Survival analysis under cross-sectional sampling: length bias and multiplicative censoring

Nonparametric inference under competing risks and selection-biased sampling

“…(1) and (2) are fulfilled (see Appendix for details). This generalizes to any bias function the results obtained by Lund [37] and Van Es et al [49] with w(x) = x, which corresponds to the homogeneous Poisson process case.…”

Accelerated failure time regression for backward recurrence times and current durations

“…Allison ( van Es et al (2000) surveyed the theory behind current duration data analysis and studied in particular proportional hazards and accelerated failure time models with a view to obtain semiparametric efficient estimators, a program carried out by Klaassen et al (2003) for the AFT models under unrealistically restrictive assumptions on the distribution of the covariates. We conclude by noting that because of the equivalence between backward and forward recurrence time distributions, accelerated failure time models would be similarly useful in situations where forward recurrence times are modelled under stationarity.…”

“…For survival analysis of dynamic populations in calendar time similar relations exist, as reviewed by van Es et al (2000): Assume that lives start at uniform rate in calendar time, and that at a certain time , we record the elapsed lifetimes Y of all individuals still alive. If…”

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

“…Then it is easy to see (Cox and Miller, 1965;Zelen, 2004;Van Es et al, 2000) that the link formula (2) holds: Let I = indicator of being included in the sample. Then…”