Estimation of the physiological length of pregnancy is a challenging prob-
lem since both the time origin of the pregnancy and the time of onset of labor are partly
observed. The time to spontaneous labor is indeed right-censored, and the time of fer-
tilization is only known up to an error. Therefore, data are subject to both censoring
and measurement errors. We focus on the case where the measurement errors affect
both the variable of interest and the censoring variable, which is the case of the timing
of spontaneous delivery among pregnant women. We propose an estimation strategy
to estimate the hazard rate of the underlying variable of interest. We explain the model
and this strategy and provide L 2 -risk bound for the data driven resulting estimator. We
also derive estimators of the survival function and the density. Simulations illustrate
the performances of the estimator. Lastly, the method is applied to an original real data
set of length of pregnancy to estimate rates of previable births, severe preterm births
and prolonged pregnancy and the influence of the cervical length of the first semester.

EB00000004451K

Available

• Hazard estimation with censoring and measurement error: application to length of pregnancy