Assessing the distribution of discrete survival time in presence of recall error

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.