  Retrospectively ascertained survival time may be subject to recall error. An
example of discrete survival time with such recall error is time-to-pregnancy
(TTP), the number of months non-contracepting couples require to get pregnant
which is a measure of human fecundity. The epidemiological literature has
demonstrated that retrospective TTP is subject to recall error and statistical
models focusing on TTP have not accounted for the recall error. We propose a
multistage model that utilizes women's retrospectively-reported TTP and
associated certainty to estimate the TTP distribution. Our proposed model
utilizes a discrete survival function that accounts for random heterogeneity
arising from between women TTP data as well as a multinomial regression model
to account for her certainty as accuracy may decline over time, i.e., depends
on time since pregnancy in estimating the TTP distribution. Other novel
features of the model include attention to whether the pregnancy was
(un)planned as well as providing an approach to predict survival function for
women without a reported TTP. Our model allows for the consideration of
covariates for each of the underlying factors of (un)planned pregnancy, measure
of certainty and TTP distribution. The proposed model is applicable for any
discrete survival time when certainty in reporting may be a consideration. We
use Monte Carlo simulations to assess the finite sample performance for the
proposed estimators. We illustrate our proposed method using data from Upstate
KIDS Study.
