- Research
- Open Access
Optimal sampling designs for estimation of Plasmodium falciparum clearance rates in patients treated with artemisinin derivatives
- Jennifer A Flegg^{1, 2}Email author,
- Philippe J Guérin^{1, 2},
- Francois Nosten^{2, 3, 4},
- Elizabeth A Ashley^{2, 3},
- Aung Pyae Phyo^{3, 4},
- Arjen M Dondorp^{2, 3},
- Rick M Fairhurst^{5},
- Duong Socheat^{6},
- Steffen Borrmann^{7},
- Anders Björkman^{8},
- Andreas Mårtensson^{8, 9},
- Mayfong Mayxay^{10},
- Paul N Newton^{2, 10},
- Delia Bethell^{11},
- Youry Se^{12},
- Harald Noedl^{13},
- Mahamadou Diakite^{14},
- Abdoulaye A Djimde^{14},
- Tran T Hien^{2, 15},
- Nicholas J White^{2, 3} and
- Kasia Stepniewska^{1, 2}
https://doi.org/10.1186/1475-2875-12-411
© Flegg et al.; licensee BioMed Central Ltd. 2013
- Received: 10 July 2013
- Accepted: 28 October 2013
- Published: 13 November 2013
Abstract
Background
The emergence of Plasmodium falciparum resistance to artemisinins in Southeast Asia threatens the control of malaria worldwide. The pharmacodynamic hallmark of artemisinin derivatives is rapid parasite clearance (a short parasite half-life), therefore, the in vivo phenotype of slow clearance defines the reduced susceptibility to the drug. Measurement of parasite counts every six hours during the first three days after treatment have been recommended to measure the parasite clearance half-life, but it remains unclear whether simpler sampling intervals and frequencies might also be sufficient to reliably estimate this parameter.
Methods
A total of 2,746 parasite density-time profiles were selected from 13 clinical trials in Thailand, Cambodia, Mali, Vietnam, and Kenya. In these studies, parasite densities were measured every six hours until negative after treatment with an artemisinin derivative (alone or in combination with a partner drug). The WWARN Parasite Clearance Estimator (PCE) tool was used to estimate “reference” half-lives from these six-hourly measurements. The effect of four alternative sampling schedules on half-life estimation was investigated, and compared to the reference half-life (time zero, 6, 12, 24 (A1); zero, 6, 18, 24 (A2); zero, 12, 18, 24 (A3) or zero, 12, 24 (A4) hours and then every 12 hours). Statistical bootstrap methods were used to estimate the sampling distribution of half-lives for parasite populations with different geometric mean half-lives. A simulation study was performed to investigate a suite of 16 potential alternative schedules and half-life estimates generated by each of the schedules were compared to the “true” half-life. The candidate schedules in the simulation study included (among others) six-hourly sampling, schedule A1, schedule A4, and a convenience sampling schedule at six, seven, 24, 25, 48 and 49 hours.
Results
The median (range) parasite half-life for all clinical studies combined was 3.1 (0.7-12.9) hours. Schedule A1 consistently performed the best, and schedule A4 the worst, both for the individual patient estimates and for the populations generated with the bootstrapping algorithm. In both cases, the differences between the reference and alternative schedules decreased as half-life increased. In the simulation study, 24-hourly sampling performed the worst, and six-hourly sampling the best. The simulation study confirmed that more dense parasite sampling schedules are required to accurately estimate half-life for profiles with short half-life (≤three hours) and/or low initial parasite density (≤10,000 per μL). Among schedules in the simulation study with six or fewer measurements in the first 48 hours, a schedule with measurements at times (time windows) of 0 (0–2), 6 (4–8), 12 (10–14), 24 (22–26), 36 (34–36) and 48 (46–50) hours, or at times 6, 7 (two samples in time window 5–8), 24, 25 (two samples during time 23–26), and 48, 49 (two samples during time 47–50) hours, until negative most accurately estimated the “true” half-life. For a given schedule, continuing sampling after two days had little effect on the estimation of half-life, provided that adequate sampling was performed in the first two days and the half-life was less than three hours. If the measured parasitaemia at two days exceeded 1,000 per μL, continued sampling for at least once a day was needed for accurate half-life estimates.
