Convergence in Mixed Effects Logistic Regression Models

Abstract

relations had been taken into account, the results would not have been significant. It has been previously reported that litter effects are a characteristic of dose response data and therefore, within-litter correlation must be included when conducting statistical analyses (Khera et al., 1989; Kupper et al., 1986). When the response is a continuous measure, adjusting for within-litter correlations is simple (Haseman and Kupper, 1979; Searle, 1971). To adjust for the within-litter correlation, when the continuous measure is normally distributed, a nested analysis of variance can be implemented (Haseman and Kupper, 1979). One paper states that adjusting for within-litter correlations is more difficult when the response is dichotomous and rare, such as the occurrence of less common tumors (Haseman and Kupper, 1979). Different statistical models have been created to include litter effect, with many undergoing constant improvement (Yamamoto and Yanagimoto, 1994). Some models must be altered to incorporate litter effect, including the dose response model (Khera et al., 1989). Haseman and Soares (1976) concluded that, when analyzing experiments that look at dichotomous fetal responses, binomial or Poisson models provide poor fits, as there is similarity between responses from the same litter (Kupper et al., 1986). It also seems that certain models such as multistage, multihit and probit, which multiple authors have used, tend to ignore litter effects (Scientific Committee of the Food Safety Council, 1978, cited in Kupper et al., 1986; Segreti, and Munson, 1981; Kupper et al., 1986; Segreti, and Munson, 1981). The beta-binomial model, considered by Williams (1975), is commonly used to account for littermate correlation when analyzing dose response data (Kupper et al., 1986; Khera et al., 1989; Convergence in Mixed Effects Logistic Regression Models