Author response: Concentration-dependent mortality of chloroquine in overdose

Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Data availability References Decision letter Author response Article and author information Metrics Abstract Hydroxychloroquine and chloroquine are used extensively in malaria and rheumatological conditions, and now in COVID-19 prevention and treatment. Although generally safe they are potentially lethal in overdose. In-vitro data suggest that high concentrations and thus high doses are needed for COVID-19 infections, but as yet there is no convincing evidence of clinical efficacy. Bayesian regression models were fitted to survival outcomes and electrocardiograph QRS durations from 302 prospectively studied French patients who had taken intentional chloroquine overdoses, of whom 33 died (11%), and 16 healthy volunteers who took 620 mg base chloroquine single doses. Whole blood concentrations of 13.5 µmol/L (95% credible interval 10.1–17.7) were associated with 1% mortality. Prolongation of ventricular depolarization is concentration-dependent with a QRS duration >150 msec independently highly predictive of mortality in chloroquine self-poisoning. Pharmacokinetic modeling predicts that most high dose regimens trialled in COVID-19 are unlikely to cause serious cardiovascular toxicity. eLife digest Hydroxychloroquine and chloroquine are closely-related drugs used for the treatment of malaria and rheumatological conditions, such as lupus. Laboratory tests have indicated that these drugs could also be used against the virus that causes COVID-19. Given the urgent need, these drugs have been fast-tracked into large-scale clinical trials, bypassing the usual stages that would provide estimates for suitable dosage. The dosage is a critical factor in a clinical trial: too low and the drug will not have an effect, too high and the side effects may counteract any potential benefits. Laboratory tests suggest that higher doses of chloroquine or hydroxychloroquine are needed for treating COVID-19 compared to malaria or lupus. However, there are concerns about the high doses used in some trials, as the drugs can have lethal side effects. Indeed, chloroquine has been used extensively in suicide attempts, particularly in France. To address these concerns, Watson et al. set out to determine the highest dosage of chloroquine (and thus of hydroxychloroquine, approximately) that does not cause unacceptable side effects. First, data was analysed regarding the concentration of chloroquine in the blood of 302 patients who had intentionally overdosed on the drug, since this concentration is tightly correlated with their risk of death. Watson et al. used a statistical model to calculate the maximal chloroquine concentration in a person’s blood associated with a one per cent risk of death. This is taken to be the threshold above which any potential benefit of chloroquine treatment would be outweighed by the possibility of lethal toxicity. Watson et al. also estimated the relationship between chloroquine concentrations and changes in electrocardiogram patterns, which record the electrical activity of the heart. This makes it possible to determine whether a high dose of chloroquine has led to dangerous levels in the blood. Using a mathematical model of how chloroquine is metabolised, Watson et al. predicted that most of the trials that tested chloroquine as a treatment for COVID-19 did not reach the calculated threshold concentration. An exception was the CloroCovid-19 trial in Brazil, which was stopped early because people in the higher dosage group suffered more heart problems and died in greater numbers than those in the lower dosage group. Two large randomised trials, RECOVERY and SOLIDARITY, have shown no benefit of hydroxychloroquine or chloroquine in the treatment of COVID-19, changing clinical practice worldwide. Both of these trials used high doses resulting in higher hydroxychloroquine or chloroquine concentrations than normally observed in the treatment of malaria or rheumatological conditions. The results from Watson et al demonstrate that the lack of benefit seen in these two large clinical trials is not due to the drug dosage being too high. Introduction Chloroquine and hydroxychloroquine are closely related 4-aminoquinoline drugs used for the treatment of malaria, amoebiasis and rheumatological conditions (World Health Organization, 2015). Until the late 1990s chloroquine was the drug of choice for the treatment of malaria. Hundreds of tons corresponding to over 200 million doses were consumed annually. Since then its use has declined because of widespread resistance in Plasmodium falciparum. Today there is greater use of hydroxychloroquine in rheumatoid arthritis and discoid and systemic lupus erythematosus. Chloroquine and hydroxychloroquine are antivirals with a broad range of activities (including flaviviruses, retroviruses, and coronaviruses) (Savarino