Partial Residual Plots as an Integrated Model Diagnostic Tool in Model-Based Meta-Analysis

The use of partial residual plots (PRPs) was explored as a model diagnostic tool in Model-based Meta-Analysis (MBMA). Mathematical derivations illustrating the concepts were followed by an MBMA example using publicly available literature data of anti-depressive treatments with fluoxetine and venlafaxine. An E_max dose-response model was identified for venlafaxine while a constant drug effect combining all dose levels vs. placebo was identified for fluoxetine. The larger the mean baseline Hamilton Depression Rating (HAMD) score, the larger the expected drug effect (P = 0.0122), based on the likelihood ratio test. Mean baseline HAMD score (range) was 25.4 (23.5, 29.4) and 20.8 (15, 26) while mean placebo change from baseline (range) was -9.02 (-12.2, -4.8) and - 6.22 (-10.9, -1.3) for venlafaxine and fluoxetine, respectively. Average baseline HAMD score appeared larger for venlafaxine compared to fluoxetine, albeit a wider range for fluoxetine. Placebo response seemed lower but also more variable in fluoxetine compared to venlafaxine studies. Observed data points tended to deviate from model predictions when the mean baseline HAMD and placebo response values associated with those data points differed substantially from the corresponding values used for the model prediction. Normalizing observed data addressed this, providing a "like-to-like" comparison with model predictions in PRP when assessing the effect of one covariate (dose) after normalizing for other covariates/effects (placebo response and mean baseline). PRPs provide a robust integrated diagnostic tool in MBMA that uses all data to show the correlation between response and any covariate while controlling for other covariates included in the model.