Semiparametric estimation for joint modeling of XXXX risk and functional biomarkers measured with errors.

@entity1 @entity2513 @entity5 @entity14
This research is motivated by a pilot @entity2513 study, where the outcome of interest is the presence of @entity2513 representing risk for @entity14 , and the predictors of interest are protein biomarkers that are repeatedly measured with errors along the length of a microscopic structure in the @entity1 colon, the colon crypt. Biomarkers of this type are referred to as functional biomarkers. The investigators are interested in identifying features of functional biomarkers that are associated with risk for @entity14 . In this paper, we investigate a joint modeling approach, where the binary clinical outcome is modeled using a logistic regression model with the unobserved true functional biomarkers as the predictors. Most existing methods are developed either for linear models or for functional biomarkers measured without errors and cannot be directly applied to our data. The applicable methods include a two-step method and a maximum likelihood method, which have some limitations. We propose a robust semiparametric method to overcome the limitations of the existing methods. We study the properties of the proposed method, and show in simulations that it compares favorably with other methods and also offers significant savings in CPU time. We analyze the pilot @entity2513 data and show that expression levels of AFC, a @entity5 suppressor gene, in the transitional area from the proliferation zone to the differentiation zone of colon crypts are likely to be associated with risk for @entity14 . Given the relatively small sample size in the pilot study, our results need to be validated in the future full-scale studies.
