Use of shared gamma frailty model in analysis of survival data in twins.

In survival analysis, the effect of a covariate on the outcome is reported in a hazard rate. However, hazards rates are hard to interpret. Here we consider differences in survival probabilities instead. Using data on twins is interesting due to the fact that many observed and unobserved factors are controlled or matched. To model the correlation between twins, some authors have proposed survival models with frailties or random effects. However, there is a potential danger of bias in the estimation if the frailty distribution is misspecified. Frailties are often assumed to follow a gamma distribution. To safeguard us from the impact of the misspecification of this distribution, we consider a flexible non-parametric baseline hazard in addition to a parametric one. We will apply this methodology to the TwinsUK cohort to predict the probability of experiencing a fracture in the next five or ten years, given their bone mineral densities (BMD) and their frailty index. The models with parametric and non-parametric baseline hazards yield very close results in estimating survival probabilities and thus a choice of parametric baseline hazard is generally preferred. We find that bone mineral density is a significant predictor in the model whereas frailty index is not. Low BMD leads to a larger probability of fracture; e.g, in 10 years, the probability of fracture is 21% for low BMD group, 16% for medium BMD group and 8% for high BMD group.