*The use of Isoniazid in HIV/TB treatment with ritonavir/lopinavir and others PIs*: The isoniazid will increase the level or effect of PIs by affecting hepatic/intestinal enzyme CYP3A4 metabolism. Avoid co-administration with others inhibitors of the hepatic/intestinal enzyme CYP3A4 metabolism such as macrolide antibiotics, itraconazole, ketoconazole,

*Isoniazid + ethambutol*: increase the risk of peripheral neuropathy: burning, tingling, pain, or

*Isoniazid + rifampin/rifabutin*: The risk of hepatotoxicity is greater when rifampin and isoniazid are given concomitantly than when either drug is given alone. Rifampin alters the metabolism of isoniazid and increase the amount of toxic metabolites. Similar reaction may occur with rifabutin and isoniazid. Patients who are elderly, have hepatic impairment, are slow acetylators of isoniazid, drink alcohol daily, are female, or are taking other CYP450 inducing agents may be at greater risk of hepatotoxicity. Recommend the monitoring for clinical or laboratory evidence of hepatic function during the treatment. Discontinuation of either or both drugs may be necessary when simptoms of hepatite such as fatigue,

*Isoniazid + food:* Food significantly reduces isoniazid absorption, increasing the risk of therapeutic failure or resistance. The mechanism is unknown. In addition, the ingestion of certain histamine-rich fish (e.g., tuna) and cheeses during isoniazid therapy may cause a flushing reaction in some patients. The proposed mechanism is inhibition of monoamine oxidase and histaminase by isoniazid, resulting in histamine intoxication. The associated symptoms is: flushing, tachycardia, chills, headache, nausea, vomiting, diarrhea, burning sensation, sweating, or shortness of breath after eating certain foods. Isoniazid cause depletion of B6 vitamin during the treatment. Since HIV-infected persons are at increased risk for isoniazid-induced peripheral neuropathy, these patients should take vitamin B6 and avoid antiretroviral drugs with potential peripheral neurotoxicity (e.g., stavudine and

**4. Adherence to therapy – Process to improve medication efficacy**

It has been reported that treatment abandonment rate reaches until 25% of all patients during the treatment (Veronesi & Focaccia, 1996). In developing countries such as Brazil, this rates decreased in the last years to 4,5%, but it is possible to find out in some regions values until 20,3% (Costa, Gonçalves & Menezes, 1998; Lima et al., 2001). The WHO's recommendation is that abandonment rates must be until 5%, however, it is possible to find in some countries such as Colombia abandonment rates of 65,6% (Mateus-Solarte &

In order to reduce the abandonment of therapy and ensure the correct treatment of patients some strategies have been adopted to improve adherence to therapy. According to WHO "Adherence corresponds to the behavior of one person - in terms of taking a drug, a diet or executing lifestyle changes - that is in accordance with recommendations arising from health

Adherence to therapy is a serious problem responsible for the evolution of diseases and complications, loss of quality of life and even death. In the United States it is estimated that

nefazodone, fluconazole, verapamil, diltiazen, grapefruit juice.

weakness, malaise, anorexia, nausea, or vomiting appears.

numbness in the hands and feet

didanosine).

Carvajal-Barona, 2008).

professionals" (WHO, 2003).

*The use of tenofovir in HIV/TB need avoid the co-administration:* with other potentially nephrotoxic agents (e.g., aminoglycosides; polypeptide, glycopeptide, and polymyxin antibiotics; amphotericin B; adefovir; cidofovir; foscarnet; cisplatin; deferasirox; gallium nitrate; lithium; mesalazine; certain immunosuppressants; intravenous bisphosphonates; intravenous pentamidine; high intravenous dosages of methotrexate; high dosages and/or chronic use of nonsteroidal anti-inflammatory agents. Renal function should be evaluated prior to and during therapy with tenofovir. Patients with renal insufficiency at baseline or during treatment may require dosage adjustment in accordance with the manufacturer's product labeling.

*The use of efavirenz in HIV/TB need avoid the co-administration:* with potentially hepatotoxicity agents: pyrazinamide, isoniazid, acetaminophen; alcohol; androgens and anabolic steroids; azole antifungal agents; ACE inhibitors; endothelin receptor antagonists; interferons; other nucleoside reverse transcriptase inhibitors; retinoids; thiazolidinediones; anticonvulsants such as carbamazepine, hydantoins, felbamate, and valproic acid; lipid-lowering medications such as fenofibrate, HMG-CoA reductase inhibitors, and niacin; herbals and nutritional supplements such as chaparral, comfrey, DHEA, kava, pennyroyal oil, and red yeast rice. Patients should be advised to seek medical attention if they experience potential signs and symptoms of hepatotoxicity such as fever, rash, itching, anorexia, nausea, vomiting, fatigue, right upper quadrant pain, dark urine, light-colored stools, and jaundice. Monitoring of liver function should occur before and during treatment, especially in patients with other hepatic disease (including hepatitis B or C co-infection) or marked transaminase elevations. The benefit of continued therapy with efavirenz should be considered against the unknown risks of significant liver toxicity in patients who develop persistent elevations of serum transaminases greater than five times the upper limit of normal.

*The use of tenofovir in HIV/TB treatment with streptomycin*: Caution for renal function impairment due to additive effects on the kidney. The deleterious effect on the kindney can occur with concomitant use of others nephrotoxic drugs such as aminoglycosides; polypeptide, glycopeptide, and polymyxin antibiotics; amphotericin B; adefovir; cidofovir; foscarnet; cisplatin; deferasirox; gallium nitrate; lithium; mesalamine; certain immunosuppressants; intravenous bisphosphonates; intravenous pentamidine; high intravenous dosages of methotrexate; high dosages and/or chronic use of nonsteroidal antiinflammatory agents. Renal function should be evaluated prior to and during therapy. Patients with renal insufficiency at baseline or during treatment may require dosage adjustment in accordance with the manufacturer's product labeling.

*The use of maraviroc in HIV/TB treatment with rifampin and others CYP 450 3A4 inhibitors:* maraviroc should be administered at a dosage of 600 mg twice daily during coadministration with potent CYP450 3A4 inducers such as efavirenz, rifampin, carbamazepine, phenobarbital, and phenytoin. However, if a potent CYP450 3A4 inhibitor such as itraconazole, ketoconazole, delavirdine, clarithromycin, telithromycin, nefazodone, or any protease inhibitor (except tipranavir + ritonavir) is also used in combination with the inducer, then maraviroc dosage should be reduced to 150 mg twice daily. Maraviroc is contraindicated for use in combination with potent CYP450 3A4 inducers in patients with severe renal impairment or end-stage renal disease (CrCl <30 mL/min).

*The use of tenofovir in HIV/TB need avoid the co-administration:* with other potentially nephrotoxic agents (e.g., aminoglycosides; polypeptide, glycopeptide, and polymyxin antibiotics; amphotericin B; adefovir; cidofovir; foscarnet; cisplatin; deferasirox; gallium nitrate; lithium; mesalazine; certain immunosuppressants; intravenous bisphosphonates; intravenous pentamidine; high intravenous dosages of methotrexate; high dosages and/or chronic use of nonsteroidal anti-inflammatory agents. Renal function should be evaluated prior to and during therapy with tenofovir. Patients with renal insufficiency at baseline or during treatment may require dosage adjustment in accordance with the manufacturer's

*The use of efavirenz in HIV/TB need avoid the co-administration:* with potentially hepatotoxicity agents: pyrazinamide, isoniazid, acetaminophen; alcohol; androgens and anabolic steroids; azole antifungal agents; ACE inhibitors; endothelin receptor antagonists; interferons; other nucleoside reverse transcriptase inhibitors; retinoids; thiazolidinediones; anticonvulsants such as carbamazepine, hydantoins, felbamate, and valproic acid; lipid-lowering medications such as fenofibrate, HMG-CoA reductase inhibitors, and niacin; herbals and nutritional supplements such as chaparral, comfrey, DHEA, kava, pennyroyal oil, and red yeast rice. Patients should be advised to seek medical attention if they experience potential signs and symptoms of hepatotoxicity such as fever, rash, itching, anorexia, nausea, vomiting, fatigue, right upper quadrant pain, dark urine, light-colored stools, and jaundice. Monitoring of liver function should occur before and during treatment, especially in patients with other hepatic disease (including hepatitis B or C co-infection) or marked transaminase elevations. The benefit of continued therapy with efavirenz should be considered against the unknown risks of significant liver toxicity in patients who develop persistent elevations of serum transaminases greater than five times the upper limit of

*The use of tenofovir in HIV/TB treatment with streptomycin*: Caution for renal function impairment due to additive effects on the kidney. The deleterious effect on the kindney can occur with concomitant use of others nephrotoxic drugs such as aminoglycosides; polypeptide, glycopeptide, and polymyxin antibiotics; amphotericin B; adefovir; cidofovir; foscarnet; cisplatin; deferasirox; gallium nitrate; lithium; mesalamine; certain immunosuppressants; intravenous bisphosphonates; intravenous pentamidine; high intravenous dosages of methotrexate; high dosages and/or chronic use of nonsteroidal antiinflammatory agents. Renal function should be evaluated prior to and during therapy. Patients with renal insufficiency at baseline or during treatment may require dosage

*The use of maraviroc in HIV/TB treatment with rifampin and others CYP 450 3A4 inhibitors:* maraviroc should be administered at a dosage of 600 mg twice daily during coadministration with potent CYP450 3A4 inducers such as efavirenz, rifampin, carbamazepine, phenobarbital, and phenytoin. However, if a potent CYP450 3A4 inhibitor such as itraconazole, ketoconazole, delavirdine, clarithromycin, telithromycin, nefazodone, or any protease inhibitor (except tipranavir + ritonavir) is also used in combination with the inducer, then maraviroc dosage should be reduced to 150 mg twice daily. Maraviroc is contraindicated for use in combination with potent CYP450 3A4 inducers in patients with

adjustment in accordance with the manufacturer's product labeling.

severe renal impairment or end-stage renal disease (CrCl <30 mL/min).

product labeling.

normal.

