Detectability of Plasmodium falciparum clones

Abstract

Background: In areas of high transmission people often harbour multiple clones of Plasmodium falciparum, but even PCR-based diagnostic methods can only detect a fraction (the detectability, q) of all clones present in a host. Accurate measurements of detectability are desirable since it affects estimates of multiplicity of infection, prevalence, and frequency of breakthrough infections in clinical drug trials. Detectability can be estimated by typing repeated samples from the same host but it has been unclear what should be the time interval between the samples and how the data should be analysed.

Methods: A longitudinal molecular study was conducted in the Kassena-Nankana district in northern Ghana. From each of the 80 participants, four finger prick samples were collected over a period of 8 days, and tested for presence of different Merozoite Surface Protein (msp) 2 genotypes. Implications for estimating q were derived from these data by comparing the fit of statistical models of serial dependence and over-dispersion.

Results: The distribution of the frequencies of detection for msp2 genotypes was close to binomial if the time span between consecutive blood samples was at least 7 days. For shorter intervals the probabilities of detection were positively correlated, i.e. the shorter the interval between two blood collections, the more likely the diagnostic results matched for a particular genotype. Estimates of q were rather insensitive to the statistical model fitted.

Conclusions: A simple algorithm based on analysing blood samples collected 7 days apart is justified for generating robust estimates of detectability. The finding of positive correlation of detection probabilities for short time intervals argues against imperfect detection being directly linked to the 48-hour periodicity of P. falciparum. The results suggest that the detectability of a given parasite clone changes over time, at an unknown rate, but fast enough to regard blood samples taken one week apart as statistically independent.

Figure 1

Study design. Blood samples were collected in four survey rounds (R1-R4), on day 1, 2, 7 and 8. The result of this study design are two sampling intervals of 1 day, one of 5, two of 6, and one of 7 days. A 48-hour periodicity of P. falciparum detectability could therefore be identified, as it should show positive correlation of detection outcomes between surveys with even-numbered interval length, and negative correlation between surveys with odd-numbered interval length (in days).

Figure 2

Expected and actual frequencies of sequence types. Comparison of sequence type frequencies in the data with their expectations from a) the binomial model (M1), and b) the Markov Chain model (M3). M3 fitted the data better, yet did not fully explain it. The beta-binomial model (M2) is not shown since it measured almost no variation in detectability among clones, and therefore effectively reduced to M1.

Figure 3

The error in prevalence measurements becomes more important at low MOI. a) Prevalence estimates are biased due to imperfect detection. Assuming that infecting clones within a particular host are independent from each other, the probability of missing all of them and therefore falsely classify an individual as negative, is highest for low multiplicity of infection. This graph shows - for different values of q - how the number of clonal infections in a host affects the estimates of prevalence. The probability of correctly recognizing a positive individual with n infections is calculated as 1 - (1 - q)ⁿ. It follows that the effect of detectability on prevalence estimates is highest at low multiplicity of infection and therefore low transmission, for example when being close to local elimination. However, low transmission intensity might prevent acquisition of immunity and therefore raise the value of detectability. It is therefore desirable to report estimates of q and multiplicity of infection together with prevalence estimates. b) The distribution of MOI. Contrary to common practice, observations from all four surveys are pooled for the calculation of MOI. This corresponds to the assumption that clones are present throughout all surveys if detected once. With the help of figure 3.a, the bias on prevalence estimates in this population, as introduced by imperfect detection, can be roughly estimated.