title: Assessment of lack of fit in simple linear regression: an application to serologic response to treatment for syphilis.
abstract: A patient treated for infectious syphilis is cured when serologic tests become non-reactive, which may take years to achieve. Our objective is to develop a method to determine, within months, whether the patient has responded adequately to treatment. Previous research and our exploratory graphical analysis suggested that treatment response is linear when we applied logarithmic transformations of the axes. If the response to treatment is linear, titres recorded within the first few months of treatment will determine the slope of the line and one can develop an action line in future research. We used a non-parametric method to assess whether the logarithmic transformation improved the linearity and then we applied three different methods of testing lack of fit in linear regression. Based upon a sample size that reflects a clinically reasonable number of data points, the results of these tests provided no evidence against linearity.
authors.affiliation: Department of Community Health Sciences, Faculty of Medicine, University of Calgary, Alberta, Canada.
authors.forename: M S
authors.initials: MS
authors.lastname: Rose
authors.forename: G H
authors.initials: GH
authors.lastname: Fick
mesh_terms: D000416:Alberta / Q000453:epidemiology; D003626:Data Display; D004196:Disease Outbreaks / Q000517:prevention & control*; D005500:Follow-Up Studies; D006801:Humans; D016014:Linear Models; D012698:Serologic Tests; D018709:Statistics, Nonparametric; D013587:Syphilis / Q000175:diagnosis / Q000453:epidemiology* / Q000628:therapy; D016896:Treatment Outcome