Pharmacokinetic-based prophylaxis of replacement factor VIII (FVIII) products has been encouraged in recent years, but the relationship between exposure (factor VIII activity) and response (bleeding frequency) remains unclear. The aim of this study was to characterize the relationship between FVIII dose, plasma FVIII activity, and bleeding patterns and individual characteristics in severe hemophilia A patients. Pooled pharmacokinetic and bleeding data during prophylactic treatment with BAY 81-8973 (octocog alfa) were obtained from the three LEOPOLD trials. The population pharmacokinetics of FVIII activity and longitudinal bleeding frequency, as well as bleeding severity, were described using non-linear mixed effects modeling in NONMEM. In total, 183 patients [median age 22 years (range, 1-61); weight 60 kg (11-124)] contributed with 1,535 plasma FVIII activity observations, 633 bleeds and 11 patient/study characteristics [median observation period 12 months (3.1-13.1)]. A parametric repeated time-to-categorical bleed model, guided by plasma FVIII activity from a 2-compartment population pharmacokinetic model, described the time to the occurrence of bleeds and their severity. Bleeding probability decreased with time of study, and a bleed was not found to affect the time of the next bleed. Several covariate effects were identified, including the bleeding history in the 12-month pre-study period increasing the bleeding hazard. However, unexplained inter-patient variability in the phenotypic bleeding pattern remained large (111%CV). Further studies to translate the model into a tool for dose individualization that considers the individual bleeding risk are required. Research was based on a post-hoc analysis of the LEOPOLD studies registered at clinicaltrials.gov identifiers: 01029340, 01233258 and 01311648.
Hemophilia A is an X-linked hereditary bleeding disorder caused by the deficiency of coagulation factor VIII (FVIII). The severity of the disease is inversely correlated with the amount of factor that an individual is able to produce, and nearly half of the cases correspond to the severe laboratory phenotype (endogenous plasma FVIII activity levels <1 IU/dL).1,2 Prophylaxis with FVIII concentrates is currently considered the treatment of choice to decrease the frequency of bleeding and preserve musculoskeletal function.3–5 The population pharmacokinetics (PK) of FVIII products has been extensively studied, and it has been seen that the elimination half-life varies substantially between patients.6,7 Thus, the individual disposition of FVIII cannot be adequately predicted by average PK parameters and demographic characteristics, and PK-based dosing has been encouraged to optimize dosing regimens in the prophylactic setting.8–10 In brief, PK-based dosing relies on Bayesian estimation to estimate the individual PK parameters by combining patient information (dose, FVIII activity measurements and demographic characteristics, e.g. age, body weight) with information previously collected from a patient population by means of a population PK model.11,12 Based on the estimated individual PK parameters, a patient-specific dosing regimen can be suggested.13 Recently, the shift from standard prophylaxis to PK-based prophylaxis was facilitated by the development of dosing tools, which are hemophilia-specific for one (e.g. my PKFit, Shire Pharmaceutical Holdings Ireland Limited, Dublin, Ireland; www.mypkfit.com) or multiple (WAPPS-Hemo, McMaster University, Hamilton, Ontario, Canada, www.wapps-hemo.org) FVIII products, or generic tools (e.g. DoseMe LLC, Taringa Qld, Australia; www.doseme-rx.com; InsightRX Inc., San Francisco, CA, USA, www.insight-rx.com), which also support drugs from other clinical areas.14
The choice of individual dosing regimens in PK-based prophylaxis is based on information about the individual PK, but is also based on other components such as the patient’s bleeding pattern, joint status or physical activity. From a PK perspective, the dose and dosing interval that generates an individual trough plasma FVIII activity above a certain target level, traditionally 1 IU/dL, is selected.1,15 However, even though this level was not supposed to be an end in itself,16 but rather an orientation, until recently it was the main target used to build prophylaxis regimens. Several studies showed that some patients still bleed with higher trough values, while others do not bleed despite having trough values below 1 IU/dL, suggesting that a “one-target-fits-all” strategy is not appropriate.16–22 Other measures of target FVIII exposure have been associated with bleeding,23 and different target levels for different patients that take into consideration individual lifestyle were recently suggested.24
One of the most important clinical endpoints to assess efficacy in hemophilia is bleeding frequency. This is often reported as the absolute number of bleeds during the study duration or annualized bleeding rate with the respective dispersion (e.g. range or standard deviation).25 Whereas these bleeding outcome measures may be useful to report efficacy, they are not adequate to study predictors of bleeding as they do not account for complex aspects, such as individual differences in FVIII disposition or bleeding phenotype, or time-varying factors, such as changes in dosing regimens or bleeding patterns. However, using an integrated model-based analysis overcomes these limitations. Repeated time-to-event modeling, an extension of parametric time-to-event survival analysis using non-linear mixed effects modeling, accounts for the occurrence of multiple events (e.g. bleeds) within an individual.26,27 This methodology enables the characterization of time-varying patterns in the occurrence of events (e.g. bleeding patterns changing over time) or predictors of events (e.g. FVIII activity) and has successfully been applied to several clinical areas, e.g. to describe the analgesic consumption in postoperative pain,28 or the time to the occurrence of epileptic seizures.29 This technique can be further extended to capture how consecutive events may be related to each other (Markovian dependence), or to include the severity of the events [repeated time-to-categorical event (RTTCE) modeling].30
To better understand the link between prophylactic FVIII replacement therapy and bleeding patterns in patients with severe hemophilia A, the aim of this study was to characterize the relationship between FVIII doses, FVIII activity in plasma, and the occurrence of bleeds, as well as bleeding severity (mild, moderate or severe).