et al., 2003; Liu et al., 2020; Wang et al., 2020; Yao et al., 2020; Mégarbane and Scherrmann, 2020). Their antiviral activity against SARS-CoV2 is expected to be weak as predicted unbound concentrations of hydroxychloroquine and chloroquine in vivo with currently recommended doses are lower than the half-maximal effect concentrations reported in Vero cell cultures (White et al., 2020). This has motivated trialling of higher loading and maintenance doses than usually given in malaria or hepatic amoebiasis (World Health Organization, 2015; Conan, 1949). As of the 11th June 2020, 77 interventional clinical trials evaluating these drugs in both the prevention and treatment of COVID-19 were registered and recruiting participants on ClinicalTrials.gov. Figure 1 shows a scatter plot of the duration versus total dose in base equivalent for the 55 trials using chloroquine or hydroxychloroquine for the treatment of hospitalised COVID-19 patients for which exact dosing could be extracted. The doses and durations varied greatly. The high doses used by some trials have caused concern over the potential for cardiovascular toxicity. Nevertheless, despite the lack of any convincing evidence of clinical benefit, these drugs are now being used extensively in COVID-19 prevention and treatment across the world. Sadly, patients who need hydroxychloroquine or chloroquine for the treatment of malaria and rheumatological conditions are often having difficulty obtaining them (Straits Times, 2020). Figure 1 Download asset Open asset The total chloroquine or hydroxychloroquine dose (in grams) and duration of 55 COVID-19 treatment trials currently recruiting participants, extracted from ClinicalTrials.gov on the 11th June 2020. The black open square boxes show the four ‘flat’ dosing chloroquine regimens simulated in this paper. Note that many trials give the same dose regimen so there are fewer than 55 unique points on the graph. Some multi-country trials such as SOLIDARITY use both hydroxychloroquine or chloroquine depending on the countries included. As the majority of countries worldwide use hydroxychloroquine we have colored these trials in red. The extracted data can be found in the supplementary materials. Figure 1—source data 1 Extracted meta-data from 55 trials registered on Clinicaltrials.gov using chloroquine or hydroxychloroquine for the treatment of COVID-19. https://cdn.elifesciences.org/articles/58631/elife-58631-fig1-data1-v2.xlsx Download elife-58631-fig1-data1-v2.xlsx Borba et al. reported results from a randomised trial in Brazil of two dose regimens of chloroquine in COVID-19 treatment (CloroCovid-19 study, ClinicalTrials.gov NCT04323527) (Borba et al., 2020). The trial was stopped early after recruiting only 81 patients because of cardiac toxicity and greater mortality in the higher dose group; two of 41 patients given the higher dose regimen developed ventricular tachycardia before death and 7 of 37 patients in this group developed electrocardiograph QTcF intervals over 500 msec compared with 4 of 36 in the lower dose group. The higher dose regimen, comprising 600 mg base chloroquine administered twice daily for ten days, is substantially higher than recommended in malaria or rheumatological conditions (World Health Organization, 2015) and represents the standard malaria loading dose repeated 19 times at 12 hr intervals. Chloroquine is dangerous in overdose and has been used extensively for suicide. High concentrations of chloroquine cause hypotension, arrhythmias, coma, acute respiratory distress syndrome (ARDS), and fatal cardiac arrest (Riou et al., 1988; Clemessy et al., 1995; Clemessy et al., 1996; Mégarbane et al., 2010). In Zimbabwe the mortality of chloroquine in overdose was approximately six times higher than for other drugs (Ball et al., 2002). In France in the early 1980s there was a suicide epidemic (Riou et al., 1988; Clemessy et al., 1995; Clemessy et al., 1996; Mégarbane et al., 2010 ) following the publication of a book entitled Suicide: mode d’emploi (Suicide: a how-to guide) (Guillon and Le Bonniec, 1982). This unfortunate experience allowed characterization of the factors associated with death from chloroquine overdose. Outcome in chloroquine self-poisoning depends on the dose ingested, the delay in reaching hospital and the quality of intensive care support. Using the blood concentration measurements taken from self-poisoning patients managed by experienced intensivists in the French National referral centre allowed development of a pharmacokinetic-pharmacodynamic model to estimate the relationship between chloroquine dosing and a fatal outcome. A pooled analysis using electrocardiograph QRS interval data from healthy volunteers (Pukrittayakamee et al., 2014) and from the French self-poisoning cohorts helped characterise the contribution of QRS prolongation to the recorded QT prolongation. These models were used to estimate the safety of the main treatment