The final data set included 246 patients, who contributed 2455 busulfan concentration–time points from 568 busulfan administrations, summarized in Table 1. Patients were treated according to several conditioning regimens: busulfan/clofarabine/fludarabine (14% of patients), busulfan/fludarabine/cyclophosphamide, busulfan/fludarabine/thiotepa, or busulfan/melphalan. A more precise breakdown of conditioning regimens was not available in the data. Following the recent implementation of Bayesian forecasting software, standard practice at UCSF is to collect four samples per dosing interval (77% of dosing intervals); more densely sampled intervals were relatively rare (16% of intervals had six or more samples collected).

The mean AUC estimated per dosing interval across all methods was 15.0 mg⋅h/L, and the four methods of AUC estimation showed good agreement in their estimation, as assessed by Bland–Altman plots (standard deviation of differences (SD) of 0.44–1.83 mg⋅h/L (i.e., 3–12% of mean AUC); Fig. 2a) and by correlation in estimates (correlation coefficients of 0.945–0.998; Fig. 2b). The two NCA methods showed the closest agreement (mean difference in AUC estimation of 0.53 mg⋅h/L, SD of 0.44 mg⋅h/L, and correlation coefficient of 0.998), which is to be expected since these methods differ only in how they estimate the shape of the concentration–time curve up until the time of the first sample collection. NCA with peak extension will always be higher than NCA without peak extension (see Fig. 1), explaining the bias observable in the Bland–Altman plot. The two PK models also showed close agreement (mean difference of 0.15 mg⋅h/L, SD of 0.96 mg⋅h/L, correlation coefficient of 0.985), suggesting that the two models arrive at similar PK parameter estimates despite differences in model structure and inter-individual variability. When comparing MAP estimates to NCA approaches, agreement was better for the first dosing interval (mean difference of 0.8–1.96, SD of 0.61–1.34, correlation of 0.982–0.994), but lower for subsequent dosing intervals (mean difference of 0.99–2.0, SD of 1.85–2.12, correlation of 0.918–0.938), with NCA methods consistently estimating lower exposures than MAP methods.

Agreement between AUC estimation methods. a Bland–Altman plots showing agreement between AUC estimation approaches. Each point representsan AUC estimate made by the corresponding method for a single dosing interval. Dashed lines indicate mean difference and the limits of agreement (mean difference ± 1.96 standard deviations). b Correlation coefficient describing correlation between AUC estimates for each dosing interval. NCA: non-compartmental analysis. MAP: maximum a posteriori estimation with either the one-compartment Shukla model (1cmt) or the two-compartment McCune (2cmt) methods on real patient data

In the simulated treatment courses, since initial dosing was weight-based, the first dose was the same for both the NCA and MAP arms. AUC estimates arising from the first dose across the full dosing interval varied by estimation method (Fig. 3a). The mean AUC estimated by NCA was 17.6 mg⋅h /L while the mean AUC estimated by MAP was 18.3 mg⋅h/L, compared to a true mean AUC of 19.7 mg⋅h /L. However, the majority of the variation arose from differences in AUC estimation during infusion: the mean AUC during infusion was 4.97 mg⋅h /L for NCA and 5.93 mg⋅h /L for MAP compared to 7.02 mg⋅h/L true AUC. In contrast, AUC estimates after infusion were similar (NCA: 12.6 mg⋅h/L, MAP: 12.3 mg⋅h/L, true: 12.7 mg⋅h/L). This trend was true for later dosing intervals too, with NCA underestimating AUC by 28% during infusion and 0.4% after infusion, and MAP underestimating AUC by 13% during infusion and 1.31% after infusion (Fig. 3b). (The differences in estimated and true AUC have been expressed as proportions and not in absolute AUC values as they cannot be compared between methods after dose adaptation has been performed.) That the two-compartment model (designated the true AUC in this experimental design) produces a higher AUC than the one-compartment model and the NCA method is consistent with the sharp peak visible in Fig. 1.

Differences between non-compartmental analysis (NCA) and maximum a posteriori Bayesian estimation (MAP) in AUC estimation and dose adjustment in a simulated trial. a AUC estimated following the first weight-based dose during infusion (t = 0–3 h), after infusion (t = 3–24 h), or across the full first dosing interval (t = 0–24 h). b Ratio of estimated AUC to true AUC across dosing intervals. c Doses selected by dosing interval, normalized to the initial dose to account for body-size dependence in doses. d AUC by dosing interval using NCA estimates for dose adjustment. e AUC by dosing interval using MAP for dose adjustment. Shaded grey region indicates a target AUC of 22.5 mg⋅h/L per day ± 15%. Concentration–time curves were simulated with the McCune model (true AUC) and estimated with NCA or with MAP using the Shukla model. Samples were collected at 3.25, 4, 6, and 8 h after the start of infusion. Boxplot indicates the median (bold line), 25th-75th percentiles (outer rectangle) and 1.5 × the interquartile range from the 25th-75th percentiles (whiskers)

