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A dynamic adaptation of the propensity score adjustment for effectiveness analyses of ordinal doses of treatment.

The propensity score adjustment is a method to reduce bias in observational studies. We propose a strategy that involves a novel combination of three data analytic techniques, which adapts the propensity adjustment for additional perturbations of longitudinal, observational studies. First, ordinal logistic regression examines propensity for ordinal doses of treatment. Second, a mixed-model approach incorporates the multiple treatment trials and multiple episodes that are characteristic of chronically ill subjects. Finally, a mixed-effects grouped-time survival model incorporates the propensity score in treatment effectiveness analyses. The strategy that is applied here to an observational study of affective illness can also be used to evaluate the effectiveness of treatments for other chronic illnesses.

Adolescent↗

PubMed1998

Propensity score methods for bias reduction in the comparison of a treatment to a non-randomized control group.

In observational studies, investigators have no control over the treatment assignment. The treated and non-treated (that is, control) groups may have large differences on their observed covariates, and these differences can lead to biased estimates of treatment effects. Even traditional covariance analysis adjustments may be inadequate to eliminate this bias. The propensity score, defined as the conditional probability of being treated given the covariates, can be used to balance the covariates in the two groups, and therefore reduce this bias. In order to estimate the propensity score, one must model the distribution of the treatment indicator variable given the observed covariates. Once estimated the propensity score can be used to reduce bias through matching, stratification (subclassification), regression adjustment, or some combination of all three. In this tutorial we discuss the uses of propensity score methods for bias reduction, give references to the literature and illustrate the uses through applied examples.

Analysis of Variance↗

PubMed2005

The use of the propensity score for estimating treatment effects: administrative versus clinical data.

There is an increasing interest in using administrative data to estimate the treatment effects of interventions. While administrative data are relatively inexpensive to obtain and provide population coverage, they are frequently characterized by lack of clinical detail, often leading to problematic confounding when they are used to conduct observational research. Propensity score methods are increasingly being used to address confounding in estimating the effects of interventions in such studies. Using data on patients discharged from hospital for whom both administrative data and detailed clinical data obtained from chart reviews were available, we examined the degree to which stratifying on the quintiles of propensity scores derived from administrative data was able to balance patient characteristics measured in clinical data. We also determined the extent to which measures of treatment effect obtained using propensity score methods were similar to those obtained using traditional regression methods. As a test case, we examined the treatment effects of ASA and beta-blockers following acute myocardial infarction. We demonstrated that propensity scores developed using administrative data do not necessarily balance patient characteristics contained in clinical data. Furthermore, measures of treatment effectiveness were attenuated when obtained using clinical data compared to when administrative data were used.

Adrenergic beta-Antagonists↗

PubMed2007

Early surgery in patients with infective endocarditis: a propensity score analysis.

BACKGROUND: An accurate assessment of the predictors of long-term mortality in patients with infective endocarditis is not possible using retrospective data because of inherent treatment biases and predictable imbalances in the distribution of prognostic factors. Largely because of these limitations, the role of surgery in long-term survival has not been adequately studied. METHODS: Data were collected prospectively from 426 patients with infective endocarditis. Variables associated with surgery in patients who did not have intracardiac devices who had left-side-associated valvular infections were determined using multivariable analysis. Propensity scores were then assigned to each patient based on the likelihood of undergoing surgery. Using individual propensity scores, 51 patients who received medical and surgical treatment were matched with 51 patients who received medical treatment only. RESULTS: The following factors were statistically associated with surgical therapy: age, transfer from an outside hospital, evidence of infective endocarditis on physical examination, the presence of infection with staphylococci, congestive heart failure, intracardiac abscess, and undergoing hemodialysis without a chronic catheter. After adjusting for surgical selection bias by propensity score matching, regression analysis of the matched cohorts revealed that surgery was associated with decreased mortality (hazard ratio, 0.27; 95% confidence interval, 0.13-0.55). A history of diabetes mellitus (hazard ratio, 4.81; 95% confidence interval, 2.41-9.62), the presence of chronic intravenous catheters at the beginning of the episode (hazard ratio, 2.65; 95% confidence interval, 1.31-5.33), and paravalvular complications (hazard ratio, 2.16; 95% confidence interval, 1.06-4.44) were independently associated with increased mortality. CONCLUSIONS: Differences between clinical characteristics of patients with infective endocarditis who receive medical therapy versus patients who receive surgical and medical therapy are paramount. After controlling for inherent treatment selection bias and imbalances in prognostic factors using propensity score methodology, risk factors associated with increased long-term mortality included diabetes mellitus, the presence of a chronic catheter at the onset of infection, and paravalvular complications. In contrast, surgical therapy was associated with a significant long-term survival benefit.

