Regression analysis of a disease onset distribution using diagnosis data.

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, Biometrics 57, 306-403) approached this problem using maximum likelihood, under the assumption that the ratio of the diagnosis and onset distributions is monotonic nondecreasing. As an alternative, we propose a two-step estimator, an extension of the approach of van der Laan, Jewell, and Petersen (1997, Biometrika 84, 539-554) in the single sample setting, which 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.