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Keywords: Missing data, survival analysis, measurement error, semiparametric theory, Huntington's Disease
Modeling the progression of Huntington's Disease is difficult because no clinical data cover the full disease course. If we conduct a study to model disease progression given age at disease onset as a covariate, the study may end before all subjects experience onset. In this case, we say that the covariate age at disease onset has been censored. Such “covariate censoring” presents a serious problem when our goal is to model the progression of Huntington’s Disease before and after onset. One contemporary solution to covariate censoring is conditional mean imputation, which is a simple way to impute unobserved disease onset times using all available data. However, there is no guarantee that an imputed disease onset time will reliably approximate the true onset time. As a result of this discrepancy, conditional mean imputation can yield biased estimates of disease progression. We actively adjust for this imputation error by directly modeling the error. Then, rather than assume a specific distributional form for this unobservable error, we incorporate it into our model by allowing this imputation error to follow any distribution. We achieve this flexibility by drawing from semiparametric theory. We illustrate this method’s effectiveness through simulations and an application to Huntington’s Disease.