ASSESSMENT OF LACK OF FIT IN SIMPLE LINEAR-REGRESSION - AN APPLICATION TO SEROLOGIC RESPONSE TO TREATMENT FOR SYPHILIS

A patient treated for infectious syphilis is cured when serologic test s become non-reactive, which may take years to achieve. Our objective is to develop a method to determine, within months, whether the patien t has responded adequately to treatment. Previous research and our exp loratory graphical analysis suggested that treatment response is linea r when we applied logarithmic transformations of the axes. If the resp onse to treatment is linear, titres recorded within the first few mont hs of treatment will determine the slope of the line and one can devel op an action line in future research. We used a non-parametric method to assess whether the logarithmic transformation improved the linearit y and then we applied three different methods of testing lack of fit i n linear regression. Based upon a sample size that reflects a clinical ly reasonable number of data points, the results of these tests provid ed no evidence against linearity.