Standardizing the measurement of parasite clearance in falciparum malaria: the parasite clearance estimator
- Jennifer A Flegg^{1, 3},
- Philippe J Guerin^{1, 3},
- Nicholas J White^{2, 3} and
- Kasia Stepniewska^{1, 3}Email author
https://doi.org/10.1186/1475-2875-10-339
© Flegg et al; licensee BioMed Central Ltd. 2011
Received: 6 September 2011
Accepted: 10 November 2011
Published: 10 November 2011
Abstract
Background
A significant reduction in parasite clearance rates following artesunate treatment of falciparum malaria, and increased failure rates following artemisinin combination treatments (ACT), signaled emergent artemisinin resistance in Western Cambodia. Accurate measurement of parasite clearance is therefore essential to assess the spread of artemisinin resistance in Plasmodium falciparum. The slope of the log-parasitaemia versus time relationship is considered to be the most robust measure of anti-malarial effect. However, an initial lag phase of numerical instability often precedes a steady exponential decline in the parasite count after the start of anti-malarial treatment. This lag complicates the clearance estimation, introduces observer subjectivity, and may influence the accuracy and consistency of reported results.
Methods
To address this problem, a new approach to modelling clearance of malaria parasites from parasitaemia-time profiles has been explored and validated. The methodology detects when a lag phase is present, selects the most appropriate model (linear, quadratic or cubic) to fit log-transformed parasite data, and calculates estimates of parasite clearance adjusted for this lag phase. Departing from previous approaches, parasite counts below the level of detection are accounted for and not excluded from the calculation.
Results
Data from large clinical studies with frequent parasite counts were examined. The effect of a lag phase on parasite clearance rate estimates is discussed, using individual patient data examples. As part of the World Wide Antimalarial Resistance Network's (WWARN) efforts to make innovative approaches available to the malaria community, an automated informatics tool: the parasite clearance estimator has been developed.
Conclusions
The parasite clearance estimator provides a consistent, reliable and accurate method to estimate the lag phase and malaria parasite clearance rate. It could be used to detect early signs of emerging resistance to artemisinin derivatives and other compounds which affect ring-stage clearance.
Keywords
malaria regression analysis parasite clearance, artemisinin resistance drug resistanceBackground
Anti-malarial drug resistance is a major cause of preventable mortality [1] and poses the main threat to current global efforts to control and eliminate malaria [2]. Replacement of failing mono-therapy with highly effective artemisinin combination therapy (ACT) and increased delivery of effective vector control measures have reversed the increasing malaria mortality trend observed in the 1980s and 1990s. ACT has now become the recommended first line treatment for falciparum malaria in nearly all malaria affected countries [3].
The recent emergence of artemisinin resistance in Plasmodium falciparum malaria in Western Cambodia represents a considerable threat to global health [4–6]. A significant reduction in the rates of parasite clearance following treatment with artesunate and increased failure rates following artemisinin combination treatments (ACT) provided definitive evidence of resistance in that region [5, 7, 8]. There is increasing concern that artemisinin resistance has spread westwards [9]. No molecular marker of artemisinin resistance has yet been identified, and in vitro assessments have given contradictory results [5–7]. The clinical phenotype of slow parasite clearance remains to date the only way to define artemisinin resistance reliably [10].
The unique ability of the artemisinin derivatives to accelerate the clearance of ring stage infected erythrocytes is their pharmaco-dynamic hallmark [11, 12]. Accurate measurement of the rate of parasite clearance is necessary to assess artemisinin susceptibility in vivo. Most in vivo assessments measure parasitaemia either daily, or only on days D0, D2 and D3, as recommended in the current World Health Organization (WHO) guidelines [6]. In most studies, the exact timing of the parasite count is not recorded and could vary by several hours depending on the timing of the visit to the clinic at inclusion and during follow-up visits. The proportion of patients with persistent parasitaemia at D3 after ACT provides a useful indicator which can be used as a simple and readily obtained measure to exclude resistance, but not to define resistance [13]. It is too inaccurate for precise assessment as it is dependent on pre-treatment parasite density, precise timing of the sample, and it requires large sample sizes for precise estimates. In previous studies, with more frequent sampling, several different methods of analysing and measuring parasite clearance have been employed but systematic analytical approaches to measurement have not been taken.
In an attempt to standardize parasite clearance assessments from parasitaemia-time profiles in P. falciparum malaria, and facilitate epidemiological investigations of artemisinin resistance a method of identifying the initial lag phase and calculating a slope of log-parasitaemia changes over time after this lag phase has been developed and implemented into the parasite clearance estimator (PCE). The algorithm chooses between three models (log-linear, log-quadratic and log-cubic) and also provides automation of the "cleaning" of parasite count data before model fitting. The PCE may be used for any anti-malarial drug assessment, although it has been tested in data from patients treated with artemisinin derivatives and various ACT.
