weech - maldonado , shea , and mor ( 2006 ) examined the cost / outcome relationship for nursing homes and found that the pattern of the relationship depended on the choice of outcome measures .
different studies examining the relationship between inefficiency and health outcomes have also yielded contradictory results .
morey et al . ( 1992 ) and deily and mckay ( 2006 ) found that a hospital 's inefficiency score was positively associated with the observed in - hospital mortality rate , whereas mckay and deily ( 2008 ) did not find any consistent association .
some studies have used cost functions with costs as the dependent variable , where outcome measures were explanatory variables in a given cost function ( fleming 1991 ; carey and burgess 1999 ; weech - maldonado , shea , and mor 2006 ) .
this cost function usually has a hybrid functional form following grannemann , brown , and pauly ( 1986 ) .
however , mukamel , zwanziger , and tomaszewski ( 2001 ) , deily and mckay ( 2006 ) , and mckay and deily ( 2008 ) used outcomes as the dependent variables , where hospital cost was one explanatory variable .
a common feature of these studies is their use of aggregate measures for costs and health outcomes .
most studies use mortality ( i.e. , usually in - hospital mortality ) as the only outcome measure ( morey et al .
1992 ; mukamel , zwanziger , and tomaszewski 2001 ; deily and mckay 2006 ; ) . using both readmissions and mortality , fleming ( 1991 ) found that the association with costs was positive at low outcome levels , negative at intermediate outcome levels , and positive again at high outcome levels for both outcomes measures .
however , mckay and deily ( 2008 ) also used readmissions in addition to mortality and found no systematic pattern .
carey and burgess ( 1999 ) used posthospitalization outcomes for mortality and readmission , as well as outpatient follow - up rates .
they found that all three outcome measures were positively associated with hospital costs ( i.e. , high levels of mortality were associated with high costs ) .
weech - maldonado , shea , and mor ( 2006 ) used pressure ulcers and mood decline as outcome measures in nursing homes .
the goal of the present study was to explore and to quantify the relationship between costs and outcomes of treatment for ami while controlling for comorbidity , input quality , and organizational hospital characteristics .
we used individual - level data for costs , outcomes , and comorbidity from the vha .
mortality and readmission , each assessed 1 year after the index hospitalization , were used as measures of clinical outcome .
we hypothesized that outcome would be a function of age , comorbidities , costs , and hospital organizational characteristics .
while age , comorbidities , and costs can differ for each treated patient , hospital organizational characteristics remain identical for all patients treated in a given hospital . as a result , observations across patients violate assumptions such as independence and common variance .
significance tests are thus not robust and would overestimate the precision of information provided by the hospital - level variables . to avoid this problem , we applied random - effects proportional hazard models , also known as frailty models ( yamaguchi et al .
, we took a two - level multilevel modeling approach , nesting treated patients as microunits within hospitals , which were , in turn , considered to be macrounits .
we used the following model : where hij(t ) is the hazard for the ith patient in the jth hospital at time t. h0(t ) is the unspecified baseline hazard .
xij is a vector of explanatory variables at the patient level , while zj is a vector of explanatory variables at the hospital level .
 and  are two vectors that measure the effects of xij and zj , respectively .
0j , or 0j ( = exp(0j ) ) , if interpreted as a factor , represent the deviation of hospital j from the overall baseline hazard .
two models were estimated , one model for time to death and one model for time to readmission .
as the event  death  is a competing risk for the event  readmission ,  that is , death at a specific point in time thereafter excludes readmission , we treated observations that died as censored at the time of death in the readmission model ( allison 2005 ; s , dismuke , and guimaras 2007 ; ) .
however , is not a competing risk for the event  death  because the data allowed a follow - up for 365 days after index admission .
we also assumed that costs were endogenous to health outcomes , which we confirmed using the hausman test ( hausman 1978 ) .
thus , we subsequently used two - stage residual inclusion ( 2sri ) based on terza , basu , and rathouz ( 2008 ) .
the two - stage approach is less efficient than full information maximum likelihood but yields consistent estimates .
