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PubMedDate not supplied

Too much ado about propensity score models? Comparing methods of propensity score matching.

OBJECTIVE: A large number of possible techniques are available when conducting matching procedures, yet coherent guidelines for selecting the most appropriate application do not yet exist. In this article we evaluate several matching techniques and provide a suggested guideline for selecting the best technique. METHODS: The main purpose of a matching procedure is to reduce selection bias by increasing the balance between the treatment and control groups. The following approach, consisting of five quantifiable steps, is proposed to check for balance: 1) Using two sample t-statistics to compare the means of the treatment and control groups for each explanatory variable; 2) Comparing the mean difference as a percentage of the average standard deviations; 3) Comparing percent reduction of bias in the means of the explanatory variables before and after matching; 4) Comparing treatment and control density estimates for the explanatory variables; and 5) Comparing the density estimates of the propensity scores of the control units with those of the treated units. We investigated seven different matching techniques and how they performed with regard to proposed five steps. Moreover, we estimate the average treatment effect with multivariate analysis and compared the results with the estimates of propensity score matching techniques. The Medstat MarketScan Data Base provided data for use in empirical examples of the utility of several matching methods. We conducted nearest neighborhood matching (NNM) analyses in seven ways: replacement, 2 to 1 matching, Mahalanobis matching (MM), MM with caliper, kernel matching, radius matching, and the stratification method. RESULTS: Comparing techniques according to the above criteria revealed that the choice of matching has significant effects on outcomes. Patients with asthma are compared with patients without asthma and cost of illness ranged from 2040 dollars to 4463 dollars depending on the type of matching. After matching, we looked at the insignificant differences or larger P-values in the mean values (criterion 1); low mean differences as a percentage of the average standard deviation (criterion 2); 100% reduction bias in the means of explanatory variables (criterion 3); and insignificant differences when comparing the density estimates of the treatment and control groups (criterion 4 and criterion 5). Mahalanobis matching with caliber yielded the better results according all five criteria (Mean = 4463 dollars, SD = 3252 dollars). We also applied multivariate analysis over the matched sample. This decreased the deviation in cost of illness estimates more than threefold (Mean = 4456 dollars, SD = 996 dollars). CONCLUSION: Sensitivity analysis of the matching techniques is especially important because none of the proposed methods in the literature is a priori superior to the others. The suggested joint consideration of propensity score matching and multivariate analysis offers an approach to assessing the robustness of the estimates.

Confounding Factors, Epidemiologic↗

PubMed2005

The effects of antipsychotic treatment on quality of life of schizophrenic patients under naturalistic treatment conditions: an application of random effect regression models and propensity scores in an observational prospective trial.

The study examines the effect of different types of antipsychotic treatment on the health related quality of life (HRQL) of people with schizophrenia under naturalistic outpatient treatment conditions. In a prospective study design, 307 schizophrenic patients were followed over a period of 2.5 years. HRQL, clinical characteristics, and type of antipsychotic medication were assessed five times every 6 months. HRQL was assessed by the SF-36. Random effect regression models were computed for the SF-36 mental (MCS) and physical (PCS) component scores. Propensity scores were included in the regression models to reduce a possible sample selection bias. Monotherapeutic treatment with new atypical neuroleptic drugs had a more positive effect on the mental health related quality of life (MCS) in comparison to treatment with polypharmacological treatment but not with oral conventional antipsychotics. Monopharmaceutical treatment with depot-antipsychotic drugs had a more positive effect on the physical health related quality of life (PCS) in comparison to polypharmacological treatment. Study results indicate that atypical antipsychotic drugs are not superior to conventional antipsychotics with regard to the effect on QOL. However, monopharmaceutical treatment can be assumed to be more effective in improving mental and physical related QOL than polypharmaceutical treatment.

Adolescent↗

PubMed1999

Invited commentary: propensity scores.

The propensity score is the conditional probability of exposure to a treatment given observed covariates. In a cohort study, matching or stratifying treated and control subjects on a single variable, the propensity score, tends to balance all of the observed covariates; however, unlike random assignment of treatments, the propensity score may not also balance unobserved covariates. The authors review the uses and limitations of propensity scores and provide a brief outline of associated statistical theory. They also present a new result of using propensity scores in case-cohort studies.