Adult↗

PubMed1996

Matching using estimated propensity scores: relating theory to practice.

Matched sampling is a standard technique in the evaluation of treatments in observational studies. Matching on estimated propensity scores comprises an important class of procedures when there are numerous matching variables. Recent theoretical work (Rubin, D. B. and Thomas, N., 1992, The Annals of Statistics 20, 1079-1093) on affinely invariant matching methods with ellipsoidal distributions provides a general framework for evaluating the operating characteristics of such methods. Moreover, Rubin and Thomas (1992, Biometrika 79, 797-809) uses this framework to derive several analytic approximations under normality for the distribution of the first two moments of the matching variables in samples obtained by matching on estimated linear propensity scores. Here we provide a bridge between these theoretical approximations and actual practice. First, we complete and refine the nomal-based analytic approximations, thereby making it possible to apply these results to practice. Second, we perform Monte Carlo evaluations of the analytic results under normal and nonnormal ellipsoidal distributions, which confirm the accuracy of the analytic approximations, and demonstrate the predictable ways in which the approximations deviate from simulation results when normal assumptions are violated within the ellipsoidal family. Third, we apply the analytic approximations to real data with clearly nonellipsoidal distributions, and show that the theoretical expressions, although derived under artificial distributional conditions, produce useful guidance for practice. Our results delineate the wide range of settings in which matching on estimated linear propensity scores performs well, thereby providing useful information for the design of matching studies. When matching with a particular data set, our theoretical approximations provide benchmarks for expected performance under favorable conditions, thereby identifying matching variables requiring special treatment. After matching is complete and data analysis is at hand, our results provide the variances required to compute valid standard errors for common estimators.

Analysis of Variance↗

PubMed2004

Assessing the effect of batterer program completion on reassault using propensity scores.

Recent experimental evaluations have suggested little or no effect of batterer programs on reassault but are compromised by methodological and analytical issues. This study assesses program effect using propensity score analysis with a quasi-experimental sample in an attempt to address these issues. The sample consisted of 633 batterers and their partners from three geographically dispersed batterer programs and a 15-month follow-up with their female partners. Subclassification on propensity scores was used to balance program completers and program dropouts. The propensity score was estimated as the probability of completing the batterer program conditional on observable characteristics. Direct adjustment indicates that program completion reduced the probability of reassault during the 15-month follow-up by 33% for the full sample, and by nearly 50% for the court-ordered men.

Adolescent↗

PubMed2004

Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study.

Estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics. The propensity score, the probability of treatment exposure conditional on covariates, is the basis for two approaches to adjusting for confounding: methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores. We review popular versions of these approaches and related methods offering improved precision, describe theoretical properties and highlight their implications for practice, and present extensive comparisons of performance that provide guidance for practical use.

Computer Simulation↗

PubMed2004

On-pump versus off-pump coronary artery bypass grafting in diabetic patients: a propensity score analysis.