Conclusions
This study has revealed important insights on sampling schedules for accurate and reliable estimation of Plasmodium falciparum half-life following treatment with an artemisinin derivative (alone or in combination with a partner drug). Accurate measurement of short half-lives (rapid clearance) requires more dense sampling schedules (with more than twice daily sampling). A more intensive sampling schedule is, therefore, recommended in locations where P. falciparum susceptibility to artemisinins is not known and the necessary resources are available. Counting parasite density at six hours is important, and less frequent sampling is satisfactory for estimating long parasite half-lives in areas where artemisinin resistance is present.
Keywords
- Plasmodium falciparum
- Malaria
- Artemisinin resistance
- Parasite clearance
- Simulation
Background
Anti-malarial drug resistance poses a serious threat to global efforts to control and eliminate malaria. During the 1980s and 1990s, malaria-related mortality increased due to the spread of Plasmodium falciparum resistance to anti-malarial drugs. This trend was reversed by replacing failing drugs with highly efficacious artemisinin-based combination therapy (ACT) and deployment of improved vector control measures. ACT is now the recommended first-line treatment for P. falciparum malaria in almost all endemic countries [1, 2]. In the past, parasite resistance to chloroquine and then to sulphadoxine-pyrimethamine spread from Western Cambodia throughout Asia and Africa. The recent emergence of artemisinin resistance in P. falciparum malaria on the Thailand-Cambodia border therefore poses a considerable global health threat [3–5].
To date, the molecular basis of artemisinin resistance has not been elucidated and conventional in vitro drug response assays have provided conflicting results. Recently, a ring stage survival assay has been proposed, but it requires specific skills, training and validation [6, 7]. Strong evidence of artemisinin resistance in Southeast Asia was recognized by the significant reduction in the parasite clearance rate following artesunate treatment and increased failure rates following ACT administration [4, 8, 9]. Until a definitive molecular marker is identified and validated in various regions, accurate and reliable measurement of parasite clearance remains a robust and simple method of assessing the spread or independent emergence of artemisinin-resistant P. falciparum in Southeast Asia and elsewhere. Furthermore, parasite clearance is becoming an essential component of the measurement of the efficacy of new anti-malarials.
Following treatment with an effective anti-malarial drug, the clearance of parasites from the peripheral blood is proportional to the parasite density (that is, a first-order process) [10, 11]. As such, the predominant relationship between the log-transformed parasite density and time is generally linear [12–14]. The slope of the log-parasitaemia versus time relationship is considered the most robust measure of parasite clearance [15], and of various different in vivo measures shows the highest heritability among P. falciparum parasites in a setting where artemisinin resistance is prevalent [16]. However, several potential sources of error can be introduced if a straight line is fitted to all log-parasite density data [14]. Previous estimates of parasite clearance rates have, therefore, been complicated by observer subjectivity in how to handle these sources of variation [14, 15].
To facilitate the standardized and accurate estimation of parasite clearance rates, the WorldWide Antimalarial Resistance Network (WWARN) previously developed the Parasite Clearance Estimator (PCE) tool, now available online [14, 17]. The PCE expresses parasite clearance in terms of the slope half-life and has been used to quantify the clearance distributions in several studies (for example, [18–21]). Using this tool, parasite clearance distributions may be compared from different study locations and times, where half-life distributions that are centered around smaller half-lives correspond to a relatively sensitive response compared to distributions centered at longer half-life values. For example, the parasite clearance distribution in Pailin, Cambodia, in 2008–2010 showed evidence of slow clearance with a median half-life of 5.8 hours [21] while the distribution in Mali in 2010 showed evidence of a sensitive response (median half-life of 1.9 hours) [19].
