Methods of utilizing baseline values for indirect response models

This study derives and assesses modified equations for Indirect Response Models (IDR) for normalizing data for baseline values (R-0) and evaluates different methods of utilizing baseline information. Pharmacodynamic response equations for the four basic IDR models were adjusted to reflect a ratio to, a change from (e.g., subtraction), or percent change relative to baseline. The original and modified IDR equations were fitted individually to simulated data sets and compared for recovery of true parameter values. Handling of baseline values was investigated using: estimation (E), fixing at the starting value (F1), and fixing at an average of starting and returning values of response profiles (F2). The performance of each method was evaluated using simulated data with variability under various scenarios of different doses, numbers of data points, type of IDR model, and degree of residual errors. The median error and inter-quartile range relative to true values were used as indicators of bias and precision for each method. Applying IDR models to normalized data required modifications in writing differential equations and initial conditions. Use of an observed/baseline ratio led to parameter estimates of k(in) = k(out) and inability to detect differences in k(in) values for groups with different R-0, whereas the modified equations recovered the true values. An increase in variability increased the % Bias and % Imprecision for each R-0 fitting method and was more pronounced for 'F1'. The overall performance of 'F2' was as good as that of 'E' and better than 'F1'. The % Bias in estimation of parameters SC50 (IC50) and k(out) followed the same trend, whereas use of 'F1' or 'F2' resulted in the least bias for S-max (I-max). The IDR equations need modifications to directly assess baseline-normalized data. In general, Method 'E' resulted in lesser bias and better precision compared to 'F1'. With rich datasets including sufficient information on the return to baseline, Method 'F2' is reasonable. Method 'E' offers no significant advantage over 'F1' with datasets lacking information on the return to baseline phase. Handling baseline responses properly is an essential aspect of applying pharmacodynamic models.