As noted above, three scenarios in which the pattern of age-specific LTP could be predicted based on epidemiologic theory were explored for purposes of validation. Figure
3 presents simulated LTP with the C parameter for incidence set at 0.01 (1% per year), the MR set to one and the false negative risk set to zero. As expected, the lifetime prevalence increases with age. Figure
4 depicts simulated lifetime prevalence under the same set of assumptions but with the
r parameter set to 0.05, depicting a 5% decline in incidence per year of age after age 15. As expected, the simulated lifetime prevalence fails to increase after several decades as the incidence becomes very small with increasing age but, consistent with expectation, LTP does not decrease. Figure
5 depicts the addition of a false negative risk of 15% per five year period (approximately 3% per year) in addition to the features of the second scenario (Figure
4). Including a false negative risk > 0 leads to deviation of actual from apparent LTP, both of which are depicted in the Figure. "Apparent" LTP does not include the false negative results in the numerator of the prevalence proportion, which produces an apparent decline in age-specific LTP. However, the actual LTP continues to increase and is identical to that depicted in Figure
4. While Figure
5 demonstrates that false negative diagnostic ratings can lead to an apparent decline in age-specific LTP when incidence declines with age, differential mortality is another possible explanation for this pattern. In the simulations depicted in Figure
6, the r parameter has been set to zero so that incidence does not decline with age and the rate of false negative ratings has also been set to zero. The Figure presents two simulations, one in which the MR is set to 1.4, consistent with existing literature, and one in which the MR is set to 2.0 (a value likely to be too high). Comparison of Figure
3 to Figure
6 confirms that differential mortality can affect age-specific LTP, but the effect tends to be evident only in elderly age groups. Combining the declining incidence depicted in Figure
4 with a MR of 1.4 leads to a lower LTP value and an earlier age for maximum LTP, see Figure
7, but the peak prevalence continues to occur at an older age group than has been reported by epidemiologic studies.