We consider methods for estimating the effect of a covariate on a disease onset distribution when the observed data structure consists of right-censored data on diagnosis times and current status data on onset times amongst individuals who have not yet been diagnosed. Dunson and Baird (2001) approached this problem using maximum likelihood, under the assumption that the ratio of the diagnosis and onset distributions is monotonic non-decreasing. As an alternative, we propose a two-step estimator, an extension of the approach of van der Laan, Jewell and Petersen (1997) in the single sample setting, that is computationally much simpler and requires no assumptions on this ratio. A simulation study is performed comparing estimates obtained from these two approaches, as well as that from a standard current status analysis that ignores diagnosis data. Results indicate that the Dunson and Baird estimator outperforms the two-step estimator when the monotonicity assumption holds, but the reverse is true when the assumption fails. The simple current status estimator loses only a small amount of precision in comparison to the two-step procedure but requires monitoring time information for all individuals. In the data that motivated this work, a study of uterine fibroids and chemical exposure to dioxin, the monotonicity assumption is seen to fail. Here, the two-step and current status estimators both show no significant association between the level of dioxin exposure and the hazard for onset of uterine fibroids; the two-step estimator of the relative hazard associated with increasing levels of exposure has the least estimated variance amongst the three estimators considered.
Young, Jessica G.; Jewell, Nicholas P.; and Samuels, Steven J., "Regression Analysis of a Disease Onset Distribution Using Diagnosis Data" (July 2007). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 218.