2sri has been used before for survival outcomes in a health care context by lindrooth and weisbrod ( 2007 ) .
the method requires the use of instrumental variables , that is , variables that are highly correlated with the endogenous variable ( costs ) , but not with unobserved determinants of the main outcome variable of interest ( time to readmission conditional on not dying , time to death ) .
these assumptions are often satisfied by variables that are correlated with the endogenous variable but have no direct effect on the outcome variable ( cameron and trivedi 2005 ) .
we believe that the medicare wage index and general overhead costs per day at the hospital level meet these criteria .
the medicare wage index adjusts hospital costs for regional differences in medical wages across the united states .
one could argue that higher wages may represent an extrinsic incentive for staff to perform better and deliver higher quality care .
however , the medicare wage index only covers wage differences between , and not within , regions and thus is unlikely to have a direct effect on health outcomes .
general overhead costs per day at the hospital level include cost elements from the nonmedical infrastructure of a hospital , for example , costs for activities such as housekeeping , engineering , and administration .
note that we excluded medical department overhead from overhead costs . the variable  general overhead costs per day  thus acts as a proxy for the price level a hospital faces to purchase certain activities excluding prices for medical personnel .
the costs are allocated by charging the same amount for each patient day irrespective of the reason for admission .
thus , this is a specific type of overhead costs , which does not relate to the actual hospital stay of each patient .
these overhead costs are predominantly fixed in the short term and are not related to ami treatment and severity of disease .
it should also be pointed out that this type of overhead costs is not related to either hospital size or angiography , because we control for both of these in the analysis at both stages of the estimation .
given our definition of general overhead costs per day at the hospital level , the variable is highly correlated with individual level costs per case but is unlikely to be associated with health outcomes .
in particular we also included the hospital 's occupancy rate and the overall hospital 's case mix .
however , their explanatory power was calculated to be low ( i.e. , with an f - value < 10 ) . because the use of weak instruments can be problematic in statistical analysis
we first estimated a generalized linear mixed model with cost as the dependent variable and all variables at the patient and hospital levels , including the medicare wage index and general overhead costs per day at the hospital level , as explanatory variables .
we assumed a gamma distribution for the variable  cost  and used a log - link function .
the functional form of the cost function incorporates variables used in structural cost functions and variables on an ad hoc basis ( grannemann , brown , and pauly 1986 ) .
subsequently , we estimated two separate random - effects proportional hazard models for mortality and readmission using the survival package of the statistical program r , which allows for frailty models .
actual costs and residuals from the first - stage regression were used in the second stage ( terza , basu , and rathouz 2008 ) .
we also reestimated including polynomials of the residuals . to adjust standard errors of the second - stage regression for including estimated residuals from the first stage , murphy 
topel adjustment was used ( murphy and topel 1985 ) . to assess the validity of the proportional hazards assumption , we plotted scaled schoenfeld residuals against event time .
in addition , according to a test suggested by grambsch and therneau ( 1994 ) , we regressed scaled schoenfeld residuals on event time for each covariate and tested for zero slope .
the goal of the present study was to explore and to quantify the relationship between costs and outcomes of treatment for ami while controlling for comorbidity , input quality , and organizational hospital characteristics .
we used individual - level data for costs , outcomes , and comorbidity from the vha .
mortality and readmission , each assessed 1 year after the index hospitalization , were used as measures of clinical outcome .
we hypothesized that outcome would be a function of age , comorbidities , costs , and hospital organizational characteristics .
while age , comorbidities , and costs can differ for each treated patient , hospital organizational characteristics remain identical for all patients treated in a given hospital . as a result , observations across patients violate assumptions such as independence and common variance .
significance tests are thus not robust and would overestimate the precision of information provided by the hospital - level variables . to avoid this problem , we applied random - effects proportional hazard models , also known as frailty models ( yamaguchi et al .
