Per K. Andersen, Mette Gerster, Mia Madsen

Let T_{i1}, T_{i2} be event times for the two members of a matched pair, e.g. a pair of twins. Inference for these event times needs to address the possible within-pair association and a possible model with this property is the shared frailty model λ_{ij}(t) = W_{i}λ_{0}(t)exp(β Z_{ij}).

Here,λ_{ij}(t) is the hazard function for subject i,j, λ_{0}(t) the baseline hazard common to all individuals, Z_{ij} are observed covariates for subject i,j. Finally, W_{i} is an unobserved random effect (“the frailty”), which is shared between the two members of the pair. The random frailty creates the desired within-pair association.

Standard inference for this model requies independence between W_{i} and Zsub]ij. We study how violations of this assumption affects inference for the regression coefficients, β, and conclude that substantial bias may occur.

We propose an alternative way of making inference for β by using a fixed-effects models for survival in matched pairs. In this model, λ_{ij}(t)=λ_{0i}(t)exp(β Z_{ij}) each pair has its own baseline hazard,λ_{0i}(t) which is eliminated from estimating equations via a partial likelihood. Fitting this model to data generated from the frailty model provides consistent and asymptotically Normal estimates for β.

The methods are exemplified by studying how length of education affects the incidence of cancer in Danish twins.

**Keywords:** Survival analysis; Matched pairs; Twin studies

**Biography:** PKA is professor at the Department of Biostatistics at University of Copenhagen, Denmark. He took his master's degree in 1978, and his ph.d. degree in mathematical statistics in 1982, and a Dr.Med.Sci. degree in 1997 - all from University of Copenhagen. His main research interests are survival/event history analysis and analysis of cohort studies and other epidemiological applications of statistics.