Linear and Non - linear modeling of a dose - response curve using SAS

In clinical trials response variables are measured at different times and doses. This paper explores methods to determine the dose that optimizes the response based on multiple responses and doses. Linear dose-response modeling can be performed using repeated measures analysis (using PROC MIXED) for change in response (Y) using dose (X) as a continuous explanatory variable with time, dose, and time-by-dose interaction as fixed effects. The error structure to model the correlation between the repeated measures needs to be determined e.g. using the Akaike information criteria. To compare the responses at each dose, additional analyses using dose as a classification variable can be performed and pairwise comparisons can be obtained. Non-linear dose response modeling can be performed using continuous dose, X (using PROC NLIN) with the following model: Percent change in Y= b0 + (X . b1)/(X + b2 ) + error, where b0 is the response at dose = 0, b1 is the optimum % change in Y compared to dose = 0 and b2 is the dose at 50% of b1. A fixed value of γ can be chosen based on minimum residual sum of squares. Predicted values are calculated and plotted against the observed % change in Y for all doses. Additionally PROC CAPABILITY can be used to determine the best fitted distribution of Y among the exponential family and plotted for different doses. These methods were applied to analyze the pooled data from two clinical trials. Various determination of the “optimal dose” was considered.