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Additional lesions with signs of cerebral atrophy in 75% of acute and 50% of subacute phases were noted buy generic clomipramine 10mg on line. Such lipophilic compounds cross the normal blood brain barrier and localize in normal brain cells by passive transport proportional to the blood flow safe 75 mg clomipramine, with an extraction efficiency of around 60% order clomipramine in india. They have many applications in the field of epilepsy cheap clomipramine 50mg mastercard, cerebrovascular strokes, traumatic lesions, dementia and brain death [1]. On the other hand, 20lTl-chloride has been shown to reflect viable malignant glioma, as its uptake is related to the pumping effect of potassium, blood brain barrier dysfunction and increased regional blood flow. Group 1 consisted of 15 patients imaged within two weeks following surgery to detect residual tumours. Group 2 consisted of ten patients with possible recurrence or post-radiation gliosis. Twenty-five out of the 30 patients (83%) were uncontrolled by medical treat­ ment. A 64 x 64 projection with 30 s per view was obtained with the camera rotated 360°. Tomographic slices were recon­ structed using filtered back projection with a Shepp-Logan filter and a power of 0. Regions of interest were drawn on the slice with the greatest tumour activity and on the contralateral scalp for calculation of the early and delayed uptake and retention index. Post-operative residual A higher mean value of early and delayed 201T1 uptake of 2. There was a significant differ­ ence with a low retention index of 9 ± 2% in high grade glioma versus a high reten­ tion index of 32 ± 1% in low grade tumours (P < 0. Tumour recurrence versus gliosis A higher mean value for early and delayed 201T1 uptake of 2. Figures 1(a)- 1(b) show a case of astrocytoma with a residual viable tumour with a high uptake of 2. Epilepsy Thirty patients ranging in age from 15 to 34 years, with a mean age of 24. They had a history of epileptic fits ranging from 4 months to 20 years which were controlled through medical treatment. Cerebrovascular stroke Thirty patients, ranging in age from 40 to 65 years, with different types of cerebrovascular strokes were included in the study. There was no evidence of other lesions, cerebellar diaschiasis or signs of cerebral atrophy. The accumulation of 210T1 in malignant tumours may be related to changes in the blood brain barrier, regional blood flow and/or increased pumping of this potas­ sium analogue by the Na+-K + adenosine triphosphate pump [3]. In this study, a significant correlation between tumour grade and retention index (r = 0. Recurrent tumours or post-radiation gliosis Following radical dose of radiation therapy, it is critical to differentiate between post-radiation necrosis, which requires conservative measures, and recurrent tumours, which may need resurgery or adjuvant therapy in order to improve the quality of life and the survival rate [6]. In this work, 8 out of 10 patients (80%) were shown as having recurrent tumours in view of the high early, late 201T1 uptake and retention index. In this work, interictal evaluation for the detection of epileptic focus showed a sensitivity of 80, 73. However, differences in sensitivity between structural and functional imaging modalities disappear within 72 h [11]. This is a common finding accompanying cortical strokes because of cortico-pontine-cerebellar linkages which lead to reduced perfu­ sion as a secondary phenomenon following cerebral ischaemia [12]. Luxury perfusion was usually evident 5 to 20 d after the attack; however, its cause was not fully understood [13]. Twenty-one patients were studied: 14 females and 7 males, ranging in age from 11 to 74 years (x = 37 years). Reconstruction was made by filtered back projection and an attenuation correction algorithm was applied. Each study was visually evaluated and a semiquantitative method was used when significant uptake in the sellar region was observed. Pathology exami­ nations revealed pituitary adenomas in 15 cases, 2 cases of craniopharyngioma and 1 of dys- germinoma. Intracellular retention related to mitochondrial membrane potentials, which depend on the metabolic activity of the tissue. There is a wide variety of adenomas depending on the proliferating cell