In order to accurately estimate parasite clearance using the current version of the PCE tool, frequent parasite counts (at least twice daily) are recommended. However, most in vivo assessments published in the literature measure parasitaemia either daily, or only on days D0, D2 and D3, as recommended by the World Health Organization [22]. The proportion of patients with detectable parasitaemia on D3 is a simple measure of parasite clearance at the population level [23], and provides a useful metric of response that can be widely applied. However, “D3-positivity” at the individual patient level is inaccurate because it depends heavily on the pre-treatment parasite density and the precise timing of sampling, and these can vary substantially within and across clinical trials. D3 can correspond to a time ranging from 60 to 80 hours after treatment, depending on the time of patient enrolment and the subsequent follow-up visits. For example, a patient first treated at 09.00 on D0 may be assessed for parasitaemia at 17.00 on D3 (80 hours later).
To compare parasite clearance rates across different study sites and times, frequent parasite counts are needed to generate accurate and reliable estimates. This method is dependent on resource and operational constraints, capacity to generate quality-assured parasite density counts, and patient convenience (in terms of how often blood samples are taken), all factors that may limit the number of measurements that can be taken at a given site. In fact, the six hourly schedule was arbitrarily defined, and there have been no studies validating that these measurements need to be, or indeed should be, collected at regular time-intervals to best facilitate clearance estimation. Schedules that produce accurate rate estimates yet minimize patient (and/or their caretakers) inconvenience (including hospitalization and night-time blood collection) would clearly be preferable. Here, the effects of potential alternative sampling schedules on the estimation of parasite clearance rates were investigated using real patient data from 13 studies with a combined sample size of 4,652 patients, conducted between 2001 and 2011 in Cambodia, Thailand, Mali, Kenya and Vietnam.
Methods
This paper used three approaches to investigate the effect of different sampling schedules on parasite clearance estimates. The first approach used a large dataset of patient data, pooled across 13 studies conducted between 2001 and 2011, to compare the HL estimates from four alternative sampling schedules. The second used statistical bootstrap method to investigate the effect on population estimates of HL when the same four alternative schedules were applied to populations that varied from short to very long geometric mean HL. In the final approach, a simulation study was designed in which parasite counts were generated so that more complicated sampling schedules could be assessed.
Study data
This work was conducted by the Parasite Clearance Study Group, under the auspices of WWARN, as part of a larger effort to combine all available data from ACT efficacy studies that measured parasite densities at least twice daily. Parasite density-time profiles from published and unpublished studies that measured six-hourly parasite densities were sought for this analysis. Studies were identified among those that used the PCE tool and through calls for data at international meetings. Only studies in which patients were treated with artesunate alone or in combination with a partner drug were considered. Within each study, only patients with parasite densities measured every six hours until parasitaemia became undetectable (i.e., “negative”) on blood smears were included.
Summary of the 13 included studies
Country | Years | Number patients | Sampling schedule | Counting method | DLM | Reference | |
---|---|---|---|---|---|---|---|
Thick (WBC) | Thin (RBC) | ||||||
Thailand1 | 2001-2010 | 3391 | SS1 | 500 | 1000 | 16 | Phyo et al.[20] |
Thailand2 | 2008 | 40 | SS3 | 200 | 1000 | 16 | Dondorp et al.[4] |
Thailand3 | 2009-2010 | 80 | SS2 | 200 | 1000 | 16 | Das et al.[21] |
Mali | 2010 | 261 | SS1 | 300 | ND | 25 | Lopera-Mesa et al.[19] |
Cambodia1 | 2007-2008 | 59 | SS2 | 200 | 1000 | 16 | Dondorp et al.[4] |
Cambodia2 | 2008-2010 | 79 | SS2 | 200 | 1000 | 16 | Das et al.[21] |
Cambodia3 | 2009 | 79 | SS1 | 200 | ND | 15 | Amaratunga et al.[18] |
Cambodia4 | 2010 | 98 | SS1 | 200 | ND | 15 | Amaratunga et al.[18] |
Cambodia5 | 2010 | 30 | SS1 | 200 | ND | 15 | Amaratunga et al.[18] |
Cambodia6 | 2010 | 55 | SS1 | 200 | ND | 15 | Unpublished |
Cambodia7 | 2008-2009 | 143 | SS2 | 200 | 5000 | 14 | Bethell et al.[24] |
Kenya | 2010-2011 | 171 | SS2 | 30 | Unpublished | ||
Vietnam | 2010-2011 | 166 | SS1 | 400 | 1000 | 8 | Hien et al.[25] |
Total | 4652 |
Parasite clearance parameters
Approach 1: Effect of alternative sampling schedules on estimation of half-life
The sampling time-points (in hours) included in the reference schedule and each of the four alternative schedules, A1-A4, for the analysis of real patient data
Sampling schedule | 0 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | Every 6 hours until negative | Every 12 hours until negative |
---|---|---|---|---|---|---|---|---|---|---|---|
Reference | X | X | X | X | X | X | X | X | X | X | |
A1 | X | X | X | X | X | X | X | ||||
A2 | X | X | X | X | X | X | X | ||||
A3 | X | X | X | X | X | X | X | ||||
A4 | X | X | X | X | X | X |
Approach 2: Sampling distribution of half-life with bootstrapping
- a)
segmented the reference HL distribution into discrete sections, S_{i}, i = 1…r. The segments were each of one hour width from zero hours to 13 hours (the range of HL is 0.7-12.9).
