G-estimation of structural nested mean models for competing risks data using pseudo-observations

Rare event approximation between subdistribution hazard ratio and cause-specific hazard ratio in survival analysis with competing risks

BackgroundDespite the fact that competing risks are inevitable in epidemiological and clinical studies, distinctions between the hazard ratio estimated by handling competing risks as censoring and the subditribution hazard ratio are often overlooked.MethodsWe derive quantitative relationships between subdistribution hazard ratio and cause-specific hazard ratio, and derive an approximate calculation method to transform the two into each other. Numerical examinations of hypothetical six scenarios and published information of a randomized clinical trial of cholesterol-lowering therapy and a registry of acute myeloid leukemia were provided.ResultsGeneral and approximate relationships under rare event assumptions between the two types of hazard ratio were given. The approximation formula is based on a survival ratio and has two possible applications. First, one can calculate a subdistribution hazard ratio from published information. Second, this formula allows sample size estimation that takes the presence of competing risks into account.ConclusionsThe distinction between the two types of hazard ratio can be addressed by focusing on two quantities. One is how the event of interest and competing risk is rare, and the other is the survival ratio.

G-estimation of structural nested mean models for interval-censored data using pseudo-observations

Two large-scale randomized clinical trials compared fenofibrate and placebo in diabetic patients with pre-existing retinopathy (FIELD study) or risk factors (ACCORD trial) on an intention-to-treat basis and reported a significant reduction in the progression of diabetic retinopathy in the fenofibrate arms. However, their analyses involved complications due to intercurrent events, that is, treatment-switching and interval-censoring. This article addresses these problems involved in estimation of causal effects of long-term use of fibrates in a cohort study that followed patients with type 2 diabetes for 8 years. We propose structural nested mean models (SNMMs) of time-varying treatment effects and pseudo-observation estimators for interval-censored data. The first estimator for SNMMs uses a nonparametric maximum likelihood estimator (MLE) as a pseudo-observation, while the second estimator is based on MLE under a parametric piecewise exponential distribution. Through numerical studies with real and simulated datasets, the pseudo-observations estimators of causal effects using the nonparametric Wellner-Zhan estimator perform well even under dependent interval-censoring. Its application to the diabetes study revealed that the use of fibrates in the first 4 years reduced the risk of diabetic retinopathy but did not support its efficacy beyond 4 years.

Causal inference for recurrent event data using pseudo-observations

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.