Evidence for over-dispersion in the distribution of clinical malaria episodes in children

Abstract

Background: It may be assumed that patterns of clinical malaria in children of similar age under the same level of exposure would follow a Poisson distribution with no over-dispersion. Longitudinal studies that have been conducted over many years suggest that some children may experience more episodes of clinical malaria than would be expected. The aim of this study was to identify this group of children and investigate possible causes for this increased susceptibility.

Methodology and principal findings: Using Poisson regression, we chose a group of children whom we designated as 'more susceptible' to malaria from 373 children under 10 years of age who were followed up for between 3 to 5 years from 1998-2003. About 21% of the children were categorized as 'more susceptible' and although they contributed only 23% of the person-time of follow-up, they experienced 55% of total clinical malaria episodes. Children that were parasite negative at all cross-sectional survey were less likely to belong to this group [AOR = 0.09, (95% CI: 0.14-0.61), p = 0.001].

Conclusions and significance: The pattern of clinical malaria episodes follows a negative binomial distribution. Use of lack of a clinical malaria episode in a certain time period as endpoints for intervention or immunological studies may not adequately distinguish groups who are more or less immune. It may be useful in such studies, in addition to the usual endpoint of the time to first episode, to include end points which take into account the total number of clinical episodes experienced per child.

Figure 1. Comparing fit for the Poisson, Pareto and Negative Binomial distributions using observed total clinical malaria episodes per child as outcome.

The X-axis is the total clinical episodes of malaria experienced per child and Y-axis is the proportion of children with given total disease episodes. The bars are the observed total number of cases per child, the black line is the predicted totals from the Poisson regression model, the dashed line represent the predicted total episodes from the negative binomial regression model while the crossed lines represents the predicted total episodes from the Pareto distribution. Figure (a) represents all the children, (b) all children under 5 years at the time the study started (who were followed up from 1998 to 2003) and (c) children ≥5 years of age (followed up from 1998 to 2001).

Figure 2. Non-admission clinical malaria episodes/child/year among children that were admitted at least once or never admitted during 3–5 years of follow-up.

Box plot of the median(central line) 25%, 75% quartile ranges around the median (box width) and the upper and lower limits (T).

Figure 3. Distribution of the total number of ‘more susceptible’ children within study households.

The clear circles represents the households that did not have any children ‘more susceptible’ than others, the circles with squares represent the households that had between 1–3 children ‘more susceptible’, the grey circles represent those that had 4–6 and the black circles represent those that had more than 7 children in the households ‘more susceptible’ than others. The smaller dots spread across the map are all the other households within the larger study area that were not included in the surveillance.

Figure 4. Kaplan-Meier survival curve of the time to first episode of clinical malaria.

Dashed line represents the ‘more susceptible’ children and the solid line represents the time to first episode for the other children.