Multistage regression, a novel method for making better predictions from your efficacy data

Abstract

Multistage regression is rarely used in therapeutic research, despite the multistage pattern of many medical conditions. Using an example of an efficacy study of a new laxative, path analysis and the 2-stage least square method were compared with standard linear regression. Standard linear regression showed a significant effect of the predictor "noncompliance" on drug efficacy at P=0.005. However, after adjustment for the covariate "counseling," the magnitude of the regression coefficient fell from 0.70 to 0.29, and the P value rose to 0.10. Path analysis was valid, given the significant correlation between the two predictors (P=0.024) and produced an increase of the regression coefficient between "noncompliance" and "drug efficacy" by 60.0%. The 2-stage least squares method, using counseling as instrumental variable, produced, similarly, an increase of the overall correlation by 66.7%. A bivariate path analysis with "quality of life" as the second outcome variable increased the magnitude of the path statistic further by 47.1%, and, thus, enabled to make still better use of the predicting variables. We conclude that (1) multistage regression methods, as used in the present article produced much better predictions about the drug efficacy than did standard linear regression; (2) the inclusion of additional outcome variables enables to make still better use of the predicting variables; (3) multistage regression must always be preceded by usual linear regression to exclude weak predictors. We recommend that researchers analyzing efficacy data of new treatments more often apply multistage regression.