Flexible regression models for estimating postmortem interval (PMI) in forensic medicine.

Correct determination of time of death is an important goal in forensic medicine. Numerous methods have been described for estimating postmortem interval (PMI), but most are imprecise, poorly reproducible and/or have not been validated with real data. In recent years, however, some progress in PMI estimation has been made, notably through the use of new biochemical methods for quantifying relevant indicator compounds in the vitreous humour. The best, but unverified, results have been obtained with [K+] and hypoxanthine [Hx], using simple linear regression (LR) models. The main aim of this paper is to offer more flexible alternatives to LR, such as generalized additive models (GAMs) and support vector machines (SVMs) in order to obtain improved PMI estimates. The present study, based on detailed analysis of [K+] and [Hx] in more than 200 vitreous humour samples from subjects with known PMI, compared classical LR methodology with GAM and SVM methodologies. Both proved better than LR for estimation of PMI. SVM showed somewhat greater precision than GAM, but GAM offers a readily interpretable graphical output, facilitating understanding of findings by legal professionals; there are thus arguments for using both types of models. R code for these methods is available from the authors, permitting accurate prediction of PMI from vitreous humour [K+], [Hx] and [U], with confidence intervals and graphical output provided.