, we took a two - level multilevel modeling approach , nesting treated patients as microunits within hospitals , which were , in turn , considered to be macrounits .
we used the following model : where hij(t ) is the hazard for the ith patient in the jth hospital at time t. h0(t ) is the unspecified baseline hazard .
xij is a vector of explanatory variables at the patient level , while zj is a vector of explanatory variables at the hospital level .
 and  are two vectors that measure the effects of xij and zj , respectively .
0j , or 0j ( = exp(0j ) ) , if interpreted as a factor , represent the deviation of hospital j from the overall baseline hazard .
two models were estimated , one model for time to death and one model for time to readmission .
as the event  death  is a competing risk for the event  readmission ,  that is , death at a specific point in time thereafter excludes readmission , we treated observations that died as censored at the time of death in the readmission model ( allison 2005 ; s , dismuke , and guimaras 2007 ; ) .
however , is not a competing risk for the event  death  because the data allowed a follow - up for 365 days after index admission .
we also assumed that costs were endogenous to health outcomes , which we confirmed using the hausman test ( hausman 1978 ) .
thus , we subsequently used two - stage residual inclusion ( 2sri ) based on terza , basu , and rathouz ( 2008 ) .
the two - stage approach is less efficient than full information maximum likelihood but yields consistent estimates .
2sri has been used before for survival outcomes in a health care context by lindrooth and weisbrod ( 2007 ) .
the method requires the use of instrumental variables , that is , variables that are highly correlated with the endogenous variable ( costs ) , but not with unobserved determinants of the main outcome variable of interest ( time to readmission conditional on not dying , time to death ) .
these assumptions are often satisfied by variables that are correlated with the endogenous variable but have no direct effect on the outcome variable ( cameron and trivedi 2005 ) .
we believe that the medicare wage index and general overhead costs per day at the hospital level meet these criteria .
the medicare wage index adjusts hospital costs for regional differences in medical wages across the united states .
one could argue that higher wages may represent an extrinsic incentive for staff to perform better and deliver higher quality care .
however , the medicare wage index only covers wage differences between , and not within , regions and thus is unlikely to have a direct effect on health outcomes .
general overhead costs per day at the hospital level include cost elements from the nonmedical infrastructure of a hospital , for example , costs for activities such as housekeeping , engineering , and administration .
note that we excluded medical department overhead from overhead costs . the variable  general overhead costs per day  thus acts as a proxy for the price level a hospital faces to purchase certain activities excluding prices for medical personnel .
the costs are allocated by charging the same amount for each patient day irrespective of the reason for admission .
thus , this is a specific type of overhead costs , which does not relate to the actual hospital stay of each patient .
these overhead costs are predominantly fixed in the short term and are not related to ami treatment and severity of disease .
it should also be pointed out that this type of overhead costs is not related to either hospital size or angiography , because we control for both of these in the analysis at both stages of the estimation .
given our definition of general overhead costs per day at the hospital level , the variable is highly correlated with individual level costs per case but is unlikely to be associated with health outcomes .
in particular we also included the hospital 's occupancy rate and the overall hospital 's case mix .
however , their explanatory power was calculated to be low ( i.e. , with an f - value < 10 ) . because the use of weak instruments can be problematic in statistical analysis
we first estimated a generalized linear mixed model with cost as the dependent variable and all variables at the patient and hospital levels , including the medicare wage index and general overhead costs per day at the hospital level , as explanatory variables .
we assumed a gamma distribution for the variable  cost  and used a log - link function .
the functional form of the cost function incorporates variables used in structural cost functions and variables on an ad hoc basis ( grannemann , brown , and pauly 1986 ) .
subsequently , we estimated two separate random - effects proportional hazard models for mortality and readmission using the survival package of the statistical program r , which allows for frailty models .
actual costs and residuals from the first - stage regression were used in the second stage ( terza , basu , and rathouz 2008 ) .
we also reestimated including polynomials of the residuals . to adjust standard errors of the second - stage regression for including estimated residuals from the first stage , murphy 
topel adjustment was used ( murphy and topel 1985 ) . to assess the validity of the proportional hazards assumption , we plotted scaled schoenfeld residuals against event time .
