Three measures of explained variation for correlated survival data under the proportional hazards mixed-effects model.

Measures of explained variation are useful in scientific research, as they quantify the amount of variation in an outcome variable of interest that is explained by one or more other variables. We develop such measures for correlated survival data, under the proportional hazards mixed-effects model. Because different approaches have been studied in the literature outside the classical linear regression model, we investigate three measures R(2) , Rres2, and ρ(2) that quantify three different population coefficients. We show that although the three population measures are not the same, they reflect similar amounts of variation explained by the predictors. Among the three measures, we show that R(2) , which is the simplest to compute, is also consistent for the first population measure under the usual asymptotic scenario when the number of clusters tends to infinity. The other two measures, on the other hand, all require that in addition the cluster sizes be large. We study the properties of the measures both analytically and through simulation studies. We illustrate their different usage on a multi-center clinical trial and a recurrent events data set.