Causal Multistate Models to Evaluate Treatment Delay

Abstract

Multistate models allow for the study of scenarios where individuals experience different events over time. While effective for descriptive and predictive purposes, multistate models are not typically used for causal inference. We propose an estimator that combines a multistate model with g-computation to estimate the causal effect of treatment delay strategies. In particular, we estimate the impact of strategies such as awaiting natural recovery for 3 months, on the marginal probability of recovery. We use an illness-death model, where illness and death represent, respectively, treatment and recovery. We formulate the causal assumptions needed for identification and the modeling assumptions needed to estimate the quantities of interest. In a simulation study, we present scenarios where the proposed method can make more efficient use of data compared to an alternative approach using cloning-censoring-reweighting. We then showcase the proposed methodology on real data by estimating the effect of treatment delay on a cohort of 1896 couples with unexplained subfertility who seek intrauterine insemination.

Keywords: causal inference; g‐computation; multistate model; observational data; survival analysis.

FIGURE 1

The illness–death setting: The three states (starting state, treatment, and recovery) are connected by arrows that represent the possible transitions between them. The respective transition intensities between states are depicted.

FIGURE 2

Visual representation of the simulation results for scenario 1, where assumptions needed for all estimation approaches are met. Cumulative recovery probabilities until time 1.5 are plotted under five treatment strategies: initiate immediately, delayed at 0.25, delayed at 0.5, delayed at 0.75, and never initiate. Four estimation approaches are reported: (i) Multistate continuous; (ii) Multistate categorical; (iii) Clone–censor–reweight continuous; (iv) Clone–censor–reweight categorical. The solid lines represent the true values, the dotted line represents the mean of the estimates, and the shaded area represents the [5th–95th] percentile of the estimates.

FIGURE 3

Estimated cumulative pregnancy probability for unexplained subfertile couples if they are assigned different treatment strategies.