A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^

Prognosis of amyotrophic lateral sclerosis

Two cohorts of amyotrophic lateral sclerosis (ALS) patients were identified. One incidence-based cohort from Harris County, Texas with 97 cases, and the other a clinic referral series from an ALS clinic in Houston, Texas with 439 cases were followed-up to evaluate the prognosis of ALS. The overall Kaplan-Meier 3-year survival after diagnosis was similar, 0.287 for the incidence cohort and 0.313 for the referral cohort. However, the 5-year survival was much lower for the incidence cohort than the referral cohort (0.037 vs. 0.206). The large difference in 5-year survival was thought to be the results of a stronger unfavorable effect of the prognostic factors in the incidence cohort than in the referral cohort.^ Cohort-specific Weibull regression models were derived to evaluate the cohort-specific prognostic factors and survival probability with adjustment of certain prognostic factors.^ The major prognostic factors were: age at diagnosis, bulbar onset, black ethnicity, and positive family history of ALS in both cohorts. Female gender, simultaneous upper and lower extremities onset were specifically unfavorable factors in the incidence cohort. In the incidence cohort the prognosis was relatively favorable for cases with duration from onset to diagnosis longer than 4 months, however in the referral cohort the relatively favorable prognosis only occurred in cases with duration from onset to diagnosis 1 year or longer and was strongest in cases with duration 5 years and longer. Age at diagnosis modified the effect of bulbar onset in the incidence cohort but not in the referral cohort. The estimated survival with presence of an unfavorable prognostic factor identified in the incidence cohort was higher for the referral cohort than for the incidence cohort. Future studies are indicated to investigate the disease heterogeneity issue of ALS based on survival distribution of ALS. ^