line, and modem classifications include immunohistochemical analysis for a proper evalu­ ation of the lesion. However, less attention has been paid to functional methods which can provide physiological information about the disease process, not only for diagnostic purposes, but also to evaluate the effects of therapy on tissue metabolism even before anatomical changes can be observed. For this reason, the search is justified for new functional imaging methods which could be used on a routine clinical basis at a lower cost. Compounds of the family of isonitriles constitute some of those new tracers and we evaluated two agents of this family for in vivo characterization of the functional aspects of pituitary tumours. Transverse, coronal and sagittal slices were generated and displayed for diagnostic evaluation. Each study was visually evaluated and a semiquantitative method was used when signifian t uptake in the sellar region was observed. This method consisted of the generation of identical regions of interest over the zone exhibiting uptake and over an adjacent area considered of normal tissue. The regions of interest were drawn on the transverse slice showing maximal uptake of the tracer in the lesion. A total count ratio between the regions of interest was then calculated (tumour/ normal (T/N)). Pathology examinations revealed various types of pituitary adenomas in 15 cases, 2 cases of craniopharyn­ gioma and 1 of dysgerminoma. All cases of pituitary adenoma had elevated hormonal serum levels, with high correlation with the radiotracer uptake ratio. In positive cases, visual inspection usually revealed intense uptake of the radio­ tracer in the mid-anterior aspect of the base of the skull, with high contrast with respect to adjacent structures (Figs 1-3). Moderate uptake on the projection of the choroid plexus was also observed, although not affecting the interpretation of the study because of the higher and lateral location. The tumour is clearly delineated (arrow) and there is no prominent uptake at the level of the choroid plexus. Since hormone secretion is a high energy demanding process, significant isonitrile uptake and retention in secreting adenomas could be anticipated, as is observed in parathyroid adenomas [8]. Further studies are warranted to establish the potential of this technique for research and routine clinical practice. Among them were 132 cases of cerebrovascular disease, 33 cases of Parkin­ son’s disease and 12 cases of dementia. Six cases of infarction of the basal ganglia accompanied by cerebral cortical hypoperfusion may be neurological functional communica­ tion disturbances (similar to diathesis). This find­ ing was not related to the Hoehn-Yahr stage and the laterality of motor symptoms. Li Ping Zhang, and Zhi Xu Gao reported that the incidence of dementia in the elderly was 3. It is thus very important to make a diagnosis and differential diagnosis of central nervous system diseases in elderly patients. After the occlusion of the middle cerebral artery, the ratio of lesion site to normal site activity in 11 rats was 0. Six cases of infarction of basal ganglia accompanied by cerebral cortical hypoperfusion were con­ sidered to be similar to the diaschiasis; this phenomenon was caused by the after­ effect of neurological functional communication disturbances. In the hemi- anopia group, as the visual function improved after light stimulation treatment, the blood perfusion increased in the occipital lobe. This finding was not related to the Hoehn-Yahr stage and the laterality of motor symptoms. In individual cases of Alzheimer’s disease, the prominent unilateral cortical hypoperfusion accompanied by unilateral basal ganglia, and contralateral regional cerebellum hypoperfusion, may also be due to diaschiasis, but cerebral vascular lesion cannot be ruled out. Multiple infarction dementia manifested multiple, irregular cortical hypoperfusion, mostly involved with basal ganglia or cerebellum lesions, which can be differentiated from Alzheimer’s disease. In the pre-surgical studies, all cases showed hypoperfusion in the bilateral temporal and parietal regions. Also, in two patients moderate striatal bilateral hypoperfusion was observed and in two other patients moderate hypoperfusion was found on the contralateral side most clinically affected.

