Cumulative and "lifetime" prevalence of delinquency

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While age-specific prevalence statistics give an idea of the development with age of delinquent and criminal activity in the population, they do not show the cumulative effect of this development. For example, knowing (from the section above on the age-specific prevalence of offending) that 0.033% of 5 year olds and 0.067% of 6 year olds were identified as offenders does not determine what proportion of the cohort were ever identified as offenders before their seventh birthday. The number is somewhere between 0.067% and 0.100% (assuming that none of them was apprehended before their 5^th birthday): the lower figure if all the apprehended 6 year olds were also apprehended as 5 year olds, and the higher figure if none of them were apprehended as 5 year olds. Thus, in order to estimate the age-specific cumulative prevalence of identified offenders in the cohort – that is, the proportion of the cohort who were ever identified as offenders up to and including a given age – it is necessary to eliminate double- or multiple-counting of persons who commit crimes at different years of age. Perhaps most interesting to know is the proportion of the cohort who were ever identified as offenders, during the period covered by the study. This ever-prevalence, or lifetime prevalence, is the same as the age-specific cumulative prevalence at the last year of age covered by the study.

Figure 12 shows the cumulative prevalence of identified offenders in each cohort, by year of age. The proportion of the cohorts ever identified as offenders rises from 0.033% of 5 year olds, or one in every 3,000 cohort members, to 18.5%, or just under one-fifth of cohort members, by the 18^th birthday. This finding is consistent with similar research conducted in other countries (reviewed in Piquero et al., 2003), and with Canadian research based on youth court records (Carrington et al., 2005).

Prior to the 13^th birthday, and especially prior to the 10^th birthday, the recorded cumulative prevalence of offenders is lower in the 1987 cohort than in the cohort born in 1990. The probable reason for this is that there are no data on offending prior to 1995, and therefore no data on offending by members of the 1987 cohort prior to their 8^th birthdays. Fortunately, the cumulative prevalence of offenders before the 8^th birthday is so small (0.22% of the 1990 birth cohort) as to be insubstantial, and the resulting underestimation of cumulative offending in this cohort appears to have cleared up entirely by the age of 13, where the two curves converge at 5.5%.¹ Apparently, most if not all of those in the 1987 cohort who would have appeared in the statistics if there had been data for years prior to 1995, were also recorded as offenders between the ages of 8 and 13, with the result that they were belatedly added to the cumulative prevalence counts. Therefore, the approach used in the following analyses of cumulative prevalence (which differs from the approach used in the discussion of age-specific prevalence in the previous chapter) is to report proportions of the cohort born in 1990 for the ages of 5 to 13, and of the 1987 cohort thereafter.

To recapitulate, the proportion of the cohorts ever recorded as offenders rises smoothly with age, reaching 18.5%, or just under one-fifth of cohort members, by the 18^th birthday. No levelling-off is evident in Figure 12: if anything, the increases in cumulative prevalence during the teenage years appear to be large and continuing. The largest annual absolute increase in cumulative prevalence takes place at the age of 15, when 3.7% of the cohort commit their first recorded offence.² Figure 13 shows the annual rate of increase in cumulative prevalence, relative to the level of the previous year. As in the analysis of the relative rate of change in age-specific prevalence (Figure 4), the largest relative increases in cumulative prevalence occur at the youngest ages, and there is a jump at 12 years old which may reflect the under-recording of crime committed by 5 to 11 year olds, due to 12 years old being the minimum age of criminal responsibility. After the age of 12, the relative rate of increase in cumulative prevalence decreases with each year of age: it is 85% at 12 and only 18% at 17. Thus, although large numbers of additional offenders are being added to the cumulative prevalence during the teenage years (Figure 12), the rate at which they are being added is decreasing.

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Notes

1. Two-tailed t-values for the differences between the cohorts in cumulative prevalence at ages 8, 9, ..., 14 are -10.18, -8.47, -5.41, -5.23, -2.34, -0.56, 2.96. These statistics should be interpreted with caution, since these are not normally distributed random samples. Satterthwaite's (1946) approximation for the degrees of freedom was used, since the variances of each pair of vectors of observations were unequal (SAS Institute, 2004). Both the differences and the t-values decrease with age. Only the t-value for 13 year olds is not significant at p<.05 (p₁₃=.58). For an explanation of the difference in recorded cumulative prevalence at 14 years of age, see note 1 in "The age-crime curve" .
2. This is the proportion of the cohort whose first recorded offence, or delinquent career onset, was at 15 years old. The age of onset of the career is discussed as a topic of interest in itself in a later section of this report.