BACKGROUND: Diabetic patients are recognized as being at high risk for adverse outcomes after coronary artery bypass grafting. We evaluated our outcomes in diabetic patients to compare the effect of off-pump with on-pump coronary revascularization. METHODS: Between April 1997 and September 2002, 951 consecutive diabetic patients underwent isolated coronary artery bypass grafting. A total of 186 (19.6%) of these patients had off-pump coronary procedures. Multivariate logistic regression was used to assess the effect of off-pump coronary procedures on adverse in-hospital outcomes, while adjusting for patient and disease characteristics by constructing a propensity score from core patient characteristics. The propensity score was the probability of receiving off-pump coronary operation, with a C-statistic of 0.81, and was included along with the comparison variable in a multivariable analysis of outcome. All analysis was performed retrospectively. RESULTS: Off-pump patients were more likely to be obese (p = 0.032), have left main stem stenosis (p = 0.034), and have undergone prior cardiac operation (p = 0.027). The off-pump group had fewer patients with three-vessel disease compared with the on-pump group. After risk adjusting with propensity score, off-pump patients had a significantly lower incidence of stroke (adjusted odds ratio 0.15; p = 0.039) and renal failure (adjusted odds ratio 0.38; p = 0.036). Off-pump patients also required less blood transfusion (p < 0.001) and had shorter lengths of stay (p < 0.001). CONCLUSIONS: Off-pump coronary operation in diabetic patients significantly reduced postoperative morbidity and length of stay compared with on-pump coronary operation, although no in-hospital survival difference was noted between the two groups.

Acute Kidney Injury↗

PubMed2004

Vascular access and all-cause mortality: a propensity score analysis.

The native arteriovenous fistula (AVF) is the preferred vascular access because of its longevity and its lower rates of infection and intervention. Recent studies suggest that the AVF may offer a survival advantage. Because these data were derived from observational studies, they are prone to potential bias. The use of propensity scores offers an additional method to reduce bias resulting from nonrandomized treatment assignment. Adult (age 18 yr or more) patients who commenced hemodialysis in Australia and New Zealand on April 1, 1999, until March 31, 2002, were studied by using the Australian and New Zealand Dialysis and Transplant Association (ANZDATA) Registry. Cox regression was used to determine the effect of access type on total mortality. Propensity scores were calculated and used both as a controlling variable in the multivariable model and to construct matched cohorts. The catheter analysis was stratified by dialysis duration at entry to ANZDATA to satisfy the proportional-hazard assumption. There were 612 deaths in 3749 patients (median follow-up, 1.07 yr). After adjustment for confounding factors and propensity scores, catheter use was predictive of mortality. Patients with arteriovenous grafts (AVG) also had a significantly increased risk of death. Effect estimates were also consistent in the smaller propensity score-matched cohorts. Both AVG and catheter use in incident hemodialysis patients are associated with significant excess of total mortality. Reducing catheter use and increasing the proportion of patients commencing hemodialysis with a mature AVF remain important clinical objectives.

Adult↗

PubMed1995

Prognostic models and the propensity score.

Subjects in observational studies of exposure effects have not been randomized to exposure groups and may therefore differ systematically with regard to variables related to exposure and/or outcome. To obtain unbiased estimates and tests of exposure effects one needs to adjust for these variables. A common method is adjustment via a parametric model incorporating all known prognostic variables. Rosenbaum and Rubin propose adjustment by the conditional exposure probability given a set of covariates which they call the propensity score. They show that, at any value of the propensity score, covariates are on average balanced between exposure groups. Thus matching on the propensity score leads to unbiased estimators and tests of exposure effect. However, the validity of the method depends on knowing the exposure probability. This quantity is usually not known in observational studies and needs to be estimated.

Bias↗

PubMed2004

Propensity score estimation with boosted regression for evaluating causal effects in observational studies.

Causal effect modeling with naturalistic rather than experimental data is challenging. In observational studies participants in different treatment conditions may also differ on pretreatment characteristics that influence outcomes. Propensity score methods can theoretically eliminate these confounds for all observed covariates, but accurate estimation of propensity scores is impeded by large numbers of covariates, uncertain functional forms for their associations with treatment selection, and other problems. This article demonstrates that boosting, a modern statistical technique, can overcome many of these obstacles. The authors illustrate this approach with a study of adolescent probationers in substance abuse treatment programs. Propensity score weights estimated using boosting eliminate most pretreatment group differences and substantially alter the apparent relative effects of adolescent substance abuse treatment.

