Propensity Score Matching in Observational Research

KEY POINT Propensity score matching can reduce confounding in observational research by creating two groups that are well balanced with respect to baseline characteristics.Related Article, see p 1618 In this issue of Anesthesia & Analgesia, Miyao and Kotake1 report results of an observational study on the association between hydroxyethyl starch (HES) and renal morbidity in surgical patients. The authors used propensity scores to match 8823 patients who received HES to 8823 controls who had not received HES. In observational research, the treatment groups are not randomly assigned. Rather, treatment assignment is typically affected by individual patient characteristics and provider preference or choice. Therefore, patients with a certain exposure (eg, HES administration) usually systemically differ from patients without the exposure, and such differences may confound the relationship with the outcome (eg, renal morbidity).2 Any direct comparison between treatment groups is therefore likely biased, and statistical methods to reduce confounding are thus required when analyzing observational outcome data. Traditionally, multivariable regression has been used for this purpose.3 More recently, methods based on propensity scores have become popular alternatives.4 This Statistical Minute focuses on propensity score matching (PSM) as applied by Miyao and Kotake.1 Alternatively, and at least equally useful, propensity scores can also be used to weight, rather than to match, observations for subsequent analyses (inverse probability of treatment weighting [IPTW]). Other propensity score–based approaches, such as using propensity scores for stratification or as covariates in regression analyses, are inferior in reducing confounding compared to PSM and IPTW.4 The propensity score is the probability of exposure to a particular treatment given baseline covariates.4 As treatment is usually a binary variable (eg, patient received HES versus did not receive HES), the propensity score is commonly estimated using logistic regression, in which the treatment assignment is the outcome variable, and in which baseline covariates are the independent variables. In PSM, patients who received the treatment are matched to one or several control patients with “similar” propensity scores. Technically, matching is often not performed on the propensity score itself, but on the logit of the propensity score (natural logarithm of the odds of treatment), and a maximum allowable distance (caliper) of 0.2 standard deviations is commonly recommended.4 This results—on average—in groups with comparable covariate patterns; in other words, there is no systematic difference and so these covariates can no longer confound the between-group comparison. This is akin to the situation in a randomized trial. However, randomization controls for both observed and unobserved confounders, while propensity scores can only balance observed confounders. Thus, residual bias is still possible. After matching, researchers should calculate standardized differences (differences in means or proportions divided by the pooled standard deviation) between the matched groups to assess whether the matching was successful in balancing baseline covariates. Generally speaking, absolute standardized differences of <0.1 indicate adequate balance. When baseline covariates are well balanced, the outcome variable(s) can be compared between the 2 groups using standard statistical techniques, including simple hypothesis tests, regression techniques, or survival analysis.3,5 However, there is a considerable debate in statistical literature about whether the matched design must be accounted for in the analysis (eg, whether to use a paired or unpaired t test to compare a continuous outcome).4Figure.: Excerpt from Table 3 and Table 4 in Miyao and Kotake.1 Table 3 shows the improvement in balance among covariates between the groups (only 2 of 36 covariates shown in this excerpt), with a marked reduction of the standardized differences (shown as percent; 1.6% ≙ 0.016) after matching. Table 4 shows the estimated risk of AKI after HES administration before and after PS matching. Note that the unadjusted analysis (crude odds ratio) substantially overestimated the relationship between HES and AKI compared to the more valid PSM analysis (adjusted odds ratio). AKI indicates acute kidney injury; CI, confidence interval; HES, hydroxyethyl starch; IQR, interquartile range; PS, propensity score.