Improvements in cancer therapies have led to an increasing number of survivors living many years after successful treatment. However, along with this encouraging success comes the realization that these survivors are at an increased risk of late adverse effects and of late mortality many years after cancer treatment. An ideal approach for estimating the incidence rates of these toxicities and developing appropriate interventions would be to systematically monitor these survivors in a longitudinal manner, but this is impractical and generally not feasible. Instead, cross-sectional surveys are conducted to estimate the cumulative incidence rates of specific toxicities at fixed time points (5 or 10 years) and the effect of specific treatment on long-term toxicity. Data obtained by using the cross-sectional approach falls into the category of current status data. In the parametric framework, piecewise exponential distribution has been used for conducting inference on the current status data. Although the approach yields a reasonable estimate of fixed-term incidence rate and treatment effect, the limitations of this approach are identifying the number of pieces, the change points, and the assumption of constant hazard within each piece. In this paper we propose the use of some general parametric models to model incidence rates in cardio-toxicity data, which to our knowledge, has not been previously. One such model is the Weibull distribution, which is very flexible in modeling monotone hazard rates and essentially takes care of the limitations mentioned above thereby presenting an attractive alternative to model such data. The Weibull distribution model is robust in terms of estimates and inferences, and, it also provides smooth estimates of the confidence intervals for the fixed-term incidence rates, which is a primary objectives of such studies.
Srivastava DK, Zhu L, Hudson M, Pan J, Rai SN. Robust estimation and inference on current status data with applications to phase IV cancer trial. Journal of Modern Applied Statistical Methods, (accepted for publication; to appear in the May 2018 issue).