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. ^

The effects of ethnicity and ethnic composition of schools on physical activity and nutrition behaviors of 8th and 11th graders in Texas

With rates of obesity and overweight continuing to increase in the US, the attention of public health researchers has focused on nutrition and physical activity behaviors. However, attempts to explain the disparate rates of obesity and overweight between whites and Hispanics have often proven inadequate. Indeed, the nebulous term ‘ethnicity’ provides little important detail in addressing potential biological, behavioral, and environmental factors that may affect rates of obesity and overweight. In response to this, the present research seeks to test the explanatory powers of ethnicity by situating the nutrition and physical activity behaviors of whites and Hispanic into their broader social contexts. It is hypothesized that a student's gender and grade level, as well as the socioeconomic status and ethnic composition of their school, will have more predictive power for these behaviors than will self-reported ethnicity. ^ Analyses revealed that while ethnicity did not seem to impact nutrition behaviors among the wealthier schools and those with fewer Hispanics, ethnicity was relevant in explaining these behaviors in the poorest tertile of schools and those with the highest number of Hispanics. With respect to physical activity behaviors, the results were mixed. The variables representing regular physical activity, participation in extracurricular physical activities, and performance of strengthening and toning exercises were more likely to be determined by SES and ethnic composition than ethnicity, especially among 8th grade males. However, school sports team and physical education participation continued to vary by ethnicity, even after controlling for SES and ethnic composition of schools. In conclusion then, it is important to understand the intersecting demographic and social variables that define and surround the individual in order to understand nutrition and physical activity behaviors and thus overweight and obesity.^

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. ^