- b)
selected one of the r segments from (a), chosen at random.
- c)
identified reference HLs from the real data that lie within the r^{th} segment, chosen in (b).
- d)
sampled one of the reference HLs identified in (c), chosen at random.
- e)
accepted the reference HL as the j^{th} bootstrap sample with a probability p, where p is the log-normal density for the given values of M and CV, for the HL chosen in (d).
- f)
repeated steps (a) – (e) until 100 patients had been accepted into the j^{th} bootstrap sample.
where ‘median SS_HL’ and ‘median R_HL’ are the median HL estimates for the alternative and reference sampling schedules, respectively.
Approach 3: Comparison of sampling schedules on simulated data
To investigate more complicated sampling schedules that included a time-point not represented in the reference schedule, a simulation study was designed. Parasite counts were generated based on the variability observed in the real patient data, so that the created profiles were realistic. The process by which parasite count data were generated, for a given HL and P0, is presented in Additional file 1. For a specified “true” HL and “true” initial parasitaemia (P0), 1,000 log-parasite density-time profiles were generated, and the HLs using a number of different sampling schedules (Table A2.1 in Additional file 2) were calculated using the PCE tool. These include regular sampling schedules (S1-S4), the best sampling schedule from the bootstrap analysis (B1 = A1), an optimal sampling schedule [28], schedules based on once daily repeated sampling (M1-M3) and slight modifications of these schedules. All combinations of “true” HLs of two, three, four, five and six hours and “true” initial parasite densities (P0) of 5,000, 10,000, 50,000, 100,000, and 200,000 per μL were examined. The effect of the sampling schedules on estimates of HL was assessed through comparisons with the “true” HL using the proportion of profiles with an absolute value of relative difference (ARD) more than 10, 20 and 30% and the proportion of profiles with an absolute value of difference (AD) greater than one hour. For the two sampling schedules that stopped at 48 hours (O1 and S1c), large values of the HL and high P0 combinations could result in a final parasite density exceeding 1,000 per μL, in which case a HL estimate is not typically available through the PCE tool [14]. To facilitate comparison of these two schedules, the PCE tool was adjusted and run separately for these two schedules such that the HL was estimated, regardless of what was the parasite density at 48 hours.
