MEDLINE, Web of Science, Embase, and Cochrane Data of Systematic Reviews were searched in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement (S1 Checklist). As previously described [9,16], prospective studies evaluating the efficacy of antimalarials against uncomplicated P. vivax that were published between January 1, 2000, and January 31, 2018, in any language were identified (S1 Text).

Two independent investigators undertook the review and extracted the data (RJC and RNP), resolving discrepancy through discussion. Principal investigators of eligible studies were invited to share individual patient data and any additional data from eligible unpublished studies. Studies were included if they assessed treatment with DP or AL with or without PQ. Studies were excluded if adjunctive drugs were given or PQ was dosed weekly. Individual patient data shared with the WorldWide Antimalarial Resistance Network (WWARN) were curated and standardised as described in a data management plan [17].

Data included in this analysis were obtained in accordance with ethical approvals from the location of origin. See S2 Text for a list of specific ethics committees. Data are requested to be shared anonymised, and additional review from an ethics committee was not required for the subsequent analysis according to guidelines of the Oxford Central University Research Ethics Committee.

Individual patient data were excluded if baseline parasitaemia involved mixed species or blood schizontocidal treatment was incomplete. Early PQ was defined as commencement of PQ within the first 3 days of ACT treatment. Drug doses were calculated from the number of tablets a patient was administered if data were available or were based on the study protocol, assuming complete adherence. ACT partner drugs were considered determinants for recurrence rather than artemisinins, which have short half-lives and are considered determinants for parasite clearance.

Study sites were classified as having short (median time to patent relapse of 47 days or less) or long P. vivax relapse periodicity based on estimates from the Malaria Atlas Program for geographical location [12]. PQ dose was defined as a low dose if the total dose was <5.0 mg/kg or high dose if the total dose was ≥5.0 mg/kg [18]. A symptomatic recurrence was defined as recurrent parasitaemia associated with a temperature of ≥37.5°C or a history of fever within the preceding 24 hours.

Underdosing of piperaquine and lumefantrine was defined as a dose less than the minimum dose recommended by current World Health Organization (WHO) guidelines for P. falciparum [19]. DP dosing guidelines were updated by WHO in 2015, after enrolment of patients in all studies included in this analysis was completed. The revised WHO guidelines recommend a minimum total dose of piperaquine of ≥60 mg/kg in patients weighing <25 kg and ≥48 mg/kg if weighing ≥25 kg [19–21]. A minimum total dose of lumefantrine of ≥29 mg/kg is recommended in patients treated with AL [19].

The primary outcome was the risk of P. vivax recurrence between days 7 and 42. The secondary outcomes were the risk of P. vivax recurrence between days 7 and 28 and days 7 and 63.

Analyses were undertaken according to an a priori statistical analysis plan [22], unless stated otherwise, using Stata (version 15.0) and R (version 3.4.0). The protocol was registered in the International Prospective Register of Systematic Reviews (PROSPERO: CRD42016053310) prior to undertaking the analysis.

To investigate inclusion bias, baseline characteristics of targeted studies not included in the analysis were compared with the characteristics of the studies included in the analysis. Study quality and risk of bias were assessed according to criteria for individual patient data meta-analyses [23].

Kaplan-Meier survival analyses were used to calculate risk of recurrence according to the treatment administered. Patients were censored at the first day of any of the following for an outcome prior to day of the end point: recurrent parasitaemia, the last clinic visit, the last visit prior to a gap of >18 days between parasite microscopy results, the day of outcome, or the day of PQ treatment (if ≥28 days after enrolment).

The association between schizontocidal treatment (AL versus DP), coadministration of PQ, and the mg/kg dose of each drug component (piperaquine and lumefantrine) with the rate of P. vivax recurrence was estimated using Cox’s proportional hazards regression. Analyses were adjusted for potential confounders: age, sex, baseline parasitaemia, baseline haemoglobin, and regional relapse periodicity, with shared frailty applied for study site. Weight was not included, because of collinearity with age and geographical region, and parasite prevalence was not included, because of collinearity with relapse periodicity. Age was categorised for analyses of mg/kg dose as defined previously by age-related dose effects in P. falciparum [21,24]. Proportional hazards assumptions were tested using Schoenfeld residuals. Figures of risk of recurrence were generated based on the Cox model, which adjusted for confounders and assumed no study-site effect. In a sensitivity analysis, the coefficient of variation was calculated for estimates of primary analyses by removal of one study site at a time to investigate study site heterogeneity. The coefficient of variation should be interpreted in association with the absolute variation of the effect size. A subgroup analysis restricted the analysis to results from studies directly comparing DP and AL.

