Stats, drugs and rock and roll : statistical applications to temporally autocorrelated substance use data

The use of illicit drugs is an area of interest across a broad range of industries and fields including public policy, law enforcement and physical and mental health. Both the field of measuring drug use in the community and understanding its cognitive impacts are therefore the subject of constant research, development and innovation. This thesis examines statistical applications to temporally autocorrelated data in both the areas of drug use extent and cognitive impact. Specifically, sampling strategies for ascertaining drug use extent from waste water through the utilisation of patterns in weekly drug use is examined. This leads to a practical example of when representative sampling is cost effective enough to be a viable alternative to random sampling. The ability to ascertain cognitive impacts of drug use at the level of the individual is then explored. Analyses of empirical models of cognitive behaviour, that have been traditionally utilised to decompose behaviour, on psychological assessment tools the Iowa Gambling Task and the Balloon Analogue Risk Task are considered. We show that empirical models can lead to an inability to uniquely describe behaviour when considering individuals with possible cognitive impairments (those with extreme behaviours) and discuss the possibility of utilising mechanistic models of the data as a more reliable source of estimating behaviour in the extreme.