in addition , according to a test suggested by grambsch and therneau ( 1994 ) , we regressed scaled schoenfeld residuals on event time for each covariate and tested for zero slope .
the primary data source in this study was a set of vha administrative files for the fiscal years 2000 through 2006 . for each ami patient , we selected the index hospitalization during which a primary diagnosis of ami was made .
we excluded all patients who were admitted and discharged on the same day , because we assumed that these patients were transferred to other hospitals or ruled out for ami .
moreover , we excluded patients who had been admitted with ami in the previous year , as well as those whose ami was coded as an in - hospital complication . ultimately , a total of 115 vha hospitals with 35,279 patients remained in the sample . for measuring costs , the vha database offers several advantages over the american hospital association data commonly used in u.s .
hospital cost estimation , because the former is based on the requirement that hospitals provide information to a standardized internal accounting system that is subject to extensive periodic audits .
the vha accounting system was established in the 1990s and has been continuously improved since then .
it provides detailed cost information for hospitalization episodes and thus individual - level cost data .
moreover , it includes the costs of physicians while , at the same time , excluding capital costs .
we eliminated the costs of postacute care , a component usually included in vha hospital costs , from the total costs , and we excluded patients whose total treatment costs were recorded as being < u.s.$100 , interpreting this as an obvious accounting error .
finally , costs were deflated to reflect year 1999 values . to control for patient comorbidities , we compiled a comprehensive list of comorbidities that have been found in other studies to affect mortality .
in doing so , we relied on the ontario acute myocardial infarction mortality prediction rules ( tu et al .
2001 ) and the charlson comorbidity index ( sundararajan et al . 2004 ) . because evans et al .
( 2007 ) have shown that comorbidities associated with mortality in ami patients are also associated with resource use , we hypothesized that these and other predictors of mortality risk would also be associated with inpatient costs .
we thus also included the full set of comorbidities for the first - stage cost estimation . for coding diagnoses
we obtained data on hospital organizational characteristics that we judged to be potentially associated with outcomes .
the number of treated ami patients per hospital was included to control for volume effects , because a larger number of treated cases has been found to be associated with superior outcomes for specific indications ( birkmeyer et al .
, we used the number of beds to control for the size of the hospital ( carey and burgess 1999 ; dudley et al .
one of these was a dummy variable for a hospital 's teaching status , which we used as a proxy for staff qualification and equipment .
each vha hospital was classified as a teaching - affiliated hospital if it was a member of the council of teaching hospitals ( coth ) . as a proxy for labor intensity
, we included the ratio of nurses per bed for each hospital ( needleman et al .
( 2004 ) , we also included a dummy variable for a hospital 's capability to perform coronary angiography ; we counted five or more claims for coronary angiography as evidence of a hospital 's capability to perform this procedure .
all hospital characteristics were also included in the first - stage cost equation . to control for regional effects
, we included regional dummies into first- and second - stage equations . as discussed previously , we estimated a cost equation in the first stage .
the additional variables included in this equation are the medicare wage index obtained from the centers for medicare and medicaid services and general overhead costs per day on hospital level .
table 2 presents coefficient estimates and p - values for the first - stage cost equation .
the signs of the estimated coefficients were generally in line with our expectations , and the variables for medicare wage index and general overhead costs per day were highly significant .
characteristics of the study sample values for mortality do not include cases who died during index hospitalization .
the coefficients for ami cases ( no . ) and beds were multiplied by 100 .
table 3 shows the results of the second - stage regression models , with mortality and readmission conditional on not dying as dependent variables . for the mortality equation ,
the majority of coefficients had the expected signs and the equation showed a highly significant negative association between costs and mortality .
every u.s.$100 less spent is associated with a 0.63 percent increase in the hazard of dying .
the risk for mortality also decreased significantly as the number of treated ami cases per hospital increased ( each additional ami case treated decreased the hazard of dying by 0.32 percent ) .
every u.s.$100 less spent is associated with a 1.24 percent increase in the hazard to be readmitted conditional on not dying . except for angiographic capability that was positively associated with readmission conditional on not dying , hospital - level variables were not significant .
