Statistical Methods for Combining Multivariate and Categorical Data in Postmortem Interval Estimation

As submitted by the proposer: Inferring time since death is a standard goal of a murder investigation. There is at this time no unified statistical methodology for this purpose. Opinions often are based on qualitative judgments rather than on systematic, quantified measures of the attendant uncertainty. We propose to create a unified statistical method for estimating the postmortem interval (PMI), or time since death, based on the simultaneous analysis of quantitative and categorical data. We will use entomological data to develop and refine our approach, but the resulting tools should be applicable to any scientific approach to PMI estimation. The sizes of insect larvae associated with a corpse may be expressed quantitatively, such as length and weight, or categorically, such as developmental stage. The presence/absence of a list of species provides another kind of biological clock; such succession data are inherently categorical. Other conditions, such as temperature and drugs, as well as geographic and environmental factors, can affect the rates of changes of growth and succession with time. Previously, we developed separate basic statistical methods for estimating PMI based on quantitative and categorical response variables, respectively, and for quantifying the uncertainty attendant on such estimates. We propose here to extend our work on quantitative responses and to develop further procedures for categorical responses, in both realms to broaden the applicability and accuracy of the methods. Finally, we propose an analytical strategy for synthesizing them into methodology to deal with both kinds of data at once. The same basic statistical questions that motivate this research in the PMI setting arise as well in other settings, not only in forensic sciences. Examples include inferring the age of a fetus from ultrasound measurements and inferring whether a given male is fertile based on semen concentration, motility, and morphology. The methods we propose to investigate have potential applicability in any setting where an attribute of an individual is to be inferred by comparing measured characteristics to training data from other subjects known to have the attribute. During phase one we will develop the mathematical and statistical methodology. For use in forensic settings, it is essential to be able to quantify the uncertainty inherent in the resulting inferences, and to provide a firm, rational, clear basis for that assessment. Our objective is to develop methodology with known statistical properties. During phase two we will test these methods and models on real data. Properties of inferences from statistical methods all depend to some extent on the assumptions on which the models are based. By use of extensive collections of real data, we will simulate samples from natural populations and quantify performance characteristics of the statistical methods that we develop. These data collections will include our own unpublished experimental data on carrion insect growth and succession. We have in hand measurements for size as a function of age from >15,000 specimens of three carrion fly species, and presence/absence data from 53 succession experiment pig carcasses exposed under relatively uniform conditions. Our development data have been checked and cleaned and assembled into consistently-formatted databases. The succession data are new, and so it will take time and effort to assemble them into a reliable database. In addition, the succession study included the collection of >36,000 carrion fly larvae corresponding to known PMI values. We will measure these (length, width, dry weight) to add quantitative information to the existing categorical dataset. We will also assemble the results from published experimental PMI studies, including both insect development and succession models. Several authors have agreed to provide their raw data, which we will assemble in a common database. ca/ncf