Evaluation Studies as Topic↗

PubMed2006

Evaluation of the risk of a nonrestorative resection for the treatment of diverticular disease: the Cleveland Clinic diverticular disease propensity score.

PURPOSE: The choice of operation for diverticular disease is a contentious issue, particularly in patients with acute symptoms. This study compares early outcomes between primary resection and anastomosis and Hartmann's resection and describes a propensity score for the selection of patients for nonrestorative procedures. METHODS: Data were collected from 731 patients undergoing primary resection and anastomosis (Group 1) and 123 patients undergoing primary Hartmann's resection (Group 2) for diverticular disease in a single tertiary referral center from January 1981 to May 2003. Multifactorial logistic regression was used to develop a propensity score for estimating the likelihood of performing a nonrestorative procedure. RESULTS: Operative 30-day mortality and surgical or medical complications were 0.7 percent, 26.0 percent, and 4.8 percent for primary resection and anastomosis and 12 percent, 43.9 percent, and 14.6 percent for Hartmann's resection, respectively (P < 0.001). There was no difference in the readmission rates between primary resection and anastomosis and Hartmann's resection (7.6 percent vs. 9.9 percent, P = 0.428). Laparoscopy was used for 32.7 percent of primary resection and anastomosis vs. 1.6 percent for Hartmann's resection (P < 0.001). Independent predictors in favor for Hartmann's resection were body mass index > or = 30 kg/m2 (odd's ratio = 2.32), Mannheim peritonitis index >10 (odd's ratio = 6.75), operative urgency (emergency, urgent vs. elective surgery, odd's ratio = 16.08 vs. 13.32), and Hinchey stage > II (odd's ratio = 27.82). The area under the receiver operating characteristic curve for the choice of operative procedure was 93.9 percent. CONCLUSIONS: Although Hartmann's resection was associated with a higher incidence of postoperative adverse events, the choice of operation was dependent on the patient presentation and intra-abdominal contamination, which can be quantified in the preoperative setting by the Cleveland Clinic diverticulitis propensity score.

Anastomosis, Surgical↗

PubMed2006

Centrum use and progression of age-related cataract in the Age-Related Eye Disease Study: a propensity score approach. AREDS report No. 21.

PURPOSE: To evaluate the effect of the multivitamin Centrum on the development and progression of age-related lens opacities. DESIGN: Clinic-based prospective cohort study. PARTICIPANTS: Four thousand five hundred ninety individuals with at least one natural lens and photographic follow-up (median, 6.3 years) were assessed for development or progression of lens opacities. MAIN OUTCOME MEASURES: Progression of "any" lens opacity or type-specific opacity was ascertained from lens photographs taken at baseline and at annual visits beginning at year 2. METHODS: The Age-Related Eye Disease Study (AREDS) showed no statistically significant effect of a high-dose antioxidant formulation on progression of lens opacities. Centrum also was provided to approximately two thirds of the study participants. Because Centrum use was elective, a logistic regression model of baseline characteristics was used to generate a propensity score for Centrum use. Repeated-measures logistic regression, adjusted for propensity score and other covariates, was used to evaluate associations of Centrum use and lens opacity. RESULTS: Centrum use, adjusted for propensity score and other covariates, was associated with a reduction in "any" lens opacity progression (odds ratio [OR] = 0.84, 95% confidence interval [CI] = 0.72-0.98, P = 0.025). Results for individual lens opacity types suggested that Centrum use was protective for nuclear opacity events (OR = 0.75, 95% CI = 0.61-0.91, P = 0.004). CONCLUSION: Observational data from the AREDS and other studies suggest that use of a multivitamin may delay the progression of lens opacities. A National Eye Institute-sponsored clinical trial scheduled for completion in 2007 will provide additional data on Centrum use and cataract development.