The bowel sounds are normoac- tive discount 50mg clomipramine visa, and the patient’s stool is hemoccult-negative order clomipramine with a mastercard. An ab- dominal ﬁlm shows an enlarged gastric bubble with decompressed small intestinal loops purchase discount clomipramine online. All the following are risk factors for the de- velopment of this disease except A clomipramine 75mg without a prescription. A 25-year-old female with cystic ﬁbrosis is diag- nosed with chronic pancreatitis. Symptoms include greasy, foul-smelling stools that an extent where the patient has not been able to tolerate are difﬁcult to ﬂush. A 64-year-old man seeks evaluation from his pri- describes vomiting partially digested foods within a half mary care physician because of chronic diarrhea. He ports that he has two or three large loose bowel has experienced an unintentional 30-lb weight loss over 6 movements daily. The patient has a history of diabetes mellitus smelling, and they often leave an oily ring in the toilet. The patient underwent partial gastrectomy heavy meals, but if he fasts or eats low-fat foods, the for peptic ulcer disease at age 52. Crohn’s disease with ileitis pain previously, but when it occurs, he will limit his oral C. He has ered her crying on the ﬂoor of their bedroom, found stopped all alcohol intake for up to a week at a time in numerous open bottles of acetaminophen scattered the past without withdrawal symptoms. She is nauseated and physical examination, the patient is thin but appears vomits once in the emergency room. Cardiac and pulmonary examinations are nor- epigastric tenderness to deep palpation. Which of the is 12 cm to percussion and palpable 2 cm below the right following statements regarding her clinical condition is costal margin. The patient should be admitted and observed for 48 What is the next most appropriate step in diagnosing to 72 h as her hepatic injury may manifest days after and managing this patient’s primary complaint? Advise the patient to stop all alcohol use and pre- who develop fulminant hepatic failure from aceta- scribe pancreatic enzymes. Normal liver function tests at presentation make scribe narcotic analgesia and pancreatic enzymes. Prescribe prokinetic agents to improve gastric emp- pain, anorexia, and fever of 4 days’ duration. A 52-year-old male with chronic hepatitis C pre- verticulitis she has increased her ﬁber intake and sents to your clinic with worsening right upper quadrant avoids nuts and popcorn. Examination shows a palpable right upper quadrant for weight loss, daily chills and sweats, and “bubbles” mass. All the following are appropri- admitted with a presumptive diagnosis of diverticuli- ate management steps except tis. A 32-year-old man who recently returned from a department with hematochezia of 4 h duration. The pa- vacation in Thailand presents with the acute onset of tient is pale but alert and oriented. He is able to tol- 82 mmHg, respiratory rate is 24 breaths/min and heart erate small amounts of food. The hematocrit is 24%, with a base- and an abdominal examination reveals a nontender liver line of 32%. Which of the following represents the best ap- edge palpable 2 cm below the right costal margin. Angiography is most appropriate for this massive hepatitis B surface antigen is negative. Angiography is of little utility since the patient is not never received a hepatitis B vaccine series. Immediate lamivudine treatment for a planned 6- guished from chronic persistent hepatitis by the presence of month course A. All the following are causes of bloody diarrhea except tion, the patient has had profound diarrhea that occurs A. A 17-year-old Asian student complains of abdom- which reveals serpiginous ulcers in the distal esophagus inal bloating and diarrhea, particularly after eating ice without vesicles. Her parents have similar biopsies are taken that show intranuclear and intracyto- symptoms. The patient denies any weight loss or systemic plasmic inclusions in large endothelial cells and ﬁbro- symptoms. What is the best treatment for this patient’s ment with which of the following medications is most esophagitis? Conjugated bilirubin is passively transported into and tender hepatomegaly but is otherwise unremarkable. A 69-year-old man with Parkinson’s disease is ad- ate next study in this patient’s management? Adenosine deaminase activity of the ascitic ﬂuid developed diarrhea 2 days ago, and this morning was B. He remains febrile and hypotensive with blood care unit with obtundation and jaundice over 1–2 days. His abdomen is tense and distended, ﬁndings are obtained: with hypoactive bowel sounds. A defect in which of the following bilirubin meta- ing but remains elevated out of proportion to the patient’s bolic processes will give rise to bilirubinuria? Which of the following statements regarding bi- ing of abdominal pain off and on for several days, but lirubin metabolism is true? Bacterial β-glucuronidases unconjugate the conju- She is able to describe a sharp, stabbing pain in her ab- gated bilirubin that reaches the distal ileum. Bilirubin solubilizes in the serum after conversion and seems to have no appetite. The patient has