Performances of the estimators of the incidence rates of an infection with a differential mortality in the case of a birth cohort with constant incidence as well as constant background and excess mortalities.

We used the exact prevalence for the simulations.
: background mortality rate;
: excess mortality rate;
: time between the two surveys;
: initial prevalence, at ;
: initial prevalence, at ;
: simulated incidence;
: incidence rate estimated using the -estimator;
: incidence rate estimated using the H-estimator which was proposed by Hallett et al. [19] for birth cohort;
: incidence rate estimated using the B-estimator which was proposed by Brookmeyer and Konikoff. [29];
: incidence rate estimated using the optimal estimator obtained by solving the maximum likelihood equations (see equation (C2) in Text S1, Appendix C).
se: Standard error; here, the standard deviations were estimated using the delta method; the ratios were calculated under the assumption that the numbers of individuals in the two surveys are the same.
*: Ratio of the se to the se of the optimal estimator.