PRM62 Visual Assessment of Fit of Equations to Predict Time-to-Event Outcomes

Graphical tests are very useful for assessing the fit of statistical models. In linear regression models, for instance, a plot of predicted means against observed values can reveal systematic over- or under-prediction. Similar graphical tests are not necessarily straightforward for other types of regression models like those based on parametric survival distributions (e.g., to predict life-expectancy, time to progression of disease), particularly when multiple predictors are included in the model. The first complicating issue is censoring, which makes a scatter plot of individual observed and predicted values difficult to interpret. A better approach is to plot the empirical distributions (i.e., Kaplan-Meier curves) derived from the observed and predicted values, which inherently accounts for censoring in observed times. The second and more intricate issue is the definition of the predicted values. In linear regression models, predictions represent the mean of the underlying normal distribution that produced the observation. Since the normal distribution is symmetric, it is reasonable to expect half of the observations to fall below their means, and the rest to fall above. Parametric survival distributions are highly skewed, however, so that the mean would generally be expected to exceed most observed values. Similar problems arise if one uses the median (or any one particular percentile) as a reference, or plots the overall predicted curve at the mean predicted value of the regression parameter (i.e., the scale of the distribution). An accurate depiction of the overall predicted curve can be obtained instead by generating multiple random event times from each individual's predicted distribution, and using these to derive the overall predicted curve. The approach will be illustrated with an example that highlights pitfalls involved with more simplistic approaches.