Case-Control Studies↗

PubMed1989

Performance of tests of significance based on stratification by a multivariate confounder score or by a propensity score.

Stratification by a multivariate confounder score or by a propensity score has been proposed for the multi-confounder situations that are commonly encountered in epidemiologic evaluations of the effects of a treatment or a triage decision. However, the use of these scores in clinical research has been limited, perhaps in part because of the concern that the stated level of statistical significance may be exaggerated when there is a high degree of correlation between the exposure and the set of confounders. We present a specific example and computer simulations to suggest that exaggeration of statistical significance occurs only under unusual circumstances when the correlation between the exposure and the confounders is extreme. Our simulations also suggest that an analysis based on stratification by a propensity score is less affected by high correlation between the exposure and the confounders than is an analysis based on a multivariate confounder score.

Computer Simulation↗

PubMed2007

The performance of different propensity score methods for estimating marginal odds ratios.

The propensity score which is the probability of exposure to a specific treatment conditional on observed variables. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. In the medical literature, propensity score methods are frequently used for estimating odds ratios. The performance of propensity score methods for estimating marginal odds ratios has not been studied. We performed a series of Monte Carlo simulations to assess the performance of propensity score matching, stratifying on the propensity score, and covariate adjustment using the propensity score to estimate marginal odds ratios. We assessed bias, precision, and mean-squared error (MSE) of the propensity score estimators, in addition to the proportion of bias eliminated due to conditioning on the propensity score. When the true marginal odds ratio was one, then matching on the propensity score and covariate adjustment using the propensity score resulted in unbiased estimation of the true treatment effect, whereas stratification on the propensity score resulted in minor bias in estimating the true marginal odds ratio. When the true marginal odds ratio ranged from 2 to 10, then matching on the propensity score resulted in the least bias, with a relative biases ranging from 2.3 to 13.3 per cent. Stratifying on the propensity score resulted in moderate bias, with relative biases ranging from 15.8 to 59.2 per cent. For both methods, relative bias was proportional to the true odds ratio. Finally, matching on the propensity score tended to result in estimators with the lowest MSE.

Bias↗

PubMed2006

Interval estimation for treatment effects using propensity score matching.

In causal studies without random assignment of treatment, causal effects can be estimated using matched treated and control samples, where matches are obtained using estimated propensity scores. Propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions. Despite its application in many applied problems, there is no universally employed approach to interval estimation when using propensity score matching. In this article, we present and evaluate approaches to interval estimation when using propensity score matching.

Adolescent↗

PubMed2005

Weaknesses of goodness-of-fit tests for evaluating propensity score models: the case of the omitted confounder.

PURPOSE: Propensity scores are used in observational studies to adjust for confounding, although they do not provide control for confounders omitted from the propensity score model. We sought to determine if tests used to evaluate logistic model fit and discrimination would be helpful in detecting the omission of an important confounder in the propensity score. METHODS: Using simulated data, we estimated propensity scores under two scenarios: (1) including all confounders and (2) omitting the binary confounder. We compared the propensity score model fit and discrimination under each scenario, using the Hosmer-Lemeshow goodness-of-fit (GOF) test and the c-statistic. We measured residual confounding in treatment effect estimates adjusted by the propensity score omitting the confounder. RESULTS: The GOF statistic and discrimination of propensity score models were the same for models excluding an important predictor of treatment compared to the full propensity score model. The GOF test failed to detect poor model fit for the propensity score model omitting the confounder. C-statistics under both scenarios were similar. Residual confounding was observed from using the propensity score excluding the confounder (range: 1-30%). CONCLUSIONS: Omission of important confounders from the propensity score leads to residual confounding in estimates of treatment effect. However, tests of GOF and discrimination do not provide information to detect missing confounders in propensity score models. Our findings suggest that it may not be necessary to compute GOF statistics or model discrimination when developing propensity score models.

Confounding Factors, Epidemiologic↗

PubMed2001

Estimating the effect of an intensive surveillance program on stage of breast carcinoma at diagnosis: a propensity score analysis.

