Proportional hazards model for competing risks data with missing cause of failure

Abstract

We consider the semiparametric proportional hazards model for the cause-specific hazard function in analysis of competing risks data with missing cause of failure. The inverse probability weighted equation and augmented inverse probability weighted equation are proposed for estimating the regression parameters in the model, and their theoretical properties are established for inference. Simulation studies demonstrate that the augmented inverse probability weighted estimator is doubly robust and the proposed method is appropriate for practical use. The simulations also compare the proposed estimators with the multiple imputation estimator of Lu and Tsiatis (2001). The application of the proposed method is illustrated using data from a bone marrow transplant study.

Semiparametric regression and risk prediction with competing risks data under missing cause of failure

“…The finite sample properties of the estimators and their robustness against misspecification of the parametric model for the probability of the cause of failure are investigated through simulations. Moreover, in the simulation studies, we also demonstrate superior finite sample performance of our estimator for the regression coefficients compared to the AIPW estimator (Gao and Tsiatis 2005;Hyun et al 2012). Finally, we apply the methodology to data sets from the EA-IeDEA HIV cohort study and a bladder cancer trial from the European Organisation for Research and Treatment of Cancer (EORTC).…”

“…To evaluate the finite sample performance of the proposed estimator, we conducted a series of simulation studies. We used similar simulation settings to those used in Hyun et al (2012). Specifically, we considered a cohort study with an observation interval [0, 2], two causes of failure, and two covariates Z = (Z 1 , Z 2 ) T , where Z 1 was generated from U (0, 1) and Z 2 from the Bernoulli(0.5) distribution.…”

“…The domain limits for the confidence bands were calculated based on {c 1 , c 2 } = {0.1, 0.9}, as described in the preceding section. Note that since the AIPW approach (Gao and Tsiatis 2005;Hyun et al 2012) and the MI estimator (Lu and Tsiatis 2001) did not consider inference about the infinite-dimensional parameters we were not able to provide results from these approaches in the latter set of simulations.…”

“…This approach utilizes parametric models for the probability of missingness and the probability of the cause of failure conditional on the fully observed data. Hyun et al (2012) applied the AIPW approach to the proportional cause-specific hazards model. These AIPW estimators are more efficient compared to the simple inverse probability weighting estimators, and possess the double-robustness property.…”

“…However, this approach considered an unspecified baseline hazard for only one cause of failure, say λ 0,1 (t), while the baseline hazards for the remaining cause of failures were assumed to satisfy a parametric hazard ratio λ 0, j (t)/λ 0,1 (t). On the contrary, the other approaches mentioned above considered unspecified baseline cause-specific hazards for all the cause of failures (Lu and Tsiatis 2001;Gao and Tsiatis 2005;Hyun et al 2012). It is important to note that, none of the aforementioned methods have considered the problem of inference for the infinite-dimensional parameters, such as the covariate-specific cumulative incidence function.…”