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Table 2 Statistical performance of selected and alternative statistical impact prediction models

From: Malaria intervention scale-up in Africa: effectiveness predictions for health programme planning tools, based on dynamic transmission modelling

Statistical model Metric Health burden outcome, and time period from intervention start
Case incidence 0–4 years, years 1–3 Case incidence 0–4 years, years 4–6 Malaria mortality 0–4 years, years 8–10 Malaria mortality 15+ years, years 8–10
Coefficient of variation, i.e. ratio of standard deviation of the simulated distribution to the mean (does not depend on the statistical model)   125 % 129 % 138 % 279 %
Variance in simulated outcomes (does not depend on statistical model)   1.1 1.2 1.04e−4 3.1e−6
Selected (best) model: simulated 0 values imputed and remaining results re-scaled in the range 0–0.99 MSE, from out-of-sample predictiona 7.5 % 17.0 % 43.4 % 73.3 %
Adjusted R2 96.5 % 92.7 % 90.3 % 74.1 %
MSE as  % of simulated variance 12.6 % 17.9 % 52.0 % 73.9 %
Simulated 0 values dropped and remaining results re-scaled in the range 0–0.99 Adjusted R2 96.6 % 92.2 % 86.8 % 70.1 %
MSE as  % of simulated variance 19.3 % 28.4 % 72.2 % 75.0 %
Dropping EIR and model variant (the two variables with no country data) Adjusted R2 88.4 % 80.4 % 72.7 % 42.6 %
MSE as  % of simulated variance 75.1 % 406 % 142 % 89.8 %
Log-transformation instead of logit-transformation of health outcomes Adjusted R2 96.0 % 93.0 % 90.6 % 77.1 %
MSE as  % of simulated variance 37.9 % 324 % 405 % 75.3 %
  1. aAverage of 25 simulations in which sub-samples of 100,000 simulations were randomly drawn to train and select the statistical model, and each time the remaining 65,888 simulations were used to assess its MSE