Results
Study data
Summary of results from 13 included studies
Country | Proportion of patients | Median HL; range; IQR | CV (%) | Std dev log(HL) | Prop NZ tlag | Median NZ tlag | Prop with tail |
---|---|---|---|---|---|---|---|
Thailand1 | 46% (1571/3391) | 3.05; 0.889-12.9; 2.37-4.24 | 46.4 | 0.438 | 26.4% (n = 415) | 6 | 42.1% (n = 662) |
Thailand2 | 82% (33/40) | 2.87; 1.48-7.54; 2.11-3.77 | 46.8 | 0.421 | 18.2% (n = 6) | 4.05 | 54.5% (n = 18) |
Thailand3 | 88% (70/80) | 3.26; 0.964-9.09; 2.36-4.42 | 50.4 | 0.49 | 24.3% (n = 17) | 6 | 41.4% (n = 29) |
Mali | 99% (258/261) | 1.87; 0.678-4.27; 1.57-2.34 | 30.0 | 0.296 | 58.1% (n = 150) | 6 | 1.55% (n = 4) |
Cambodia1 | 97% (57/59) | 6.11; 2.53-9.5; 4.93-7.18 | 26.1 | 0.285 | 21.1% (n = 12) | 12 | 45.6% (n = 26) |
Cambodia2 | 94% (74/79) | 5.79; 2.07-9.37; 4.85-7.32 | 31.1 | 0.359 | 24.3% (n = 18) | 6.02 | 40.5% (n = 30) |
Cambodia3 | 99% (78/79) | 6.09; 1.71-11.2; 4.69-7.15 | 32.4 | 0.377 | 7.69% (n = 6) | 6 | 14.1% (n = 11) |
Cambodia4 | 100% (98/98) | 6.5; 2.13-11.3; 5.14-7.73 | 29.2 | 0.329 | 6.12% (n = 6) | 15 | 2.04% (n = 2) |
Cambodia5 | 100% (30/30) | 5.75; 2.66-10.5; 4.12-7.48 | 34.5 | 0.363 | 33.3% (n = 10) | 15 | 13.3% (n = 4) |
Cambodia6 | 78% (43/55) | 2.62; 1.13-4.43; 2.31-3 | 25.9 | 0.278 | 6.98% (n = 3) | 6 | 27.9% (n = 12) |
Cambodia7 | 98% (140/143) | 7.03; 1.7-11.8; 5.6-8.11 | 31.6 | 0.397 | 6.43% (n = 9) | 6 | 57.1% (n = 80) |
Kenya | 93% (159/171) | 2.49; 0.956-5.19; 1.89-3.09 | 33.1 | 0.354 | 19.5% (n = 31) | 6 | 0% (n = 0) |
Vietnam | 81% (135/166) | 2.9; 1.02-10.2; 2.04-5.46 | 59.3 | 0.572 | 34.1% (n = 46) | 6.23 | 40.7% (n = 55) |
Total | 59% (2746/4652) | 3.13; 0.678-12.9; 2.29-5 | 53.8 | 0.519 | 26.5% (n = 729) | 6 (6–6.25) | 34% (n = 933) |
Parasite clearance parameters
The median, range and interquartile range (IQR) of parasite HLs for individual studies and all studies combined are presented in Table 3. The median (range) HL of all studies was 3.1 hours (0.7-12.9) and varies between studies, ranging from 1.9 hours to 7.0 hours. The proportion of profiles with a non-zero lag-phase (tlag) was 26.5% for all studies, and ranged from six to 58% (Table 3). Of those profiles with a non-zero tlag, the median lag-phase duration of all studies was six hours, and ranged from four to 15 hours. The coefficient of variation of HL estimates for all studies was 54%, and ranged between 26 and 59%. The proportion of profiles showing a tail (i.e., the terminal part of the profile when parasitaemia remains close to the detection limit) for all studies was 34% and between 0 and 57% in individual studies.
Approach 1: Effect of alternative sampling schedules on estimation of half-life
Summary of results from reference and alternative schedules
Schedule | Prop OE (of 2746 profiles) | (IQR) | CV (%) | Std dev log(HL) | Prop NZ tlag | Median (IQR) NZ tlag | Prop tail | Prop (%) profiles misclassified, with HL cutoff of: | |||
---|---|---|---|---|---|---|---|---|---|---|---|
3 h | 4 h | 5 h | 6 h | ||||||||
Ref | 0% | 0 (0–0) | 54.5 | 0.52 | 26.5 (n = 729) | 6 (6–6.25) | 34% (n = 933) | 0 | 0 | 0 | 0 |
A1 | 49.9% | 0.01 (-0.15-0.21) | 51.6 | 0.503 | 22.1 (n = 606) | 6 (6–6.27) | 9.36% (n = 257) | 7.7 | 3.9 | 2.7 | 2.2 |
A2 | 60.2% | 0.06 (-0.10-0.29) | 51.1 | 0.482 | 17.4 (n = 478) | 6 (6–6.03) | 9.87% (n = 271) | 8.6 | 4.4 | 3 | 2.2 |
A3 | 59.8% | 0.09 (-0.09-0.34) | 50.9 | 0.484 | 12.5 (n = 344) | 12 (12–12) | 9.91% (n = 272) | 9.5 | 4.5 | 3 | 2.1 |
A4 | 66.3% | 0.15 (-0.06-0.46) | 47.7 | 0.435 | 6.96 (n = 191) | 12 (12–12) | 9.25% (n = 254) | 10 | 4.6 | 3.4 | 2.2 |
The 12-hourly schedule (A4) was the worst performing schedule when the real patient data were used. The main determinants of the discrepancy between the reference and A4 schedules were the presence of a lag-phase in the reference profile and a small number of measurements, which resulted in a simple regression model fitted for the A4 schedule (with the first zero replaced by the detection limit) as opposed to a tobit regression fitted for the reference data (Table A3.2, Additional file 3). A six-hour delay in the time when the first negative parasitaemia was recorded (when using A4 versus the reference schedule) did not matter overall.