been treated with gem- periences diarrhea that is hemoccult positive. The patient has had biliary stents placed with- men is mildly distended and she has hypoactive bowel out complication for obstructive jaundice. She does not exhibit rebound tenderness or weight is stable and he is able to perform activities of daily guarding. The patient wants to know what “the Several hours after admission she becomes unrespon- next step” is now that gemcitabine has seemed to fail. Blood pressure is difﬁcult to obtain and at best ap- is the most appropriate recommendation at this time? The lack of acute abdominal signs in this case is un- binemia from other causes except usual for mesenteric ischemia. The differential diagnosis of an isolated unconju- head gated (indirect) hyperbilirubinemia is limited. Characteristics of the ulcer at endoscopy provide important prognostic information. One-third of pa- tients with an active bleeding vessel or a nonbleeding visible vessel will have rebleeding that requires surgery. Any ﬁnding other than a clean-based ulcer should prompt admis- sion and monitoring for 3 days, as most rebleeding occurs within 3 days. Finding a clean- based ulcer is reassuring, and if the patient is stable and has no other indication for hos- pitalization, he may be safely discharged. Unlike some other causes of cirrhosis, pathologically it is characterized by small, ﬁne scarring and small regenerative nodules. There is clear evidence that excessive alco- hol use in the setting of chronic hepatitis C strongly increases the risk of development of cirrhosis; therefore, screening and appropriate counseling are essential. The intrinsic pathway contains many other unaf- fected factors, and the activated partial thromboplastin time is often normal. Unlike the case in acute viral hepatitis, acetaminophen toxicity, and vascular congestion, alcoholic injury to the liver rarely elevates the transaminases above levels in the hundreds. During the initial phase, pancreatic injury leads to intrapancreatic activa- tion of digestive enzymes with subsequent autodigestion and acinar cell injury. Acinar in- jury is primarily attributed to activation of zymogens (proenzymes), particularly trypsinogen, by lysosomal hydrolases.

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A second major advan- ing of the complex mechanism of hearing has increased enor- tage of the gene is its very small size cheap clomipramine 50mg mastercard, which makes genetic mously 25mg clomipramine otc. Promising tions generic clomipramine 75 mg mastercard, the genetic causes are distributed over dozens of genes cheap clomipramine 10mg line, results have recently been reported about phenotypic variability some of which are very large in size and hence expensive to in hearing loss caused by modiﬁer genes. Screening all known deafness genes for mutations characterisation of these modiﬁers will deﬁnitely be a new chal- would be extremely expensive with current technology, pro- lenge for deafness research. This can either be the analysis of help in reducing the increasing gap between scientiﬁc research many known mutations or be the complete mutation analysis of and diagnostic applications for hearing loss. Cell Tissue in connexin26, D66H, causes mutilating keratoderma with sen- Res 1998; 294:415–420. Am J Med Genet 2003; ciated with the most common form of non-syndromic neurosensory 117A:89–91. Nat speciﬁc spectrum of mutations in Japan, including a frequent Genet 1997; 17:411–422. A gene responsible membrane protein is mutated in patients with diabetes mellitus for a dominant form of neurosensory non-syndromic deafness and optic atrophy (Wolfram syndrome). J Cell Sci tiguous gene deletion causing infantile hyperinsulinism, enteropa- 2001; 114:2105–2113. J Cell Biol 1993; R143W mutation associated with recessive nonsyndromic sen- 123:1777–1788. Ann N Y Acad Sci 2000; glucose is decreased in embryonic lethal connexin26-deﬁcient 915:129–135. Targeted ablation of adhesion molecule, a novel member of the immunoglobulin super- connexin26 in the inner ear epithelial gap junction network family that distributes at intercellular junctions and modulates causes hearing impairment and cell death. Nat Genet 2000; mouse ortholog of the Pendred’s syndrome gene (Pds) suggests a 26:142–144. Mutations in connexin31 underlie and genotype of mutation in Pendred syndrome gene. Nat Rev Cx26 resulting from a heterozygous missense mutation in a family Genet 2004; 5:489–498. Mutations in cadherin 23 mice, is mutated in autosomal dominant nonsyndromic hearing affect tip links in zebraﬁsh sensory hair cells. Science stereocilin and otoancorin points to a uniﬁed mechanism for 2004; 303:2007–2010. Nat Genet 2001; has a mutation in the gene encoding the espin actin-bundling 29:345–349. Espin cross-links cause surface of sensory epithelia and their overlying acellular gels, is the elongation of microvillus-type parallel actin bundles in vivo. J Med in the human alpha-tectorin gene cause autosomal dominant Genet 2004; 41:591–595. Hum Mol Genet tion in alpha-tectorin reveals that the tectorial membrane is 2003; 12:1155–1162. Nat Genet induced and nonsyndromic deafness