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ASSESSMENT OF LACK OF FIT IN SIMPLE LINEAR REGRESSION: AN APPLICATION TO SEROLOGIC RESPONSE TO TREATMENT FOR SYPHILIS
Author(s) -
ROSE M. SARAH,
FICK GORDON H.
Publication year - 1997
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19970228)16:4<373::aid-sim419>3.0.co;2-o
Subject(s) - syphilis , serology , simple (philosophy) , statistics , linear regression , generalized linear model , linear model , simple linear regression , regression , econometrics , medicine , computer science , mathematics , immunology , human immunodeficiency virus (hiv) , antibody , philosophy , epistemology
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. © 1997 by John Wiley & Sons, Ltd.