Assessing time-dependent risk factors in relation to the risk of disease progression is challenging, yet important, especially for chronic diseases with slow progression. In this paper, the partly conditional model is extended for characterizing disease progression at time t with longitudinal ordinal outcomes in the presence of time-dependent covariates at time s \((s < t)\) and time-dependent effects. Advantages of the method include direct modeling of disease progression, use of longitudinal risk factors, and flexibility in target period of progression \(u = t - s\) . A generalized estimating equation approach is adopted for parameter estimation, and a new regularity condition requiring a fixed prediction time window \(u_0\) is established to consistently estimate the covariance of the estimated parameters. Extensive simulation studies are conducted to assess the properties of the proposed model alongside with an explicit demonstration of the implementation using existing statistical software. The proposed method is applied to a longitudinal Alzheimer’s disease dataset from the National Alzheimer’s Coordinating Center to assess effect of time-dependent cognitive complaint on Alzheimer’s Disease progression.