dependent variables : time to death and time to readmission within 1 year of discharge .
the coefficients for ami cases ( no . ) and beds were multiplied by 100 .
we tested the robustness of our findings in five ways . to begin with , we reestimated the first- and second - stage regressions using readmission and mortality assessed 1 year after admission from the index hospitalization instead of discharge .
thus , in these reestimated models mortality and readmission are dated from the admission to the hospital because one could argue that if dated from discharge some individuals would be observed shorter than others due to longer hospitalization .
second , we ran the models by excluding cases that were transferred between different hospitals during index hospitalization ( 3,131 cases ) .
the modification had very little impact on the coefficient of the cost variable , which remained highly significant in both equations .
third , we reestimated both models without a multilevel approach dropping the higher level variables . in doing so
, we made a correction for clusters of the variance  covariance matrix to obtain a robust estimate in the second stage .
the size of the coefficients decreased slightly in both equations , but it remained highly significant .
fourth , we ran the models with an extended observation period of 2 years instead of 1 year for both outcomes .
again the modification had very little impact on the coefficient of the cost variable , which remained highly significant in both equations .
fifth , we obtained f - statistics to test the reliability of our instrument ( i.e. , whether our instrument was correlated with the costs ) . because the f
- statistics for the medicare wage index and general overhead per day were 23.69 and 58.91 , respectively , weak correlation is unlikely to be a source of bias ( bound , jaeger , and baker 1995 ; staiger and stock 1994 ) .
when plotting scaled schoenfeld residuals against event time for the survival models , the mortality model appeared to be a good fit to the data .
according to the regressions , the proportional assumption seems to have been violated for the variable  chronic renal failure ,  and some of the dummy variables for year of treatment .
however , this might also be due to the ols regression being heavily influenced by outliers ( thompson et al .
2003 ) that could be identified in the plots . in the readmission model , however , the proportional hazard assumption seems to have been violated more often .
therefore , and as an additional sensitivity analysis , we also fitted a weibull model for mortality and readmission , respectively .
the results in both models , that is , the sign of the coefficient for the variable cost and the p - value , remained robust .
if parameter estimates of the weibull models are transformed to hazard ratios , every u.s.$100 less spent is associated with a 0.64 percent increase in the hazard of dying and a 1.27 percent increase in the hazard of a readmission conditional on not dying .
in this paper , we investigated and we quantified the relationship between hospital costs and health outcomes for patients with ami using a two - step random intercept cox proportional hazard model to obtain consistent estimates of the effects of costs on outcomes .
we followed a more refined approach than previous studies investigating this relationship by ( a ) focusing on one episode of care , ( b ) using patient - level data , and ( c ) applying a survival model .
we found that costs were negatively associated with mortality and with readmission conditional on not dying .
outcome relationship appears to be very clear in both cases , although costs were more significant in the readmission equation compared with the mortality equation .
the finding that the relationship between costs and outcomes is negatively correlated for both outcome measures is at odds with the results obtained by carey and burgess ( 1999 ) , who also based their analysis on vha data .
they found that both 1-year mortality and 1-year readmissions were positively associated with hospital costs .
they suggested that differences in severity of illness unmeasured by the case mix were a likely explanation for this result .
however , comparability to our study is limited by the fact that carey and burgess ( 1999 ) did not concentrate solely on ami as one episode of care and by that they used aggregate hospital costs instead of patient - level costs .
in addition , they did not use a survival model and did not control for competing risks . in general , none of the previous studies used a survival model to investigate the cost  outcome relationship , making any comparison with our study difficult .
the negative association between costs and the risk for mortality / readmission conditional on not dying confirms the often - stated hypothesis that increased resource input for patients should clearly lead to better outcomes .
some of the hospital - level variables had unexpected signs , although most of them ( e.g. , coth ) were not significant .
however , the positive coefficient for the variable for capability of angiography in both equations suggests that the risk for an event , that is , readmission conditional on not dying or death , increases significantly with capability of angiography .
one potential explanation for this pattern may be that certain measures for case mix are not included .
thus , the positive coefficients for angiography capability may reflect higher severity rather than input quality .
