Case‐parent Triads: Estimating Single‐ and Double‐dose Effects of Fetal and Maternal Disease Gene Haplotypes

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Abstract
Case-parent triad data are considered a robust basis for studying association between variants of a gene and a disease. Methods evaluating statistical significance of association, like the TDT-test and its extensions, are frequently used. When there are prior hypotheses of a causal effect of the gene under study, however, methods measuring penetrance of alleles or haplotypes as relative risks will be more informative. Log-linear models have been proposed as a flexible tool for such relative risk estimation. We demonstrate an extension of the log-linear model to a natural framework for also estimating effects of multiple alleles or haplotypes, incorporating both single- and double-dose effects. The model also incorporates effects of single- and double-dose maternal haplotypes on a fetus during pregnancy. Unknown phase of haplotypes as well as missing parents are accounted for by the EM algorithm. A number of numerical improvements to maximum likelihood estimation are also implemented to facilitate a larger number of haplotypes. Software for these analyses, HAPLIN, is publicly available through our web site. As an illustration we have re-analyzed data on the MSX1 homeobox-gene on chromosome 4 to show how haplotypes may influence the risk of oral clefts.