Approach 2: Sampling distribution of half-life with bootstrapping
Examining the estimates of the proportion of profiles with a HL above a value of three, four, five and six hours, of all the alternative schedules applied to all bootstrap datasets, 7,981 bootstrap datasets gave different estimates of these proportions by absolute 10% difference or more. Of these, 7,224 (91%) occurred when the HL was above three hours. Among these profiles, 69% were for bootstrap samples with a geometric mean HL of two hours and 30% for a geometric mean HL of three hours, and <1% for all other HL.
Approach 3: Comparison of sampling schedules on simulated data
In the final approach, a simulation study was designed to assess the effect of more complicated sampling schedules on parasite clearance estimation. Table A3.3, Additional file 3 summarizes the performance of the 16 sampling schedules in the simulation study, with results pooled for all values of HL and P0 considered. That is, for each schedule 25,000 profiles were used to create the summary statistics in Table A3.1, Additional file 3 (1,000 from each combination of HL and P0). For each simulation schedule, the proportion of profiles with AD (absolute value of the difference) more than one hour between the HL estimate under the schedule and the “true” HL, and the proportion of profiles with ARD (absolute value of relative difference) more than 10, 20 and 30% were calculated.
The worst-performing schedules, in terms of the highest ARD, were S4, M1 and S3, having 66, 53 and 52% of profiles with ARD > 10%; 49, 31 and 26% of profiles with ARD > 20% and 38, 19 and 13% with ARD > 30% (Table A3.3, Additional file 3). The best-performing schedule, in terms of the lowest ARD, for all HL and P0 values was the six-hourly schedule (S1). The eight-hourly sampling schedule (S2) had a consistently higher number of discrepant profiles (ARD > 10%) than S1, but the difference in the proportion of profiles with discrepant estimates was never more than 6%. More dense sampling than every 12 hours (S3) was required in the first 24 hours to accurately estimate HL for profiles with short HL and/or low initial parasite density. For HL ≤ 3, ARD > 20% was 19 and 34% for S1 and S3, respectively, compared to 14 and 20% for HL ≥ 4. Similarly for P0 ≤ 10,000 ARD > 20% was 24 and 39% for S1 and S3, respectively, compared to 11 and 17% for P0 ≥ 100,000. Among modified schedules (M1, M2 and M3), M2 had lower ARD > 20% and ARD > 30% than M1 while M2 performed better or similarly as M3, in terms of ARD > 20% and ARD >30%, except in simulations where HL = 2 and P0 ≤ 10,000.
For all schedules, except those involving 12 or 24-hourly sampling (i.e., S3, S4, M1, M2 and M3), the proportion of profiles with an absolute value of difference (AD) greater than one hour between the estimated HL and “true” HL increased with HL, but decreased with the initial parasitaemia. On the other hand, the proportion of profiles with an absolute value of the relative difference (ARD) greater than 10% (or 20%), was generally highest for a “true” HL of two hours and then remained constant or slightly decreased with HL. For schedules except S4, M2, and M3 the ARD slightly decreased with initial parasitaemia, but this effect was much less pronounced than for AD.
