Propensity scores with misclassified treatment assignment: a likelihood-based adjustment

Abstract

Propensity score methods are widely used in comparative effectiveness research using claims data. In this context, the inaccuracy of procedural or billing codes in claims data frequently misclassifies patients into treatment groups, that is, the treatment assignment ($T$) is often measured with error. In the context of a validation data where treatment assignment is accurate, we show that misclassification of treatment assignment can impact three distinct stages of a propensity score analysis: (i) propensity score estimation; (ii) propensity score implementation; and (iii) outcome analysis conducted conditional on the estimated propensity score and its implementation. We examine how the error in $T$ impacts each stage in the context of three common propensity score implementations: subclassification, matching, and inverse probability of treatment weighting (IPTW). Using validation data, we propose a two-step likelihood-based approach which fully adjusts for treatment misclassification bias under subclassification. This approach relies on two common measurement error-assumptions; non-differential measurement error and transportability of the measurement error model. We use simulation studies to assess the performance of the adjustment under subclassification, and also investigate the method's performance under matching or IPTW. We apply the methods to Medicare Part A hospital claims data to estimate the effect of resection versus biopsy on 1-year mortality among $10\,284$ Medicare beneficiaries diagnosed with brain tumors. The ICD9 billing codes from Medicare Part A inaccurately reflect surgical treatment, but SEER-Medicare validation data are available with more accurate information.

Keywords: Comparative effectiveness; Measurement error; Observational data; Propensity scores; Validation data.

Fig. 1.

Error in the treatment assignment (T) will always directly influence the propensity score estimation and outcome analysis, and will “sometimes” directly influence the propensity score implementation as well. In contrast, error in the confounders () will only influence the propensity score estimation.

Fig. 2.

Bias and MSE of the ATE estimator, under simulation setting with a moderate association between and and measurement error dependent of (Table 1). Gold Standard is based on the true treatment assignment. No Adj is based on the error-prone treatment assignment. Two-step Adj is based on the error-prone treatment assignment with the proposed two-step likelihood-based adjustment, adjusting both the propensity score and outcome model. Average sensitivity is 0.46 and average specificity is 0.47. The true treatment effect is .

Fig. 3.

Histograms of the adjusted propensity score, , in blue for and in red for . The left panel shows differences in weights, , under matching for one simulation, shown as dots in the figure, in blue for and in red for . are weights obtained by matching individuals based on their adjusted propensity score using the error-prone treatment assignment and are weights obtained by matching individuals based on their adjusted propensity score using the true treatment assignment. The right panel shows differences in weights, , under IPTW for one simulation, shown as dots in the figure, in blue for and in red for . are weights obtained by weighting individuals based on their adjusted propensity score using the error-prone treatment assignment and are weights obtained by weighting individuals based on their adjusted propensity score using the true treatment assignment (Note, a color version of this figure is available in the online version).