*The use of Isoniazid in HIV/TB treatment with ritonavir/lopinavir and others PIs*: The isoniazid will increase the level or effect of PIs by affecting hepatic/intestinal enzyme CYP3A4 metabolism. Avoid co-administration with others inhibitors of the hepatic/intestinal enzyme CYP3A4 metabolism such as macrolide antibiotics, itraconazole, ketoconazole, nefazodone, fluconazole, verapamil, diltiazen, grapefruit juice.

*Isoniazid + ethambutol*: increase the risk of peripheral neuropathy: burning, tingling, pain, or numbness in the hands and feet

*Isoniazid + rifampin/rifabutin*: The risk of hepatotoxicity is greater when rifampin and isoniazid are given concomitantly than when either drug is given alone. Rifampin alters the metabolism of isoniazid and increase the amount of toxic metabolites. Similar reaction may occur with rifabutin and isoniazid. Patients who are elderly, have hepatic impairment, are slow acetylators of isoniazid, drink alcohol daily, are female, or are taking other CYP450 inducing agents may be at greater risk of hepatotoxicity. Recommend the monitoring for clinical or laboratory evidence of hepatic function during the treatment. Discontinuation of either or both drugs may be necessary when simptoms of hepatite such as fatigue, weakness, malaise, anorexia, nausea, or vomiting appears.

*Isoniazid + food:* Food significantly reduces isoniazid absorption, increasing the risk of therapeutic failure or resistance. The mechanism is unknown. In addition, the ingestion of certain histamine-rich fish (e.g., tuna) and cheeses during isoniazid therapy may cause a flushing reaction in some patients. The proposed mechanism is inhibition of monoamine oxidase and histaminase by isoniazid, resulting in histamine intoxication. The associated symptoms is: flushing, tachycardia, chills, headache, nausea, vomiting, diarrhea, burning sensation, sweating, or shortness of breath after eating certain foods. Isoniazid cause depletion of B6 vitamin during the treatment. Since HIV-infected persons are at increased risk for isoniazid-induced peripheral neuropathy, these patients should take vitamin B6 and avoid antiretroviral drugs with potential peripheral neurotoxicity (e.g., stavudine and didanosine).

#### **4. Adherence to therapy – Process to improve medication efficacy**

It has been reported that treatment abandonment rate reaches until 25% of all patients during the treatment (Veronesi & Focaccia, 1996). In developing countries such as Brazil, this rates decreased in the last years to 4,5%, but it is possible to find out in some regions values until 20,3% (Costa, Gonçalves & Menezes, 1998; Lima et al., 2001). The WHO's recommendation is that abandonment rates must be until 5%, however, it is possible to find in some countries such as Colombia abandonment rates of 65,6% (Mateus-Solarte & Carvajal-Barona, 2008).

In order to reduce the abandonment of therapy and ensure the correct treatment of patients some strategies have been adopted to improve adherence to therapy. According to WHO "Adherence corresponds to the behavior of one person - in terms of taking a drug, a diet or executing lifestyle changes - that is in accordance with recommendations arising from health professionals" (WHO, 2003).

Adherence to therapy is a serious problem responsible for the evolution of diseases and complications, loss of quality of life and even death. In the United States it is estimated that

Health Interventions to Improve the Medication Efficacy in Tuberculosis Treatment 545

therapy is not immediately improve the main symptoms, should be established an accord with the patients which should be aware of the goals of therapy. Treatment should be simplified to suit the patient's situation. Complex dosing regimens tend have higher dropout rates. The health system has an important role in the adherence. Access to professional and medicines is a determining factor for treatment. There is no possibility to discuss adherence even if the patients do not have access to health care. In this case, it is essential to adopt policies to control diseases such as tuberculosis ensuring access to the

Several strategies have been described in the literature to promote adherence to therapy. Educational interventions may involve pedagogical strategies (oral or written) aiming increase the knowledge. This strategy can be used individually or collectively. The uses of

Behavioral interventions aimed changing certain habits. They are guided by theories about behavior change. In these strategies the role of health professionals is essential in promoting adherence. This one can work with combinations of rewards and communication strategies, such as reminders to join the proposed therapy. Praise for the efforts is the reward commonly used. The possibility of monitoring the condition at home is also very useful and

Interventions with affective character take into account social relationships and may be done with the patient or the family. Family visits provide a good opportunity for this type of intervention. The professional can intervene, in educational way, with all the family doing them to understand the situation and help the patient. In TB intervention the combination of

Some care should be taken into account in monitoring patients for tuberculosis to detect adverse effects or ineffective therapy since the beginning of treatment. After 3 months of treatment, most patients (90-95%) will have negative smears (American Thoracic Society, 2003). Thus, situations of therapeutical inefficacy will be characterized with smear-positive after this period. Among factors responsible for ineffective treatment can be mentioned: bacterial resistance, poor absorption of drugs, inadequate adherence to treatment and drug

Some adverse effects such as peripheral neuritis induced by isoniazid can be prevented by supplementation with vitamin B6 (pyridoxine). This approach should be considered in special situations such as malnutrition, pregnancy, HIV co-infection and alcohol abuse.

Monitoring liver function is especially important for patients with any risk factor. About 20% of patients will have elevated levels of liver transaminases without symptoms. In such cases, after treatment the enzymes return to levels considered normal. Hepatitis should be suspected only when the elevation of transaminases is three to five times higher than considered normal associated with symptoms such as nausea, vomiting and abdominal pain. Some risk factors for hepatotoxicity are: chronic liver disease or hepatitis, alcohol abuse, use of isoniazid, female, HIV infection, low body mass index and age over 60 years

written or audiovisual materials help the patient to understand the strategy.

strategies seems to be more appropriate to increase therapy adherence.

enables patient involvement in the action plan proposed.

**5. Pharmacotherapeutic monitoring**

interactions (Figure 3).

entire population.

the cost of low compliance reach over \$ 147 billion (Council on Patient Information and Education, 2007). WHO estimate that rate of adherence of patients which treat chronic diseases is only 50% (WHO, 2003). These same values were found in a study with TB patients (Cuneo, 1989).

Literature reports show that interventions to promote adherence are effective in short treatments, but these same interventions are less effective in prolonged treatments. In the latter situation it requires a combination of strategies, becoming more complex the interventions performed by health professionals (Haynes et al., 2009).

Several methods are available in the literature to assess adherence to treatment. These methods can be divided into direct and indirect. In direct methods is possible to quantify the drug in the body. These methods are expensive, invasive and not available for all drugs, however are suitable methods to say whether or not adherence to therapy allowing include adjust the dose. The indirect methods allow assessing the use of medicines by health professionals. These methods are usually overestimated and with low sensitivity. Among the indirect methods can include: patient's self-report; prescriber's report; pill count; measurement of prescription replacement (allowing indirect evaluation of non-compliance by the lack of access to medication). Strategies using devices of separation and counting of medicines may be useful for patients who do not understand the regimen. These devices can be purchased at pharmacies and separate properly in accordance with the therapy the patient by the pharmacist.

However, in the therapy of tuberculosis, one of the strategies most used and recommended by the World Health Organization (WHO) treatment involves supervised therapy (DOTS - Directly Observed Therapy). DOTS strategy includes the delivery of a short course of standard drugs, lasting 6 months for new Patients (and 8 months for retreatment Patients). The delivery includes the direct observation of therapy (DOT), either by a health worker or by caregiver (WHO, 2002).

During the promotion of strategies to increase adherence is important to consider some factors related to therapy adherence that may be related to: patient, health professional, the disease condition, treatment and health care system (and the policies government).