Among schedules in the simulation study with six or fewer measurements in the first 48 hours, when HL ≤ 4, the best performing schedules included B1, O1 and M2. Overall, the B1 and M2 schedules performed slightly better than O1, with 20, 19 and 22% of profiles with ARD > 20%, respectively. The three schedules gave similar results for slow clearing profiles, but not in the case of very fast clearance. For HL = 2, M2 had the lowest proportion of profiles with ARD > 10% (37 versus 52 for B1 and 52% for O1), and ARD > 20% (19 versus 25 and 26%) but similar proportions of profiles with ARD > 30% (13 versus 12 and 12%). The three schedules gave comparable results for high initial parasitaemia, but for low initial parasitaemia M2 performed better: ARD > 20% for M2, B1 and O1 were 22, 31 and 33% (P0 = 5,000), respectively compared to 19, 18 and 19% (P0 ≥ 10,000).
Continued sampling after 48 hours was important for slow clearing profiles. All six-hourly schedules (S1, S1a, S1b, S1c) gave the same results for HL ≤ 3, due to very few positive parasitaemias values recorded after 48 hours. The six-hourly schedules with 12-hourly (S1a) and six-hourly (S1) measurements after 48 hours gave similar results for longer HLs, while S1b and S1c performed worse. For HL ≥ 4, for example, the proportion of discrepant profiles for S1a and S1 were, 43 and 41% (ARD > 10%) and 16 and 14% (ARD > 20%), respectively. For S1b and S1c, these values increased to 46 and 45% (ARD > 10%); and 18 and 18% (ARD > 20%), respectively. When the optimal schedule (O1) was extended beyond 48 hours, the O1a (12-hourly) schedule gave slightly better estimation results while the O1b (24-hourly) schedule gave comparable results. All three schedules gave nearly identical results for HL ≤ 3 hours (ARD > 10% and ARD > 20% always within 1%) while for HL ≥ 4 hours there was a noticeable difference: the ARD > 20% was 22, 19 and 22% for the O1, O1a and O1b schedules, respectively, and 48, 45 and 49% for ARD >10%.
When the restriction of the final parasite density being less than 1,000 per μL was removed from the PCE algorithm, it was clear that the accuracy of the O1 and S1c schedules was poor if the measured parasitaemia at 48 hours was more than 1,000: ARD > 20% was 68% for O1 when the parasite density at 48 hours exceeded 1,000 compared to 33% for O1a. When the parasite density at 48 hours was less than 1000 the ARD > 20% was comparable: 24 and 19% for O1 and O1a, respectively. The same trend was observed for S1c versus S1: when the parasite density at 48 hours exceeded 1,000 ARD > 20% was 64 and 24% for S1c and S1, respectively (compared to 20 and 16% when the parasite density at 48 hours was less than 1,000).
Discussion
A bootstrapping algorithm was used to study the effect of different sampling schedules on population estimates of HL, for populations with different geometric mean HLs and coefficients of variation. Schedule A1 consistently performed better than the other schedules over a range of different geometric mean HLs. Its superiority was greater for profiles with shorter HLs (Figure 3). The 12-hourly A4 schedule performed the worst (Figure 3).
To investigate more complicated sampling schedules that included a time-point not present in the reference schedule, a simulation study was performed using “true” HLs of two, three, four, five and six hours and initial parasite densities (P0s) of 5,000, 10,000, 50,000, 100,000 and 200,000 per μL. The schedules which performed worst were 24-hourly sampling (S4), 12-hourly sampling (S3) and the modified 24-hour schedule (M1) (Table A3.1, Additional file 3), and the best-performing schedule was six-hourly sampling (S1). The simulation study confirmed that more dense parasite sampling schedules are required to accurately estimate half-life for profiles with short half-life (≤3 hours) and/or low initial parasite density (≤10,000 per μL). Among schedules in the simulation study with a limited number of measurements, when HL ≤ 4 hours, the best performing schedules included B1, O1 and M2.
