Abstract
To date, most statistical developments in QTL detection methodology have been directed at continuous traits with an underlying normal distribution. This paper presents a method for QTL analysis of non-normal traits using a generalized linear mixed model approach. Development of this method has been motivated by a backcross experiment involving two inbred lines of mice that was conducted in order to locate a QTL for litter size. A Poisson regression form is used to model litter size, with allowances made for under- as well as over-dispersion, as suggested by the experimental data. In addition to fixed parity effects, random animal effects have also been included in the model. However, the method is not fully parametric as the model is specified only in terms of means, variances and covariances, and not as a full probability model. Consequently, a generalized estimating equations (GEE) approach is used to fit the model. For statistical inferences, permutation tests and bootstrap procedures are used. This method is illustrated with simulated as well as experimental mouse data. Overall, the method is found to be quite reliable, and with modification, can be used for QTL detection for a range of other non-normally distributed traits.
Highlights
Various methods have been developed to detect a quantitative trait locus, ranging from the simpler regression based and method of moments, to maximum likelihood and Markov Chain Monte Carlo methods
The current paper provides a framework for QTL detection for non-normal traits with the addition of random polygenetic and/or environmental effects, and is an expansion of the method presented previously by Thomson [38]
Note that we do not assume γQq = γqQ since these heterozygous genotypes have different amounts of background genes coming from the appropriate parental strain (BC1 has 75% of genetic material originating from S1 compared with 25% originating from S1 for BC2)
Summary
Various methods have been developed to detect a quantitative trait locus, ranging from the simpler regression based and method of moments, to maximum likelihood and Markov Chain Monte Carlo methods. During the 1970s and 1980s, the generalized linear model (GLM1) was developed as a uniform approach to handling all these above classes of data [27], and these procedures are included in most major statistical packages. These methods would be applicable if data could be modeled as coming from one of the distributions of the exponential family (including Poisson for counts, binomial for binary and proportions data, as well as the normal distribution). Models to detect QTLs differ fundamentally from the standard statistical linear models (LM), linear mixed models (LMM), as well as the models for non-normal data mentioned above (GLM and GLMM). The method will be derived in terms of the mouse litter size model
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