With regard to the patient an important strategy to be adopted is empowerment. This strategy is an educational intervention that aims to transfer responsibilities to patients which is tone of the most important person responsible to conduct the therapy, based in the principle that the decision to follow or not the treatment is only taken by the patient. The patient must know about the disease and treatment to participate in the process of using the medicine. Factors such as social stigma are common in patients with tuberculosis, however, this factor must be worked in the intervention. Economic factors and access to health services are factors that also interfere with the patient's decision to adhere to therapy or not.

With regard to health professionals, active participation is required in treating patients, because is often the situation that them cannot understand the proper way to use the antitubercular drugs. The treatment cannot be seen as the sole responsibility of the patient. Health professionals have a large portion of the contribution of adherence to treatment. With regard to health status, disease severity and the observation of improvement with the medicines use is important for maintenance adherence. In situations where the goal of

the cost of low compliance reach over \$ 147 billion (Council on Patient Information and Education, 2007). WHO estimate that rate of adherence of patients which treat chronic diseases is only 50% (WHO, 2003). These same values were found in a study with TB

Literature reports show that interventions to promote adherence are effective in short treatments, but these same interventions are less effective in prolonged treatments. In the latter situation it requires a combination of strategies, becoming more complex the

Several methods are available in the literature to assess adherence to treatment. These methods can be divided into direct and indirect. In direct methods is possible to quantify the drug in the body. These methods are expensive, invasive and not available for all drugs, however are suitable methods to say whether or not adherence to therapy allowing include adjust the dose. The indirect methods allow assessing the use of medicines by health professionals. These methods are usually overestimated and with low sensitivity. Among the indirect methods can include: patient's self-report; prescriber's report; pill count; measurement of prescription replacement (allowing indirect evaluation of non-compliance by the lack of access to medication). Strategies using devices of separation and counting of medicines may be useful for patients who do not understand the regimen. These devices can be purchased at pharmacies and separate properly in accordance with the therapy the

However, in the therapy of tuberculosis, one of the strategies most used and recommended by the World Health Organization (WHO) treatment involves supervised therapy (DOTS - Directly Observed Therapy). DOTS strategy includes the delivery of a short course of standard drugs, lasting 6 months for new Patients (and 8 months for retreatment Patients). The delivery includes the direct observation of therapy (DOT), either by a health worker or

During the promotion of strategies to increase adherence is important to consider some factors related to therapy adherence that may be related to: patient, health professional, the

With regard to the patient an important strategy to be adopted is empowerment. This strategy is an educational intervention that aims to transfer responsibilities to patients which is tone of the most important person responsible to conduct the therapy, based in the principle that the decision to follow or not the treatment is only taken by the patient. The patient must know about the disease and treatment to participate in the process of using the medicine. Factors such as social stigma are common in patients with tuberculosis, however, this factor must be worked in the intervention. Economic factors and access to health services are factors that also interfere with the patient's decision to adhere to therapy or not. With regard to health professionals, active participation is required in treating patients, because is often the situation that them cannot understand the proper way to use the antitubercular drugs. The treatment cannot be seen as the sole responsibility of the patient. Health professionals have a large portion of the contribution of adherence to treatment. With regard to health status, disease severity and the observation of improvement with the medicines use is important for maintenance adherence. In situations where the goal of

disease condition, treatment and health care system (and the policies government).

interventions performed by health professionals (Haynes et al., 2009).

patients (Cuneo, 1989).

patient by the pharmacist.

by caregiver (WHO, 2002).

therapy is not immediately improve the main symptoms, should be established an accord with the patients which should be aware of the goals of therapy. Treatment should be simplified to suit the patient's situation. Complex dosing regimens tend have higher dropout rates. The health system has an important role in the adherence. Access to professional and medicines is a determining factor for treatment. There is no possibility to discuss adherence even if the patients do not have access to health care. In this case, it is essential to adopt policies to control diseases such as tuberculosis ensuring access to the entire population.

Several strategies have been described in the literature to promote adherence to therapy. Educational interventions may involve pedagogical strategies (oral or written) aiming increase the knowledge. This strategy can be used individually or collectively. The uses of written or audiovisual materials help the patient to understand the strategy.

Behavioral interventions aimed changing certain habits. They are guided by theories about behavior change. In these strategies the role of health professionals is essential in promoting adherence. This one can work with combinations of rewards and communication strategies, such as reminders to join the proposed therapy. Praise for the efforts is the reward commonly used. The possibility of monitoring the condition at home is also very useful and enables patient involvement in the action plan proposed.

Interventions with affective character take into account social relationships and may be done with the patient or the family. Family visits provide a good opportunity for this type of intervention. The professional can intervene, in educational way, with all the family doing them to understand the situation and help the patient. In TB intervention the combination of strategies seems to be more appropriate to increase therapy adherence.

#### **5. Pharmacotherapeutic monitoring**

Some care should be taken into account in monitoring patients for tuberculosis to detect adverse effects or ineffective therapy since the beginning of treatment. After 3 months of treatment, most patients (90-95%) will have negative smears (American Thoracic Society, 2003). Thus, situations of therapeutical inefficacy will be characterized with smear-positive after this period. Among factors responsible for ineffective treatment can be mentioned: bacterial resistance, poor absorption of drugs, inadequate adherence to treatment and drug interactions (Figure 3).

Some adverse effects such as peripheral neuritis induced by isoniazid can be prevented by supplementation with vitamin B6 (pyridoxine). This approach should be considered in special situations such as malnutrition, pregnancy, HIV co-infection and alcohol abuse.

Monitoring liver function is especially important for patients with any risk factor. About 20% of patients will have elevated levels of liver transaminases without symptoms. In such cases, after treatment the enzymes return to levels considered normal. Hepatitis should be suspected only when the elevation of transaminases is three to five times higher than considered normal associated with symptoms such as nausea, vomiting and abdominal pain. Some risk factors for hepatotoxicity are: chronic liver disease or hepatitis, alcohol abuse, use of isoniazid, female, HIV infection, low body mass index and age over 60 years

Health Interventions to Improve the Medication Efficacy in Tuberculosis Treatment 547

postpone antiretroviral therapy until TB treatment is complete. However, the optimal time for starting ATR therapy should be individualized based on initial response to TB treatment

A patient who cannot take efavirenz, and when rifabutin is not available, the alternative is nevirapine - with rifampin. The pharmacokinetic effect of the rifamycin is moderate in this regimen. When used with isoniazid, rifampin, and pyrazinamide, there is some concern about hepatotoxicity. However, given the risk of reduced viral susceptibility and resistance development associated with subtherapeutic antiretroviral drug levels of nevirapine, some experts recommend that alternative antimycobacterial agents be considered in patients

Other alternatives for patients who cannot take efavirenz, and when rifabutin is not available, are as follows: rifampin with a) zidovudine/lamivudine/abacavir/tenofovir treatment; b) zidovudine/lamivudine/tenofovir or c) zidovudine/lamivudine/abacavir. The toxicity of these alternative regimens is primarily anemia. Pharmacokinetic concerns are a 50% decrease in zidovudine and the effect on abacavir is not yet evaluated. For the treatment of latent TB infection, a nine-month regimen of isoniazid may be

In general, treatment of TB /HIV in the context of ATR therapy is complex and requires an individualized approach. Experts in the treatment of HIV-related tuberculosis should be consulted, and TB and HIV care providers should work in close coordination throughout

Additional care should be conducted with patients who have resistant infection. To decrease the resistance some principles should be adopted: a) the scheme more effective should be adopted, b) the therapeutic regimen should include at least three antimycobacterial drugs, c) the treatment should be daily and preferably monitorate by health professional and d)

In situations of resistance to isoniazid, one possibility is the use of rifampicin, pyrazinamide, ethambutol (and some fluoroquinolone) for a period of 6 months. For resistance to rifampicin and isoniazid regimen can be use fluoroquinolone, pyrazinamide and ethambutol associated with some other drug for a period of 18-24 months. In situations of resistance to rifampin, isoniazid, pyrazinamide (or ethambutol) the scheme would be to use a fluoquinolone (ethambutol or pyrazinamide depending on the susceptibility) and two

In cases of latent infection, correctly detected, should be assessed the risk and benefit of treatment. People living with HIV, immunocompromised, malnourished, drug users and from endemic regions with positive test to TB are considered at risk of developing tuberculosis. A study by Wilkinson and colleagues (1998) demonstrated that treatment for latent infection in HIV people decreased by 43% the risk of developing tuberculosis (Wilkinson et al., 1998). Among the schemes that have been proposed that it should be noted: a) isoniazid for 6-9 months in the absence of active infection b) rifampicin and

isoniazid for 3 months and others (Balcells et al. 2006; Ena et al., 2005).

already receiving effective nevirapine-containing antiretroviral therapy.

and occurrence of adverse effects such as IRIS.

the best treatment considering patient quality of life.

medicines should not be left for possible "future use".

alternative agents for a period of 24 months.

considered.

