Causal inference in survival analysis using longitudinal observational data: Sequential trials and marginal structural models

Abstract

Longitudinal observational data on patients can be used to investigate causal effects of time-varying treatments on time-to-event outcomes. Several methods have been developed for estimating such effects by controlling for the time-dependent confounding that typically occurs. The most commonly used is marginal structural models (MSM) estimated using inverse probability of treatment weights (IPTW) (MSM-IPTW). An alternative, the sequential trials approach, is increasingly popular, and involves creating a sequence of "trials" from new time origins and comparing treatment initiators and non-initiators. Individuals are censored when they deviate from their treatment assignment at the start of each "trial" (initiator or noninitiator), which is accounted for using inverse probability of censoring weights. The analysis uses data combined across trials. We show that the sequential trials approach can estimate the parameters of a particular MSM. The causal estimand that we focus on is the marginal risk difference between the sustained treatment strategies of "always treat" vs "never treat." We compare how the sequential trials approach and MSM-IPTW estimate this estimand, and discuss their assumptions and how data are used differently. The performance of the two approaches is compared in a simulation study. The sequential trials approach, which tends to involve less extreme weights than MSM-IPTW, results in greater efficiency for estimating the marginal risk difference at most follow-up times, but this can, in certain scenarios, be reversed at later time points and relies on modelling assumptions. We apply the methods to longitudinal observational data from the UK Cystic Fibrosis Registry to estimate the effect of dornase alfa on survival.

Keywords: cystic fibrosis; inverse probability weighting; marginal structural model; registries; sequential trials; survival; target trials; time-dependent confounding.

FIGURE 1

Directed acyclic graph (DAG) illustrating relationships between treatment $A$, time‐dependent covariates $L$, discrete time outcome $Y$, and unmeasured covariates $U$. Time‐fixed covariates $Z$ are omitted from the diagram but are assumed to potentially affect all other variables.

FIGURE 2

Causal tree diagram illustrating a study with a binary treatment $A_t$ and binary covariate $L_t$, both measured at two time points ($t=0,1$). $Y_t$ is a discrete time survival outcome. Thick lines indicate branches for groups of individuals who were untreated or treated at both time points.

FIGURE 3

Illustration of the sequential trials approach using causal tree diagram from Figure 2. (A) Trial starting at $t=0$ . (B) Trial starting at $t=1$. (A) In the trial starting at time $t=0$ individuals with $Y_1=0$ are censored at time 1 if $A_1\ne A_0$. (B) The trial starting at time $t=1$ is restricted to individuals with $A_0=0$ (and $Y_1=0$).

FIGURE 4

Simulation results: mean estimated survival curves obtained using the sequential trials analysis and the MSM‐IPTW analysis. The faded lines show the estimates from each of the 1000 simulated datasets and the thick lines are the point‐wise averages.

FIGURE 5

Simulation results: bias in estimation of the risk difference using the sequential trials analysis and the MSM‐IPTW analysis. The black line shows the bias at each time point and the grey area shows the Monte Carlo 95% CI at each time point.

FIGURE 6

Simulation results: relative efficiency of the sequential trials analysis compared with the MSM‐IPTW analysis, defined as the inverse of the ratio of the empirical variances of the risk difference estimates at each time.

FIGURE 7

Simulation results: Plots of the largest weight (by time period) in each of the 1000 simulated data sets under the sequential trials analysis (IPACW) compared with the inverse probability weighted estimation of marginal structural model analysis. The weights are time‐dependent and change at event visit $k=0,\dots ,4$. We obtained the largest weight in each time period, where in the sequential trials the time refers to time since the start of the trial. In the sequential trials analysis, the IPACW are equal to 1 up to time 1.

FIGURE 8

Estimated survival curves under the “always treated” and “never treated” with DNase strategies from the MSM‐IPTW and sequential trials analyses. The shaded areas show the 95% confidence intervals.

FIGURE 9

Estimated risk difference (“always treated” vs “never treated” with DNase) from the MSM‐IPTW and sequential trials analyses. The shaded area shows the 95% confidence intervals.