Causal inference for recurrent event data using pseudo-observations

Robust inference for causal mediation analysis of recurrent event data

Recurrent events, including cardiovascular events, are commonly observed in biomedical studies. Understanding the effects of various treatments on recurrent events and investigating the underlying mediation mechanisms by which treatments may reduce the frequency of recurrent events are crucial tasks for researchers. Although causal inference methods for recurrent event data have been proposed, they cannot be used to assess mediation. This study proposed a novel methodology of causal mediation analysis that accommodates recurrent outcomes of interest in a given individual. A formal definition of causal estimands (direct and indirect effects) within a counterfactual framework is given, and empirical expressions for these effects are identified. To estimate these effects, a semiparametric estimator with triple robustness against model misspecification was developed. The proposed methodology was demonstrated in a real-world application. The method was applied to measure the effects of two diabetes drugs on the recurrence of cardiovascular disease and to examine the mediating role of kidney function in this process.

Propensity score weighting methods for causal subgroup analysis with time-to-event outcomes

Evaluating causal effects of an intervention in pre-specified subgroups is a standard goal in comparative effectiveness research. Despite recent advancements in causal subgroup analysis, research on time-to-event outcomes has been lacking. This article investigates the propensity score weighting method for causal subgroup survival analysis. We introduce two causal estimands, the subgroup marginal hazard ratio and subgroup restricted average causal effect, and provide corresponding propensity score weighting estimators. We analytically established that the bias of subgroup-restricted average causal effect is determined by subgroup covariate balance. Using extensive simulations, we compare the performance of various combinations of propensity score models (logistic regression, random forests, least absolute shrinkage and selection operator, and generalized boosted models) and weighting schemes (inverse probability weighting, and overlap weighting) for estimating the causal estimands. We find that the logistic model with subgroup-covariate interactions selected by least absolute shrinkage and selection operator consistently outperforms other propensity score models. Also, overlap weighting generally outperforms inverse probability weighting in terms of balance, bias and variance, and the advantage is particularly pronounced in small subgroups and/or in the presence of poor overlap. We applied the methods to the observational Comparing Options for Management: PAtient-centered REsults for Uterine Fibroids study to evaluate the causal effects of myomectomy versus hysterectomy on the time to disease recurrence in a number of pre-specified subgroups of patients with uterine fibroids.

Analysis of survival data with cure fraction and variable selection: A pseudo-observations approach

In biomedical studies, survival data with a cure fraction (the proportion of subjects cured of disease) are commonly encountered. The mixture cure and bounded cumulative hazard models are two main types of cure fraction models when analyzing survival data with long-term survivors. In this article, in the framework of the Cox proportional hazards mixture cure model and bounded cumulative hazard model, we propose several estimators utilizing pseudo-observations to assess the effects of covariates on the cure rate and the risk of having the event of interest for survival data with a cure fraction. A variable selection procedure is also presented based on the pseudo-observations using penalized generalized estimating equations for proportional hazards mixture cure and bounded cumulative hazard models. Extensive simulation studies are conducted to examine the proposed methods. The proposed technique is demonstrated through applications to a melanoma study and a dental data set with high-dimensional covariates.

C-index regression for recurrent event data

Recurrent event data analysis plays an important role in many fields, e.g., medicine, social science, and economics. While the existing approaches under the proportional rates or mean model yield poor performance when the underlying model is misspecified, we propose a novel model-free approach by introducing a lower bound on the concordance index (C-Index). We develop an estimation method through deriving a continuous lower bound on the C-Index based on the log-sigmoid function and also provide a variable selection procedure in high dimensional settings. Under both low and high dimensional settings, simulation results show that the proposed methods outperform the gamma frailty recurrent event model when the proportional mean assumption is violated. Moreover, an application to the hospital readmission dataset shows results in line with previous studies and a higher C-Index value further assures model decency.

The semiparametric accelerated trend-renewal process for recurrent event data

Recurrent event data arise in many biomedical longitudinal studies when health-related events can occur repeatedly for each subject during the follow-up time. In this article, we examine the gap times between recurrent events. We propose a new semiparametric accelerated gap time model based on the trend-renewal process which contains trend and renewal components that allow for the intensity function to vary between successive events. We use the Buckley-James imputation approach to deal with censored transformed gap times. The proposed estimators are shown to be consistent and asymptotically normal. Model diagnostic plots of residuals and a method for predicting number of recurrent events given specified covariates and follow-up time are also presented. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to two real data sets.