Semiparametric linear transformation models for indirectly observed outcomes

We propose a regression framework to analyze outcomes that are indirectly observed via one or multiple proxies. Semiparametric transformation models, including Cox proportional hazards regression, turn out to be well suited to model the association between the covariates and the unobserved outcome. By coupling this regression model to a semiparametric measurement model, we can estimate these associations without requiring calibration data and without imposing strong functional assumptions on the relationship between the unobserved outcome and its proxy. When multiple proxies are available, we propose a data-driven aggregation resulting in an improved proxy. We empirically validate the proposed methodology in a simulation study, revealing good finite sample properties, especially when multiple proxies are aggregated. The methods are demonstrated on two case studies.