, it is the first study , to our knowledge , to examine the trade - off between costs and outcomes using patient - level cost and outcome data .
the use of patient - level data enabled us to obtain more consistent estimates on the relationship between costs and outcomes .
second , we focused on ami as one episode of care , which allowed us to control appropriately for case mix .
third , we are the first study exploring this trade - off using a cox proportional hazard model and considering the competing risk nature of the data .
fourth , the rich data sample containing information at the patient and hospital levels allowed us to use a multilevel model combined with a 2sri model .
first , certain undocumented health - related conditions or factors may explain part of the variation in our outcome variables , thus potentially affecting the relationship between costs and outcomes . also , the validity of the instruments relies on the assumption that the error structure follows a random effects model
. another limitation may be this study 's focus on mortality and readmissions as opposed to clinical - outcome measures .
although the vha has a standardized internal accounting system , certain variations in costs may be explained by the different accounting systems used in different vha hospitals , which is a factor we were unable to control for .
finally , our study uses only vha data , which raises the question of generalizability beyond the vha .
it is likely that the relationship between costs and outcomes varies according to the health care context , differing , for example , between fragmented and integrated health care systems .
for instance , an integrated delivery system with managed care elements , such as the vha , is more likely than fragmented health care systems to avoid or substitute readmissions .
thus , in the vha context , it is conceivable that patients with multiple conditions  for which acute hospital treatment was not appropriate  were less likely to be readmitted . in spite of the clear findings
certainly , the negative association between costs and mortality and costs and readmission conditional on not dying does not mean that every clinical intervention is justified , especially if the costs of the intervention are greater than the benefits .
however , this negative association does suggest that reductions in costs may indeed lead to poorer outcomes .
because of this , outcomes should be monitored closely when introducing cost - containment programs . moreover , linking reimbursement rates to outcomes , as is practiced in reimbursement programs such as  pay for performance  in the united states or 
payment by results  in the united kingdom , might represent a promising approach to overcoming the trade - off between costs and outcomes , supplying providers with incentives to keep outcomes stable in spite of decreasing costs .
outcome relationship for conditions other than ami to see whether our results are consistent . with this in mind , examining the various treatment processes within organizations would also seem a fruitful way of gaining a greater understanding of this relationship .
additional supporting information may be found in the online version of this article : appendix sa1 : author matrix .
please note : wiley - blackwell is not responsible for the content or functionality of any supporting materials supplied by the authors .
any queries ( other than missing material ) should be directed to the corresponding author for the article .
 objectiveto investigate and to quantify the relationship between hospital costs and health outcomes for patients with acute myocardial infarction ( ami ) in veterans health administration ( vha ) hospitals using individual - level data for costs and outcomes.data sourcesvha administrative files for the fiscal years 20002006.study designcosts were defined as costs incurred during the index hospitalization for treatment of ami . 
 mortality and readmission , assessed 1 year after the index hospitalization , were used as measures of clinical outcome . 
 we examined health outcomes as a function of costs and other patient - level and hospital - level characteristics using a two - stage cox proportional hazard model that accounted for competing risks within a multilevel framework . to control for patient comorbidities , we compiled a comprehensive list of comorbidities that have been found in other studies to affect mortality and readmissions.principal findingswe found that costs were negatively associated with mortality and readmissions . 
 every u.s.$100 less spent is associated with a 0.63 percent increase in the hazard of dying and a 1.24 percent increase in the hazard to be readmitted conditional on not dying . 
 this main finding remained unchanged after a number of sensitivity checks.conclusionsour results suggest that there is a trade - off between costs and outcomes . 
 the negative association between costs and mortality suggests that outcomes should be monitored closely when introducing cost - containment programs . 
 additional studies are needed to examine the cost  
 outcome relationship for conditions other than ami to see whether our results are consistent . 
PREVIOUS RESEARCH
METHODOLOGY
Empirical Model
Estimation Issues
DATA
RESULTS
DISCUSSION
SUPPORTING INFORMATION