regimens currently used in COVID-19 clinical trials and of the standard malaria treatment regimen for comparison. Results Predicting mortality in self-poisoning from peak chloroquine concentrations We pooled individual patient whole blood chloroquine + desethylchloroquine concentrations and outcomes from three large prospectively studied hospital self-poisoning cohorts (n = 302, Figure 2, top panel) (Riou et al., 1988; Clemessy et al., 1995; Clemessy et al., 1996; Mégarbane et al., 2010). All the patients included in this analysis were treated in the same hospital in Paris and all had whole blood concentrations measured on admission. The overall mortality was 11% (33 of 302). Of the patients with multiple concentration measurements (n=173), 61 (35%) reached their peak whole blood chloroquine concentrations after admission. The distribution of differences on the log scale between admission whole blood concentrations and peak concentrations in patients who peaked after hospital admission was used to estimate a correction term for all other patients. Bayesian logistic regression was used to estimate the relationship between mortality and inferred whole blood peak chloroquine concentrations (Figure 2, bottom panel) specifically adjusted for the desethyl metabolite levels and for the non-observed peak concentrations in 241 (80%) of the patients. The model also adjusted for differences in treatment received between cohorts. The whole blood chloroquine concentration associated with 1% mortality was 13.5 µmol/L (95% C.I. 10.1 to 17.7). 1% is the lowest mortality for which a reliable estimate can be derived from these data. The 1% threshold value was then used to evaluate the risk of fatal toxicity in chloroquine treatment regimens under evaluation in COVID-19. Figure 2 Download asset Open asset Pharmacokinetic-pharmacodynamic model of chloroquine induced mortality. Top: pooled whole blood chloroquine + desethylchloroquine concentrations from admission samples in 302 prospectively studied self-poisoning patients (Riou et al., 1988; Clemessy et al., 1995; Clemessy et al., 1996; Mégarbane et al., 2010). The data are shown as overlapping histograms for survivors (yellow, n=269) and fatal cases (red, n=33). Bottom: Bayesian posterior distribution over the concentration-response curve (mean and 95% credible interval) describing the relationship between inferred whole blood chloroquine peak concentrations (after adjustment for the desethyl metabolite) and death, with the chloroquine concentration shown on the log10 scale. The vertical lines show the upper 99 percentiles of the predicted Cmax distribution in a 70 kg adult under the whole blood pharmacokinetic model for the six adult dose regimens considered (pink: 10 day regimen with 12 hourly maintenance dose of 600 mg (base); brown: 10 day regimen with 12 hourly maintenance dose of 310 mg (base); green: 7 day regimen with 12 hourly maintenance dose of 310 mg (base) ; grey: malaria treatment regimen). The vertical light pink shaded area shows the posterior credible interval over the concentrations associated with 1% mortality. The equivalent output with the plasma pharmacokinetic model is shown in Appendix 4. Predicting mortality from peak blood concentrations in COVID-19 treatment regimens We used two pharmacokinetic models to predict peak chloroquine concentrations for six chloroquine regimens. Five of the simulated regimens are potential COVID treatment regimens, and one is the standard malaria treatment regimen. A very wide range of chloroquine and hydroxychloroquine regimens are currently in use for the treatment of COVID-19 (Figure 1). The COVID-19 regimens we simulated correspond to the highest chloroquine treatment regimen (in terms of total dose) registered at ClinicalTrials.gov (Borba et al., 2020); the regimen given in the World Health Organization SOLIDARITY trial (NCT04330690); a lower 7 day adaptation of the SOLIDARITY regimen; and weight-optimised equivalent regimens. The pharmacokinetic model estimated from whole blood concentrations (Höglund et al., 2016) predicted a slightly wider range of values for maximum chloroquine concentrations (Cmax) than the plasma-based model (Appendix 3 shows the predicted Cmax distributions for both models in a 70 kg adult). Assuming a whole blood to plasma concentration ratio of 4, the whole blood-based model and the plasma-based model predicted approximately identical median Cmax values. Thus, the whole blood pharmacokinetic model provides higher estimates for fatal toxicity because it predicts a larger variance for the Cmax distribution and hence more extreme outliers. As a sensitivity analysis, the equivalent outputs for the plasma-based model are shown in Appendix 4. Based on the whole blood model, the median Cmax following a chloroquine dose of 600 mg base equivalent given twice daily for ten days to a 70 kg adult is 10.7 µmol/L (Figure 3, panel A). This is more than three times