Following the first dose, subsequent doses were adjusted based on AUC estimates to attain a cAUC of 90 mg⋅h/L (Fig. 3c, expressed normalized to the initial dose to control for differences in patient weight). The weight-based starting dose of 3.2 mg/kg per day, which is more aggressive than the FDA label recommendation of 3.2 mg per kilogram adjusted body weight (the minimum of IBW and total body weight) divided over four doses, led to underexposure during this first dosing interval (Fig. 3d, e). Both estimation methods correctly identified this underexposure and increased dosing accordingly. However, the value of the second dose greatly varied between the two methods (Fig. 3c): the second dose was on average 63% higher than the first dose for NCA, and 28% higher than the first dose for MAP (paired t-test comparing NCA versus MAP: p-value < 0.0001). In part, this difference is related to how the PK models describe clearance over time. Busulfan clearance is reported to decrease over time [5, 6, 15], and both PK models incorporate this change in clearance. In the McCune model, clearance decreases by 6.8% after 6 h of therapy and by 8.1% after 36 h of therapy relative to initial clearance, while in the Shukla model, clearance decreases by 13.5% after 24 h of therapy. In contrast, NCA does not incorporate time-dependent changes in clearance. As a result, this method overpredicted busulfan clearance on day 2 of therapy, resulting in too high of a dose and too high an exposure (Fig. 3c–d). To balance out this overexposure, doses and exposures for day 3 and day 4 were, on average, lower. Because the Shukla model expects a larger decrease in clearance from day 1 to day 2 than described in the model used for simulation (McCune), it resulted in a smaller dose than necessary to make up the underexposure from day 1, and as a result, doses and exposures were higher for day 3 and day 4 (Fig. 3c,e).

The variation in dose recommendations and estimated AUC was substantially narrower in MAP-guided dose adjustment, consistent with prior prospective trials [5]. MAP-guided dose adjustment also led to less variation in true AUC (Fig. 3d–e).

Attainment of the cAUC target also varied by estimation method. Simulated patients were deemed “on target” if their cumulative exposure was within 15% of the target cAUC of 90 mg⋅h /L. For both estimation methods, estimated target attainment following all four doses was high: 98.7% for NCA and 99.9% for MAP (Fig. 4 and Table 2, “4 samples”). However, both methods overestimated target attainment compared to true target attainment. This misestimation was considerably larger for NCA (65.0% true target attainment) than for MAP (92.1% true target attainment). Variability in estimated cAUC was higher for simulated patients dosed using NCA (standard deviation: 4.5 mg⋅h/L) compared to MAP (standard deviation: 3.3 mg⋅h/L), consistent with findings in real patients [5]. True variability was higher than estimated variability in both methods (standard deviation, NCA: 7.6 mg⋅h/L; MAP: 5.7 mg⋅h/L).

Cumulative AUC target attainment in a simulation study using either non-compartmental analysis (NCA) or maximum a posteriori Bayesian estimation (MAP) to estimate AUC and personalize doses. a True AUC versus estimated AUC by method, with shaded regions indicating the target AUC (90 mg⋅h/L) ± 15%. b Percentage of simulated patients achieving a true cumulative AUC within 15% of the target

This simulated trial used the sampling strategy that is standard practice at UCSF. Increasing the number of samples to five samples per interval (collected at sample times described by Yeh et al. [16]) to include a final sample at 11 h improved true target attainment slightly for both estimation methods (Supplementary Fig. 1 and Table 2, “5 samples”. NCA: 66.2%, MAP: 93%). Reducing the samples per interval to three did not adversely impact true AUC estimation when the final sample at 8 h was retained but did lead to lower true target attainment when the final sample was at 6 h (Supplementary Fig. 1 and Table 2). Because the McCune model has two compartments, this later time point is likely quite informative for estimating clearance during the elimination phase. This model also includes mid-interval changes in clearance (at 6 and 36 h after the first dose), and so later collection points (samples at 8 h, 11 h) would also allow better capture of these dynamics.

Interestingly, increasing sample density to every 30 min starting 15 min after the end of infusion did not substantially improve true target attainment (Supplementary Fig. 1 and Table 2, “dense, post-infusion”: NCA: 67.6%, MAP: 91.3%). Hypothesizing that this difference between NCA and model-based AUC may be due to mis-estimations of AUC during infusion (Fig. 3a–b), we repeated this experiment with samples during infusion and observed a marked increase in target attainment for both estimation strategies (Supplementary Fig. 1 and Table 2, “dense, full interval”: NCA: 97.3%, MAP 96.6%).

In the real-world data, NCA and MAP showed greater disagreement after the first dosing interval (Fig. 2). Hypothesizing that this difference was because NCA uses samples only from the most recent dosing interval while MAP can leverage all samples collected to-date, we lastly assessed the impact of using MAP with only samples from the most recent dosing interval (Supplementary Fig. 2). Overall, the difference in error in estimating true AUC was relatively minor, dropping to a mean absolute percent error of 6.1% when only samples from the most recent interval were used compared to 5.8% in standard MAP. This difference in estimation error resulted in a decrease in true target attainment to 90.3%, a reduction of 1.8 percentage points.