Fig. 3. Some factors responsible to inefficacy.

The action plan for monitoring patients with hepatotoxicity during the treatment includes withdrawal of all medicines. After the reduction of transaminases levels, reintroduction of individual drug must be re-thinking. It is recommended to start treatment with rifampicin (less hepatotoxic), and between 3-7 days to introduce a new drug. Treatment regimens without isoniazid are possible. In this last case, one possibility is treating the patient with rifampicin, ethambutol and pyrazinamide for six months.

Drug interactions should be identified and prevented. Beyond the hepatotoxic effect already discussed, some antituberculosis drugs like rifampicin are metabolic enzymatic inducers and may interfere with the metabolism of many drugs. One example is the oral contraceptive whose effectiveness can be compromised with concomitant use of rifampicin. In these situations alternative reproductive control methods should be used. Isoniazid may increase serum levels of drugs of narrow therapeutic index such as theophylline used by asthma patients.

Regimen that includes rifabutin is generally preferred, as rifabutin appears to be as effective as rifampin but is a much less potent inducer of CYP450 3A4. Non rifamycin-containing regimens is related to higher rates of treatment relapse and failure; longer treatment duration with increased adverse effects and higher mortality rates. This regimen is only recommended to patients who are intolerant of rifamycins or are infected with rifamycinresistant strains.

Usual dosages of rifampin may be used in patients receiving ritonavir 600 mg twice/day or ritonavir 400 mg twice/day in combination with another PI at reduced dosage (e.g., saquinavir 400 mg twice/ day). If the patients have not begun antiretroviral therapy at the time TB treatment is initiated, clinicians may also consider using rifampin and postponing ATR therapy, because in the early HIV stage of the disease, there is low risk of HIV disease progression or death. During this period the physician may monitor CD4 cell count and

The action plan for monitoring patients with hepatotoxicity during the treatment includes withdrawal of all medicines. After the reduction of transaminases levels, reintroduction of individual drug must be re-thinking. It is recommended to start treatment with rifampicin (less hepatotoxic), and between 3-7 days to introduce a new drug. Treatment regimens without isoniazid are possible. In this last case, one possibility is treating the patient with

Drug interactions should be identified and prevented. Beyond the hepatotoxic effect already discussed, some antituberculosis drugs like rifampicin are metabolic enzymatic inducers and may interfere with the metabolism of many drugs. One example is the oral contraceptive whose effectiveness can be compromised with concomitant use of rifampicin. In these situations alternative reproductive control methods should be used. Isoniazid may increase serum levels of drugs of narrow therapeutic index such as theophylline used by

Regimen that includes rifabutin is generally preferred, as rifabutin appears to be as effective as rifampin but is a much less potent inducer of CYP450 3A4. Non rifamycin-containing regimens is related to higher rates of treatment relapse and failure; longer treatment duration with increased adverse effects and higher mortality rates. This regimen is only recommended to patients who are intolerant of rifamycins or are infected with rifamycin-

Usual dosages of rifampin may be used in patients receiving ritonavir 600 mg twice/day or ritonavir 400 mg twice/day in combination with another PI at reduced dosage (e.g., saquinavir 400 mg twice/ day). If the patients have not begun antiretroviral therapy at the time TB treatment is initiated, clinicians may also consider using rifampin and postponing ATR therapy, because in the early HIV stage of the disease, there is low risk of HIV disease progression or death. During this period the physician may monitor CD4 cell count and

Fig. 3. Some factors responsible to inefficacy.

asthma patients.

resistant strains.

rifampicin, ethambutol and pyrazinamide for six months.

postpone antiretroviral therapy until TB treatment is complete. However, the optimal time for starting ATR therapy should be individualized based on initial response to TB treatment and occurrence of adverse effects such as IRIS.

A patient who cannot take efavirenz, and when rifabutin is not available, the alternative is nevirapine - with rifampin. The pharmacokinetic effect of the rifamycin is moderate in this regimen. When used with isoniazid, rifampin, and pyrazinamide, there is some concern about hepatotoxicity. However, given the risk of reduced viral susceptibility and resistance development associated with subtherapeutic antiretroviral drug levels of nevirapine, some experts recommend that alternative antimycobacterial agents be considered in patients already receiving effective nevirapine-containing antiretroviral therapy.

Other alternatives for patients who cannot take efavirenz, and when rifabutin is not available, are as follows: rifampin with a) zidovudine/lamivudine/abacavir/tenofovir treatment; b) zidovudine/lamivudine/tenofovir or c) zidovudine/lamivudine/abacavir. The toxicity of these alternative regimens is primarily anemia. Pharmacokinetic concerns are a 50% decrease in zidovudine and the effect on abacavir is not yet evaluated. For the treatment of latent TB infection, a nine-month regimen of isoniazid may be considered.

In general, treatment of TB /HIV in the context of ATR therapy is complex and requires an individualized approach. Experts in the treatment of HIV-related tuberculosis should be consulted, and TB and HIV care providers should work in close coordination throughout the best treatment considering patient quality of life.

Additional care should be conducted with patients who have resistant infection. To decrease the resistance some principles should be adopted: a) the scheme more effective should be adopted, b) the therapeutic regimen should include at least three antimycobacterial drugs, c) the treatment should be daily and preferably monitorate by health professional and d) medicines should not be left for possible "future use".

In situations of resistance to isoniazid, one possibility is the use of rifampicin, pyrazinamide, ethambutol (and some fluoroquinolone) for a period of 6 months. For resistance to rifampicin and isoniazid regimen can be use fluoroquinolone, pyrazinamide and ethambutol associated with some other drug for a period of 18-24 months. In situations of resistance to rifampin, isoniazid, pyrazinamide (or ethambutol) the scheme would be to use a fluoquinolone (ethambutol or pyrazinamide depending on the susceptibility) and two alternative agents for a period of 24 months.

In cases of latent infection, correctly detected, should be assessed the risk and benefit of treatment. People living with HIV, immunocompromised, malnourished, drug users and from endemic regions with positive test to TB are considered at risk of developing tuberculosis. A study by Wilkinson and colleagues (1998) demonstrated that treatment for latent infection in HIV people decreased by 43% the risk of developing tuberculosis (Wilkinson et al., 1998). Among the schemes that have been proposed that it should be noted: a) isoniazid for 6-9 months in the absence of active infection b) rifampicin and isoniazid for 3 months and others (Balcells et al. 2006; Ena et al., 2005).

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All these factors must be taken into account during the pharmacotherapeutic monitoring of tuberculosis patients to adequate the therapy and improve quality of life of patients with tuberculosis.

#### **6. Conclusion**

The current TB treatment presents several challenges. The absence of development new drugs is the cruelest face of this disease. This fact associated with inadequate treatment and TB-drug resistance contributes to survival of the disease today. Anti-TB therapy has several problems relate to noncompliance, lack of adherence to therapy, patients with comorbidity, socio-economic factors, environmental factors and problems related to drugs such as adverse effects and drug interactions. Health interventions can improve the medication efficacy, reduce the resistance and improve patients quality of life. Pharmacotherapeutic follow-up and adequate strategies to increase therapy adherence are important factors to be monitored during TB therapy. It is important to keep in mind that interventions that guarantee the adequate use of the medication are the first step to improve TB treatment.

#### **7. References**

All these factors must be taken into account during the pharmacotherapeutic monitoring of tuberculosis patients to adequate the therapy and improve quality of life of patients with

The current TB treatment presents several challenges. The absence of development new drugs is the cruelest face of this disease. This fact associated with inadequate treatment and TB-drug resistance contributes to survival of the disease today. Anti-TB therapy has several problems relate to noncompliance, lack of adherence to therapy, patients with comorbidity, socio-economic factors, environmental factors and problems related to drugs such as adverse effects and drug interactions. Health interventions can improve the medication efficacy, reduce the resistance and improve patients quality of life. Pharmacotherapeutic follow-up and adequate strategies to increase therapy adherence are important factors to be monitored during TB therapy. It is important to keep in mind that interventions that guarantee the adequate use of the medication are the first step to

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*Article* **Numerical Studies of Statistical Management Decisions in Conditions of Stochastic Chaos**

**Alexander Musaev 1 and Dmitry Grigoriev 2,\***

**Abstract:** The research presented in this article is dedicated to analyzing the acceptability of traditional techniques of statistical management decision-making in conditions of stochastic chaos. A corresponding example would be asset management at electronic capital markets. This formulation of the problem is typical for a large number of applications in which the managed object interacts with an unstable immersion environment. In particular, this issue arises in problems of managing gasdynamic and hydrodynamic turbulent flows. We highlight the features of observation series of the managed object's state immersed in an unstable interaction environment. The fundamental difference between observation series of chaotic processes and probabilistic descriptions of traditional models is demonstrated. We also present an additive observation model with a chaotic system component and non-stationary noise which provides the most adequate characterization of the original observation series. Furthermore, we suggest a method for numerically analyzing the efficiency of conventional statistical solutions in the conditions of stochastic chaos. Based on numerical experiments, we establish that techniques of optimal statistical synthesis do not allow for making effective management decisions in the conditions of stochastic chaos. Finally, we propose several versions of compositional algorithms focused on the adaptation of statistical techniques to the non-deterministic conditions caused by the specifics of chaotic processes.

