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 varianceâ€“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 caseâ€“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.
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