  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 (IPD) 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 (MDR-TB), where multiple antimicrobial
agents are taken concurrently to cure the infection. We propose a marginal
structural model (MSM) for effect modification by different patient
characteristics and co-medications in a meta-analysis of observational IPD. We
develop, evaluate, and apply a targeted maximum likelihood estimator (TMLE) for
the doubly robust estimation of the parameters of the proposed MSM 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.
