Measurement Error for Age of Onset in Prevalent Cohort Studies
- 1 Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
- 2 Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada
Abstract
Prevalent cohort studies involve screening a sample of individuals from a population for disease, recruiting affected individuals, and prospectively following the cohort of individuals to record the occurrence of disease-related complications or death. This design features a response-biased sampling scheme since individuals living a long time with the disease are preferentially sampled, so naive analysis of the time from disease onset to death will over-estimate survival probabilities. Unconditional and conditional analyses of the resulting data can yield consistent estimates of the survival distribution subject to the validity of their respective model assumptions. The time of disease onset is retrospectively reported by sampled individuals, however, this is often associated with measurement error. In this article we present a framework for studying the effect of measurement error in disease onset times in prevalent cohort studies, report on empirical studies of the effect in each framework of analysis, and describe likelihood-based methods to address such a measurement error.
- Zelen, M. and Feinleib, M. (1969) On the Theory of Screening for Chronic Diseases. Biometrika, 56, 601-614. http://dx.doi.org/10.1093/biomet/56.3.601
- Zelen, M. (2004) Forward and Backward Recurrence Times and Length Biased Sampling: Age Specific Models. Lifetime Data Analysis, 10, 325-334. http://dx.doi.org/10.1007/s10985-004-4770-1
- Lagakos, S.W., Barraj, L.M. and De Gruttola, V. (2006) Nonparametric Analysis of Truncated Survival Data, with Applications to AIDS. Biometrika, 75, 515-523. http://dx.doi.org/10.1093/biomet/75.3.515
- Wolfson, C., Wolfson, D.B., Asgharian, M., M’Lan, C.E., ?stbye, T., Rockwood, K. and Hogan, D.B. (2001) A Reevaluation of the Duration of Survival after the Onset of Dementia. New England Journal of Medicine, 344, 1111-1116. http://dx.doi.org/10.1056/NEJM200104123441501
- Asgharian, M., M’Lan, C.E. and Wolfson, D.B. (2002) Length-Biased Sampling with Right Censoring: An Unconditional Approach. Journal of the American Statistical Association, 97, 201-209. http://dx.doi.org/10.1198/016214502753479347
- Rothman, K.J., Greenland, S. and Lash, T.L. (2008) Modern Epidemiology. Lippincott Williams & Wilkins, Philadelphia.
- Cox, D.R. and Miller, H.D. (1965) The Theory of Stochastic Processes. Chapman, London.
- Kalbfleisch, J.D. and Lawless, J.F. (1991) Regression Models for Right Truncated Data with Applications to AIDS incubation Times and Reporting Lags. Statistica Sinica, 1, 19-32.
- Turnbull, B.W. (1976) The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data. Journal of the Royal Statistical Society, Series B (Methodological), 38, 290-295.
- Wang, M.-C. (1991) Nonparametric Estimation from Cross-Sectional Survival Data. Journal of the American Statistical Association, 86, 130-143. http://dx.doi.org/10.1080/01621459.1991.10475011
- Keiding, N. and Moeschberger, M. (1992) Independent Delayed Entry, Survival Analysis: State of the Art. Springer, New York, 309-326. http://dx.doi.org/10.1007/978-94-015-7983-4_18
- Wang, M.-C., Brookmeyer, R. and Jewell, N.P. (1993) Statistical Models for Prevalent Cohort Data. Biometrics, 49, 1-11. http://dx.doi.org/10.2307/2532597
- Vardi, Y. (1982) Nonparametric Estimation in the Presence of Length Bias. The Annals of Statistics, 10, 616-620. http://dx.doi.org/10.1214/aos/1176345802