is associated with the 2002; 30:257–258. Am J Hum Genet 2004; gene Tmie results in sensory cell defects in the inner ear of 74:139–152. Maternally inherited hear- drial transcription factor B1 as a modiﬁer gene for hearing loss ing loss, ataxia and myoclonus associated with a novel point associated with the mitochondrial A1555G mutation. Unfortunately, these are only suitable The next 50 years will witness a signiﬁcant increase in ageing in for a limited number of people. Although hearing aids succeed in the European Union, the United States, and Japan, with the sufﬁcient ampliﬁcation of sound, the gain in speech recognition number of people aged 65 and above growing signiﬁcantly. This is, at least partly, due to the misconception that aged between 61 and 70 have a signiﬁcant hearing loss of at least hearing impairment is an inevitable burden of ageing, rather than 25 dB (1). In addition, hearing loss may have a major inﬂuence on their quality of life and their feeling of well-being. These ﬁgures are compara- stria vascularis, which can all degenerate independently. The latter study revealed prevalence ﬁg- vascularis and the spiral ganglion, respectively, are the major ures of 44% for the age range 60 to 69 years and 66% for the 70 affected structures (10,11). According to Schuknecht, audio- to 79 age range (pure tone thresholds averaged for 0. In addition, 25% of all cases cannot be classiﬁed accord- lower frequencies, while women hear better than men at fre- ing to Schuknecht’s scheme. For instance, at 60 years of age, the function of age remain, therefore, controversial (17). Areas of degeneration were concentrated in the Age-related hearing impairment: ensemble playing of environmental 81 apex and the base (25). In the Framingham seemed to be best correlated with changes in the supporting cells cohort, a relation between auditory and cognitive dysfunction of the basal half of the cochlea and with alterations in the spiral was observed. Moreover, aberrant test results for central audi- limbus in the apical part of the cochlea (27). In addition, apical neuronal loss was accompanied by responding neurons survive alongside slowly responding neu- abnormalities in pillar cells and the Reissner’s membrane and loss rons in older mice, indicating that wastage of individual neu- of ﬁbrocytes in the spiral limbus at the apical cochlear turn (28). Finally, an increase in the spontaneous activity of rabbit, gerbil, dog, and guinea pig. The tional studies gathered different types of evidence of the role of advantage of studying house dogs instead of laboratory animals is the central auditory pathway in presbyacusis. In subsequent studies, the variation in hearing ability in the high frequencies is due to an Ahl gene was shown to be a major contributor to the hearing loss interaction of genetic and environmental effects. The gene responsible was iden- the population variance for high-frequency hearing ability tiﬁed in 2003; in exon 7 of cadherin 23 (Cdh23), a hypomorphic above the age of 65 is caused by genetic differences, and half by single-nucleotide polymorphism (753A), leading to in-frame environmental differences (37). Johnson More recently, a Danish twin study evaluated the self- and Zheng demonstrated that the hearing loss attributable to reported reduced hearing abilities in 3928 twins of 75 years of Ahl2 is dependent on a predisposing Ahl genotype (46). The effect of tobacco smoking tive effects of disease, ototoxic agents, and other environmental and of alcohol (ab)use on hearing loss remains controversial (including noise) and dietary factors that act together with (57,62–67). Hearing loss due to head trauma could possibly be hereditary factors to inﬂuence the cochlear ageing process. The nutritional status Environmental risk factors also seems to have importance (69), while caloric-restriction Several environmental risk factors have been put forward as does not seem to have much effect (70). However, considerable controversy exists Interestingly, this effect remained even when noise exposure concerning the role of many of the risk factors. Clearly, it will be very difﬁcult to and the most studied risk factor for hearing loss is noise expo- assess what the contribution of all separate factors will be on sure. Also, noise exposure hypertension, diabetes, smoking, weight, and serum lipid levels) due to leisure activities (rock, classical or jazz music, personal lis- was investigated in the Framingham cohort (65). Of the cardiovascu- on hearing capabilities results from recreational hunting or tar- lar disease risk factors, hypertension and systolic blood pressure get shooting (50). It has been a point of debate whether ageing and noise cies (66), while Lee et al. The assumption of an additive effect has been most cation that vascular abnormalities might be important in the widely accepted. Either the disease itself (due to uraemic neuropathy, elec- eral, there is agreement on the fact that age-related changes trolyte imbalance, premature cardiovascular disease, shared exceed noise-induced changes for the 0. The detrimental effects of some chemicals on hearing tigators have observed an