Maximum of the Weighted Kaplan‐Meier Tests with Application to Cancer Prevention and Screening Trials

A class of maximum weighted Kaplan-Meier test statistics is described where the weight functions are chosen from a family of smooth functions. The investigated test statistic is robust and sensitive to a variety of alternatives that are often observed in cancer prevention and screening trials. A simulation study is performed to compare the size and power properties between the proposed test statistics and some existing ones. We illustrate the procedure using data from a clinical trial of a breast cancer screening program.

[1]  Monitoring a general class of two-sample survival statistics with applications , 1999 .

[2]  R. Gill.  Large Sample Behaviour of the Product-Limit Estimator on the Whole Line , 1983 .

[3]  D. Harrington.  A class of rank test procedures for censored survival data , 1982 .

[4]  S G Self,et al.  An adaptive weighted log-rank test with application to cancer prevention and screening trials. , 1991, Biometrics.

[5]  L Ryan,et al.  Survival analysis in natural history studies of disease. , 1989, Statistics in medicine.

[6]  K. Kafadar,et al.  A data-analytic approach for estimating lead time and screening benefit based on survival curves in randomized cancer screening trials. , 1994, Statistics in medicine.

[7]  R. Tarone,et al.  Analysis of breast cancer mortality and stage distribution by age for the Health Insurance Plan clinical trial. , 1988, Journal of the National Cancer Institute.

[8]  Z. Ying,et al.  A Class of Weighted Log-Rank Tests for Survival Data When the Event is Rare , 2000 .

[9]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[10]  M S Pepe,et al.  Weighted Kaplan-Meier statistics: a class of distance tests for censored survival data. , 1989, Biometrics.

[11]  L. Stitt,et al.  Evaluating the survival of cancer cases detected by screening. , 1987, Statistics in medicine.

[12]  David P. Harrington,et al.  A class of hypothesis tests for one and two sample censored survival data , 1981 .

[13]  J. Wittes,et al.  The Evaluation of Medical Screening Procedures , 1981 .

[14]  Ruth Etzioni,et al.  On the catch-up time method for analyzing cancer screening trials. , 1995, Biometrics.

[15]  Ruth Etzioni,et al.  A likelihood ratio test for cancer screening trials. , 1995, Biometrics.

[16]  S. Shapiro,et al.  Evidence on screening for breast cancer from a randomized trial , 1977, Cancer.

[17]  R. Tarone,et al.  On the distribution of the maximum of the longrank statistic and the modified Wilcoxon statistic , 1981 .

[18]  Thomas R. Fleming,et al.  Weighted Kaplan‐Meier Statistics: Large Sample and Optimality Considerations , 1991 .