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A Bounded Integer Model for Rating and Composite Scale Data
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Pharmacometrics Research Group)ORCID iD: 0000-0002-7228-0422
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Pharmacometrics Research Group)ORCID iD: 0000-0003-3531-9452
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Pharmacometrics Research Group)ORCID iD: 0000-0003-1258-8297
2019 (English)In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 21, no 4, article id 74Article in journal (Refereed) Published
Abstract [en]

Rating and composite scales are commonly used to assess treatment efficacy. The two main strategies for modelling such endpoints are to treat them as a continuous or an ordered categorical variable (CV or OC). Both strategies have disadvantages, including making assumptions that violate the integer nature of the data (CV) and requiring many parameters for scales with many response categories (OC). We present a method, called the bounded integer (BI) model, which utilises the probit function with fixed cut-offs to estimate the probability of a certain score through a latent variable. This method was successfully implemented to describe six data sets from four different therapeutic areas: Parkinson's disease, Alzheimer's disease, schizophrenia, and neuropathic pain. Five scales were investigated, ranging from 11 to 181 categories. The fit (likelihood) was better for the BI model than for corresponding OC or CV models (ΔAIC range 11-1555) in all cases but one (ΔAIC -63), while the number of parameters was the same or lower. Markovian elements were successfully implemented within the method. The performance in external validation, assessed through cross-validation, was also in favour of the new model (ΔOFV range 22-1694) except in one case (ΔOFV -70). A residual for diagnostic purposes is discussed. This study shows that the BI model respects the integer nature of data and is parsimonious in terms of number of estimated parameters.

Place, publisher, year, edition, pages
2019. Vol. 21, no 4, article id 74
Keywords [en]
Bounded integer model, Categorical data, Composite scale, Nonlinear mixed-effects modelling, Probit regression, Rating scale
National Category
Pharmaceutical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-388766DOI: 10.1208/s12248-019-0343-9ISI: 000470776700002PubMedID: 31172350OAI: oai:DiVA.org:uu-388766DiVA, id: diva2:1342113
Funder
Swedish Research Council, 2018-03317Available from: 2019-08-12 Created: 2019-08-12 Last updated: 2019-08-12Bibliographically approved

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Wellhagen, Gustaf J.Kjellsson, Maria C.Karlsson, Mats O.

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