Windows of Selection for Anti-Malarial Drug Treatments
Windows of Selection for Anti-Malarial Drug Treatments
The 'true' WoS are shown on Fig. 2 and the raw data are given on the left hand panels of Fig. 3 and Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional. All ACT regimens routinely cleared infections emerging from the liver on the first day post-treatment irrespective of their IC50 value (Fig. 2). Thereafter the probability of an infection successfully establishing in patients was highly dependent on the parasite IC50. The probability of surviving showed the largest increase between days 2 and 3. This is likely to be due to the presence of the artemisinin component on day 2 and its absence by day 3 (by convention, treatment starts on day 0 so artemisinins are present on days 0, 1 and 2). The probabilities that an established, patent infection survived direct treatment with the partner drug monotherapy are given in Fig. 2 for each resistant 'genotype' in the column labelled 'POST'. The POST was always greater than the probability of parasites surviving emergence on day 0 for two plausible reasons. Firstly, the established, patent infections treated on day 0 are present in much greater numbers (10 –10 parasites) than the newly emerging infections on day 0 (10 parasites). Secondly, POST is calculated for the partner drug monotherapy, whereas emergence on day 0 encounters both partner drug and an artemisinin derivative.
The presence or absence of a true WoS between the different genotypes can be determined from Fig. 2. As expected, the true WoS is closed in the initial days post-treatment (survival probability is around zero for all alleles) and closed again at later time points (when all alleles have a near 100% probability of surviving). The WoS is however open during the intermediary days and, interestingly, the probability changes between genotypes are roughly parallel. The true WoS was therefore arbitrarily defined as the time difference between the days when an allele has a 50% change of successful emergence (the dashed lines in Fig. 2).
The pattern of treatment outcome following AR-LF (Fig. 2a) was broadly similar to that noted with AS-MQ (Fig. 2b). Both ACT regimens kept the probability of successful emergence below 10% with sensitive infections (i.e., IC50 increases <fivefold) for ten to 20 days post-treatment (AR-LF and AS-MQ, respectively). As expected, the probability of successful emergence increased as infections became more resistant. The probability of an infection successfully becoming established just 10 days after treatment with the most resistant genotypes (50-fold IC50 increase) was as high as 60–80% following AR-LF and AS-MQ treatment, respectively. Treatment with DHA-PPQ was much more sensitive to increases in IC50 (Fig. 2c) than AR-LF and AS-MQ, suggesting it had a much shorter period of post-treatment prophylaxis (discussed later). Ten days after treatment, infections with PPQ-sensitive parasites had a 40% chance of successful emergence while infections with an IC50 increase of twofold and fivefold had a 68 and 95% chance of resulting in a successful emergence. Twenty days post-treatment, these probabilities increased to 60, 80 and 97%, respectively. Given that the probability of acquiring a new infection associated with a fivefold IC50 increase reached >95% almost immediately after the artemisinin component (DHA) was eliminated, it was unnecessary to illustrate greater increases in PPQ IC50 as the results would follow the same pattern.
The clinical WoS were formally defined as the differences between genotypes based on the tenth, 25th and 50th (i.e., median) centile values of patient data and are given on Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional with the raw data shown on the middle and right hand panels of Fig. 3 for AR-LF, and Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional for AS-MQ and DHA-PPQ, respectively. Figure 3 shows the clinical WoS for AR-LF opens much later using Method 2 (right hand panel) than Method 1 (central panel) and shifts the distribution of earliest patent infections (used to define the opening of the WoS) significantly to the right (i.e., to later days). Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional show this result was consistent following AS-MQ and DHA-PPQ treatment.
The key research question addressed here is whether the clinical WoS reliably estimates the 'true' WoS; the estimates are given on Table 1 and Additional file 1: Tables S2 and S3 http://www.malariajournal.com/content/14/1/292/additional. This does not appear to be true if the clinical WoS is estimated using Method 1, which ignored new infections occurring after the follow-up period (Table 1 and Additional file 1: Tables S2, S3 http://www.malariajournal.com/content/14/1/292/additional). Following treatment, the clinical WoS consistently underestimated the true WoS by as much as 9 days for AR-LF, 33 days for AS-MQ and 7 days for DHA-PPQ (Method 1, Table 1). One notable exception to this rule occurs when DHA-PPQ resistance is increased from twofold to fivefold, the clinical WoS over estimates the true WoS by up to 6 days (Method 1, Table 1).
