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Table 4 Mathematical details of the Newcombe method

From: Composite endpoints for malaria case-management: not simplifying the picture?

1. For each value of prevalence (p) from 0 to 1, the difference in probability of correct management between the strategies, denoted f , is obtained by calculating a (weighted) mean of the difference in the PMR between the two strategies (θ1) and the difference in the NMRs (θ2):
  f = λθ1 + (1 - λ)θ2
  where the weight, λ is calculated as λ= 1 1 + c 2 1 - p c 1 p and
  c1 = subjective weight indicating ‘importance’ of treating a malaria patient (avoiding false negatives)
  c2 = subjective weight indicating ‘importance’ of avoiding treating a patient without malaria (false positives)
2. For clarity of presentation the relative importance of false negatives to false positives is defined as
  R = c1/c2
  If c1 = c2 (R = 1) the equation for λ simplies to λ= 1 1 + 1 - p p i.e. λ = p
3. A confidence interval for f can be calculated as described in Newcombe [13] and http://medicine.cf.ac.uk/primary-care-public-health/resources/.