Scenario comparisons: How much good can we do?

Applied scientists, especially public health scientists, frequently want to know how much good can be caused by a proposed intervention. For instance, they might want to estimate how much we could decrease the level of a disease, in a dream scenario where the whole world stopped smoking, assuming that a regression model fitted to a sample is true. Alternatively, they may want to compare the same scenario between regression models fitted to different datasets, as when disease rates in different subpopulations are standardized to a common distribution of gender and age, using the same logistic regression model with different parameters in each subpopulation. In statistics, scenarios can be defined as alternative versions of a dataset, with the same variables, but with different values in the observations or even with noncorresponding observations. Using regression methods, we may estimate the scenario means of a Y-variable in scenarios with specified X-values and compare these scenario means. In Stata Versions 11 and 12, the standard tool for estimating scenario means is margins. A suite of packages is introduced for estimating scenario means and their comparisons using margins together with nlcom to implement Normalizing and variance–stabilizing transformations. margprev estimates scenario prevalences for binary variables. marglmean estimates scenario arithmetic means for non-negative valued variables. regpar estimates two scenario prevalences, together with their difference, the population attributable risk (PAR). punaf estimates two scenario arithmetic means from cohort or cross-sectional data, together with their ratio, the population unattributable fraction (PUF), which is subtracted from 1 to give the population attributable fraction (PAF). punafcc estimates an arithmetic mean between-scenario rate ratio for cases or nonsurvivors in case–control or survival data, respectively. This mean rate ratio, also known as a PUF, is also subtracted from 1 to estimate a PAF. These packages use the log transformation for arithmetic means and their ratios, the logit transformation for prevalences, and the hyperbolic arctangent or Fisher's z transformation for differences between prevalences. Examples are presented for these packages.