In this paper, the details of a simple calculator (PCE) that provides measures of parasite clearance from serial parasite count data are presented including the background, terminology, method of use, and examples of its application to real data.
Methods
Parasite clearance following any effective anti-malarial treatment is a first order process, resulting in killing of a fixed fraction of the parasite population in each asexual cycle, and can be considered as the reciprocal of parasite multiplication [11, 17]. The predominant relationship between log-transformed parasite density and time is generally linear [14, 18, 19]. Key terminology in relation to parasite clearance estimation is presented below.
Ideally the white blood cell (wbc) count is measured by an automated cell counter or manually. If this is not available then the counts are assumed to be 8,000/uL.
When the white blood cell count is assumed 8,000 for all patients, then the detection limit will be 40/uL for counting per 200 wbc and 16/uL for counting per 500 wbc.
Negative parasite slide - when no parasites are seen while the full number of white cells have been counted then the parasite count is recorded as zero. Of course this means only that the count is below the limit of detection, although it is often reported or modeled as 0/uL.
Outliers - parasite counts which are not biologically possible or are highly unlikely based on other parasite measurements in the same individual. These often result from transcription errors.
Lag phase - initial part of the parasite clearance profile which has a much flatter slope that the remaining part of the profile. It is important to note that a lag phase is not observed in all profiles.
Tail - terminal part of the parasite clearance profile when parasitaemia remains close to the detection limit (i.e. a few parasites per slide) and does not decrease over a number of measurement time-points. Tails are not observed in all profiles.
Serial parasitaemia-time data obtained from several published studies carried out between 2001 and 2010, at sites located in Tak province in north-western Thailand, Chittagong and Bandarban in Bangladesh, Savannakhet province in Laos, western Cambodia and Mali were used in the analysis. All studies investigated the use of artemisinin combination therapies. The algorithm was also tested on data from patients treated with quinine, enrolled in a study in Ho Chi Minh City, Vietnam between 1991-1996.
The latent variable is modelled in the standard way: ${\mathsf{\text{Y}}}_{\mathsf{\text{i}}}^{*}={\mathsf{\text{X}}}_{\mathsf{\text{i}}}\mathrm{\beta}+\mathrm{\epsilon}$. The regression model is solved using maximum likelihood techniques, however the likelihood function is now a truncated normal distribution in the case when ${\mathsf{\text{Y}}}_{\mathsf{\text{i}}}^{*}\le {\mathsf{\text{Y}}}_{\mathsf{\text{L}}}$.
- 1.
Linear: X_{i} = [1, t_{i}], β = [b_{0}, b_{1}]
- 2.
Quadratic: ${\mathsf{\text{X}}}_{\mathsf{\text{i}}}=\left[\mathsf{\text{1}},{\mathsf{\text{t}}}_{\mathsf{\text{i}}},{\mathsf{\text{t}}}_{\mathsf{\text{i}}}^{2}\right]$, β = [c_{0}, c_{1}, c_{2}]
- 3.
Cubic: ${\mathsf{\text{X}}}_{\mathsf{\text{i}}}=\left[\mathsf{\text{1}},{\mathsf{\text{t}}}_{\mathsf{\text{i}}},{\mathsf{\text{t}}}_{\mathsf{\text{i}}}^{2},{\mathsf{\text{t}}}_{\mathsf{\text{i}}}^{3}\right]$, β = [d_{0}, d_{1}, d_{2}, d_{3}]
For subjects with only four positive parasite measurements, the cubic regression model could not be fitted so a linear regression model starting from the second parasite measurement was fitted if this second measurement exceeded the first measurement (at time 0) by more than 25%. These "maximum regression" models often fitted better than the quadratic models that typically do not fit well for data with a steep increase in parasitaemia.
Linear, quadratic and cubic models fitted to the same data were compared using Akaike Information Criterion (AIC) [21] and the model that minimised the AIC was selected as best describing changes in log-parasitaemia over time. For subjects with a "maximum regression" model fitted, the sum of the squared residuals for the observations common to all three models (RSS_{shared}) was used instead and the model that minimised the RSS_{shared} was selected. From the selected best fitting model the lag phase was identified and the clearance rate constant was estimated using the algorithm described below.