BACKGROUND: The authors used propensity score adjustment to investigate the impact of intensive screening on stage of breast carcinoma at diagnosis in women who were at elevated risk for breast carcinoma. METHODS: The authors compared 58 women participating in a surveillance program at the Columbia Presbyterian Medical Center of New York Presbyterian Hospital who developed breast carcinoma with 3022 nonparticipating breast carcinoma patients. A propensity score was constructed for each woman by using important background covariates, and multivariable regression modeling was used to estimate the association of program membership with disease stage after adjusting for the propensity score. RESULTS: Before propensity score adjustment, nine baseline covariates significantly differed between the two groups (number of pregnancies, number of births, age at first delivery, race, how the tumor was discovered, history of prior breast disease, breast carcinoma in mother, breast carcinoma in maternal aunt, and breast carcinoma in sister), and there was a significant difference in stage at diagnosis. After adjustment, no significant differences remained. Program participants were more likely to have lower stage tumors at diagnosis than nonparticipants, but this association did not reach statistical significance (odds ratio, 1.52; 95% confidence interval, 0.94--2.46). CONCLUSIONS: Propensity score methods can remove bias in treatment comparisons in observational studies. An intensive surveillance program at a major cancer center may have had some effect on improving stage at diagnosis, but this effect was not statistically significant.

Breast Neoplasms↗

PubMed2005

Propensity scores: an introduction and experimental test.

Propensity score analysis is a relatively recent statistical innovation that is useful in the analysis of data from quasi-experiments. The goal of propensity score analysis is to balance two non-equivalent groups on observed covariates to get more accurate estimates of the effects of a treatment on which the two groups differ. This article presents a general introduction to propensity score analysis, provides an example using data from a quasi-experiment compared to a benchmark randomized experiment, offers practical advice about how to do such analyses, and discusses some limitations of the approach. It also presents the first detailed instructions to appear in the literature on how to use classification tree analysis and bagging for classification trees in the construction of propensity scores. The latter two examples serve as an introduction for researchers interested in computing propensity scores using more complex classification algorithms known as ensemble methods.

Algorithms↗

PubMed2007

A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a Monte Carlo study.

The propensity score--the probability of exposure to a specific treatment conditional on observed variables--is increasingly being used in observational studies. Creating strata in which subjects are matched on the propensity score allows one to balance measured variables between treated and untreated subjects. There is an ongoing controversy in the literature as to which variables to include in the propensity score model. Some advocate including those variables that predict treatment assignment, while others suggest including all variables potentially related to the outcome, and still others advocate including only variables that are associated with both treatment and outcome. We provide a case study of the association between drug exposure and mortality to show that including a variable that is related to treatment, but not outcome, does not improve balance and reduces the number of matched pairs available for analysis. In order to investigate this issue more comprehensively, we conducted a series of Monte Carlo simulations of the performance of propensity score models that contained variables related to treatment allocation, or variables that were confounders for the treatment-outcome pair, or variables related to outcome or all variables related to either outcome or treatment or neither. We compared the use of these different propensity scores models in matching and stratification in terms of the extent to which they balanced variables. We demonstrated that all propensity scores models balanced measured confounders between treated and untreated subjects in a propensity-score matched sample. However, including only the true confounders or the variables predictive of the outcome in the propensity score model resulted in a substantially larger number of matched pairs than did using the treatment-allocation model. Stratifying on the quintiles of any propensity score model resulted in residual imbalance between treated and untreated subjects in the upper and lower quintiles. Greater balance between treated and untreated subjects was obtained after matching on the propensity score than after stratifying on the quintiles of the propensity score. When a confounding variable was omitted from any of the propensity score models, then matching or stratifying on the propensity score resulted in residual imbalance in prognostically important variables between treated and untreated subjects. We considered four propensity score models for estimating treatment effects: the model that included only true confounders; the model that included all variables associated with the outcome; the model that included all measured variables; and the model that included all variables associated with treatment selection. Reduction in bias when estimating a null treatment effect was equivalent for all four propensity score models when propensity score matching was used. Reduction in bias was marginally greater for the first two propensity score models than for the last two propensity score models when stratification on the quintiles of the propensity score model was employed. Furthermore, omitting a confounding variable from the propensity score model resulted in biased estimation of the treatment effect. Finally, the mean squared error for estimating a null treatment effect was lower when either of the first two propensity scores was used compared to when either of the last two propensity score models was used.

