Predictive Models for Trajectory Risks Prediction from Repeated Ordinal Outcomes

This paper proposes new regressive proportional and partial proportional odds models and a framework to predict trajectories of repeated ordinal outcomes, which is a new development. We illustrated the proposed models using repeated ordinal responses on activities of daily living from older adults collected biannually through the Health and Retirement Study in the USA. The proposed framework uses the marginal and conditional modeling approach to obtain the joint model and predict the joint probability of a sequence of ordinal outcomes and trajectories. Besides, these models significantly reduce over-parameterization, as one needs to fit one model for each follow-up. This model allows assessing the effect of prior responses on current outcomes, including interaction terms among previous responses and between prior outcomes and covariates in the model. Also, it permits the varying number of risk factors for each follow-up. The prediction accuracy for full, training, and test data is close and varies between 0.91 and 0.94. The bootstrap simulation demonstrates the bias of parameter estimates, accuracy, and predicted joint probabilities are negligible with very low mean squared error. This model and framework would be instrumental in studying trajectories generated from longitudinal studies. The proposed framework can be used to analyze big data generated from repeated measures. This model readily uses a divide and recombine approach for big data in a statistically valid manner.