The O1 schedule was identified by Jamsen et al.[28] as an optimal sampling schedule through a different methodological approach, and this was also investigated in the present simulation study. Jamsen et al. used a robust T-optimal design methodology to allow for discrimination across models that best describe an individual patient’s parasite-time profile. The design was based on the constraint that no more than six samples would be taken per patient within 48 hours of initial treatment. The T-optimal sampling times (windows) were: 0 (0–1.1), 5.8 (4.0-6.0), 9.9 (8.4-11.5), 24.8 (24.0-24.9), 36.3 (34.8-37.2) and 48 (47.3-48.0) hours after treatment initiation. It is interesting and lends support to our results that a sampling schedule driven by practicalities (B1) turned out to be a variant of a schedule identified by optimal design theory (O1).
In the simulation study, sampling after two days was found to give little additional improvement in parasite clearance HL estimates for fast clearing parasites (HL ≤ 3 hours). This observation is supported by the work of Nkhoma et al.[16], a study in which the majority of the profiles had cleared or reached very low parasitaemia levels by 48 hours. The reduced sampling schedule M2 performed very well in the simulation study; however, further investigation of this schedule in the field is required before it can be recommended widely. The simulation results will be extended to examine factors affecting HL estimates (eg, the thick and thin smear counting method combinations) and patient factors that affect clearance, notably the potential interaction between parasite clearance and clinical immunity. It is also important to recognize that high quality quantitative microscopy to measure the parasite density in the peripheral blood is essential for accurate estimation of parasite clearance rates.
The clinical phenotype of slow P. falciparum clearance is likely to remain a critical indictor of artemisinin resistance to be correlated with molecular markers when they are identified and validated. Furthermore, in the context of detecting the emergence and spread of artemisinin resistance, it is important to establish reliable baselines of parasite clearance for the different ACT available. Indeed, depending on the type and dosage of artemisinin derivatives in the various ACT (eg, artemether 1.7 mg/kg body weight in fixed-dose combination (FDC) of artemether-lumefantrine per dose; artesunate 4 mg/kg in FDC of artesunate-amodiaquine per day; and dihydroartemisinin 2 mg/kg in FDC of dihydroartemisinin-piperaquine), and the impact of the partner drugs, parasite clearance profiles may vary substantially. Hence, accurate and reliable estimation of parasite clearance rates is essential to monitor changes in artemisinin susceptibility within and between malaria-endemic regions. In investigating the effect of different sampling schedules on the accuracy of HL estimation, this study has shown that HL is best estimated by including samples at six and 12 hours (A1), and that 12-hourly sampling may be satisfactory in patients with slow-clearing parasites. It is particularly challenging to accurately estimate the HL in profiles with fast parasite clearance and low initial parasite density, the conditions usually encountered in high-transmission areas where individuals have significant levels of immunity.
Conclusions
This study reveals important insights on sampling designs for accurate and reliable estimation of P. falciparum HL following treatment with artesunate alone or in combination with a partner drug. Including a parasite measurement at six hours is important, especially in regions with unknown P. falciparum susceptibility to artemisinins. Schedules with measurements at times (windows) of 0 (0–2), 6 (4–8), 12 (10–14), 24 (22–26), 36 (34–36) and 48 (46–50) hours, or at six, seven (two samples from 5–8), 24, 25 (two samples from 23–26), 48 and 49 (two samples from 47–50) hours, until negative are recommended. If the measured parasitaemia at two days exceeds 1,000 per μL, continued sampling at least once a day is suggested. A measure at 72 hours should be considered if the goal is to assess drug efficacy overall, and to conform to existing recommendations.
Declarations
Acknowledgements
This study was supported by the Bill and Melinda Gates Foundation and in part by the Intramural Research Program of the NIAID, NIH. Francois Nosten, Elizabeth Ashley, Aung Pyae Phyo, Arjen M, Mayfong Mayxay, Paul N Newton, Tran Tinh Hien, and Nicholas J White are all supported by the Wellcome Trust. All clinical studies were approved by the respective ethics committees or institutional review boards of each collaborative entity and host country of conduct. All subjects provided informed consent before study participation, and parents or legal guardians provided informed consent on behalf of their children.
Authors’ Affiliations
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