**Keywords:** currency market; Forex risk control models; chaotic processes; trends prediction

#### **1. Introduction**

A distinctive feature of dynamic open systems that interact with unstable immersion environments is the presence of random perturbations associated with unpredictable physical, economical, political, natural, etc. factors. At each moment of time any given (often latent) factor may start to dominate, which makes many explicitly pronounced local trends appear. The presence of such trends and large areas of observation series that are oscillatory non-periodic processes exactly satisfies the description of chaotic processes [1–6]. The chaotic nature of observation series violates the established constraints that are required for statistical estimates to be consistent, efficient, and non-biased. In particular, this refers to the stationarity of the noise, independence of increments, normality (gaussianity) of value variations, and others. The full list of conditions that provide effectiveness and consistency of statistical solutions can be found in classical and modern textbooks on mathematical statistics [7–12]. At the same time, as dedicated statistical studies [5,6] show, the most adequate model for describing observation series of the state of unstable objects is an additive combination of a system component consisting of an oscillatory non-periodic process with many local trends, and a random component that is a nonstationary random process. It is obvious that in these conditions, aptly named stochastic chaos, the most important assumption about the repeatability of events which underlies the

**Citation:** Musaev, A.; Grigoriev, D.; Numerical Studies of Statistical Management Decisions in Conditions of Stochastic Chaos. *Mathematics* **2022**, *10*, 226. https://doi.org/10.3390/ math10020226

Academic Editors: Mihaela Neamt,u, Eva Kaslik and Anca R ˘adulescu

Received: 2 December 2021 Accepted: 6 January 2022 Published: 12 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

probabilistic-statistical paradigm has been violated. At the same time, statistical analysis methods remain the primary tool of management decision-making in the conditions of non-determinism. Hence, there is a problem of evaluating the effectiveness of statistical methods of data analysis in conditions in which they are obviously not optimal. Moreover, the estimates made in the conditions of stochastic chaos generally are not unbiased and effective. Therefore, the question about the effectiveness of management decisions based on them remains open. Currently, there are no analytical methods for assessing the quality of statistical estimates generated for chaotic data. The only available assessment means are numerical studies. Therefore, this is the methodology we use in the present article. Note that the specifics of chaotic dynamics do not allow us to obtain a stable result that determines the effectiveness of the estimation procedures themselves. However, considering the management task for which such estimates are made, it would be more sensible to assess the quality of the used algorithms via terminal performance indicators of the constructed strategies. We propose and examine the corresponding technique in this study.

#### **2. Materials and Methods**

#### *2.1. Generalized Statistical Decision-Making*

Decision-making via statistical synthesis requires constructing a statistical model of the trading situation state. A traditional example of such a model is the statement that an observation series of financial instrument quotations *y*1, *y*2, ... , *yn* are independent, identically distributed random variables with a total density *f*(*y*, *θ*), *y* ∈ *R*1, where *θ* ∈ Θ ⊂ *Rm* is the set of market parameters, *Rm* is an *m*-dimensional real Euclidean space, and *D* is the decision space. It is assumed that information about *X* is needed to select a trading decision *d* ∈ *D* from a predetermined set of management decisions *D*. In general, *d* is the result of a certain predictive analysis procedure concerning the trading situation, which includes formalized data processing and interpretation of the obtained results. In practice, a trading decision *d* is made based on the predicted values of the trading situation state vector *X*+.

A trading strategy (*a decision function*) is a map *S* : *Y* → *D*, i.e., a rule according to which, within the framework of a given statistical model, a set of observations of a trading situation *y*1, *y*2, ... *yn* ∈ *Y* corresponds to a trading decision *d* ∈ *D*. Thus, a trading strategy is essentially a procedure for analyzing and processing observation series, and a rule for interpreting the result.

The fundamental task of statistical synthesis of management decisions is to choose a strategy that is optimal with respect to some specific quality measure. Such a choice requires the introduction of "more—less", "better—worse" order relations to the class of all strategies. Strategy *S*0 is called *feasible* if it provides management decisions that satisfy a given class of constraints. Strategy *S*∗ is optimal in a given class of feasible strategies *S* ∈ {*S*0} if, taking into account the existing constraints, it outperforms any other strategy from this class by a specified effectiveness measure *μ*(*S*): *S* = *S*∗ : *μ*(*S*∗) > *μ*(*S*), ∀*S* ∈ {*S*0}.

The most common method of ordering a set of strategies requires *a loss function w*(*X*, *d*) that maps *X*+*τ* × *D* → R+, where R+ is the positive semi-axis of the real axis R, which represents the loss of a trading decision *d* ∈ *D* based on forecast *X*+*τ* in conditions when the true state of the trading environment is described by a vector parameter *Xτ*, and *τ* is the forecasting interval. In estimation problems,the full square of the forecast error is often used as a loss function: *w*(*Xτ*, *X*+*τ*)=(*X*+*τ* − *Xτ*)2, i.e., the square of the Euclidean distance between *X*+*τ* and *Xτ*. Sometimes the loss function is made more complex by adding a weight, thus becoming a weighted sum: *w*(*Xτ*, *X*+*τ*) = *λ*(*Xτ*)(*X*+*τ* − *Xτ*)2, where the weight *λ*(*Xτ*) is selected from the condition of a specific task.

#### *2.2. Specifics of Asset Management in the Conditions of Dynamic Chaos*

During the construction of Bayesian management strategies, each acceptable trading strategy *S* ∈ {*S*0} is mapped to an average loss or *risk RS*(*X*) = *E*{*w*(*X*, *d*)}, where *E* is the symbol of mathematical expectation. In the tasks of proactive (i.e., forecast-based) management, which is typical for trading, the main cause of risk is errors in predicting the market situation state vector *X*+*τ* for the forecast interval *τ* chosen by the trader. In the case of a point state vector of a particular financial instrument based on an independent sample of observations *y*1, *y*2, ... , *yN* with a distribution density *f*(*Y*), the average loss from the selected trading decision will have the form

$$R\_S(\mathbf{x}\_\tau) = \int \dots \int\_{R^n} w(\mathbf{x}\_\tau, \hat{\mathbf{x}}\_\tau(y\_1, \dots, y\_n)) \prod\_{i=1}^n f(y\_i \mid \mathbf{x}\_\tau) dy. \tag{1}$$

In the conditions of chaotic dynamics, the observed process does not meet the conditions of stationarity and ergodicity [5,6], the distribution function continuously changes in time and it is not possible to restore it from the previous sample of observations. In this case, the quality of the forecast itself is often estimated based *on average square error RS* = *E*{(*X*+*τ* − *Xτ*)2} = *D*{*X*+*τ*} + (*E*{*X*+*τ*} − *Xτ*)2, where *D*{*X*+*τ*} is the variance of the forecast *X*+*τ*. The trading risk from adopting a management strategy S is mainly related to the probabilistic scatter of *X*+*τ* near the true value *Xτ* for time *t* + *τ*. For a normal distribution law, variance lim*n*→∞*E*{*X*+*τ* − *X*} = lim*n*→∞*D*{*X*+*τ*} = *σ*2 *τ* is a natural scatter measure. However, for chaotic processes, there is no natural general measure of scatter, and the choice has to be made in accordance with the conditions of a specific task.

The risk *RS*(*X*) associated with the application of strategy *S* introduces a partial order in the set of strategies so that *S*1 ≥ *S*2 ⇔ *RS*1 (*X*) ≤ *RS*2 (*X*) ∀*X* ∈ {*X*}.

Generally, in chaotic conditions curves *RS*1 (*X*) and *RS*2 (*X*) intersect and, therefore, the corresponding strategies are generally incomparable. Only in very rare cases there may exist a curve in this class that lies uniformly below all the others at ∀*X* ∈ {*X*}, and thus corresponds to the optimal strategy according to the criterion of minimum trading risk.