Calculating the clinical WoS using Method 2 generally provided better estimates of the true WoS (Table 1 and Additional file 1: Tables S2, S3 http://www.malariajournal.com/content/14/1/292/additional). However, alleles that were particularly sensitive to the drug had such a low probability of becoming patent during the 63-day follow-up that the earliest patent infection (for a given centile value) often fell within the group of censored data arbitrarily assigned to day 70; the WoS was recorded as occurring 'beyond follow-up' (BF) in these circumstances. Following treatment with AR-LF, the clinical WoS accurately estimated the true WoS for all IC50 increases when defined using the tenth or 25th centile and for larger LF IC50 increases (i.e., >15-fold) defined using the 50th centile (Method 2 in Table 1 and Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). If MQ IC50 was increased twofold or more, the tenth and 25th centile estimates of WoS were accurate to within one to 2 days (depending on the magnitude of the IC50 increase and the centile cut-off, Method 2, Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). When MQ IC50 was equal to the default value, or when the 50th centile cut-off was used to define WoS, estimates of the AS-MQ clinical WoS were not possible as new infections occurred beyond the follow-up period (Method 2 in Table 1 and Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). Estimates of clinical WoS following DHA-PPQ treatment were accurate when PPQ IC50 increased twofold (defined by the 25th centile, Method 2, Table 1) but overestimate the true WoS by as much as 6–13 days when IC50 increases from two to fivefold.
In summary, Table 1 shows that clinical WoS calculated using Method 1 (i.e., as currently estimated) were consistently shorter than the true WoS. Clinical WoS calculated using Method 2 were far more consistent with the true WoS; it appears that Method 2 based on the 25th centile provides the best match between true and clinical WoS. The exception was DHA-PPQ, which was overestimated by both methods when PPQ IC50 was increased more than twofold.
These results were determined assuming patients acquire 16 new infections per year (see Additional file 1 http://www.malariajournal.com/content/14/1/292/additional for details); note results were consistent when the number of new infections was reduced to eight per year (Additional file 1: Table S3 http://www.malariajournal.com/content/14/1/292/additional).
Results
The 'true' WoS are shown on Fig. 2 and the raw data are given on the left hand panels of Fig. 3 and Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional. All ACT regimens routinely cleared infections emerging from the liver on the first day post-treatment irrespective of their IC50 value (Fig. 2). Thereafter the probability of an infection successfully establishing in patients was highly dependent on the parasite IC50. The probability of surviving showed the largest increase between days 2 and 3. This is likely to be due to the presence of the artemisinin component on day 2 and its absence by day 3 (by convention, treatment starts on day 0 so artemisinins are present on days 0, 1 and 2). The probabilities that an established, patent infection survived direct treatment with the partner drug monotherapy are given in Fig. 2 for each resistant 'genotype' in the column labelled 'POST'. The POST was always greater than the probability of parasites surviving emergence on day 0 for two plausible reasons. Firstly, the established, patent infections treated on day 0 are present in much greater numbers (10 –10 parasites) than the newly emerging infections on day 0 (10 parasites). Secondly, POST is calculated for the partner drug monotherapy, whereas emergence on day 0 encounters both partner drug and an artemisinin derivative.
The presence or absence of a true WoS between the different genotypes can be determined from Fig. 2. As expected, the true WoS is closed in the initial days post-treatment (survival probability is around zero for all alleles) and closed again at later time points (when all alleles have a near 100% probability of surviving). The WoS is however open during the intermediary days and, interestingly, the probability changes between genotypes are roughly parallel. The true WoS was therefore arbitrarily defined as the time difference between the days when an allele has a 50% change of successful emergence (the dashed lines in Fig. 2).