higher than the median Cmax for the chloroquine malaria treatment regimen at the same body weight. Approximately 60% of 70 kg adults continuing to receive the twice daily 600 mg dose have blood concentrations which rise into the ‘danger zone’ defined as whole blood concentrations above 10 µmol/L. In comparison, only two in a thousand 70 kg adults receiving the twice daily 310 mg base maintenance dose (as given in the SOLIDARITY and RECOVERY trials) for ten days would reach concentrations above 10 µmol/L (approximately the lower bound for the 1% mortality threshold). Taking into account the uncertainty around this threshold value, the model estimates that fewer than one per thousand receiving the twice daily 310 mg dose would have peak concentrations above the 1% mortality threshold (Figure 3, panel B). Clearly body weight is an important determinant of exposure if doses are not adjusted for weight, as is common with oral administration (chloroquine and hydroxychloroquine tablets usually contain 155 mg base). At most, two in a thousand 40 kg adults receiving the 3 day malaria treatment regimen without weight adjustment (i.e. an unusually high mg/kg dose) are predicted to reach peak concentrations above 10 µmol/L. Figure 3 Download asset Open asset The predicted risk of potentially fatal chloroquine toxicity across the six regimens simulated under the whole blood pharmacokinetic model. Panel A shows the simulated distribution of Cmax values in a 70 kg adult for the five COVID-19 treatment regimens under evaluation and the standard malaria treatment regimen. The vertical light pink shaded area shows the 95% credible interval for the 1% mortality threshold concentration. Panel B shows the probability that an individual will cross the 1% mortality threshold value as a function of body weight for the different chloroquine regimens (log10 scale on the y-axis). Panel C shows the predicted mortality per thousand for the six chloroquine regimens as a function of body weight. The equivalent output using the plasma pharmacokinetic model is given in Appendix 4. Coupling the pharmacokinetic model with the pharmacodynamic model, we estimated the expected weight-dependent fatality ratios for the five COVID-19 chloroquine treatment regimens, truncating the concentration-fatality curve at the 1% mortality threshold (only taking into account concentrations going above this threshold). Administering 600 mg base equivalent of chloroquine phosphate twice daily for ten days as in the CloroCovid-19 trial is predicted to result in absolute mean fatality ratios ranging between 0.05% (90 kg, 95% credible interval (C.I.), 0% to 0.3%) and 3.5% (40 kg, 95% C.I. 1.0% to 8.0%), Figure 3, panel C. In comparison, only the flat dosing regimens are predicted to result in fatality ratios greater than one per thousand, and then only for weights less than 55 kg: for a 40 kg adult the 10 day SOLIDARITY regimen could result in 0.2% mortality (95% CI, 0 to 0.8). The 10 day flat regimen (without a loading dose) of 500 mg chloroquine phosphate salt (310 mg base equivalent) twice daily was recommended by the Health Commission of Guangdong Province for adults weighing more than 50 kg (Multicenter collaboration group of Department of Science and Technology of Guangdong Province and Health Commission of Guangdong Province for chloroquine in the treatment of novel coronavirus pneumonia, 2020). This is not predicted to incur a significant risk of cardiotoxicity. Overall the model predictions support this body weight threshold for dose reduction. Concentration-dependent electrocardiograph QRS prolongation We pooled individual electrocardiograph QRS intervals and chloroquine concentration data from 16 healthy volunteers (Pukrittayakamee et al., 2014, for each individual the QRS interval was measured twice at rest and 12 times in presence of detectable plasma chloroquine concentrations after a single 620 mg base oral dose of chloroquine phosphate), and 290 self-poisoning patients (no QRS data from Riou et al., and one missing QRS measurement from the Clemessy cohort), Figure 4. We fitted a hierarchical Bayesian Emax sigmoid regression model to the paired concentration-QRS data and the steady state QRS data (healthy volunteers only), a total of n=514 datapoints. A whole blood chloroquine concentration of 3 µmol/L (usually observed in malaria treatment) is associated with a slight QRS prolongation of 6.7 msec (95% credible interval, 5.5–7.8). Clinically significant intraventricular conduction delay (QRS prolongation), resulting in durations greater than 150 msec, was strongly associated with observed chloroquine concentrations above 10 µmol/L. In self-poisoning, 1 out of 108 patients with admission whole blood concentrations less than 10 µmol/L had a QRS interval longer than 150 msec (this accounts for the bias term estimated in the Clemessy cohort). In comparison, QRS durations longer than 150 msec were recorded in 36 out