Log Likelihood Ratio Tests for Safety Data Analysis

Abstract

For Gandhi non-violence was a primary invariance principle, while for his political successor Nehru justice was so. Invariance principles signify that while everything changes in life, some laws of life do not. Consequently, these laws of life do not include a measure of error. For example, Einstein’s invariance principle is expressed in the famous equation E  =  mc². Most statistical tests, including t- (and z-) tests, F-tests, chi-square tests, odds ratio tests, do not meet the invariance principle, because they apply estimated likelihoods like averages and proportions that have their standard errors as a measure of uncertainty. However, a few statistical tests use likelihoods without standard error. These tests, called exact tests, should, by their very nature, provide the best precision and sensitivity of testing. They include, among others, the Fisher exact test and the log likelihood ratio test. Particularly, the log likelihood ratio test, avoiding some of the numerical problems of the other exact likelihood tests, is straightforward, and is available through most major software programs (BUGS y WinBUGS 2011; S plus 2011; Stata 2011; StatsDirect 2011; StatXact 2011; True Epistat 2011; SAS 2011; SPSS 2011), although infrequently used so far. This chapter reviews the advantages and problems of the log likelihood ratio test, and gives real and hypothesized data examples supporting its better sensitivity. We do hope that the chapter will stimulate researchers to more often apply this test.