Log‐rank permutation tests for trend: saddlepoint p‐values and survival rate confidence intervals

Suppose p + 1 experimental groups correspond to increasing dose levels of a treatment and all groups are subject to right censoring. In such instances, permutation tests for trend can be performed based on statistics derived from the weighted log-rank class. This article uses saddlepoint methods to determine the mid-P-values for such permutation tests for any test statistic in the weighted log-rank class. Permutation sim- ulations are replaced by analytical saddlepoint computations which provide extremely accurate mid-P-values that are exact for most practical purposes and almost always more accurate than normal approximations. The speed of mid-P-value computation allows for the inversion of such tests to determine confidence intervals for the percentage increase in mean (or median) survival time per unit increase in dosage. The Canadian

[1]  E. Venkatraman,et al.  RESAMPLING PROCEDURES TO COMPARE TWO SURVIVAL DISTRIBUTIONS IN THE PRESENCE OF RIGHT-CENSORED DATA , 1996 .

[2]  Robin Henderson,et al.  Aalen Plots under Proportional Hazards , 1991 .

[3]  J. Peto,et al.  Asymptotically Efficient Rank Invariant Test Procedures , 1972 .

[4]  Richard Routledge,et al.  Practicing safe statistics with the mid-p* , 1994 .

[5]  D. Cox.  The Regression Analysis of Binary Sequences , 1958 .

[6]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[7]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[8]  A. Agresti.  [A Survey of Exact Inference for Contingency Tables]: Rejoinder , 1992 .

[9]  Alan Agresti,et al.  Improved Exact Inference about Conditional Association in Three-Way Contingency Tables , 1995 .

[10]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[11]  Ehab F. Abd-Elfattah,et al.  The weighted log-rank class of permutation tests: P-values and confidence intervals using saddlepoint methods , 2007 .

[12]  Saddlepoint approximations as smoothers , 2002 .

[13]  Ib M. Skovgaard,et al.  Saddlepoint expansions for conditional distributions , 1987, Journal of Applied Probability.

[14]  D G Thomas,et al.  Trend and homogeneity analyses of proportions and life table data. , 1977, Computers and biomedical research, an international journal.

[15]  R. Butler.  SADDLEPOINT APPROXIMATIONS WITH APPLICATIONS. , 2007 .

[16]  G. J. Hahn,et al.  A Simple Method for Regression Analysis With Censored Data , 1979 .

[17]  R. Prentice.  Linear rank tests with right censored data , 1978 .

[18]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[19]  N. Breslow.  A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship , 1970 .

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

[21]  Ronald W. Butler,et al.  Randomization distributions and saddlepoint approximations in generalized linear models , 1990 .

[22]  Donald A. Pierce,et al.  Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families , 1992 .

[23]  E. Gehan.  A GENERALIZED WILCOXON TEST FOR COMPARING ARBITRARILY SINGLY-CENSORED SAMPLES. , 1965, Biometrika.

[24]  N. Mantel.  Evaluation of survival data and two new rank order statistics arising in its consideration. , 1966, Cancer chemotherapy reports.

[25]  D. Cox.  Regression Models and Life-Tables , 1972 .

[26]  James H. Ware,et al.  On distribution-free tests for equality of survival distributions , 1977 .