Testing the Non‐Unity of Rate Ratio under Inverse Sampling

Abstract

Inverse sampling is considered to be a more appropriate sampling scheme than the usual binomial sampling scheme when subjects arrive sequentially, when the underlying response of interest is acute, and when maximum likelihood estimators of some epidemiologic indices are undefined. In this article, we study various statistics for testing non-unity rate ratios in case-control studies under inverse sampling. These include the Wald, unconditional score, likelihood ratio and conditional score statistics. Three methods (the asymptotic, conditional exact, and Mid-P methods) are adopted for P-value calculation. We evaluate the performance of different combinations of test statistics and P-value calculation methods in terms of their empirical sizes and powers via Monte Carlo simulation. In general, asymptotic score and conditional score tests are preferable for their actual type I error rates are well controlled around the pre-chosen nominal level, and their powers are comparatively the largest. The exact version of Wald test is recommended if one wants to control the actual type I error rate at or below the pre-chosen nominal level. If larger power is expected and fluctuation of sizes around the pre-chosen nominal level are allowed, then the Mid-P version of Wald test is a desirable alternative. We illustrate the methodologies with a real example from a heart disease study.

Confidence intervals for odds ratio in matching pairs under inverse sampling

“…Inverse sampling scheme, first proposed by Haldane [8] , suggests that one continues to sample subjects until a pre-specified number of index subjects with the rare event of interest is observed. Inverse sampling is found to be useful for epidemiologic investigation in casecontrol studies [9,10] and sample surveys [11] . Again, when the underlying response of interest is acute and subjects arrive sequentially, inverse sampling can also be an useful alternative to binomial sampling in cohort studies [12,13] .…”

Confidence intervals for relative difference in matching pairs under inverse sampling

“…Lui [10] consider the interval estimation of rate ratio and relative difference in matched-pairs under inverse sampling, and provide the confidence interval based on Filler theorem. Tang et al [11] provide various test statistics (Wald-type, score and likelihood ratio test statistics) for testing non-unity risk ratio under standard inverse sampling scheme. All the abovementioned works are confined to test the equivalence or noninferiority based on risk difference and risk ratio under matched-pair or standard inverse sampling.…”

Confidence interval for relative difference under inverse sampling

“…For instance, Lui [5] considered the asymptotic conditional test procedures for relative difference under inverse sampling. Tang [6] developed a procedure for testing whether the rate ratio is 0 R under standard inverse sampling. They evaluate the performance of different test procedures in terms of their type I error rates and powers via a Monte Carlo simulation study.…”