A total of 18 people had blood draws after receiving a single 70-mg dose of caspofungin. Their demographic features are shown in . The weight distribution is shown in , which also breaks down weight by gender. Two persons developed adverse events, none of which were considered severe. One person developed a mild headache, which resolved about 30 min after the participant was given 650 mg of acetaminophen. The participant had reported a history of headaches and migraines. Another participant developed hot flashes and sweating after being discharged from the CTRC, where she had completed the 24-h procedures without any adverse events. These symptoms resolved on their own after a few hours without an intervention.

| **Table 1**Demographic characteristics of study participants |

Naïve pooled data of caspofungin concentrations are shown in . The immediate postinfusion peak concentration varied from 3.14 mg/liter to 25.3 mg/liter. The 72-h trough varied from 0 to 2.7 mg/liter. Thus, there is wide variability even after receipt of the same dose. also demonstrates a biphasic decline in the naïve pooled concentrations in the patients. This suggests that the pharmacokinetics are likely described by at least a two-compartment model.

Examination of different compartmental models using the MLEM algorithm led to the information criterion scores shown in . In this case, AIC and −2LL would suggest that the two-compartment model is the best model. The evidence ratio calculated using the AIC score is that the two-compartment model is >4 × 10^{8} more likely to be the model than the one-compartment model. However, the BIC score, which penalizes for more complexity of the model, suggests that the one-compartment model is better than the two-compartment model. Nevertheless, based on the preponderance of evidence, a two-compartment model was chosen as the base model. The observed versus predicted concentrations in this model are shown . Pharmacokinetic parameter estimates in this model are shown in .

| **Table 2**Comparison of compartment models for caspofungin pharmacokinetics^{a} |

Next, the relationships between caspofungin pharmacokinetic parameter estimates in the base model and demographic characteristics were examined. There were no obvious relationships between any of the pharmacokinetic parameters and many of the demographic factors. Specifically, BMI demonstrated no obvious relationships to any pharmacokinetic parameter. However, the slopes of patient weight or mass (M) versus either the volume of the central compartment (

*V*_{c}) or the volume of the peripheral compartment (

*V*_{p}) were found to differ significantly from zero (). The double-log plot for M versus

*V*_{c} had a slope of 0.75 or 3/4 (). This suggests that the relationship between weight and

*V*_{c} obeyed the 3/4 power law that has been used to scale weight to systemic clearance (SCL) for several anti-infective agents, including micafungin (

7,

9,

11,

12,

16). Therefore, we examined if inclusion of M as covariate for

*V*_{c} in the MLEM algorithm of ADAPT improved the two-compartment model. The AIC score was −91.98, the BIC score 12.67, and −2LL is −165.98; all were an improvement over the base models scores in .

*V*_{c} and M were related as follows:

*V*_{c} = 4.2(M/53.6)

^{3/4} liters, with a total clearance of 0.506 ± 0.221 liters/h, intercompartmental clearance of 0.242 ± 0.231 liters/h, and a

*V*_{p} of 4.51 ± 5.90 liters.

On the other hand, while the log-log slope of plot for M versus

*V*_{p} significantly differed from zero, the slope was 1.67 ± 0.78 (). We were interested in determining whether this was a reflection of some

*b*/4 power laws that have been used to scale the relationship between M and various physiological functions (

17–

19). In this case, given the large standard deviation, the values encompassed include 4/4, 5/4, 6/4, 7/4, and 8/4; they just miss encompassing 3/4. We examined M as a covariate of

*V*_{p} for M raised to either 3/4, 4/4, 5/4, 6/4, or 7/4 in ADAPT and compared these models to the base model using several information criteria. All led to worse scores than the base model, except the 6/4 power model (i.e., a 3/2 exponent), which improved the AIC score to −99.75, BIC to 4.89, and −2LL to −173.75. The relative likelihood that the M

^{3/2} covariate led to an improved model compared to the base model was 33,076. Thus, scaling using the 3/2 power law markedly improved the scores over those of the base model in . The relationship between

*V*_{p} and M was as follows:

*V*_{p} = 2.53(M/53.6)

^{6/4} liters.

Next, based on our results with micafungin in which systemic clearance changed with weight only above 66.3 kg, we examined the relationship between weight and pharmacokinetic parameters only in the 14 patients with higher weights than this. Scatter plots demonstrated that slopes differed significantly from zero for *V*_{p} and *V*_{c}; however the slopes were identical to those of the entire data set of 18 patients, as discussed above. However, in this subset of patients, weight was now significantly associated with both SCL and intercompartmental clearance (). The slope for the intercompartmental clearance was negative and the inverse of 3/2. However, the standard deviations were large, likely due to the diminished sample size when leaner patients were excluded. We then examined inclusion of M^{3/4} as a covariate for SCL and compared information criterion scores to those of a base model derived for the 14 patients. This was followed by inclusion of M^{−3/2} as a covariate for intercompartmental clearance. Scores are shown in , which demonstrates that the model improved with inclusion of M as a covariate. Moreover, the BIC score, which penalizes for more complexity of the model, also improved (), which means that the improved model performance was not due merely to an increased number of parameters.

| **Table 4**Effect of weight as a covariate using different quarter power laws |

If it is true that there is an increased central volume with increase in M, then one would expect there to be a decrease in observed (or measured) peak concentration, since peak is inversely proportional to the volume of distribution. demonstrates that indeed the relationship between observed caspofungin peak concentration and M was characterized by a slope of −0.15 ± 0.03, which deviated significantly from zero (*P* < 0.001), with an *r*^{2} of 0.63. Similarly, if SCL truly increases at higher M, then the observed areas under the concentration-time curve (AUCs) will decrease as M increases. demonstrates that the observed 72-h AUC, as calculated by the trapezoidal rule, indeed decreases as M increases, with a slope of −1.48 ± 0.47 (*r*^{2} = 0.40) which differed significantly from zero (*P* = 0.007). Thus, the observed (and not model-derived) concentrations confirm that AUC and decreases as M increases, consistent with the population pharmacokinetic modeling results.