Estimating mean time to reach a milestone, using retrospective data.

In surveys to estimate the mean age at menarche (or another milestone reached by the whole population), interviewed girls in the age range can respond that menarche (a) has not occurred or (b) has occurred or (c) occurred at a certain age t. Answers of type (a) and (b) are called status quo data. Answers of type (a) and (c) are called retrospective data.One kind of data is assumed. The distribution of age at menarche may also be assumed to be normal or not necessarily normal. This gives four possible sets of assumptions. Estimators, with their asymptotic distributions and optimal sampling allocations, are found for the case of retrospective data and non-normal distribution. These estimators are compared in examples with previously proposed estimators based on the other sets of assumptions. In these examples, retrospective data should certainly be used if available and reliable.