Parametric Bootstrap for Assessment of Goodness of Fit of Models for Block Haplotype Structure

Abstract

Our ultimate interest is in formalization of models for high-resolution haplotype structure in such a way that they can be useful in statistical methods for linkage disequilibrium (LD) mapping. Some steps in that direction have been taken by Daly et al.(2001) who describe a block structure of haplotypes. They outline a hidden Markov model (HMM) that allows for common haplotypes in each block. We propose somewhat different models that also use HMM, which allow for haplotypes in a block that are not one of the common types and more complex graph structure of preferred and non-preferred transitions between haplotypes in adjacent blocks. In this paper, we also address the problem of assessing goodness of fit of such models to data when only unphased genotype data on individuals or trios are available. We find that the traditional parametric bootstrap method to assess the goodness of fit of models does not have the right type I error in our case, where we have multinomial-type models with many cells having very low probabilities and only a moderate sample size.