Aged↗

PubMed2007

Analysis of observational studies in the presence of treatment selection bias: effects of invasive cardiac management on AMI survival using propensity score and instrumental variable methods.

CONTEXT: Comparisons of outcomes between patients treated and untreated in observational studies may be biased due to differences in patient prognosis between groups, often because of unobserved treatment selection biases. OBJECTIVE: To compare 4 analytic methods for removing the effects of selection bias in observational studies: multivariable model risk adjustment, propensity score risk adjustment, propensity-based matching, and instrumental variable analysis. DESIGN, SETTING, AND PATIENTS: A national cohort of 122,124 patients who were elderly (aged 65-84 years), receiving Medicare, and hospitalized with acute myocardial infarction (AMI) in 1994-1995, and who were eligible for cardiac catheterization. Baseline chart reviews were taken from the Cooperative Cardiovascular Project and linked to Medicare health administrative data to provide a rich set of prognostic variables. Patients were followed up for 7 years through December 31, 2001, to assess the association between long-term survival and cardiac catheterization within 30 days of hospital admission. MAIN OUTCOME MEASURE: Risk-adjusted relative mortality rate using each of the analytic methods. RESULTS: Patients who received cardiac catheterization (n = 73 238) were younger and had lower AMI severity than those who did not. After adjustment for prognostic factors by using standard statistical risk-adjustment methods, cardiac catheterization was associated with a 50% relative decrease in mortality (for multivariable model risk adjustment: adjusted relative risk [RR], 0.51; 95% confidence interval [CI], 0.50-0.52; for propensity score risk adjustment: adjusted RR, 0.54; 95% CI, 0.53-0.55; and for propensity-based matching: adjusted RR, 0.54; 95% CI, 0.52-0.56). Using regional catheterization rate as an instrument, instrumental variable analysis showed a 16% relative decrease in mortality (adjusted RR, 0.84; 95% CI, 0.79-0.90). The survival benefits of routine invasive care from randomized clinical trials are between 8% and 21%. CONCLUSIONS: Estimates of the observational association of cardiac catheterization with long-term AMI mortality are highly sensitive to analytic method. All standard risk-adjustment methods have the same limitations regarding removal of unmeasured treatment selection biases. Compared with standard modeling, instrumental variable analysis may produce less biased estimates of treatment effects, but is more suited to answering policy questions than specific clinical questions.

Aged↗

PubMed2005

Application of a propensity score approach for risk adjustment in profiling multiple physician groups on asthma care.

OBJECTIVES: To develop a propensity score-based risk adjustment method to estimate the performance of 20 physician groups and to compare performance rankings using our method to a standard hierarchical regression-based risk adjustment method. DATA SOURCES/STUDY SETTING: Mailed survey of patients from 20 California physician groups between July 1998 and February 1999. STUDY DESIGN: A cross-sectional analysis of physician group performance using patient satisfaction with asthma care. We compared the performance of the 20 physician groups using a novel propensity score-based risk adjustment method. More specifically, by using a multinomial logistic regression model we estimated for each patient the propensity scores, or probabilities, of having been treated by each of the 20 physician groups. To adjust for different distributions of characteristics across groups, patients cared for by a given group were first stratified into five strata based on their propensity of being in that group. Then, strata-specific performance was combined across the five strata. We compared our propensity score method to hierarchical model-based risk adjustment without using propensity scores. The impact of different risk-adjustment methods on performance was measured in terms of percentage changes in absolute and quintile ranking (AR, QR), and weighted kappa of agreement on QR. RESULTS: The propensity score-based risk adjustment method balanced the distributions of all covariates among the 20 physician groups, providing evidence for validity. The propensity score-based method and the hierarchical model-based method without propensity scores provided substantially different rankings (75 percent of groups differed in AR, 50 percent differed in QR, weighted kappa=0.69). CONCLUSIONS: We developed and tested a propensity score method for profiling multiple physician groups. We found that our method could balance the distributions of covariates across groups and yielded substantially different profiles compared with conventional methods. Propensity score-based risk adjustment should be considered in studies examining quality comparisons.