Following preplanned statistical analyses, a post hoc analysis was undertaken to investigate whether a delay in recurrence was associated with a benefit in clinically relevant outcomes. In patients with a P. vivax recurrence between day 7 and day 63, the delay in recurrence was correlated with the mean haemoglobin at the day of recurrence using linear regression, adjusting for confounding factors (age, sex, baseline parasitaemia, baseline haemoglobin, parasitaemia at recurrence, regional relapse periodicity, and PQ use), and with random effects for study site. Analysis was undertaken separately for all recurrences and just symptomatic recurrences.

Among the 812 patients treated with DP alone, the median total dose of dihydroartemisinin administered was 6.4 mg/kg (IQR 6.0–7.1; range 3.5–10.6), and the median total dose of piperaquine administered was 51.4 mg/kg (IQR 48.0–56.5; range 28.2–84.7) (S2 Fig). In total, 181 patients (22.3%) were administered less than the former WHO target dose, and 303 (37.3%) patients were administered less than the revised WHO target dose (S3 Fig).

Following DP alone, 50 of 812 patients had a recurrence between days 7 and 42, the cumulative risk of recurrence being 1.2% (95% confidence interval [CI] 0.6–2.3) at day 28 and 9.3% (95% CI 7.1–12.2) at day 42. Of the 505 patients from nine studies with follow-up beyond day 42, an additional 105 patients had a recurrence up to day 63, cumulative risk 39.9% (95% CI 33.9–46.7) at day 63. Risks for individual studies are presented in the Supporting information (S4 Fig). After adjusting for age, sex, baseline parasitaemia, baseline haemoglobin, regional relapse periodicity, and study-site clustering, an increased piperaquine dose was associated with a reduced rate of recurrence between days 7 and 42 (adjusted hazard ratio [AHR] for every 5-mg/kg increase 0.63, 95% CI 0.48–0.84, p = 0.0013) (Table 2). Other factors associated with P. vivax recurrence were short relapse periodicity (AHR 27.28, 95% CI 4.53–164.14, p < 0.001) and lower baseline haemoglobin (AHR per g/dL 0.83, 95% CI 0.68–0.99, p = 0.0432). When the method of calculating the dose of drug was included in the model, it was not an independent predictor of recurrence. In the sensitivity analysis, the coefficient of variation for piperaquine dose estimate was 6.08%, with AHRs ranging from 0.60 to 0.75 (S7 Table). The association between increased piperaquine dose and a reduced rate of recurrence was also apparent when the follow period was extended to day 63 (AHR for every 5-mg/kg increase 0.83, 95% CI 0.73–0.94, p = 0.0033).

To investigate the current WHO guidelines for DP dosing, piperaquine dosing was dichotomised into a dose above and below the minimum WHO-recommended dose for P. falciparum in the model. A piperaquine dose under the minimum WHO-recommended dose was associated with an increased rate of recurrence by day 42 (AHR 2.49, 95% CI 1.19–5.22, p = 0.0159). By day 63, the association between piperaquine dose and the rate of recurrence was attenuated (AHR 1.47, 95% CI 0.96–2.26, p = 0.0797), although it remained significant in children weighing <25 kg (AHR 2.33, 95% CI 1.18–4.62, p = 0.0149).

A total of 384 patients were treated with AL alone. The median total dose administered was 10.0 mg/kg (IQR 8.6–12.0; range 4.6–20.0) of artemether and 60.0 mg/kg (IQR 51.4–72.0; range 27.7–120.0) of lumefantrine (S5 Fig and S6 Fig).

Following AL alone, 136 of 395 patients had a recurrence between days 7 and 42, with a cumulative risk of recurrence of 21.0% (95% CI 16.9–25.8) at day 28 and 44.0% (95% CI 38.7–49.8) at day 42. Of 14 patients with follow-up beyond day 42 and up to day 63, 11 (78.6%) had recurrent parasitaemia. Only one patient (0.3%) was administered less than the current dose of lumefantrine recommended by WHO for P. falciparum (<29 mg/kg), and this patient did not have a recurrent infection (S6 Fig). The median dose of lumefantrine was 65.5 mg/kg in patients younger than 5 years and 53.3 mg/kg in those older than 5 years. After adjusting for confounders and study-site clustering, there was no significant effect of lumefantrine dose on rate of P. vivax recurrence (AHR per 5 mg/kg 1.07, 95% CI 0.99–1.16, p = 0.0869). Low baseline haemoglobin was a risk factor for recurrence (Table 3).

