A General Statistical Framework for Adjustment of Rates

A general framework is presented that integrates standardization procedures common in demography, biometrics, and other areas with statistical methodology for the analysis of log-linear models. A family of rate-adjustment methods is derived from the log-linear model; the conventional method of direct standardization is a special case. Extensions of earlier methods include (a) adjustment for three-factor interaction, (b) adjustment for marginal association between composition and group, (c) adjustments that use a standard group, and (d) adjustments that control for both marginal composition-group interaction and three-factor interaction. Statistical inference for adjusted rates is facilitated in several ways: (a) by presenting key hypotheses that can be tested routinely with log-linear methods, (b) by efficient point and interval estimation of rates, (c) by assessing the sampling variability of absolute or relative comparisons of rates across groups, and (d) by smoothing the data. Examples illustrate the flexibility of the proposed framework.