association between diabetes mellitus 84 Genetics and hearing impairment Table 6. This has been demonstrated with oversupplementa- The dissection of complex traits in humans has been particularly tion of vitamins E and C (85), and with two mitochondrial problematic. However, presently, many of the initial problems metabolites (acetyl-1-carnitine and alpha-lipoic acid) (86). Caloric for complex diseases: linkage studies on one hand and association restriction, which is also thought to reduce levels of oxidative studies on the other hand. These can be microsatellites (poly- ies in humans no, or only a very small, effect had been observed morphic tandem repeat consisting of small repeat units of 2 to for caloric restriction (Table 6. If marker alleles from a certain called common ageing mitochondrial deletion involves 4977 bp region are coinherited with the disease more than can be expected in humans (87–89), 4834 bp in rats (87,90), and 3867 bp in mice by chance, this region is said to be linked to the disease under (91).

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Normally only one type of coefﬁcient would Correlation and regression 201 be requested but to illustrate the difference between the correlation coefﬁcients buy generic clomipramine 10 mg, all three are requested in this example buy clomipramine online pills. If a left diagonal line was drawn through the matrix effective clomipramine 75mg, it can be seen that the information above the diagonal line is the same as the information below the line buy clomipramine canada. The correlation values would have a single asterisk if they were signiﬁcant at the P < 0. A comparison of the Pearson correlations (r values) in the Correlations table shows that the best predictor of weight is length with an r value of 0. Despite their differences in magnitude, the correlation coefﬁcients are all highly sig- niﬁcant at the P < 0. In the Non-parametric Correlations table, the Kendall’s tau-b coefﬁcients are all lower than the Pearson’s coefﬁcients indicating that there are some tied ranks in the data set, that is, babies with the same weight and length as one other. The Spearman’s coefﬁcients are similar in magnitude to the Pearson’s correlation coefﬁcients. Non-parametric Correlations Correlations Head circumference Weight (kg) Length (cm) (cm) Kendall’s Weight (kg) Correlation coefﬁcient 1. With this type of correlation, the linear relationship between two variables can be examined, while controlling or holding constant the effects of another confounding variable. The null hypothesis for a partial correlation is that there is no linear relationship between two variables after controlling for the effects of a confound- ing variable. For example, partial correlations could be conducted for the association between weight and head circumference after controlling for body length. The assump- tions for a partial correlation are the same as for Pearson’s correlation shown in Box 7. Therefore, both the effect size and the sample size should be considered when interpreting P values and statistical signiﬁcance. Conversely, a large effect size will be statistically signiﬁcant with a relatively small sample size. To examine the correlation in a selected sample, the data set can be restricted to babies less than 55. In addition, a ﬁlter variable to indicate the status of each case in the analysis is generated at the end of the spreadsheet with the coding 0 = not selected and 1 = selected. Correlations Correlations Head circumference Weight (kg) Length (cm) (cm) Weight (kg) Pearson correlation 1 0. When compared with Pearson’s r values from the full data set, the correlation coefﬁ- cient between weight and length is substantially reduced from 0. In general, r values are higher when the range of the explanatory variable is wider even though the relationship between the two variables is unchanged. For this reason, only the coefﬁcients from random population samples have an unbiased value and can be compared with one another. Once the correlation coefﬁcients are obtained, the full data set can be reselected using the command sequence Data → Select Cases → All cases. In reporting Pearson’s correlation coefﬁcient in this example, it could be reported as ‘The weight of babies at 1 month was signiﬁcantly related to their length (r = 0. There was also a signiﬁcant association between the length of babies and their head circumference (r = 0. These results indicate that as the length of babies increases, so does their head circumference and weight’. In this, a regression model is used to ﬁt a straight line through the data, where the regression line is the best predictor of the outcome variable using one or more explanatory variables. Normal values are the range of values that occur naturally in the general population. In developing a model to predict normal values, the emphasis is on building an accurate predictive model. The second purpose of using a regression model is to examine the effect of an explana- tory variable on an outcome variable after adjusting for other important explanatory factors. By using regression, additional information about the rela- tionships