The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.     

The Monofactorial Model for Recurrence Risks with Generalized Penetrance

Recurrence risks are derived explicitly in terms of gene frequencies and penetrance coefficients for the general case in which all genotypes have incomplete penetrance. Maximum likelihood estimation of recurrence risks is achieved through the use of the semi-symmetric intraclass contingency table. The resulting formulas and estimation procedure can be useful for the analysis of population and family data, and in genetic counselling.     

Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

Introducing the Multivariate Dale Model in Population‐Based Genetic Association Studies

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic regressions and at the haplotype level, haplotype analyses. An alternative modeling approach, based on the case/control principle, is to regard exposures (e.g., genetic data such as derived from Single Nucleotide Polymorphisms – SNPs) as random and disease status as fixed and to use a marginal multivariate model that accounts for inter‐relationships between exposures. One such model is the multivariate Dale model. This model is based on multiple logistic regressions. That is why the model, applied in a case/control setting, leads to straightforward interpretations that are similar to those drawn in a classical logistic modeling framework. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)