Adult↗

PubMed2005

A propensity score approach to estimating the cost-effectiveness of medical therapies from observational data.

Health summary measures are commonly used by policy makers to help make decisions on the allocation of societal resources for competing medical treatments. The net monetary benefit is a health summary measure that overcomes the statistical limitations of a popular measure namely, the cost-effectiveness ratio. We introduce a linear model framework to estimate propensity score adjusted net monetary benefit. This method provides less biased estimates in the presence of significant differences in baseline measures and demographic characteristics between treatment groups in quasi-randomized or observational studies. Simulation studies were conducted to better understand the utility of propensity score adjusted estimates of net monetary benefits when important covariates are unobserved. The results indicated that the propensity score adjusted net monetary benefit provides a robust measure of cost-effectiveness in the presence of hidden bias. The methods are illustrated using data from SEER-Medicare for the treatment of bladder cancer.

Aged↗

PubMed2006

Variable selection for propensity score models.

Despite the growing popularity of propensity score (PS) methods in epidemiology, relatively little has been written in the epidemiologic literature about the problem of variable selection for PS models. The authors present the results of two simulation studies designed to help epidemiologists gain insight into the variable selection problem in a PS analysis. The simulation studies illustrate how the choice of variables that are included in a PS model can affect the bias, variance, and mean squared error of an estimated exposure effect. The results suggest that variables that are unrelated to the exposure but related to the outcome should always be included in a PS model. The inclusion of these variables will decrease the variance of an estimated exposure effect without increasing bias. In contrast, including variables that are related to the exposure but not to the outcome will increase the variance of the estimated exposure effect without decreasing bias. In very small studies, the inclusion of variables that are strongly related to the exposure but only weakly related to the outcome can be detrimental to an estimate in a mean squared error sense. The addition of these variables removes only a small amount of bias but can increase the variance of the estimated exposure effect. These simulation studies and other analytical results suggest that standard model-building tools designed to create good predictive models of the exposure will not always lead to optimal PS models, particularly in small studies.

Confounding Factors, Epidemiologic↗

PubMed2002

Comparing mortality of elderly patients on hemodialysis versus peritoneal dialysis: a propensity score approach.

The objective of this study was to evaluate differences in mortality over the first year of renal replacement therapy (RRT) between elderly patients starting treatment on hemodialysis (HD) versus peritoneal dialysis (PD). For the period of 1991 to mid-1996, this study defined an inception cohort of all patients aged >65 yr with new-onset chronic RRT who were New Jersey Medicare and/or Medicaid beneficiaries in the year before RRT and who had been diagnosed with renal disease more than 1 yr before RRT. Propensity scores were calculated for first treatment assignment from a large number of baseline covariates. Mortality was then compared among patients initially assigned to HD versus PD using multivariate 90-d interval Cox models controlled for propensity scores and center stratification. Peritoneal dialysis starters had a 16% higher rate of death during the first 90 d of RRT compared with HD patients (hazard ratio [HR], 1.16; 95% confidence interval [CI], 0.96 to 1.42)]. Mortality did not differ between day 91 and 180 (HR, 1.03; 95% CI, 0.71 to 1.51). Thereafter, PD starters again died at a higher rate (HR, 1.45; 95% CI, 1.07 to 1.98). These findings were more pronounced among patients with diabetes. Sensitivity analyses using more stringent criteria to ensure that first treatment choice reflected long-term treatment choice confirmed the presence of an association between PD and mortality. In conclusion, compared with HD, peritoneal dialysis appears to be associated with higher mortality among older patients, particularly among those with diabetes, even after controlling for a large number of risk factors for mortality, propensity scores to control for nonrandom treatment assignment, and center stratification.

Aged↗