between variables and the between-group differences is obtained. In regres- sion, the distance between an observed value and the overall mean is partitioned into two components – the variation about the regression, which is also called the residual 206 Chapter 7 10 Variation about the regression 8 Variation due to the regression 6 Mean of the outcome value (Y) 4 2 Regression line 0 0 Explanatory variable Figure 7. The variation about the regression is the explained variation and the variation due to the regression is the unexplained variation. The F value, which is calculated as the regression mean square divided by the residual mean square, ranges from 1 to a large number. If the two sources of variance are similar, there is no association between the variables and the F value is close to 1. If the variation due to the regression is large compared to the variation about the regression, then the F value will be large indicating a strong association between the outcome and explanatory variables. When there is only one explanatory variable, the equation is called a simple lin- ear regression. When there is more than one explanatory variable in the model, the equation is called a multiple linear regression. With a regression model, an estimation of the best ﬁtting straight line through the data that minimizes the residual variation is calculated. Correlation and regression 207 In practice, the slope of the line, as estimated by ‘b’, represents the unit change in the outcome variable ‘y’ with each unit change in the explanatory variable ‘x’. If the slope is positive, ‘y’ increases as ‘x’ increases and if the slope is negative, ‘y’ decreases as ‘x’ increases. The intercept is the point at which the regression line intersects with the y-axis when the value of ‘x’ is zero. This value is part of the regression equation but does not usually have any clinical meaning. The ﬁtted regression line passes through the mean values of both the explanatory variable ‘x’ and the outcome variable ‘y’. When using regression, the research question must be framed so that the explanatory and outcome variables are classiﬁed correctly. An important concept is that regression predicts the mean y value given the observed x value and in this, the error around the explanatory variable is not taken into account. Therefore, measurements that can be taken accurately, such as age and height, are good explanatory variables. Variables that are difﬁcult to measure accurately or are subject to bias, such as birth weight recalled by parents when the baby has reached school age, should be avoided as explanatory variables. Regression models are robust to moderate degrees of non-normality provided that the sample size is large and that there are few multivariate outliers in the ﬁnal model. In general, the residuals but not the outcome variable have to be normally distributed. Also, the sam- ple does not have to be selected randomly because the regression equation describes the relation between the variables and is not inﬂuenced by the spread of the explanatory variable. However, it is important that the ﬁnal prediction equation is only applied to populations with the same characteristics as the study sample. For example, in building a model to predict normal values for blood pressure, the data must be collected when the participants have been resting rather than exercising and participants taking anti-hypertensive medications should be excluded. It is also important that all known covariates such as age and gender are included in the model before testing the effects of new variables in the model. The two assumptions of independence between observations and explanatory vari- ables are important. When explanatory variables are signiﬁcantly related to each other, a decision needs to be made about which variable to include and which variable to exclude. The remaining assumptions about the nature of the data can be tested when building the model. In this chapter, the assumptions are tested after obtaining a parsimonious model but in practice the assumptions should be tested at each step in the model building process. In simple linear regression, R is the absolute value of Pearson’s correlation coefﬁcient between the outcome and explanatory variable. R square has a valuable interpretation in that it indicates the per cent of the variance in the outcome variable that can be explained or accounted for by the explanatory variables. Hence, it is a measure of the ‘goodness of ﬁt’ of the regression line to the data. The adjusted R square value is the R value adjusted for the number of explanatory variables included in the model and can therefore be compared between models that include different numbers of explanatory variables. The R value for the model is equivalent to r when there is one explanatory variable in the model and can be used as a measure of effect size. Alternatively, Cohen’s f discussed in Chapter 5 can be extended to simple linear and multiple regressions using the R2 value rather than an eta squared value as follows: √ R2 Cohen’s f = (1 − R2) Correlation and regression 209 7.

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