In the subgroup of patients not treated with PQ, the rate of P. vivax recurrence between days 7 and 42 was significantly greater following AL than DP after adjusting for confounders and study-site clustering (AHR 12.63, 95% CI 6.40–24.92, p < 0.001) (Table 4). Because of violation of the proportional hazards assumption, the analysis was undertaken separately, stratifying by relapse periodicity. The high rate of recurrence after AL was apparent both in regions of short relapse periodicity (AHR 6.56, 95% CI 4.04–10.65, p < 0.001) and long relapse periodicity (AHR 81.40, 95% CI 19.58–338.45, p < 0.001) (Fig 2 and Table 4). In the sensitivity analysis, there was minimal bias related to individual study sites (S8 Table). The difference between DP and AL was also apparent in a subgroup analysis of the two studies comparing the treatments directly (AHR 10.27, 95% CI 3.99–26.45, p < 0.001). The method of drug dose calculation was not an independent predictor of recurrence when included in the overall model (AHR 0.57 [95% CI 0.19–1.70] for dosing based on the actual number of tablets administered compared with that expected from study protocol; p = 0.3137).

The median dose of PQ was 6.6 mg/kg (IQR 4.7–7.0; range 2.6–8.9) in patients treated with DP and 3.3 mg/kg (IQR 3.1–3.8; range 0.3–9.1) in patients treated with AL. Of the patients treated with DP + PQ, 173 (28.2%) received a low-dose PQ regimen (<5 mg/kg), and 440 (71.8%) received a high-dose regimen (≥5.0 mg/kg). The corresponding figures for AL + PQ were 191 (91.8%) and 17 (8.2%).

There were three recurrences between days 7 and 42 in patients treated with DP + PQ, with a cumulative risk of recurrence of 0.2% (95% CI 0.0–1.2) at day 28 and 1.0% (95% CI 0.3–3.2) at day 42. Of the 55 patients with follow-up beyond day 42, a further two patients had a recurrence between days 42 and 63: cumulative risk 5.2% (95% CI 1.7–15.5) at day 63. There were nine recurrences between days 7 and 42 in patients treated with AL + PQ, with a cumulative risk of recurrence of 2.7% (95% CI 1.1–6.3) at day 28 and 5.3% (95% CI 2.8–10.0) at day 42. Two of five patients followed beyond day 42 had a recurrence between days 42 and 63.

In a multivariable model of patients treated with DP, recurrence by day 42 was not reduced significantly by coadministration of PQ (AHR = 0.23, 95% CI 0.04–1.28, p = 0.0933). However, in patients treated with AL, coadministration of PQ reduced the rate of recurrence (AHR = 0.20, 95% CI 0.10–0.41, p < 0.001) (Fig 3 and S9 Table). When PQ dose was included in the model of patients treated with DP, neither low-dose PQ (AHR = 0.28, 95% CI 0.04–1.99, p = 0.2031) nor high-dose PQ (AHR = 0.15, 95% CI 0.01–1.96, p = 0.1494) was associated with reduced rate of recurrence. In patients treated with AL, low-dose PQ reduced the rate of recurrence (AHR = 0.21, 95% CI 0.10–0.41, p < 0.001; of note, only 17 patients received high-dose PQ) (S10 Table). In a subset analysis including five studies following patients to day 63 or more, coadministration of any dose of PQ with DP reduced the rate of recurrence (AHR = 0.06, 95% CI 0.01–0.63, p = 0.0196) (S11 Table). In a sensitivity analysis, reductions in rate of recurrence with PQ were unlikely to be attributable to bias from individual study sites (S12 Table). Because of the low number of recurrences, a multivariable analysis comparing the risk of recurrence with DP + PQ and AL + PQ could not be done.

In total, of the 160 patients with recurrence between day 7 and day 63 treated with DP with or without PQ, 12 had available data on the haemoglobin at the day of recurrence, 6 (50.0%) of which were symptomatic recurrences. The corresponding numbers for patients treated with AL were 109 patients with available data out of 158 patients with recurrence between day 7 and day 63, with 70 (64.2%) of these patients having symptomatic recurrence.

Because of the low number of recurrences after DP +/− PQ, a multivariable analysis assessing the effect of day of recurrence on haemoglobin could not be undertaken. For patients treated with AL +/− PQ, there was a nonsignificant increase in haemoglobin of 0.07 g/dL (95% CI −0.06 to 0.20), p = 0.3130 for every 5 days that recurrence was delayed. When the analysis was restricted to symptomatic recurrences, the mean haemoglobin at recurrence increased 0.13 g/dL (95% CI 0.01–0.26) for every 5 days that recurrence was delayed (p = 0.0407) (S13 Table).

Data included in this analysis were obtained in accordance with ethical approvals from the location of origin. See S2 Text for a list of specific ethics committees. Data are requested to be shared anonymised, and additional review from an ethics committee was not required for the subsequent analysis according to guidelines of the Oxford Central University Research Ethics Committee.