Multiple sources of bias for acute phase estimates.

<p>(A) The log-normal distributions used to model variability in individual hazard of infection (color-coding of σ_hazard used throughout the figure). (B and C) Estimated excess hazard-months attributable to the acute phase (EHM_acute) versus the true (simulated) EHM_acute when analyzing simulated cohort data with the (B) Wawer et al. [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001801#pmed.1001801.ref017" target="_blank">17</a>] Poisson regression and (C) Hollingsworth et al. [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001801#pmed.1001801.ref018" target="_blank">18</a>] variable hazard survival model. Thick gray diagonal lines represent unbiased estimates. Arrows 1–4 indicate how each bias affects estimates of EHM_acute. Arrow locations along the <i>x</i>-axis are chosen for ease of display only; for any true EHM_acute, each bias is quantified by the vertical separations between lines. Dotted lines show the “best case” scenario for these models: if the underlying population is truly homogenous, the analysis includes all seroincident couples, and late and chronic phase infectivity are equal. The small downward bias (1) in the Poisson regression arises from assumptions regarding person-time at risk. The dashed lines reveal additional downward bias (2) in both models stemming from misclassification of late couples as prevalent couples (assuming the excess hazard-months attributable to the late phase was 40). Solid lines show estimates from simulated cohorts when seroincident couples lost to follow-up are excluded (<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001801#pmed.1001801.g004" target="_blank">Fig. 4</a>), causing bias (3). Finally, both analyses are further biased upward (4) when used to analyze heterogeneous populations. (D) The same trends for σ_hazard = 0 and 3 from (B), but also showing how bias (4) can be partly mitigated (4*) when variance between individuals is controlled for by adjusting for measured covariates corresponding to some (but not all) of the heterogeneity. (B–D) were created by fitting smoothers through individual simulations (<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.1001801#pmed.1001801.s004" target="_blank">S3 Fig</a>.).