Monte Carlo sensitivity analysis for unmeasured confounding in dynamic treatment regimes

Abstract

Data-driven methods for personalizing treatment assignment have garnered much attention from clinicians and researchers. Dynamic treatment regimes formalize this through a sequence of decision rules that map individual patient characteristics to a recommended treatment. Observational studies are commonly used for estimating dynamic treatment regimes due to the potentially prohibitive costs of conducting sequential multiple assignment randomized trials. However, estimating a dynamic treatment regime from observational data can lead to bias in the estimated regime due to unmeasured confounding. Sensitivity analyses are useful for assessing how robust the conclusions of the study are to a potential unmeasured confounder. A Monte Carlo sensitivity analysis is a probabilistic approach that involves positing and sampling from distributions for the parameters governing the bias. We propose a method for performing a Monte Carlo sensitivity analysis of the bias due to unmeasured confounding in the estimation of dynamic treatment regimes. We demonstrate the performance of the proposed procedure with a simulation study and apply it to an observational study examining tailoring the use of antidepressant medication for reducing symptoms of depression using data from Kaiser Permanente Washington.

Keywords: adaptive treatment strategies; bias; precision medicine.

FIGURE 1

Boxplots of the point estimates for $\psi$ under an unadjusted model and when using Monte Carlo sensitivity analysis to adjust for bias due to unmeasured confounding for the one-stage data-generating model.

FIGURE 2

Boxplots of the point estimates for $\psi$ under an unadjusted model and when using G-estimation sensitivity analysis to adjust for bias due to unmeasured confounding for the one-stage data-generating model when we assume we know ${\xi }_{11}$ and ${\xi }_{12}$.

FIGURE 3

Boxplots of the point estimates for ${\psi }_2$ under an unadjusted model and when using Monte Carlo sensitivity analysis to adjust for bias due to unmeasured confounding for the two-stage data-generating model.

FIGURE 4

Boxplots of the point estimates for ${\psi }_1$ under an unadjusted model and when using Monte Carlo sensitivity analysis to adjust for bias due to unmeasured confounding for the two-stage data-generating model.