Sequential Analysis of Censored Data with Linear Transformation Models

Abstract

Sequential tests have been used commonly in clinical trials to compare treatments. For sequential analysis of right-censored survival data with covariate adjustment, several different methods have been studied based on either Cox proportional hazards model or accelerated failure time model. Here we propose a test process based on linear transformation models for staggered entry data. The proposed test process is motivated by Chen et al.'s (2002) estimating equations for linear transformation models. We show that the test process can be approximated by a mean 0 multidimensional Gaussian process. A consistent estimator of its covariance matrix function is provided. For given interim analysis time points, a repeated significant test is developed based on the boundaries procedure proposed by Slud and Wei (1982). Numerical studies show that the proposed test process performs well.

Keywords:

• Censoring
• Gaussian process
• Linear transformation models
• Repeated significant test
• Sequential analysis

Subject Classifications:

• 62L10
• 62N01
• 62N03

ACKNOWLEDGMENT

We would like thank the Associate Editor and two anonymous referees for insightful comments which helped improve this article.

Notes

The values without parentheses are empirical type I errors when γ = 0 and are empirical powers when γ = −0.5 or γ = −1 respectively.

The values within parentheses are empirical standard errors of the type I errors and powers of simulation.

The maximal sample size for each simulation is 200.

The values within parentheses are the empirical standard deviation for sample size.

Total five analyses (four interim and one final) were planned.

The values within parentheses are empirical standard deviation for the number of analyses conducted.

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