Aged↗

PubMed2007

Statistical and regulatory issues with the application of propensity score analysis to nonrandomized medical device clinical studies.

Propensity score analysis is a versatile statistical method used mainly in observational studies for improving treatment comparison by adjusting for up to a relatively large number of potentially confounding covariates. Recently, there has been an increased interest in applying this method to nonrandomized medical device clinical studies. In the application of the methodology, some statistical and regulatory issues arise in both study design and analysis of study results, such as the need for pre-specifying clinically relevant covariates to be measured, appropriate patient populations, and the essential elements of statistical analysis, planning sample size in the context of propensity score methodology, handling missing covariates in generating propensity scores, and assessing the success of the propensity score method by evaluating treatment group overlap in terms of the distributions of propensity scores. In this paper, the advantages and limitations of this methodology will be revisited, and the above issues will be discussed and illustrated with examples from a regulatory perspective.

Algorithms↗

PubMed2006

Indications for propensity scores and review of their use in pharmacoepidemiology.

Use of propensity scores to identify and control for confounding in observational studies that relate medications to outcomes has increased substantially in recent years. However, it remains unclear whether, and if so when, use of propensity scores provides estimates of drug effects that are less biased than those obtained from conventional multivariate models. In the great majority of published studies that have used both approaches, estimated effects from propensity score and regression methods have been similar. Simulation studies further suggest comparable performance of the two approaches in many settings. We discuss five reasons that favour use of propensity scores: the value of focus on indications for drug use; optimal matching strategies from alternative designs; improved control of confounding with scarce outcomes; ability to identify interactions between propensity of treatment and drug effects on outcomes; and correction for unobserved confounders via propensity score calibration. We describe alternative approaches to estimate and implement propensity scores and the limitations of the C-statistic for evaluation. Use of propensity scores will not correct biases from unmeasured confounders, but can aid in understanding determinants of drug use and lead to improved estimates of drug effects in some settings.

Bias↗

PubMed2007

Conditioning on the propensity score can result in biased estimation of common measures of treatment effect: a Monte Carlo study.

Propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature. Conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments. The degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio, which are frequently used as measures of treatment effect in observational studies, has not been extensively studied. We conducted Monte Carlo simulations to determine the degree to which propensity score matching, stratification on the quintiles of the propensity score, and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios, hazard ratios, and rate ratios. We found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio. In all scenarios examined, treatment effects were biased towards the null treatment effect. However, conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio. In contrast, conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model. The observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects, whereas propensity score methods allow one to estimate marginal treatment effects. In several settings with non-linear treatment effects, marginal and conditional treatment effects do not coincide.

Bias↗

PubMed2006

A comparison of propensity score methods: a case-study estimating the effectiveness of post-AMI statin use.

There is an increasing interest in the use of propensity score methods to estimate causal effects in observational studies. However, recent systematic reviews have demonstrated that propensity score methods are inconsistently used and frequently poorly applied in the medical literature. In this study, we compared the following propensity score methods for estimating the reduction in all-cause mortality due to statin therapy for patients hospitalized with acute myocardial infarction: propensity-score matching, stratification using the propensity score, covariate adjustment using the propensity score, and weighting using the propensity score. We used propensity score methods to estimate both adjusted treated effects and the absolute and relative risk reduction in all-cause mortality. We also examined the use of statistical hypothesis testing, standardized differences, box plots, non-parametric density estimates, and quantile-quantile plots to assess residual confounding that remained after stratification or matching on the propensity score. Estimates of the absolute reduction in 3-year mortality ranged from 2.1 to 4.5 per cent, while estimates of the relative risk reduction ranged from 13.3 to 17.0 per cent. Adjusted estimates of the reduction in the odds of 3-year death varied from 15 to 24 per cent across the different propensity score methods.

Acute Disease↗

PubMed2004

[Suppressive effect of angiotensin converting enzyme inhibitor (ACEI) on the progression of renal insufficiency: a propensity score analysis].

