ABSTRACT
A survey of statistical methods for validation of shape-scale families of probability distributions from type II censored samples is given. We propose "integrated likelihood ratio tests" which are modifications of Zhang's tests from complete to type II censored data. We also give modifications of Cramér-von-Mises and Anderson-Darling tests using integration with respect to non-parametric estimators of the cumulative distribution function. Explicit formulas for modified chi-squared tests from censored data with data driven choice of partitioning are given. Powers of tests against most used alternatives to the Weibull, loglogistic and lognormal distribution are compared.
Subject(s)
Biostatistics/methods , Animals , Chi-Square Distribution , Gamma Rays/adverse effects , Humans , Likelihood Functions , Logistic Models , Male , Mice , Radiation Injuries, Experimental/mortality , Statistics, NonparametricABSTRACT
We propose new two and k-sample tests for evaluating the equality of survival distributions against alternatives that include crossing of survival functions, and proportional and monotone hazard ratios. The tests allow for right censored data. The asymptotic power against local alternatives is investigated. Simulation results demonstrate that the new tests are more powerful than known tests when survival functions cross. We apply the tests to a well known study of chemo- and radio-therapy conducted by the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller than for other known tests.
