Modeling treatment effect modification in multidrug-resistant tuberculosis in an individual patientdata meta-analysis

Abstract

Effect modification occurs while the effect of the treatment is not homogeneous across the different strata of patient characteristics. When the effect of treatment may vary from individual to individual, precision medicine can be improved by identifying patient covariates to estimate the size and direction of the effect at the individual level. However, this task is statistically challenging and typically requires large amounts of data. Investigators may be interested in using the individual patient data from multiple studies to estimate these treatment effect models. Our data arise from a systematic review of observational studies contrasting different treatments for multidrug-resistant tuberculosis, where multiple antimicrobial agents are taken concurrently to cure the infection. We propose a marginal structural model for effect modification by different patient characteristics and co-medications in a meta-analysis of observational individual patient data. We develop, evaluate, and apply a targeted maximum likelihood estimator for the doubly robust estimation of the parameters of the proposed marginal structural model in this context. In particular, we allow for differential availability of treatments across studies, measured confounding within and across studies, and random effects by study.

Keywords: Conditional average treatment effect; double robustness; individual patient data; marginal structural model; meta-analysis; multidrug-resistant tuberculosis; targeted maximum likelihood estimation.

Figure 1.

Error of TMLE estimates under four scenarios and three different sample sizes without random effects. The $x$ -axis represents the number of studies. Coverage rates based on the clustered sandwich estimators of the standard error are presented in blue boxes. The four scenarios are as follows: Scenario 1 – both $Q$ and $g$ models are correct; Scenario 2 – $Q$ model is correct, $g$ is null; Scenario 3 – $Q$ model is null, $g$ model is correct; Scenario 4 – both $Q$ and $g$ models are null.

Figure 2.

Error of TMLE estimates under four scenarios and three different sample sizes with random effects. The $x$ -axis represents the number of studies for three sample sizes. Coverage rates based on the clustered sandwich estimators of the standard error are presented in blue boxes. The four scenarios are as follows: Scenario 1 – both $Q$ and $g$ models are correct; Scenario 2 – $Q$ model is correct, $g$ is null; Scenario 3 – $Q$ model is null, $g$ model is correct; Scenario 4 – both $Q$ and $g$ models are null.

Figure 3.

Estimated coefficients and the corresponding $95\text{\%}$ confidence interval for 14 medications relative to the intercept and six demographic or clinical covariates. None of the coefficients reached statistical significance. # Larger scale for the $y$ -axis of the LgFQ plot.

Figure 4.

Estimated coefficients of potential effect modifiers and the corresponding $95\text{\%}$ confidence intervals for EMB, CAP, CIP, CS, ETO and OFX. Significant results are shown in red and indicated with an $*$ .

Figure 5.

Estimated coefficients of potential effect modifiers and the corresponding $95\text{\%}$ confidence intervals for PAS, PTO, RIF, SM, PZA, KM/AM, LgFQ and Gp5. None of the coefficients reached statistical significance. # Larger scale for the $y$ -axis of the RIF and LgFQ plots.

Figure 6.

Estimated coefficients of potential effect modifiers and the corresponding $95\text{\%}$ confidence intervals for ethionamide (ETO) in the study by Mitnick et al. (left column) and in the meta-analysis (right column). Significant results are shown in red and indicated with an $*$ .