To clarify the renal protection conferred by angiotensin II converting enzyme inhibitor(ACEI), we compared an ACEI group and a conventional therapy (control) group with matched propensity scores. The propensity score is used to control imbalances in the conditional probability of a subject receiving a particular exposure given a set of defined confounders. To calculate the propensity score, the confounders are used in a logistic regression to predict the exposure of interest, without including the outcome. We used a database of the characteristics and clinical data for 1,309 renal insufficiency cases who visited our out-patient clinic between 1986 and 2001. The major contributing factors in the patient characteristics were primary disease, blood pressure, renal function(serum creatinine levels; sCr), urinary protein excretion (UP), and gender. The primary end-point was the doubling of the baseline sCr noted at the time of enrollment or endstage renal failure. The major characteristics of the two groups were not statistically different. An incidence of 90% was obtained at 95 months in the control group and at 183 months in the ACEI group. Using a Kaplan-Meier survival analysis, the survival rates of the two groups were found to be significantly different (p < 0.001 by log-rank test), with ACEI having a beneficial effect on the survival rate and renal function. Using a sub-analysis, neither the starting point of ACEI treatment, based on an sCr above or below 2 mg/dl, nor the amount of UP, more or less than 1 g/day, affected the superiority of ACEI in the prevention of renal failure progression. The ACEI treatment was superior to conventional therapy in patients with renal insufficiency, and this superiority was independent of blood pressure, renal function and the amount of UP, based on the analysis of an observational database of renal insufficiency cases with matched propensity scores.

Adult↗

PubMed2005

Propensity score methods gave similar results to traditional regression modeling in observational studies: a systematic review.

OBJECTIVE: To determine whether adjusting for confounder bias in observational studies using propensity scores gives different results than using traditional regression modeling. METHODS: Medline and Embase were used to identify studies that described at least one association between an exposure and an outcome using both traditional regression and propensity score methods to control for confounding. From 43 studies, 78 exposure-outcome associations were found. Measures of the quality of propensity score implementation were determined. The statistical significance of each association using both analytical methods was compared. The odds or hazard ratios derived using both methods were compared quantitatively. RESULTS: Statistical significance differed between regression and propensity score methods for only 8 of the associations (10%), kappa = 0.79 (95% CI = 0.65-0.92). In all cases, the regression method gave a statistically significant association not observed with the propensity score method. The odds or hazard ratio derived using propensity scores was, on average, 6.4% closer to unity than that derived using traditional regression. CONCLUSIONS: Observational studies had similar results whether using traditional regression or propensity scores to adjust for confounding. Propensity scores gave slightly weaker associations; however, many of the reviewed studies did not implement propensity scores well.

Bias↗

PubMedDate not supplied

The multiple propensity score for analysis of dose-response relationships in drug safety studies.

In order to detect adverse drug reactions, large observational drug safety studies are necessary as randomized clinical trials rarely have enough power. However, in order to obtain reliable results the issue of confounding, especially confounding by indication, should be addressed. We proposed a multiple propensity score, which is an extension of the propensity score, to reduce the bias in a dose-response analysis in a drug safety study. The multiple propensity score has similar properties to the propensity score in Rosenbaum and Rubin.(1) Using the propensity score for bias reduction of the risk ratio was considered. We used the multiple propensity score in a study of the dose-response relationship between diclofenac prescriptions and hospitalization for gastrointestinal bleeding and perforation using a record linkage database. We found that the unadjusted risk ratios were biased downwards due to confounders and that this bias was reduced by using stratification based on the multiple propensity score.

Adult↗

PubMed2004

Principles for modeling propensity scores in medical research: a systematic literature review.

PURPOSE: To document which established criteria for logistic regression modeling researchers consider when using propensity scores in observational studies. METHODS: We performed a systematic review searching Medline and Science Citation to identify observational studies published in 2001 that addressed clinical questions using propensity score methods to adjust for treatment assignment. We abstracted aspects of propensity score model development (e.g. variable selection criteria, continuous variables included in correct functional form, interaction inclusion criteria), model discrimination and goodness of fit for 47 studies meeting inclusion criteria. RESULTS: We found few studies reporting on the propensity score model development or evaluation of model fit. CONCLUSIONS: Reporting of aspects related to propensity score model development is limited and raises questions about the value of these principles in developing propensity scores from which unbiased treatment effects are estimated.

Bias↗