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Previously, the cluster-specific concordance probability estimates were pooled with the number of usable subject pairs as weights [ 7, 8].
For a usable subject pair the predictions are concordant with the outcomes if the ordering of the predictions is equal to the ordering of the outcomes.
Analogous to the definition of the c-index a fourth option is the number of usable subject pairs as weights, w k = n k (method 4).
We denote the number of usable subject pairs – pairs of subjects for whom we can determine the ordering of their outcomes – in cluster k by n k.
The number of usable subject pairs n u, the number of concordant subject pairs n c and the number of tied subject pairs n t are: (6) n u = ∑ i ∑ j I y i < y j n c = ∑ i ∑ j I y i < y j and y ^ i < y ^ j n t = ∑ i ∑ j I y i < y j and y ^ i = y ^ j For time-to-event outcomes y, pairs of subjects are usable if their survival times are not equal and at least the smallest survival time is uncensored.
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We failed to collect urine or tissue from five subjects, resulting in a total usable study population of 139 individuals.
The pooled estimate is then equal to the proportion of all usable within-cluster subject pairs in which the predictions and outcomes are concordant.
Data for 7 consecutive days were usable from six subjects, data for 4 consecutive days were usable from two subjects, and data for 3 consecutive days were usable from two subjects.
For binary outcomes, pairs of subjects are usable if one of the subjects had an event and the other did not.
We estimated the concordance probability within each cluster by Harrell's c-index [ 2], i.e. the proportion of all usable pairs of subjects in which the predictions are concordant with the outcomes.
For this study we had usable data on 5,450 subjects.
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