{"title":"A Non-Parametric Approach to Scale Reduction for Uni-Dimensional Screening Scales","authors":"Xinhua Liu, Zhezhen Jin","doi":"10.2202/1557-4679.1094","DOIUrl":null,"url":null,"abstract":"To select items from a uni-dimensional scale to create a reduced scale for disease screening, Liu and Jin (2007) developed a non-parametric method based on binary risk classification. When the measure for the risk of a disease is ordinal or quantitative, and possibly subject to random censoring, this method is inefficient because it requires dichotomizing the risk measure, which may cause information loss and sample size reduction. In this paper, we modify Harrell's C-index (1984) such that the concordance probability, used as a measure of the discrimination accuracy of a scale with integer valued scores, can be estimated consistently when data are subject to random censoring. By evaluating changes in discrimination accuracy with the addition or deletion of items, we can select risk-related items without specifying parametric models. The procedure first removes the least useful items from the full scale, then, applies forward stepwise selection to the remaining items to obtain a reduced scale whose discrimination accuracy matches or exceeds that of the full scale. A simulation study shows the procedure to have good finite sample performance. We illustrate the method using a data set of patients at risk of developing Alzheimer's disease, who were administered a 40-item test of olfactory function before their semi-annual follow-up assessment.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"23 1","pages":"1-22"},"PeriodicalIF":1.2000,"publicationDate":"2009-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1094","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biostatistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2202/1557-4679.1094","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
To select items from a uni-dimensional scale to create a reduced scale for disease screening, Liu and Jin (2007) developed a non-parametric method based on binary risk classification. When the measure for the risk of a disease is ordinal or quantitative, and possibly subject to random censoring, this method is inefficient because it requires dichotomizing the risk measure, which may cause information loss and sample size reduction. In this paper, we modify Harrell's C-index (1984) such that the concordance probability, used as a measure of the discrimination accuracy of a scale with integer valued scores, can be estimated consistently when data are subject to random censoring. By evaluating changes in discrimination accuracy with the addition or deletion of items, we can select risk-related items without specifying parametric models. The procedure first removes the least useful items from the full scale, then, applies forward stepwise selection to the remaining items to obtain a reduced scale whose discrimination accuracy matches or exceeds that of the full scale. A simulation study shows the procedure to have good finite sample performance. We illustrate the method using a data set of patients at risk of developing Alzheimer's disease, who were administered a 40-item test of olfactory function before their semi-annual follow-up assessment.
期刊介绍:
The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.