Supervised learning of outcome-relevant items from a questionnaire via mixed integer optimization

Questionnaires are among the oldest and most widely used instruments in practice to measure variables relevant to traits of interest that cannot be easily measured by physical devices, for example, depression. In many clinical settings, the scope of an existing questionnaire is often unfit to apply to a new study population, whose underlying characteristics are different from those of the original population used for the questionnaire's development and/or validation. Motivated by a cohort study of elderly asthma patients, we aim to examine associations between clinical outcomes and quality of life (QoL) measured by a QoL questionnaire. To increase comparability, we consider a supervised learning method to identify a subset of questions whose summary score is strongly associated with a specific clinical outcome under investigation. The resultant set of selected items gives an optimal summary metric of the questionnaire, which improves both statistical power and clinical interpretation. Our item extraction procedure is built upon the best subset algorithm implemented by a mixed integer programming, which enjoys both theoretical guarantee of selection consistency and flexibility of handling nonresponse missing data. Moreover, estimation uncertainty is analyzed by the means of noise perturbation. Our methodology is first evaluated by extensive simulation studies with comparisons to existing methods and then applied to derive tailored QoL scores adaptive to two clinical outcomes of lung function measure (FEV1) and asthma control test (ACT), respectively, among elderly people with persistent asthma.