- 1.
as described in this paper on a subset of patients with measurements taken every six hours in the first two days; with every second data-point excluded from the estimation;
- 2.
linear regression (tobit or normal regression as appropriate), i.e. ignoring the lag phase;
- 3.
normal regression where all zero-counts were excluded from the estimation, but the lag-phase was evaluated as described.
Algorithm
Before model selection and fitting, the data are checked for problem data points, possible outliers, and persistent parasite tails in an automated fashion. The data cleaning process is outlined briefly in Additional File 1. Having determined that it is appropriate to fit a model to the subject's parasite count data, the model fitting and estimation of the clearance rate constant (K) and duration of lag phase (t_{lag} ) is performed. The methodology is summarized in the following steps:
For each patient separately:
Step 1: Perform data cleaning, as described in Additional File 1. All further steps are performed on data with outliers, tails, extreme values and trailing zeros removed. For convenience of notation, if there is a zero parasitaemia that directly follows the last positive parasitaemia, it is replaced with the detection limit. This data point is subsequently counted as a non-zero parasite count.
- (i)
Number of non-zero parasite measurements (including a zero replaced with the detection limit) less than three
- (ii)
Initial parasitaemia too low: initial parasitaemia < 1,000 parasites per microlitre
- (iii)
Final recorded parasitaemia too high: final parasitaemia ≥ 1,000 parasites per microlitre
- (iv)
A zero parasitaemia has been recorded, but the last positive parasitaemia is too high and the zero count is uninformative: last non-zero parasitaemia ≥ 1,000 parasites per microlitre
A zero parasitaemia is defined to be uninformative if the normal linear regression fitted to all the data points (excluding the zero count) gives a confidence interval for the time when the parasitaemia is below the level of detection which includes the time-point when the zero parasitemia was recorded.
- (v)
There are fewer than three measurements in the first 24 hours or a time difference between measurements in the first 24 hours is more than 14 hours;
Step 4: Perform model fitting.
If none of the exclusion criteria (i)-(iv) in Step 2 are satisfied but exclusion criterion (v) in Step 3 is satisfied fit tobit linear regression if a zero parasitaemia has been recorded or linear regression otherwise.
If one or more of the exclusion criteria are satisfied in Step 2, the clearance rate constant and duration of lag phase cannot be estimated so proceed to Step 6.
Step 6: END
Estimation of clearance rate constant and duration of lag phase
The procedure to estimate the parasite clearance rate constant depends on the shape of the parasite profile, i.e. the shape of the best polynomial model fitted and the amount of data available. For profiles with only three parasite counts, infrequent parasite measurements in the first 24 hours, profiles which are linear or exhibit concave curvature, the minus slope of the linear regression model or tobit linear model (where appropriate) is used as an estimate of the clearance rate constant. Profiles which exhibit convex curvature are examined further to define the lag phase. If a lag phase is not identified in the profile, then the minus slope of the linear regression model or tobit linear model is used as an estimate of the clearance rate constant.
For profiles with convex curvature the assessment is performed on the best model predicted values with respect to changes in pair-slopes - slopes calculated between two neighbouring data points. Most pair-slopes are negative since the parasitaemia is decreasing and the smallest slope corresponds to the fastest parasite clearance. First, the minimum possible pair-slope is found for the entire profile within the time interval of detectable parasite measurements. If the profile is linear then all pair-slopes would be similar to this minimum slope, but if there is pronounced curvature in the profile, then there would be pair-slopes which are near to zero (corresponding to the flat part of the curve). If this flat part of the curve occurs at the initial time-points then it is called the lag phase and is excluded from the estimation of the parasite clearance rate constant. However the data-point which is the upper limit for the lag phase period is included in calculations (i.e. if the duration of lag phase is 12 hours then the data-point at 12 hours is included in the final estimation of the clearance rate constant).
Results
Breakdown of models fitted.
Number of models fitted (% of total) | |
---|---|
Linear fit | 1146 (28.6%) |
Max reg fit | 10 (0.3%) |
Quadratic fit (total) | 998 (24.9%) |
t_{lag} = 0 | 704 (17.6%) |
t_{lag} > 0 | 294 (7.3%) |
Cubic fit (total) | 1854 (46.2%) |
t_{lag} = 0 | 971 (24.2%) |
t_{lag} > 0 | 883 (22.0%) |
Of the 228 profiles that did not pass the requirements for clearance rate estimation, 112 were not fitted because of a lack of data (< 3 positive parasite readings), 27 because the initial parasitaemia was too low, and 89 because the parasitaemia was not cleared (last recorded parasitaemia was above 1,000 parasites per microlitre). Among 4,008 patients for whom estimation could be performed, tails were identified in 1,070 profiles (27%). In the automated cleaning process, a total of 31 outliers were identified. These points were not included in any subsequent clearance rate calculations. A lag phase was estimated in 30% (1,187/4,008) of profiles; the median (IQR; range) duration of lag phase was six (6-9; 1-60) hours.
