Table 4 Mathematical details of the Newcombe method

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 $\mathrm{\lambda }=\frac{1}{1+\frac{c_2\left(1-p\right)}{c_{1}p}}$ 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 $\mathrm{\lambda }=\frac{1}{1+\frac{\left(1-p\right)}{p}}$ 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/.