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Accelerated failure time regression for backward recurrence times and current durations. (English) Zbl 1217.62152
Summary: Backward recurrence times in stationary renewal processes and current durations in dynamic populations observed at a cross-section may yield estimates of underlying interarrival times or survival distributions under suitable stationarity assumptions. Regression models have been proposed for these situations, but accelerated failure time models have the particularly attractive feature that they are preserved when going from the backward recurrence times to the underlying survival distribution of interest. This simple fact has recently been noticed in a sociological context and is here illustrated by a study of current duration of time to pregnancy.

62N05 Reliability and life testing
62P25 Applications of statistics to social sciences
62G08 Nonparametric regression and quantile regression
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62G05 Nonparametric estimation
62N02 Estimation in survival analysis and censored data
Full Text: DOI
[1] Ali, M.M.; Marshall, T.; Babiker, A.G., Analysis of incomplete durations with application to contraceptive use, Journal of the royal statistical society. series A, 164, 549-563, (2001) · Zbl 1002.62537
[2] Allison, P.D., Survival analysis of backward recurrence times, Journal of the American statistical association, 80, 315-322, (1985)
[3] Balabdaoui, F., Jankowski, H., Pavlides, M., Seregin, A., Wellner, J., 2009. On the Grenander estimator at zero. Tech. Report 554. Department of Statistics. University of Washington. · Zbl 1214.62037
[4] Brookmeyer, R.; Gail, M.H., Biases in prevalent cohorts, Biometrics, 43, 739-749, (1987) · Zbl 0715.62221
[5] Cosslett, S.R., Efficient semiparametric estimation of censored and truncated regression via a smoothed self-consistency equation, Econometrica, 72, 1277-1293, (2004) · Zbl 1142.62329
[6] Farewell, V.T.; Prentice, R.L., A study of distributional shape in life testing, Technometrics, 19, 69-75, (1977) · Zbl 0352.62018
[7] Keiding, N., Independent delayed entry (with discussion), (), 309-326 · Zbl 0761.62156
[8] Keiding, N.; Kvist, K.; Hartvig, H.; Tvede, M.; Juul, S., Estimating time to pregnancy from current durations in a cross-sectional sample, Biostatistics, 3, 565-578, (2002) · Zbl 1138.62353
[9] Klaassen, C.A.J., Mokveld, P.J., van Es, B., 2003. Efficient estimation in the accelerated failure time model under cross sectional sampling. Math. Preprint Series 03-06. University of Amsterdam.
[10] Kulikov, V.N.; Lopuhaä, H.P., The behavior of the NPMLE of a decreasing density near the boundaries of the support, The annals of statistics, 34, 742-768, (2006) · Zbl 1092.62044
[11] Mokveld, P.J., 2007. The accelerated failure time model under cross sectional sampling schemes. Ph.D. Thesis. University of Amsterdam.
[12] Mukherjee, R., 2006. On accelerated failure time models for forward and backward recurrence times. Ph.D. Thesis. University of Wisconsin-Madison.
[13] Scheike, T.; Keiding, N., Design and analysis of time to pregnancy, Statistical methods in medical research, 15, 127-140, (2006) · Zbl 1122.62374
[14] Slama, R.; Ducot, B.; Carstensen, L.; Lorente, C.; de La Rochebrochard, E.; Leridon, H.; Keiding, N.; Bouyer, J., Feasibility of the current duration approach to study human fecundity, Epidemiology, 17, 440-449, (2006)
[15] Sun, J.; Woodroofe, M., Adaptive smoothing for a penalized NPMLE of a non-increasing density, Journal of statistical planning and inference, 52, 143-159, (1996) · Zbl 0848.62020
[16] van Es, B.; Klaassen, C.A.J.; Oudshoorn, K., Survival analysis under cross sectional sampling: length bias and multiplicative censoring, Journal of statistical planning and inference, 91, 295-312, (2000) · Zbl 0969.62062
[17] Weinberg, C.S.; Gladen, B.C., The beta-geometric distribution applied to comparative fecundabilty studies, Biometrics, 42, 547-560, (1986)
[18] Woodroofe, M.; Sun, J., A penalized maximum likelihood estimate of \(f(0 +)\) when \(f\) is non-increasing, Statistica sinica, 3, 501-515, (1993) · Zbl 0822.62020
[19] Yamaguchi, K., Accelerated failure-time mover – stayer regression models for the analysis of last episode data, Sociological methodology, 33, 81-110, (2003)
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