The pattern of treatment outcome following AR-LF (Fig. 2a) was broadly similar to that noted with AS-MQ (Fig. 2b). Both ACT regimens kept the probability of successful emergence below 10% with sensitive infections (i.e., IC50 increases <fivefold) for ten to 20 days post-treatment (AR-LF and AS-MQ, respectively). As expected, the probability of successful emergence increased as infections became more resistant. The probability of an infection successfully becoming established just 10 days after treatment with the most resistant genotypes (50-fold IC50 increase) was as high as 60–80% following AR-LF and AS-MQ treatment, respectively. Treatment with DHA-PPQ was much more sensitive to increases in IC50 (Fig. 2c) than AR-LF and AS-MQ, suggesting it had a much shorter period of post-treatment prophylaxis (discussed later). Ten days after treatment, infections with PPQ-sensitive parasites had a 40% chance of successful emergence while infections with an IC50 increase of twofold and fivefold had a 68 and 95% chance of resulting in a successful emergence. Twenty days post-treatment, these probabilities increased to 60, 80 and 97%, respectively. Given that the probability of acquiring a new infection associated with a fivefold IC50 increase reached >95% almost immediately after the artemisinin component (DHA) was eliminated, it was unnecessary to illustrate greater increases in PPQ IC50 as the results would follow the same pattern.
The clinical WoS were formally defined as the differences between genotypes based on the tenth, 25th and 50th (i.e., median) centile values of patient data and are given on Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional with the raw data shown on the middle and right hand panels of Fig. 3 for AR-LF, and Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional for AS-MQ and DHA-PPQ, respectively. Figure 3 shows the clinical WoS for AR-LF opens much later using Method 2 (right hand panel) than Method 1 (central panel) and shifts the distribution of earliest patent infections (used to define the opening of the WoS) significantly to the right (i.e., to later days). Additional file 1: Figures S1 and S2 http://www.malariajournal.com/content/14/1/292/additional show this result was consistent following AS-MQ and DHA-PPQ treatment.
The key research question addressed here is whether the clinical WoS reliably estimates the 'true' WoS; the estimates are given on Table 1 and Additional file 1: Tables S2 and S3 http://www.malariajournal.com/content/14/1/292/additional. This does not appear to be true if the clinical WoS is estimated using Method 1, which ignored new infections occurring after the follow-up period (Table 1 and Additional file 1: Tables S2, S3 http://www.malariajournal.com/content/14/1/292/additional). Following treatment, the clinical WoS consistently underestimated the true WoS by as much as 9 days for AR-LF, 33 days for AS-MQ and 7 days for DHA-PPQ (Method 1, Table 1). One notable exception to this rule occurs when DHA-PPQ resistance is increased from twofold to fivefold, the clinical WoS over estimates the true WoS by up to 6 days (Method 1, Table 1).
Calculating the clinical WoS using Method 2 generally provided better estimates of the true WoS (Table 1 and Additional file 1: Tables S2, S3 http://www.malariajournal.com/content/14/1/292/additional). However, alleles that were particularly sensitive to the drug had such a low probability of becoming patent during the 63-day follow-up that the earliest patent infection (for a given centile value) often fell within the group of censored data arbitrarily assigned to day 70; the WoS was recorded as occurring 'beyond follow-up' (BF) in these circumstances. Following treatment with AR-LF, the clinical WoS accurately estimated the true WoS for all IC50 increases when defined using the tenth or 25th centile and for larger LF IC50 increases (i.e., >15-fold) defined using the 50th centile (Method 2 in Table 1 and Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). If MQ IC50 was increased twofold or more, the tenth and 25th centile estimates of WoS were accurate to within one to 2 days (depending on the magnitude of the IC50 increase and the centile cut-off, Method 2, Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). When MQ IC50 was equal to the default value, or when the 50th centile cut-off was used to define WoS, estimates of the AS-MQ clinical WoS were not possible as new infections occurred beyond the follow-up period (Method 2 in Table 1 and Additional file 1: Table S2 http://www.malariajournal.com/content/14/1/292/additional). Estimates of clinical WoS following DHA-PPQ treatment were accurate when PPQ IC50 increased twofold (defined by the 25th centile, Method 2, Table 1) but overestimate the true WoS by as much as 6–13 days when IC50 increases from two to fivefold.
In summary, Table 1 shows that clinical WoS calculated using Method 1 (i.e., as currently estimated) were consistently shorter than the true WoS. Clinical WoS calculated using Method 2 were far more consistent with the true WoS; it appears that Method 2 based on the 25th centile provides the best match between true and clinical WoS. The exception was DHA-PPQ, which was overestimated by both methods when PPQ IC50 was increased more than twofold.
These results were determined assuming patients acquire 16 new infections per year (see Additional file 1 http://www.malariajournal.com/content/14/1/292/additional for details); note results were consistent when the number of new infections was reduced to eight per year (Additional file 1: Table S3 http://www.malariajournal.com/content/14/1/292/additional).