Summary of model outputs and examples of fit
For the 4,008 profiles fitted, the median (IQR; range) parasite clearance rate constant was 0.22 (0.16-0.30; 0.02-1.18) per hour. The corresponding slope half-life had a median (IQR; range) of 3.11 (2.33-4.24; 0.59-34.28) hours. It should be noted that the data used in this paper has come from multiple study sites, across a range of patient demographics and, as such, should not be used as a reference point for comparison to other parasite clearance data.
Goodness of fit
Comparison between lag regression and linear regression
Frequency of sampling
For profiles with no lag phase identified by six-hourly measurements, the percentage of profiles with an absolute relative difference in slope half-life above 10% was 19% for sample size of four or more counts (of the linear part of the 12 hour data), decreasing to 7% for a sample size of at least six and 0.6% for nine or more data points. The corresponding figures for an absolute difference of 20% or more were 7%, 3% and 0.3%.
Summary of changes in lag phase when 12-hourly parasite counts were used instead of six-hourly counts.
Duration of lag phase (hours)^{a} | ||||
---|---|---|---|---|
Change in t _{ lag } | 0 hours ^{ b } | 6 hours | 12 hours | 18 hours ^{ c } |
Decreased | 0 (0%) | 354 (84%) | 42 (53%) | 12 (80%) |
Remains unchanged | 1167 (99%) | 0 (0%) | 37 (47%) | 0 (0%) |
Increased | 12 (1%) | 69 (16%) | 0 (0%) | 3 (20%) |
Of 517 profiles with a lag phase detected by the six-hourly measurements, the majority (79%) had the estimate of the duration of lag phase shortened when 12-hourly measurements were used, resulting in a systematic overestimation of the slope half-life. The median (IQR; range) relative difference in slope half-life for those profiles that had both a lag phase detected with the six-hourly measurements and this lag phase shortened under the 12-hourly measurements was -25.1% (-40.2% to -16.0%; -190.9% to 28.8%). Overall this analysis indicates that parasite clearance profiles with a lag phase are poorly characterised if the first parasite count after baseline is taken at 12 hours.
Use of tobit regression
Agreement between tobit regression and linear regression estimates of slope half-life.
Relative Difference in Slope half-life^{a} | |||
---|---|---|---|
Sample size ^{ b } | < 10% | < 30% | < 50% |
3 < N ≤ 5 | 620 (90%) (26, 44) | 669 (97%) (9, 12) | 683 (99%) (5, 2) |
5 < N ≤ 10 | 1104 (81%) (19, 242) | 1281 (94%) (2, 82) | 1352 (99%) (1, 12) |
10 < N ≤ 15 | 331 (96%) (7, 8) | 346 (100%) (0, 0) | 346 (100%) (0, 0) |
Different anti-malarial drug treatments
The algorithm was tested on data from a study of 382 patients investigating the effect of quinine on parasite clearance. The median number (range) of positive parasite counts from slide readings was seven (three-30) per patient. Overall, 285 profiles were suitable for estimation of parasite clearance rates, of which 36 profiles were best fit with a quadratic model and a nonzero lag phase, 70 profiles were best fit with a cubic model and nonzero lag phase, and 179 were best fit with a linear model (either directly, or by a higher order model with zero lag phase). Of the 97 profiles that did not pass the requirements for clearance rate estimation, four were not fitted because of lack of data (< 3 positive parasite counts), 15 because the initial parasitaemia was too low, and 78 because the parasitaemia was not cleared (last recorded parasitaemia was above 1,000 parasites per microlitre). Among the patients for whom estimation could be performed, tails were identified in 45 profiles (16%) and 106 had a non-zero lag phase (37%).
Overall, the median (IQR; range) slope half-life for patients treated with quinine was 5.15 (3.83-6.68; 0.86-105.5) hours and, as expected, was longer than for ACT. Median (IQR; range) slope half-life for ACT was 3.11 (2.33-4.24; 0.59-34.28) hours. Patients treated with quinine were more likely to have a lag phase (37% versus 30% in the ACT group) and the duration of lag phase was significantly longer: median (IQR; range) of 10.0 (6.31-18.13; 0.5-81.97) hours as compared to six (6-9; 1-60) hours in ACT group.