of 182 (20%) of the patients with whole blood concentrations greater than 10 µmol/L. In self-poisoning patients, QRS duration was an independent predictor of death (adjusted odds ratio for death of 1.3 for each 10 msec increase in QRS, p<10-5). Figure 4 Download asset Open asset Electrocardiograph QRS interval duration as a function of whole blood chloroquine concentrations. The data shown in the scatter plot are from 16 healthy volunteers who took a single 620 mg base oral dose (green circles, 192 paired concentration-QRS data-points, plasma concentrations were multiplied by 4) and 290 chloroquine self-poisoning patients (red and blue, hospital admission concentrations). Random normal jitter (standard deviation of 1 ms) was added to the Clemessy cohort self-poisoning QRS values for improved visualization. Survivors are shown as circles and fatal cases as triangles. The self-poisoning electrocardiograph QRS values from the Clemessy series (Clemessy et al., 1995; Clemessy et al., 1996) were read manually and are adjusted for a bias term (see Materials and methods, non-adjusted data are shown in Appendix 5). The grey line (grey area) shows the estimated median QRS duration (range) in the 16 healthy volunteers in absence of measurable drug. The thick black line shows the mean posterior Emax sigmoid regression model, fitted to the pooled data. The dashed green and blue lines show the posterior predictive distribution under the error distributions for the healthy volunteers and Megarbane self-poisoning cohort (smaller measurement error than in the Clemessy cohort), respectively (see Materials and methods for the full specification of the model). Note that the Emax regression model does not account for concentration-dependent heteroskedasticity but only inter-individual variation for healthy volunteers and inter-study variation (differences in measurement). Discussion Chloroquine is dangerous in overdose. The risk of death is proportional to drug exposure. Mortality rises steeply at whole blood chloroquine concentrations above 10 µmol/L. This corresponds very approximately to a plasma concentration of 3 µmol/L, and a combined chloroquine and desethylchloroquine concentration (as in a spectrophotometric assay) of 14 µmol/L. Importantly the electrocardiograph is a valuable indicator of toxicity as potentially lethal levels are associated with significant QRS complex widening. A QRS duration of less than 100 msec makes lethal toxicity very unlikely. When using high-dose treatments weight adjusted dosing is important to avoid toxicity. Implications for COVID treatment regimens Chloroquine and hydroxychloroquine are already being used extensively, and often in high doses, to prevent and treat COVID-19 despite the current lack of convincing evidence of benefit. Use of these drugs has become extremely politicised. The first large randomised trial in the treatment of hospitalised patients has just reported (RECOVERY, NCT04381936: press release only at the time of writing, results are not yet peer reviewed). This result strongly suggests that hydroxychloroquine (and also lopinavir-ritonavir) does not benefit hospitalised patients. The preliminary results of the same trial show that dexamethasone has a major life saving benefit in patients receiving oxygen or being ventilated. This supports a paradigm of early benefit from an effective antiviral and late benefit from an anti-inflammatory drug. Thus there remains a potential role for chloroquine and hydroxychloroquine in prevention and early treatment. However the prevention trials will not report for many months hence. Confusion over the risks associated with chloroquine and hydroxychloroquine has been compounded by a recent high profile claim of increased mortality and high rates of ventricular arrhythmia in a very large observational data set. This data set was almost certainly fabricated (and the paper was subsequently retracted, Mehra et al., 2020). Unfortunately over-reactions by some regulatory agencies, unjustified extrapolations of risk from QT measurements, failure to distinguish the effects of the drugs given alone from the combination with azithromycin, and misunderstanding of their clinical pharmacology have conspired to reduce confidence in these drugs and jeopardise the very trials needed to characterise risks and benefits in the prevention and treatment of COVID-19 (White et al., 2020). Chloroquine and hydroxychloroquine have unusual pharmacokinetic properties with very large total apparent volumes of distribution (Vd) (chloroquine > hydroxychloroquine) and very slow terminal elimination rates (terminal half-lives exceed one month) which cannot be measured accurately. Thus, distribution processes, rather than elimination, govern the blood concentration profiles in the first days following the start of treatment. Large single doses (as in self-poisoning) are very dangerous because they result in high blood concentrations