Causal inference for recurrent event data using pseudo-observations

Abstract

Summary Recurrent event data are commonly encountered in observational studies where each subject may experience a particular event repeatedly over time. In this article, we aim to compare cumulative rate functions (CRFs) of two groups when treatment assignment may depend on the unbalanced distribution of confounders. Several estimators based on pseudo-observations are proposed to adjust for the confounding effects, namely inverse probability of treatment weighting estimator, regression model-based estimators, and doubly robust estimators. The proposed marginal regression estimator and doubly robust estimators based on pseudo-observations are shown to be consistent and asymptotically normal. A bootstrap approach is proposed for the variance estimation of the proposed estimators. Model diagnostic plots of residuals are presented to assess the goodness-of-fit for the proposed regression models. A family of adjusted two-sample pseudo-score tests is proposed to compare two CRFs. Simulation studies are conducted to assess finite sample performance of the proposed method. The proposed technique is demonstrated through an application to a hospital readmission data set.

Propensity Score Weighting Analysis of Survival Outcomes Using Pseudo-Observations

“…For example, Andersen et al (2017) considered an IPW estimator to estimate the causal risk difference and difference in restricted mean survival time. Their approach was further extended to enable doubly robust estimation with survival and recurrent event outcomes (Wang, 2018;Su et al, 2020).…”

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

“…The censoring times are independently generated from Uniform(0,c), where c is chosen so that 10% of the censored subjects are susceptible. Tables 3 and 4 presented in Web Appendix E show the results of estimators (γ PO 0,KM , γPO 1,KM ) and (γ PO 0,NP , γPO 1,NP ) obtained from (18) and estimators ( φPO 1,NP , φPO 2,NP ) and ( φPO 1,KM , φPO 2,KM ) obtained from (20), respectively. A maximum likelihood estimator (MLE) is implemented for comparison.…”

“…The top panel of Table 3 presents the results from the PHMC model obtained by ( 14) and ( 16) with g 1 (x) = log {x/(1 − x)}, g 2 (x) = log { − log (x)}, and ξ t h = log Λ 0 (t h ). The lower panel of Table 3 presents the results from the PHPH model obtained by (18) and ( 20) with g 3 (x) = log (x), g 4 (x) = log {− log (x)}, and ς t h = log { − log ( F(t h ))}. For comparison, we included the estimator 6 based on the EM-algorithm with standard errors obtained from 500 bootstrapped samples.…”

“…where θi is the pseudo-observations for θ, and V 3,i is a working variance of θi . Let (γ PO 0,KM , γPO KM ) and (γ PO 0,NP , γPO NP ) be the estimators obtained from (18) when θi is replaced by θi KM and θi NP in ( 9) and (10), respectively. Under the assumption…”

“…Since then, the pseudo-observations approach has been applied to many settings in survival analysis, including survival estimates, 13 the restricted mean survival times, 14 the cumulative incidence function, 15 the relative survival function, 16 the illness-death model with interval-censored data, 17 and the causal inference for recurrent event data. 18 Large sample properties have also been thoroughly investigated. 19 – 21 However, the pseudo-observations approach has not been applied to the analysis of survival data with a cure fraction.…”