A model for setting analytical quality specifications and design of control for measurements on the ordinal scale

A model for characterization of measurements on the ordinal scale is presented. It is based on transformation of the calculated fractions (fractiles) of positives from measurements on samples with known concentrations to a probit-natural log (probit-ln) scale. Such measurements could be made by other methods on ratio or difference scales but, for convenience (for example for speed or low cost), are measured on the ordinal scale by "simple" methods. The model is examined, and verified, using three examples from published data (haemoglobin, glucose, and leukocytes) and an external quality assessment survey on measurements of streptococcus. We show that it is possible to obtain reliable analytical quality specifications and to establish design of control systems for measurements on the ordinal scale. It is concluded that the presented probit-ln model for the ordinal scale is a tool which can improve and facilitate (i) characterizing methods with measurements on the ordinal scale, (ii) defining analytical quality specifications, (iii) designing external assessment as well as internal control schemes, (iv) validation of methods with measurements on the ordinal scale according to the analytical quality specifications, and further, (v) reduction of the number of samples required for method validation and the number of replicate measurements needed.