as the drugs distribute out from a central ‘compartment’ that is hundreds of times smaller than the total apparent Vd (compartmental modeling of chloroquine pharmacokinetics provides only an approximation of the distribution processes). These high concentrations can cause potentially lethal cardiovascular and nervous system toxicity. Chloroquine affects cardiac muscle depolarization, repolarization and contractility and also causes vasodilation. There is concentration-dependent electrocardiograph QRS widening and JT prolongation (Clemessy et al., 1995; Clemessy et al., 1996) which both contribute to QT prolongation. Death usually results from refractory hypotension or ventricular fibrillation. Self-poisoning with chloroquine has provided an unfortunate opportunity to correlate drug exposure with the risk of iatrogenic death. As chloroquine has relatively weak antiviral activity, if there is benefit in COVID-19 infections, it is likely to require high drug exposures. At the beginning of the COVID-19 pandemic a large number of investigators started studies of chloroquine and hydroxychloroquine. The toxicity thresholds were not well defined and a range of dose regimens were evaluated in the hope that benefits would exceed risks (Figure 1). The high dose chloroquine regimen evaluated by Borba et al. in Brazil did encounter cardiac toxicity. This study referenced the recommendations by the Health Commission of Guangdong Province based on the Chinese experience, but there may have been confusion between salt and base weights (Multicenter collaboration group of Department of Science and Technology of Guangdong Province and Health Commission of Guangdong Province for chloroquine in the treatment of novel coronavirus pneumonia, 2020). Whereas the Chinese authorities recommended 500 mg salt twice daily (two tablets of chloroquine phosphate 250 mg, comprising 155 mg base each), the Brazil study (Borba et al., 2020) gave doses in base equivalent (600 mg base 12 hourly) which were consequently much higher. Importantly the patients in the Brazilian study also received azithromycin (which also prolongs the QT interval, and this may well have contributed to ventricular arrhythmias, Saleh et al., 2020; Lane et al., 2020). This pharmacometric analysis of the French self-poisoning cohorts provides an evidence-based toxicity threshold. It suggests that a continued regimen of 600 mg twice daily can be directly lethal. Lower dose regimens such as those evaluated in the large RECOVERY and SOLIDARITY trials, and the original Guangdong recommendations, are predicted to be safe. Doses of chloroquine alone, resulting in peak concentrations greater than 10 µmol/L are associated with more than 1% risk of fatal toxicity. Limitations There are several limitations to this study. It is a retrospective individual patient data analysis. In the suicide attempts, other drugs or alcohol were often taken as well, although none with the acute lethal toxicity of chloroquine. Patients were managed by experienced intensivists on intensive care units where there was close clinical and laboratory monitoring. Mortality might be higher in less well supported settings, or in overloaded hospitals in high-income settings. The age range in self-poisoning is also younger than in the majority of more seriously ill COVID-19 patients. The spectrophotometric assay method does not separate chloroquine from its desethylated metabolite, and is relatively insensitive. Desethychloroquine has generally similar biological properties, and the assay performs well at the high concentrations of relevance to this study. We corrected for the presence of the metabolite under the Bayesian model, but this correction increases uncertainty around the threshold concentration associated with 1% mortality. The predictions of absolute mortality under the regimens simulated in this work are sensitive to the parameterization of the pharmacokinetic model. Cmax is not observed directly but is an output model-based quantity estimated from data. There are no large population pharmacokinetic studies to verify the precision of the Cmax predictions, especially for the critical upper tails of the distribution. The pharmacokinetic-pharmacodynamic model developed here was based on the largest prospective series of chloroquine self-poisonings studied in a single referral centre. However, it was not possible to apply a standard pharmacokinetic model to the observed data in order to estimate the individual Cmax values. Mainly because of vomiting, admission blood concentrations only weakly correlate with the self-administered chloroquine doses (Clemessy et al., 1995). Our model was based on a majority of admission whole blood concentrations. The data from patients whose peak drug concentrations occurred after hospital admission were used to approximate the difference between unobserved peak concentrations and admission concentrations in the remaining patients. Ove