Understanding How Offending Prevalence and Frequency Change with Age in the Cambridge Study in Delinquent Development Using Bayesian Statistical Models

Objectives
To provide a detailed understanding of how the prevalence and frequency of offending vary with age in the Cambridge Study in Delinquent Development (CSDD) and to quantify the influence of early childhood risk factors such as high troublesomeness on this variation.

Methods
We develop a statistical model for the prevalence and frequency of offending based on the hurdle model and curves called splines that allow smooth variation with age. We use the Bayesian framework to quantify estimation uncertainty. We also test a model that assumes that frequency is constant across all ages.

Results
For 346 males from the CSDD for whom the number of offenses at all ages from 10 to 61 are recorded, we found peaks in the prevalence of offending around ages 16 to 18. Whilst there were strong differences in prevalence between males of high troublesomeness and those of lower troublesomeness up to age 45, the level of troublesomeness had a weaker effect on the frequency of offenses, and this lasted only up to age 20. The risk factors of low nonverbal IQ, poor parental supervision and low family income affect how prevalence varies with age in a similar way, but their influence on the variation of frequency with age is considerably weaker. We also provide examples of quantifying the uncertainty associated with estimates of interesting quantities such as variations in offending prevalence across levels of troublesomeness.

Conclusions
Our methodology provides a quantified understanding of the effects of risk factors on age-crime curves. Our visualizations allow these to be easily presented and interpreted.