Standardizing estimates of the Plasmodium falciparum parasite rate

Abstract

Background: The Plasmodium falciparum parasite rate (PfPR) is a commonly reported index of malaria transmission intensity. PfPR rises after birth to a plateau before declining in older children and adults. Studies of populations with different age ranges generally report average PfPR, so age is an important source of heterogeneity in reported PfPR data. This confounds simple comparisons of PfPR surveys conducted at different times or places.

Methods: Several algorithms for standardizing PfPR were developed using 21 studies that stratify in detail PfPR by age. An additional 121 studies were found that recorded PfPR from the same population over at least two different age ranges; these paired estimates were used to evaluate these algorithms. The best algorithm was judged to be the one that described most of the variance when converting the PfPR pairs from one age-range to another.

Results: The analysis suggests that the relationship between PfPR and age is predictable across the observed range of malaria endemicity. PfPR reaches a peak after about two years and remains fairly constant in older children until age ten before declining throughout adolescence and adulthood. The PfPR pairs were poorly correlated; using one to predict the other would explain only 5% of the total variance. By contrast, the PfPR predicted by the best algorithm explained 72% of the variance.

Conclusion: The PfPR in older children is useful for standardization because it has good biological, epidemiological and statistical properties. It is also historically consistent with the classical categories of hypoendemic, mesoendemic and hyperendemic malaria. This algorithm provides a reliable method for standardizing PfPR for the purposes of comparing studies and mapping malaria endemicity. The scripts for doing so are freely available to all.

Figure 1

The average distribution of sample sizes, S(A), from 21 studies that report PfPR by age, A. The lines show, by age, the mean (blue), the trimmed mean (red, with 10% of extreme values eliminated), the median (thick black), the interquartile range (thin black), and the 5^th and 95^th quantiles (dashed lines).

Figure 2

The 21 training sets, ordered by peak PfPR. The PfPR data (black) have been plotted against the root of age in years, along with the confidence limits by the exact test for each proportion (grey). The maximum likelihood best-fit for the modified Pull & Grab model (orange) was also plotted; the plateau (horizontal dashed red line) and the age when PfPR begins to decline (vertical dashed red line) are indicated and the other fitted parameters are reported on each graph. The algorithm (blue) fitted to the data (i.e. four parameters were fixed at their trimmed mean values and the fifth parameter was fitted).

Figure 3

Theory predicts that the slope of PfPR in young children (i.e. b) and the PfPR in older children (i.e. the plateau, P') should be correlated. The best-fit parameters describing these two quantities are plotted here. Two extreme values were excluded from this plot. There was no correlation with (p = 0.23) or without (p = 0.56) the extreme values.

Figure 4

Predicted PfPR plotted against observed PfPR for the four candidate algorithms for the testing set.

Figure 5

The age-PR relationship as generated by the algorithm. Holoendemic areas are colored dark green, hyper-endemic areas green, meso-endemic areas light green, and hypoendemic olive.

Figure 6

The graphs plot a subset of 87 PfPR estimates (i.e. PR₁) in the testing set that were already standard (i.e. L₁ ≥ 2 and U₁ ≤ 10) and the predicted PfPR using either the PfPR pair (i.e. PR₂, left) or the selected standardization algorithm (right). The dashed lines show the cutoffs for the classical categories [18]. The colors highlight properly classified hypoendemic (blue), mesoendemic (grey), and hyperendemic (orange) populations, as well as misclassified populations. Some mesoendemic populations were misclassified as hypoendemic (green) and some hyperendemic populations were misclassified as mesoendemic (orange). After standardizing, a few populations were mistakenly misclassified moved from hypoendemic to mesoendemic (cyan), or from mesoendemic to hyperendemic (tan). In sum, the PfPR would have been misclassified by the paired estimate (i.e. PR₂) in 33/87 cases (38%). Using the selected Pull & Grab modified algorithm, the standardized values were misclassified in 16/87 cases (18%).