Pseudo-likelihood estimates of the cumulative risk of an autosomal dominant disease from a kin-cohort study

Wacholder et al. [1998: Am J Epidemiol 148:623-629] and Struewing et al. [1 997: N Engl J Med 336:1401-1408] have recently proposed a design called the kin-cohort design to estimate the probability of developing disease (penet rance) associated with an autosomal dominant gene. In this design, voluntee rs (probands) agree to be genotyped and one also determines the disease his tory (phenotype) of first-degree relatives of the proband. They used this d esign to estimate that the chance of developing breast cancer by age 70 in Ashkenazi Jewish women who carried mutations of the genes BRCA1 or BRCA2 wa s 0.56, a figure that was lower than previously estimated from highly affec ted families. The method that they used to estimate the cumulative risk of breast cancer, while asymptotically correct, does not necessarily produce m onotone estimates in small samples. To obtain monotone, weakly parametric e stimates, we consider separate piece-wise exponential models for carriers a nd non-carriers. As the number of intervals on which constant hazards are a ssumed increases, however, the maximum likelihood score equations become un stable and difficult to solve. We, therefore, developed alternative pseudo- likelihood procedures that are readily solvable for piecewise exponential m odels with many intervals. We study these techniques through simulations an d a re-analysis of a portion of the data used by Struewing et al. [1997] an d discuss possible extensions. (C) 2001 Wiley-Liss, Inc.