Applying the jackknife method to significance tests of diagnostic diversity

The sample theory of normal diversity indices is complex. Distribution free methods, such as the jackknife method, can easily be used to determine confidence intervals and testing diversity. Jackknife estimates and their variances for a number of different diversity indices are described in this paper. A simple numerical example is given for demonstrating this method. Discrimination based on confidence intervals is also discussed. It is assumed that there is a special correlation between the sensitivity parameter m and the relative width of confidence intervals in the Hurlbert index family. It is shown that the usual estimation of the Hurlbert index coincides with the relating jackknife estimate. For demonstration, diagnoses registered in a set of death certificates are used. There is a considerable diversity in diagnoses among different diagnostic groups: the diversity is largest in autopsy reports, whereas it is non-significant in GP's reports and in reports of physicians authorized to issue death certificates. Knowing that autopsy reports tend to be fairly accurate, our research findings seem to confirm the hypothesis that there is a correlation between reliability and diversity of diagnoses.