Making the most of case-mother/control-mother studies

Abstract

The prenatal environment plays an important role in many conditions, particularly those with onset early in life, such as childhood cancers and birth defects. Because both maternal and fetal genotypes can influence risk, investigators sometimes use a case-mother/control-mother design, with mother-offspring pairs as the unit of analysis, to study genetic factors. Risk models should account for both the maternal genotype and the correlated fetal genotype to avoid confounding. The usual logistic regression analysis, however, fails to fully exploit the fact that these are mothers and offspring. Consider an autosomal, diallelic locus, which could be related to disease susceptibility either directly or through linkage with a polymorphic causal locus. Three nested levels of assumptions are often natural and plausible. The first level simply assumes Mendelian inheritance. The second further assumes parental mating symmetry for the studied locus in the source population. The third additionally assumes parental allelic exchangeability. Those assumptions imply certain nonlinear constraints; the authors enforce those constraints by using Poisson regression together with the expectation-maximization algorithm. Calculations reveal that improvements in efficiency over the usual logistic analysis can be substantial, even if only the Mendelian assumption is honored. Benefits are even more marked if, as is typical, information on genotype is missing for some individuals.

FIGURE 1.

Noncentrality parameter and power as a function of allele frequency for the case-mother/control-mother design and case-parent triad design. The vertical axes show, in the left column, the χ² noncentrality parameter for a 4-df likelihood ratio test, and, in the right column, the power of a corresponding test with α = 0.05. Left column (panels A–C): no missing data; right column (panels D–F): 20% of genotypes missing. First row (panels A and D): R₁ = 2, R₂ = 3, S₁ = 1, S₂ = 1; second row (panels B and E): R₁ = 1, R₂ = 3, S₁ = 1, S₂ = 1; third row (panels C and F): R₁ = 1, R₂ = 3, S₁ = 2, S₂ = 2. Curves for a case-mother/control-mother design with 150 case-mother pairs and 150 control-mother pairs: logistic regression using all pairs (solid line: —), logistic regression omitting pairs with missing genotypes (short-dashed line: – – – (panels D–F only)), log-linear Poisson regression using all pairs and imposing only the family relationship constraint (dotted line: - - -), similar analysis that additionally imposes mating symmetry (dashed-dotted line: – - –), and similar analysis that additionally imposes parental allelic exchangeability (long-dashed line: — — —). Curve for a case-parent triad design with 150 triads: log-linear Poisson regression using all triads (dashed-dotted-dotted line: – - - –). For panels A and D, curves for the model imposing mating symmetry (dashed-dotted line: – - –) and the model imposing parental allelic exchangeability (long-dashed line: — — —) overlap.