Defining the relationship between Plasmodium vivax parasite rate and clinical disease

Plasmodium vivax clinical incidence data were identified in 99 publications. Following checks that the studies met the inclusion criteria described above, these data were abstracted into 388 reports of incidence. The majority of the data came from CSE Asia (80%, 311/388), as shown in Table 1, with ten records from Africa and 67 from the Americas. Data originated from 18 countries in total: ten from CSE Asia, five from the Americas and three from Africa. The incidence measures observed ranged from zero to 1.6 per person year observed. The highest incidence values observed were in CSE Asia in Papua New Guinea (PNG). Summary statistics of the incidence observed by MAP region are shown in Table 2, and the violin plots in Figure 5.

Slightly less than half of the records (46%, 180/388) had a prevalence value available from the same reference. An additional 31 prevalence values were added to records using entries in the MAP database that were collected in the same site during the same year. This provided a space-time matched PR for approximately half (54%, n = 211) of the incidence records. A PvPR value for each of the remaining 177 incidence records was obtained from the MAP P. vivax endemicity surface [19]. The MAP-based PvPR values represent all-age estimates, and 123 (69%) of the incidence records without concurrent PvPR were also measured in all ages. Of the incidence records with a concurrent PvPR estimate, 154 (73%) of PvPR surveys were conducted in the same age group as the ACD cohort. The 110 PvPR values that were not age-matched to the incidence data were age-standardized to the same age-range as the incidence data [36,38]. The PvPR estimates for all records ranged from zero to just over 30%. The highest estimates were again observed in PNG. PvPR data summary statistics are shown in Table 3.

The prevalence values extracted from the P. vivax endemicity map had a similar range to the PvPR estimates measured alongside incidence (from close to zero to ~25%), but less variation (Additional file 2: Figure S2). This was because multiple incidence records that came from the same or nearby locations were matched to a PvPR from the same or similar pixels in the predicted PvPR map. Statistically, incidence records with only PvPR values derived from the map were excluded because their uncertainties (in part due to the mismatch between the scale of MAP pixels and the scale of PvPR variation within a pixel) were so large that the inclusion of these points did not add to the model fits. That is, only concurrently measured PvPR values – reported from the same reference or another paper from the MAP database – were used. This also facilitated development of the statistical model as the selected studies all presented counts of the number examined and positive, and thus the same type of uncertainty was manifest for both the incidence and PvPR estimates used in the analysis, whereas this would not be true for excluded PvPR surveys that did not report the numerators or denominators (n = 35). Following all exclusions (Figure 3), 176 records from 75 sources remained to be used in the analysis. The temporal distribution and study size, based on person-time observed, of these records are shown in Figure 6.

The approximation of person-time in the majority of the selected records (76%, 133/176) was determined not to be an exclusion criterion. As illustrated in Additional file 3: Figure S3, there was a comparable level of noise in both those records with exact and approximate reported person-time. The data are plotted on both standard and logarithmic scales to also demonstrate that using the logarithm of incidence against the logarithm of prevalence better represents the distribution of the data. Note, however, that only 151 points appear in those panels using logarithmic scales because 25 records had a value of zero (four incidence and 21 prevalence) and could not be readily plotted on these axes.

A specific parasite density threshold in the case definition used in ACD studies was also set aside as an exclusion criterion. The majority of studies specified a case of P. vivax as a symptomatic episode at any detectable level of parasitaemia (≥1 asexual stage parasite per μl of blood), but nine of the 176 records included in the analysis specified a parasite density cut-off. Seven records were from studies applying a parasite density threshold of 500 parsites/μl to limit their Type II error rate (false attribution of vivax causality to a background fever) and an additional two applied a cut-off 1,000 parasites/μl. These studies were expected to return lower incidence estimates, but in fact were not observed to be outliers here, as seen in Additional file 4: Figure S4. That the application of the cut-off did not result in lower estimates suggests that vivax-targeting ACD studies are less sensitive to case definition than is the experience for falciparum [41].

The posterior for the non-parametric fitted function modelling the impact of ACD regularity on the rate of detected clinical incidence cases is illustrated in Additional file 5: Figure S5. In the subsequent Figures 7 and 8 the (point-wise) mean of this function was used to correct all observed incidence counts to a benchmark of fortnightly ACD. It was estimated that daily ACD studies report on average 12.2 (2.7,42) times (median and 95% credible interval, CrI) the number of fevers identified in studies with fortnightly ACD, whereas the scaling from fortnightly to monthly ACD is less marked at 0.81 (0.34,0.99). Some degree of variation in the dependence of observed incidence on ACD regularity among the geographic zones was expected, such that frequency of ACD would have a greater effect in areas with high risk of recurrence. The model of a shared effect was deemed sufficient, however, because a re-fit of the model allowing each zone to be assigned to one of two separate relationships failed to identify any significant difference in the resulting prevalence-incidence relationship.

The broad posterior credible intervals for the pair of scaling coefficients used here to account for age-dependence of the clinical incidence rate (namely, -0.28 [-0.83,0.27] for c ₁ and 0.08 [-0.40,0.66] for c ₂) suggest that these terms do not play a crucial role in these fits, a conclusion supported by visual inspection of the zone-specific prevalence – incidence relationships inferred upon exclusion of these terms from the model. However, the consequent inference that exposure-based immunity is unimportant for vivax malaria should be taken with caution: rather the present dataset is underpowered to investigate this effect since over 75% of the studies included here effectively report an all-ages incidence estimate.

The geographic origin of the studies was, however, of importance in the prevalence – incidence model. Figure 9 illustrates the distribution of the matched incidence and prevalence records shaded by the mean time to first relapse in each geographic zone. A significant degree of clustering between zones was identified through the fitted model. In particular, zones 8 and 11 (Monsoon Asia, and northern Asia and Europe) were found to share a common relationship in 50% of the posterior samples. These zones are characterized by long-latency relapse phenotypes (zone 11) or a combination of short and long latency (zone 8). At least three of the four remaining zones (2 - Central America, 3 - South America, 10 - Southeast Asia, and 12 - Melanesia) share a common relationship at a comparable rate. The zone-specific PvPR and clinical incidence relationships thus recovered are illustrated as point-wise 68 and 95% CrIs in Figure 7 and their parameter estimates are summarized in Table 4. In the Table, α is the natural logarithm of incidence per person-year observed at a prevalence of 2.5%; in the model this is the intercept of the (logarithm of) prevalence – (logarithm of) incidence curve, such that the exponent of α is the intercept in cases per person year. Accordingly, β in Table 4 is the slope of the curve, such that if the prevalence were to increase from 2.5 to 7%, the incidence would increase by a factor of exp(β). By weighting the posterior for each zone by the proportion of observations from that zone in the dataset, a pooled relationship was produced for the entire dataset, as illustrated in Figure 8. For reference, the corresponding aggregate parameter estimates of the pooled relationship are α = -3.0 (-3.5,-2.4) and β = 0.71 (0.41,1.10). In other words, based on the pooled relationship a prevalence of 2.5% would correspond to an incidence of 49.8 cases per 1,000 person years (see Table 4).

The results benefit from the model structure by producing associated measures of uncertainty. As shown in Figures 7 and 8, the point-wise CrIs are narrowest around the axis of the regression model at 2.5% prevalence. Zone-specific relationships informed by few data points (zones 2, 11 and 12) have wider CrIs. Based on these wide uncertainty bands, the predicted incidence can change by a factor of 100. While this appears to be a large range, it is representative of the data; Figure 8 illustrates the wide range of incidence measures that were observed in communities with nearly the same PvPR.