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Disease prediction is one of the central problems in biostatistical research.Some biomarkers are not only helpful in diagnosing and screening diseases butalso associated with the severity of the diseases. It should be helpful toconstruct a prediction model that can estimate severity at the diagnosis orscreening stage from perspectives such as treatment prioritization. We focus onsolving the combined tasks of screening and severity prediction, considering acombined response variable such as \{healthy, mild, intermediate, severe\}.This type of response variable is ordinal, but since the two tasks do notnecessarily share the same statistical structure, the conventional cumulativelogit model (CLM) may not be suitable. To handle the composite ordinalresponse, we propose the Multi-task Cumulative Logit Model (MtCLM) withstructural sparse regularization. This model is sufficiently flexible that canfit the different structures of the two tasks and capture their sharedstructure of them. In addition, MtCLM is valid as a stochastic model in theentire predictor space, unlike another conventional and flexible model, thenon-parallel cumulative logit model (NPCLM). We conduct simulation experimentsand real data analysis to illustrate the prediction performance andinterpretability.

Simultaneous Modeling of Disease Screening and Severity Prediction: A Multi-task and Sparse Regularization Approach