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Appendix E. Bias in apparent prevalence as a function of a range of differences in health-state-specific detection probabilities.

To give readers an idea of the general form of bias to be expected in estimated apparent prevalence when health-state-specific detection probabilities differ, we calculated both expected bias (Fig. E1) and percent relative bias (%RB) (Fig. E2) for eight pairs of differential detection probability representing a range of potential differences across probability space. There are three major influences on the magnitude of bias in apparent prevalence when we consider health state as the primary source of detection heterogeneity. These include (i) the magnitude of estimated apparent prevalence, (ii) the magnitude of the difference between health state-specific detection probabilities, and (iii) the location of detection probabilities in probability space (0–1.0). Relating to point (i), as estimated apparent prevalence approaches 0.5 for a given pair of detection probabilities, the magnitude of bias increases. With respect to point (ii), bias is positively related to the magnitude of difference in detection probability between infected and uninfected individuals. As for point (iii), for a given absolute difference in detection probability (e.g., 0.10), bias will generally be higher when detection probabilities are low (e.g., examine bias in apparent prevalence as a function of = 0.15, = 0.25 vs. = 0.75, = 0.85). We highlight these results to show researchers that the relationship between detection probabilities and bias in apparent prevalence may not be straightforward.

FIG. E1. Bias in apparent prevalence as a function of a range of differences in health state-specific detection probabilities. In the figure key, (pU, pI) are the values for detection probability of uninfected and infected individuals, respectively.

FIG. E2. Percent relative bias (%RB) as a function of a range of differences in health state-specific detection probabilities. In the figure key, (pU, pI) are the values for detection probability of uninfected and infected individuals, respectively.