Estimating the causal effects in randomized trials for survival data with a cure fraction and non compliance

ABSTRACT

We consider causal inference in randomized studies for survival data with a cure fraction and all-or-none treatment non compliance. To describe the causal effects, we consider the complier average causal effect (CACE) and the complier effect on survival probability beyond time t (CESP), where CACE and CESP are defined as the difference of cure rate and non cured subjects’ survival probability between treatment and control groups within the complier class. These estimands depend on the distributions of survival times in treatment and control groups. Given covariates and latent compliance type, we model these distributions with transformation promotion time cure model whose parameters are estimated by maximum likelihood. Both the infinite dimensional parameter in the model and the mixture structure of the problem create some computational difficulties which are overcome by an expectation-maximization (EM) algorithm. We show the estimators are consistent and asymptotically normal. Some simulation studies are conducted to assess the finite-sample performance of the proposed approach. We also illustrate our method by analyzing a real data from the Healthy Insurance Plan of Greater New York.

KEYWORDS:

• All-or-none compliance
• Cure model
• EM algorithm
• Non parametric likelihood
• Transformation model.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N01
• 62N02
• 62E20

Acknowledgments

The authors thank anonymous reviewer for his(or her) helpful comments and suggestions that have led to significant improvements. The authors also thank Dr Wen Yu for his helpful suggestions for the manuscript.

Funding

The research was supported by the National Natural Science Foundation of China (11271081).