Evaluation of diagnostic scores with adjustment for covariates

Diagnostic tests yield measurements on very different types of scales. Quantitative scales may consist of non-negative integers, either unbounded or bounded, with a fixed number of different values, or they may consist of continuous or percentage values. Remembering a different threshold value for each diagnostic variable would be cumbersome, in particular if covariates have to be taken into account. As a convenient way to overcome such problems we propose to compute z-scores for all measurements. They will be adjusted for covariates so that any individual can be judged on any test result on one single scale with an appropriate standard normal quantile as threshold. Two issues need to be addressed: Selection of covariates in the regression model which delivers the adjustment and normality of the residuals. The first will be treated by cross-validation and the latter by applying an appropriate transformation. We apply this methodology to neuropsychological tests and adjust for age, length of education and sex. Normality of residuals is needed on the diagnostically relevant side only. This allows to use parametric transformations, which can be easily implemented, e.g. in database systems. Since we have measurements at baseline and at follow-up we also analyze change values in a similar manner. For ease of interpretation, we transform the resulting z-scores back to the original scale.