#### *2.3. Specifics of Applying Statistical Synthesis of Management Strategies in Asset Management*

Making control decisions, according to the general theory of statistical decisions, is a procedure for choosing a decision *d* ∈ *D*0 from a set of acceptable decision *D*0 based on the results of observations of the state of the trading situation of interest to us, described by the process *Xt*, *t* = 1, ... , *n*. In a real situation, this vector process can not always be observed directly and a judgment about it is made on the basis of functionally related, technically accessible observations *Yt*, *t* = 1, ... , *n*. In other words, an investor or trader usually only has access to direct or indirect observations that are functionally related to the considered trading situation. It would be interesting to consider a generalized representation of an asset's state phase trajectory in a visual coordinate system "profit *P* — risk *R* — state *X*" using posterior observation data. The trading situation is described by the respective estimates of the specified parameters (*P*, *R*, *X*)*t*at the time *t* = 1, ... , *n*. In some cases, in particular forecasting changes in the trading situation, the estimated parameters include estimates of the speed and acceleration of changes in the expected profit and risk measures. Then, the vector of the estimated parameters of the phase trajectory at the time *t* = 1, ... , *n* will have the form (*P*, *P* , *P*, *R*, *R* , *R*, *X*, *X* , *X*)*t*. Observations *Yt*, *t* = 1, ... , *n* are the values of quotation vector of financial instruments *Xt*, *t* = 1, ... , *n* and, possibly, some other econometric, political, social and other values, the ensemble of which determines the dynamics of expected changes in profit and risk. The perturbations that a submersion environment exerts on a trading situation ensures that observations contain a random component in all cases. The association between the the parameter vector and observation series *Yt*, *t* = 1, ... , *n* can be expressed with a (generally non-linear) one-dimensional operator: Φ : *y* = Φ(*x*, *v*), *y* ∈ *Y*0, *x* ∈ *X*0.

A management decision *d* ∈ *D* is chosen based on observations *Yt*, *t* = 1, ... , *n* and all prior information available to the trader. Thus, the procedure for making a management decision, which is the main subject of statistical synthesis, can be written in the form of an operator *S* : *d* = *S*(*Y*, *x*). In the ideal case, this operator inverts Φ. The quality of a decision is substantially determined by the availability and reliability of prior information. The lack of reliable prior and current information relating to the trading situation defines the level of uncertainty at which a trading decision is made.

The most complete prior information consists of a probabilistic description of the observation and state spaces that uses a prior distribution of state *g*(*x*) and a family of distributions of observations *f*(*y*|*x*) for all *x* ∈ *X*0. In this case, the management decision is chosen in accordance with the Bayesian ordering of strategies (1) described above, and the preference rule is based on Bayesian risk

$$R\_S(f, \ g) = \int\_{\Theta} R\_S(\mathbf{x}, f) g(\mathbf{x}) d\mathbf{x} = \int\_X g(\mathbf{x}) \int\_{R^n} w(\mathbf{x}\_{\tau}, \hat{\mathbf{x}}\_{\tau}(y\_1, \dots, y\_n)) \prod\_{i=1}^n f(y\_i, \mathbf{x}) dy\_i,\tag{2}$$

where *h*(*x*) is the prior distribution density of the estimated parameter. This approach provides the most effective management decisions for conventional statistical synthesis problems. However, in the conditions of non-stationary dynamics of observation series, prior information turns out to be unsuitable for dynamic reconstruction of distribution functions. The transition to conventional non-Bayesian techniques eliminates the need to restore the prior distribution of the forecast parameter. However, statistical technologies remain inapplicable due to the non-stationarity of the observed process, i.e., the dependence of observation distribution density *f*(*Y* | *x*) on time. In particular, maximum likelihood estimation (MLE) [1–4], which is based on minimization of the joint distribution of observations *L*(*X*) = ∏*n i*=1 *f*(*yi*, *x*) and is widely used in statistical synthesis problems [1–4], turns out to be unsuitable for the same reason — the non-stationarity of observation series.

At the same time, it is known [1–6] that the purely random component of observations consisting of the difference between the values of observations, and the smoothed (or system) component of quotation dynamics, will tend to a Gaussian distribution by the central limit theorem. This convergence is approximate, and its degree remains undetermined, due to the impossibility to strictly separate the system component of observation series (deterministic chaos) and the random component.

Nevertheless, even for an approximate Gaussian scheme, using MLE (for a Gaussian model, this leads to the well-known least squares method (LSM)) it is possible to build constructive computational schemes intended to generate predictive management decisions. However, analytical estimates of the quality of such decisions are impossible due to the aforementioned uncertainty regarding the structure of the source data. The only possible way to analyze the problem is thus via numerical studies based on computational experiments. This article is dedicated to the investigation of these issues.

#### *2.4. Observation Model in Asset Management*

Figure 1 shows several examples of changes in various currency instrument quotations on a 250-day observation interval.

**Figure 1.** Change dynamics of EURUSD, EURJPY, and USDJPY during 250 observation days.

A visual examination of asset price observation series reveals that their nature is chaotic and can be described by an additive model of form:

$$y\_k = \mathbf{x}\_k + v\_{k\prime} \ k = 1, \ldots, n,\tag{3}$$

in which the systemic component of the observed process *xk*, *k* = 1, ... , *n* used to make a decision is an implementation of dynamic chaos [1–10,13], and usually is an oscillatory non-periodic process with a large quantity of false local trends of undetermined length. The noise *vk*, *k* = 1, ... , *n* , as shown by applying statistical hypothesis tests [5,6], is a non-stationary heteroscedastic process with a non-degenerate time-dependent autocorrelation function.

Further on, we evaluate the feasibility of using decisions made based on conventional statistical methods in asset management described by the observation model (3). In order to do so, we have constructed a method based on the general theory of evaluating the effectiveness of *IT systems* presented in [14].

#### *2.5. Analysing the Effectiveness of Statistical Decision-Making in Asset Management*

According to the aforementioned theory, the effectiveness of IT systems (in this case, data analysis algorithms) should be assessed according to the performance of the metasystem, in interests of which it is utilized. In the trading case, the management decision is proactive, i.e., it is based on the forecast of the development of the observed process. Conventional statistical synthesis provides an ability to construct an optimal forecast based on well-known methods such as Bayesian estimation, maximum likelihood estimation, least squares method, etc. [1–4,7], as shown above. It is impossible to analytically estimate whether such methods are effective if the observed processes present chaotic and nonstationary dynamics. Considering that, we present numerical studies based on the terminal estimate of the efficiency of the forecast algorithms and proactive management decisions for real trading asset quotation dynamics processes.

In particular, we consider extrapolation-based computational schemes of optimal statistic forecasting, which estimate the parameters of a polynomial forecast model via the least squares method.

The movement model undergoes statistical identification on the segment of observations that corresponds to the time interval of a financial instrument's price changing by a specific value *dL*. This approach corresponds to the problem in which the entire range of price changes of a financial instrument is divided into uniform segments of width *dL*. A positive or correct decision based on statistical trend identification accounts for the ability of the considered process to preserve the previously identified trend from the level it was detected at to the crossing of the next level in its direction. In the cases when the process turns around and reaches the opposite level, the respective experiment fragment will be considered to be a false decision. This approach is quite compatible with the tasks of electronic trading, when the gain (TP, Take Profit) is achieved when the process reaches a given level before it reverses and reaches the level of limiting losses (SL, Stop Loss).

Thus, the criterion of decision effectiveness is defined as the estimated probability (frequency) of the process intersecting the trend presence and identification level earlier than the Stop Loss level.

It should be noted that visual posterior observation of chaotic processes reflecting the currency instrument quotation dynamics confirms the assumption that there are local areas with pronounced trends which can be described by low-order polynomials. If this can be proven mathematically, then we can say that the degree of chaos of the observed process decreases locally. This, in turn, opens up prospects for constructing effective trading strategies. Areas that preserve trend direction can be described via conventional statistical methods. If this assumption turns out to be incorrect, it will not be possible to construct effective management strategies based on statistical methods of identifying trends.

As a typical process with non-stationary dynamics, we will consider changes in the quotations of currency pairs at the electronic FOREX market. To study this question, a number of computational experiments for the most commonly used currency instruments are carried out in this paper.

#### **3. Computational Experiments**

#### *3.1. Description*

The area on which the studied process *Yt* changes is divided into equal sectors that are *dL* points in percentage (pipses) long. Suppose that the process has moved from level *dL* to the level *Lk*+1 above it. We can loosely consider this to be an appearance of a positive trend. Such a transition will be denoted as *Lk* → *Lk*+1. Conversely, we can understand *Lk* → *Lk*−1 as negative dynamics [15].

The main problem that we focus on consists in proving the persistence of process *Yt* defined as it arriving at the next level of the detected trend.

We assess positive outcome probability, i.e., *Yt* going from *Lk* → *Lk*+1 after it has gone from *Lk*−1 → *Lk*. We define a negative outcome as a opposite transition to the level below *Lk* → *Lk*+1 directly after an upwards transition *Lk*−1 → *Lk*. Due to symmetry, similar measurements work for downwards transitions as well. Therefore, the set of exhaustive events consists of two positive outcomes (*Lk* → *Lk*+1 | *Lk*−1 → *Lk*),(*Lk* → *Lk*−1 | *Lk*+1 → *Lk*) and two negative outcomes (*Lk* → *Lk*−1 | *Lk*−1 → *Lk*),(*Lk* → *Lk*+1 | *Lk*+1 → *Lk*).

