Inferences for Ratios of Normal Means

Inferences concerning ratios of means of normally distributed random variables or ratios of regression coefficients arise in a variety of problems in biomedical research. For example, in tests for non-inferiority of one or more experimental treatments against a positive control, it is often easier to define and also to interpret the non-inferiority margin as percentage changes (or fraction retained compared to the mean of the control group). In bioassay problems, one is also interested in ratios of regression coefficients, for instance in parallel line or slope ratio assays. Our aim here is to introduce an R extension package called mratios which can perform inferences about one or more such ratio parameters in the general linear model. For two-sample problems, the package is capable of constructing Fieller confidence intervals and perform the related tests when the group variances are assumed homogeneous or heterogeneous. In simultaneous inferences for multiple ratios, the package can (i) perform multiple tests, (ii) construct simultaneous confidence intervals using a variety of techniques, and (iii) calculate the sample sizes required for many-to-one comparisons in simultaneous tests for non-inferiority (or superiority) based on relative margins. We demonstrate the functionality of the package by using several data examples.