Bayesian Models for PCR Stutter

Abstract

For several decades, increasing attention has been given to the improvement of the quality of DNA mixture evidence interpretation, because of its importance in resolving problems in criminal investigations. Peaks at different positions along a molecular weight axis in an electropherogram (epg) are known to correspond to the alleles in a DNA sample, and these alleles can be used to describe differences between individuals. The process of DNA mixture interpretation largely involves probability and statistical models. Continuous probabilistic models ensure relatively greater objectivity and consistency between analysts than do other types of models. Implementing such models requires statistical models for PCR phenomena such as stutter. A peak at an allelic position, generally one repeat unit lower than a ‘parental’ peak, and usually with a height lower than the parent peak height, is called a ‘stutter’. The presence of stutters in an epg presents a problem in DNA mixture evidence interpretation. Therefore, practitioners search for sophisticated methodologies to model the contributions of stutters and real alleles to the peak height in order to make the interpretation more accurate. In modelling PCR stutter, the stutter ratio (SR) which represents the proportion between the observed stutter peak height and the parent allelic peak height is generally used. This research reviews the existing models for SR and develops new, advanced, Bayesian models for increased accuracy in predicting stutter. The developed models include nonhierarchical, hierarchical, and infinite mixture models. In these models, the longest uninterrupted sequence (LUS) of an allele was used as the key covariate in explaining the behaviour of SR. For hierarchical and non-hierarchical models, standard model evaluation techniques, including information criteria such as AIC, BIC, DIC, and WAIC, crossvalidation measures, and Bayesian p-values, were used considering their limitations and appropriateness under different modelling conditions. Initially, eleven non-hierarchical models, including six new models and five models developed in previous studies for predicting SR, were evaluated. Next, hierarchical models corresponding to seven of these models were investigated. Finally, the study used an algorithm based on the collapsed Gibbs sampling that uses the Chinese restaurant process as a non-parametric Dirichlet process prior, for fitting an infinite mixture of simple linear regression models for SR using LUS as the predictor. The overall contribution includes improvements in the prediction of PCR stutter through various Bayesian modelling techniques, an extension of infinite mixtures to the linear regression case, and advances to the collapsed Gibbs sampling algorithm that uses CRP as a non-parametric Dirichlet prior.