As in illustration, Figure 2 presents an example of EURUSD quotation dynamics on a 10-day observation interval with segmentation boundaries and marks denoting boundary intersections.

**Figure 2.** An example of EURUSD quotation dynamics on a 10-day observation interval.

The figure presents both the *Yt*, *t* = 1, ... , *n* process and its smoothed version *Y*˜ *t*, *t* = 1, ... , *n*. It was smoothed via a simple exponential filter *Y*˜ *t* = *αYt* + *βY*˜ *t*−1, *t* = 1, ... , *n*, in which *α* ∈ (0, 1), *β* = 1 − *α*.

Examples of positive outcomes are shown in Figure 3, and negative ones in Figure 4.

**Figure 3.** Examples of positive outcomes of management decisions.

**Figure 4.** Examples of negative outcomes of management decisions.

Assume that *N* experiments were run, each of which has identified a transition from level to level, interpreted as a trend. If this direction persists until the process intersects the next level, this outcome will confirm the trend. Conversely, if the process reverses and reaches the previous level, it will point to trend absence. Suppose that as the result of *N* consecutive experiments *m* outcomes prove trend presence, and *N* − *m* outcomes disprove it.

Thus, this can be considered as an alternative *H*1 : *p* = 0.5 to the null hypothesis *H*0 : *p* = 0.5 of trend absence, in which *pn* = *m n* is the frequency of experiments that confirm trend presence. If an experiment is repeated a sufficient number of times, the frequency of observed event is considered to be an estimate of the probability of the corresponding assumption. To test the *H*0 hypothesis, it is possible to use a well-known rule *u* < *u*∗, where *u* = (*fn* − 0.5)(0.25/*n*)1/2 [8–10]. The critical value *u*∗ for the right-tailed criterion is found using the Laplace function Φ table of values, considering that Φ(*u*∗) = (1−2*γ*) 2 . Here, *γ* is the significance level of the null hypothesis.

#### *3.2. Results*

In order to cover as many variations of chaotic dynamics in electronic trading as possible, we have considered five 100-day segments for three most widespread financial instruments: *EURUSD*, *EURJPY*, and *USDJPY*. We have used the *dL* = 100 (pipses) as the size of the inter-level interval.

Probability is estimated using the frequency of positive outcomes, that is, the ratio of positive outcomes to the total number of experiments. The corresponding results of the computational experiment are presented in Table 1.

**Table 1.** Positive outcome frequency at *dL* = 100.

The presented data clearly indicates complete absence of any inertia in quotation dynamics. This statement can be verified with statistical hypothesis testing. As mentioned above, the null hypothesis *H*0 : *p* = 0.5 is tested against the alternative *H*1 : *p* = 0.5.

As an example, consider an experiment for the 100-day interval of EURUSD observation. It resulted in *N* = 76 closes, out of which *m* = 42 corresponded to the inertia condition at *dL* = 100. The relative frequency *m N* = 0.552 corresponds to the value of the decision statistic

$$\mu = \frac{(\# - p\_0)\sqrt{N}}{\sqrt{p\_0 q\_0}} = \frac{0.052\sqrt{76}}{\sqrt{0.25}} = 0.91.$$

Here, *q*0 = 1 − *p*0, *u* ∈ *N*(0, 1), i.e., it is subject to the standard Gaussian distribution with the (0, 1) parameters. The assumption about the normal distribution of the criterion follows from Laplace's theorem (for a sufficiently large *n*, the relative frequency can be approximately considered normally distributed with the mathematical expectation *p* and standard deviation *pq N* ). In the general case, this assumption needs additional verification.

The critical area for the symmetrical competing hypothesis *H*1 : *p* = 0.5 is determined based on the selected significance level *α* = 0.99. For a two-sided critical area, *ucr* is determined via the Laplace function value table according to Φ(*ucr*) = 1−*α* 2 = 0.005. Using the distribution tables of the Laplace function, we determine *ucr* = 2.85. Therefore, the calculated value of statistic *u* = 0.91 belongs to the area of hypothesis acceptance *H*0 : *p* = 0.5, which means that statistical solutions are unsuitable for the considered processes.

The conclusion that inertia is absent in the previous experiment may be caused by an excessively large confirmation interval *dL* = 100 p. Let us check whether we can confirm the presence of inertia on smaller segmentation levels. Note that the considered process contains a significant completely random component. Considering the random value spread relatively to the smoothed process from *Y*˜ *t*, *t* = 1, ... , *n α* = 0.02 then its SD on 100-day observation segments oscillates within 11–14 pipses for various currency instruments. Decreasing *α* to 0.01, the corresponding SD changes within 15–20 pipses, which is due to a lower degree of smoothness and therefore a smaller difference between the initial and smoothed processes.

The width of the spread is responsible for random decisions that do not correspond to systemic processes of quotation dynamics and therefore skews the conclusions on inertia presence. Thus, in order to obtain a correct conclusion on inertia, the size of the segmentation step (system dynamics) must be significantly larger than the random component.

As an example that illustrates the minimum feasible segmentation step for the presented *SD* values, consider the same task with *dL* = 50. The frequencies of positive outcomes that confirm process inertia can be found in Table 2.

**Table 2.** Positive outcome frequency at *dL* = 50.

The results, similarly to the previous case, confirm the stability of the hypothesis *H*0 : *p* = 0.5, which refutes the use of statistical management techniques in a chaotic environment. The positive asymmetry is too small to accept the null hypothesis on the significance of the difference between the frequency of positive outcomes and 50%. The difference between the following series of experiments is that the beginning of each stage of the management process is fixed when the segmentation level is crossed not by the process itself, but by its smoothed version. Positions are closed (i.e., establishing the fact of recognizing or not recognizing inertia in each experiment) by the process *Yt*, *t* = 1, . . . , *n* itself.

Obviously, the higher the degree of smoothness, the less the result will depend on the fluctuating component of the process randomly crossing the levels. On the other hand, a higher degree of smoothness inevitably leads to a lag in the smoothed process relative to the original one, which skews the resulting estimates. As a compromise, we will use values *α* = 0.005 − 0.02. The segmentation step, as in the first experiment, is equal to 100 p. The results of estimating the probability of a positive outcome confirming the alternative *H*1 for five 100-day observation intervals and different values of the exponential filter transfer coefficient *α* are presented in Table 3.

**Table 3.** Positive outcome frequency: opening by smoothed curve.

It can be seen from the above data that the smoothed version of the process has more inertia, which in general is suitable for making useful trading recommendations. However, one should keep in mind that negative decisions are more drastic in terms of loss, since in this case the dynamics of the quote reverse, and the departure of the process *Yt*, *t* = 1, ... , *n* during the time when the smoothed curve *Y*˜ *t*, *t* = 1, ... , *n* crosses the opening level can be very large.

The final computational experiment is similar to the previous one, but both were carried out by a smoothed process *Y*˜ *t*, *t* = 1, ... , *n* at the intersection of the corresponding level. The results of the experiment are shown in Table 4.

**Table 4.** Positive outcome frequency: opening and closing by smoothed curve.

It is easy to see that the presented results are quite close to the corresponding estimates given in Table 3. In other words, using a smoothed curve did not change the final result. This is due to the fact that the probability of process *Yt*, *t* = 1, ... , *n* reaching the decision level will be higher both with a positive and negative outcome.

The disadvantage of the analysis method proposed above is that it does not take into account the quality of the transitions on which the local trend is detected. For example, transition *Y*(*k*) → *Y*(*k*) + *dY* can go on for a long time, with fluctuations and with a large negative "sagging" (it is only necessary that it does not turn around and does not reach level *Y*(*k*) − *dY*). Such a process is quite difficult to perceive as a trend. However, in accordance with the above formalization, such a transition will also be interpreted as a positive trend. In this regard, it makes sense to move on to a more complex trend detection criterion, based, for example, on the average rate of change in the state of the process on a sliding time window of size *l*:

$$
\Delta \mathcal{Y}(k, l) = \mathcal{Y}(k - l + 1, k) = \left[ \mathcal{Y}(k - l + 1), \mathcal{Y}(k - l + 2), \dots, \mathcal{Y}(k) \right] \tag{4}
$$