For the quinine data-set, as with the data-set from patients treated with ACT, the agreement between the predicted and measured log-parasitaemia was better for the final linear models derived from the polynomial models than for the linear regression models fitted to all data points: the residuals had smaller variation over the data used to calculate the clearance rate constant: the mean (standard deviation) for the time points included in estimation of the clearance rate constant was 0.00 (0.39) for the polynomial models and 0.17 (1.08) for the corresponding linear models.
Conclusions
Prolonged parasite clearance is the only way artemisinin resistance can be identified currently. In this paper a new standardized approach to the estimation of the malaria parasite clearance rate has been presented. The algorithm takes into consideration the potentially confounding effects of the lag phase and removes these initial data before calculating the rate constant of the log-linear phase of parasite clearance. An outline of the algorithm is presented and its use has been evaluated with a large series of serial parasite counts from treatment studies in patients with acute falciparum malaria. Current evidence suggests that the main effect of artemisinin resistance is on the slope of the log-linear decline and for this reason this paper has focussed on characterizing this variable. The slope measure which may be most readily interpreted by malariologists is the half-life (which is inversely proportional to the first order rate constant).
The clinical phenotype of delayed parasite clearance is likely to remain the main proxy of artemisinin resistance until molecular markers are identified or in vitro methods adapted which provide better characterization. Parasite clearance rates are affected by drug blood concentration profiles as well as their pharmaco-dynamic properties. Immunity also increases parasite clearance rates. Other factors such as splenic function, age, anaemia and co-infections may also affect parasite clearance and require further investigations.
Whilst artemisinin resistance in P. falciparum is confined to a relatively small geographic area in SE Asia, it is important to establish in other areas baseline parasite clearance data for the different ACT provided through the public sector, so trends can be followed prospectively across malaria endemic countries. The accurate assessments of parasite clearance in this "early warning system" require frequent blood sampling and accurate counting and the additional workload and the necessary quality assurance of such monitoring measures will undoubtedly raise serious operational challenges.
How frequent do parasite counts need to be to provide reliable calculation of estimates is still unclear. Measuring parasitaemia every 12 hours after starting treatment until counts are below the level of detection, allows the calculation of parasite clearance rates but systematically overestimates the slope half-life compared to measurement every six hours. The difference observed is greater when there is a lag phase, and is more evident with certain anti-malarials, e.g. quinine compared to artemisinin derivatives.
More data are needed to estimate the optimal sampling design for parasite clearance characterisation. However, considering the field challenges of performing systematic measures of parasitaemia more frequently than 12-hourly, this sampling interval could be considered as the minimum.
The WorldWide Anti-malarial Resistance Network (WWARN) has developed the Parasite Clearance Estimator or PCE (see http://www.wwarn.org/research/parasite-clearance-estimator for details), which uses the methodology described above to estimate parasite clearance measures. WWARN aims at providing a platform of partnership, which facilitates gathering the necessary data across endemic countries, needed to answer to the different methodological questions raised above.
Identifying the clearance rate constant and lag phase with the improved method outlined here will provide necessary standardized information in order for warning signs of resistance to be detected, so that appropriate actions to contain resistance can be initiated [6].
Declarations
Acknowledgements
We would like to thank Prakaykaew Charunwatthana (Department of Clinical Tropical Medicine, Faculty of Tropical Medicine, Mahidol University and Mahidol-Oxford Tropical Medicine Research Unit), Nick Day (Mahidol-Oxford Tropical Medicine Research Unit and University of Oxford), Arjen Dondorp (Mahidol-Oxford Tropical Medicine Research Unit and University of Oxford), Rick M. Fairhurst (National Institute of Allergy and Infectious Diseases), Chanaki Amaratunga (National Institute of Allergy and Infectious Diseases), Duong Socheat (Cambodia National Malaria Center), Tran Tinh Hien (Hospital for Tropical Diseases, Vietnam), Mayfong Mayxay (Mahosot Hospital, Laos), Paul Newton (Mahosot Hospital, University of Oxford and WorldWide Antimalarial Resistance Network), Harald Noedl (Medical University of Vienna), Francois Nosten (Shoklo Malaria Research Unit, Mahidol-Oxford Tropical Medicine Research Unit and University of Oxford) and Nguyen Hoan Phu (Oxford University Clinical Research Unit, Hospital for Tropical Diseases, Vietnam), who provided parasite data which allowed us to test our algorithm and Stata- and R- programs.
We would also like to thank the following for assistance with the R code: Marcel Wolbers and the R-help forum. NJ White is a Wellcome Trust Principal Research Fellow. WWARN is supported by a Bill and Melinda Gates Foundation grant.
We would like to thank the anonymous referees for their comments on the manuscript and Dr Valerie Tate for editorial services.
Authors’ Affiliations
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