Trend detection in this case is exceeding the value of the linear approximation coefficient *a*1(*k*) calculated at the observation site Δ*Y*(*k*, *l*) of a certain critical value *a*1(*k*) > *a*∗. This approach can be generalized to more complex trend detection rules. In particular, we can consider a version of trend detection based on linear approximation coefficients calculated on two observation windows of different lengths Δ*Y*(*k*, *l*1) and Δ*Y*(*k*, *l*2), *l*1 > *l*2, or a version that uses a sliding approximation by a second-order polynomial. The second half of the proposed effectiveness analysis approach, namely, confirming the existence of a trend, remains unchanged. The *H*0 hypothesis of trend absence in the prolongation of the detected trend means that the process, after its detection at *t*0, reaches threshold values *Y*(*t*0) + *dL* and *Y*(*t*0) − *dL* with the same probability, i.e., *H*0 : *p* = *p*0 = 0.5, *p* being the value of the observed process at the time of trend detection. An alternative hypothesis indicating the possibility of using such strategies in conditions of market chaos will have the form *H*1 : *p* = *p*0 = 0.5. As in previous experiments, in addition to the main chaotic process *Y*(*t*), we will use its smoothed version *Ys*(*t*) (4) with a transmission coefficient. The process *Ys*(*t*), which simulates the system component of chaotic dynamics makes it possible to isolate the purely random component of the initial noise chaotic process *v*(*t*) = *Y*(*t*) − *Ys*(*t*), which is a centered random process with a distribution that is close to Gaussian. The variance of the residual process *D*(*v*(*t*)) , in turn, allows us to estimate the lower bound of the parameter *dL* that determines the level of confirmation or denial of the trend presence hypothesis. The method of conducting computational experiments is close to its prototype described above. An observation series of a trading asset's state at various non-intersecting 100-day observation intervals is considered as the polygon of chaotic data. Next, we form a sliding observation window Δ*Y*(*k*, *l*) of size *l*, on which we calculate approximating polynomials *P*(*q*, *l*), *q* being their degree. A decision about the presence of a trend is made based on the comparison of estimated coefficients of *a* with critical values *a*∗ . The number of outcomes corresponding to the process reaching a predetermined level *dL* is calculated to statistically verify the effectiveness of management decisions made following trend-based strategies. Due to the symmetry of the task, the negative result consists in a trend reversal and reaching the −*dL* level. If the ratio of reaching *dL* to the total number of position openings *m*/*n* (the frequency of the event) is close to 0.5, then this confirms the hypothesis *H*0 that it is impossible to successfully implement trend-based management strategies. The parameters of the computational experiment are observation window *l*, degree of smoothing polynomial *q*, threshold values of trends *a*∗, and trend confirmation level *dL* . The simplest linear approximation scheme *Y*˜(*t*) = *a*0 + *a*1*t* is used on a sliding observation window Δ*Y*(*k*, *l*). A trend is confirmed when the linear approximation coefficient *a*1 exceeds a pre-set value *a*∗ : *a*1 ≥ *a*∗. Trend presence is either denied or confirmed when the condition *Y*(*t*) = *Y*0 ± *dL* is met, in which *Y*0 = *Y*(*t*0) is the value of the process at the time of trend detection *t*0, and *dL* = 30, 50, 100 are the trend confirmation levels. The size of the observation window *l* varies in the (0.1–0.5) day range. A trend is detected if

**Table 5.** Trend confirmation frequency for different parameter values.

The presented data clearly confirms that it is impossible to successfully prolongate *Ys*(*t*) in a wide range of changes in intensity values, fixation levels and trend confirmation levels. The disadvantage of this experiment is the fixed length of the sliding observation window *l*. A large window causes a significant delay in trend detection, which leads to a delayed decision and, as a result, to an incorrect assessment of the probability of trend confirmation. An example is shown in Figure 5.

**Figure 5.** Examples of incorrect conclusions about the presence of a trend associated with a delay in decision-making.

A small window leads to an increased sensitivity of the trend detection procedure to the random component, which, in turn, leads to statistical errors of Type II (false alarms), that is, to the detection of a non-existent trend. In this regard, it makes sense to consider the problem of trend detection based on a complex criterion that uses two sliding observation windows of different sizes.

Unlike the previous experiment, in this one we consider two trends. In this case, linear approximations *q* = 1 are used for two sliding observation windows of size *l*1 and

*l*2, *l*1 > *l*2. It is obvious that the first trend has stronger smoothing characteristics, and the second is more sensitive to both systemic process changes and "false alarms". Let *l*1 = 300, *l*2 = 90 minute counts, critical values of the linear regression coefficient *a*∗ 1 = 0.05, *a*∗ 2 = 0.1 , the level of trend confirmation *dL* = 75. The decision on the presence of a trend is made if both linear regression coefficients exceed their critical values by the absolute value. An example of the implementation of such a scheme is shown in Figure 6.

**Figure 6.** Example of a decision-making scheme with two trends

Longer trends correspond to larger observation windows. Let us consider the result of using this method for four 100-day intervals with different levels of trend confirmation *dL* = 25 : 25 : 100. The corresponding data is presented in Table 6. It is easy to see that the modification did not have a positive effect.

**Table 6.** Trend confirmation frequency for various time intervals.

Obviously, the issues of the previous version of this approach have not been resolved. Additionally, the method, as a rule, detects a trend at the time of confirmation (or denial) of the previous trend. At the same time, there is no new trend detection during the confirmation time: this would require a method that simultaneously analyzes several trends. The provided data clearly illustrates the extremely insignificant fluctuations in the frequency of trend confirmation relative to the 0.5 value. This conclusion is easily confirmed by testing the statistical hypothesis *H*0 : *p* = 0.5 about the absence of a trend using U-statistics and confidence level *α* = 0.99.

#### **4. Discussion**

The applicability of statistical techniques for making management decisions for chaotic processes with a non-stationary random component is a key question in applied problems of asset management. An example of such a problem are effective management strategies based on statistical trend analysis. It is impossible to make analytical estimates of unstable inertia-less system management strategies because the observed processes are unstable parameter-wise. Thus, such studies can be conducted as numerical studies exclusively, considering large observation intervals that cover the variety of stochastic chaos. The technique proposed in the article uses segmentation of the area of change of the considered random process. Thus, it allows us to build a visual system for analyzing the effectiveness

of statistical management decisions. The use of the process itself to fix the levels of confirmation or denial of the management effectiveness does not lead to a stable solution due to the high degree of its stochastic spread. The process reaches decision-making levels more often due to high variance than as a result of an inertial trend. This leads to the idea of using a smoothed process for analysing inertia. In particular, good results are obtained with smoothing via an exponential filter with transfer coefficient *α* = 0.005 − 0.02.

A better management result can be expected from more efficient computational schemes for the extraction of the system component in observation series. This issue is currently under study.

Trend analysis that we have conducted does not confirm the effectiveness of trendbased statistical decisions. The trend management strategy for areas with a weak trend of chaotic variations of the immersion environment is essentially non-profitable. Detecting a trend on such segments of price dynamics indicates an upcoming change in the near future and, therefore, it being appropriate to open a position in the opposite direction. In other words, the problem lies not in the statistical methods of estimation themselves, but in the infinite variety of dynamic forms generated by market chaos, which makes it impossible to utilize simple stationary observation models.

It should be noted that currency market inertia is still not confirmed with statistical significance. Some facts that are observed at financial markets confirm this point. If a trend is detected, it is highly likely that in the next moment it will reverse. This means strategies that were effective on backtest could accidentally be effective in the future. The inability of the trend to continue its development can be explained by the fact that most of the time the composition of trading participants is in an equilibrium balance. The influence of trend-following traders (momentum traders) is compensated by market makers and mean reversion traders [16]. At the same time, according to the inaction inertia theory [17], individual investors who missed the opportunity to enter a position at a good price prefer to hold back from a trade at a less favorable price, thereby preventing the trend from developing. However, these factors become insignificant when the fundamental valuation of the asset is changed. When this view is shared by the majority of traders, a continuous trend may develop [18].

This leads to the conclusion that the market situation needs multilateral analysis. In particular, the use of the considered types of statistical solutions combined with an automatic text analyzer, which would assess the general "mood" in relation to the financial instruments used, would significantly increase the effectiveness of the generated decisions.

Therefore, the most promising direction in the development of the task of automatic management of market assets is the development of trading robots based on multi-expert systems. Our current and planned publications will be dedicated to the development of the conceptual and practical aspects of such systems.

**Author Contributions:** Conceptualization, A.M. and D.G.; methodology, A.M.; software, A.M.; validation, A.M. and D.G.; formal analysis, A.M.; investigation, A.M.; resources, A.M. and D.G; data curation, A.M.; writing-original draft preparation, A.M.; writing—review and editing, D.G.; visualization, A.M.; supervision, A.M.; project administration, D.G.; funding acquisition, D.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research of Alexander Musaev described in this paper is partially supported is partially supported by the Russian Foundation for Basic Research (grant 20-08-01046), state research FFZF-2022-0004. Dmitry Grigoriev research for this paper was funded by a Support from The Endowment Fund of St Petersburg University.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The source of data—Finam.ru (https://www.finam.ru/, accessed on accessed on 1 December 2021).

**Acknowledgments:** The authors are grateful to participants at the Center for Econometrics and Business Analytics (ceba-lab.org, CEBA) seminar series for helpful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**