For a detailed description of the methods used, see the Online Supplementary Appendix.
This post-hoc analysis was based on dosing, PK, bleeding and patient characteristics data obtained from the three LEOPOLD trials (LEOPOLD I clinicaltrials.gov identifier: 01029340, LEOPOLD II clinicaltrials.gov identifier: 01233258 and LEOPOLD kids clinicaltrials.gov identifier: 01311648),31–33 evaluating efficacy, safety and PK of a full-length recombinant human FVIII product, BAY 81-8973 (octocog alfa, Kovaltry®),34 in severe hemophilia A (endogenous FVIII activity <1 IU/dL) patients. Previously treated patients with no history of FVIII inhibitors, receiving on-demand or prophylactic treatment at screening, aged 12-64 years (LEOPOLD I and II) and ≤12 years (LEOPOLD kids) were included. Single doses of 50 IU/kg or 20-50 IU/kg 2-3 times/week (LEOPOLD I), 20-40 IU/kg 2-3 times/week (LEOPOLD II), and 25-50 IU/kg at least 2 times/week (LEOPOLD kids) were administered. The study protocols were reviewed and approved by each site’s independent ethics committee or institutional review board.
Factor VIII activity was measured by the chromogenic assay. Bleeding episodes observed during prophylactic treatment were included in the analysis, which included spontaneous, trauma-related and untreated bleeds (i.e. bleeds not requiring FVIII infusions in addition to scheduled treatment), and unspecified events requiring FVIII treatment. Date and time of injection, and bleeding data (date, time, severity and location) were self-reported by the patient or caregiver using an electronic patient diary. A maximum of one bleed per calendar day was recorded, and spontaneous joint or muscle bleeds were not registered if occurring within 72 hours (h) of another bleed at the same site or respective infusion.
Model estimation was performed using non-linear mixed effects modeling in NONMEM® 220.127.116.11 The PK and RTTCE models were estimated simultaneously and covariates integrated afterwards. Model assessment was based on scientific plausibility, changes in the objective function value (OFV, −2·log-likelihood), goodness-of-fit plots and precision of parameter estimates. For nested models, the likelihood ratio test was used [difference in OFV (ΔOFV) >6.64 considered significant at =0.01, 1 d.f.].
The population PK analysis started from the model by Garmann et al. using the corresponding set of data.36 The included association between lean body weight (LBW) and clearance (CL) and central volume of distribution (V1) was retained given the wide age range of patients. The previous model assumptions were comprehensively assessed.
The probability density of each bleed, as well as the probability associated with each severity was estimated from the observed time of bleeding and severity score (mild, moderate, severe) using a combination of parametric survival analysis and proportional odds model for ordered categorical data,26,27,37,38 i.e. the RTTCE model.30 The distribution of time of bleeds was explored using exponential, Weibull and Gompertz hazard functions. Inter-individual variability was considered on the overall bleeding hazard and on the logit transform of the severity probability. The censoring time for bleeds was set at the end of the individual bleeding observation period (right-censored observation).
The influence of individual plasma FVIII activity predicted from the estimated individual PK parameters and recorded dose information was explored on the baseline hazard using either a linear, exponential or maximum inhibition (Imax) model. Furthermore, a time-dependency between consecutive bleeds was assessed with a Markov hazard rate through a function depending on the time since the previous bleed.
The final RTTCE model, developed based on data of all bleeds, was re-estimated including only data concerning joint spontaneous bleeds from the studies LEOPOLD I and II to characterize the joint bleeding patterns in patients aged 12 years or older.
The correlation between covariates (patient and study characteristics), PK, bleeding hazard (all bleeds), and bleeding severity were evaluated using full random effects modeling.39,40 This methodology allows the characterization of all model parameter-covariate relationships in a single step and does not require imputation of pre-defined values when covariate data are missing. The covariates explored were: age, body weight, body mass index, lean body weight, race, von Willebrand factor (vWF), number of bleeds in the 12-month pre-study period, previous therapy history, on-demand or prophylaxis treatment, number of target joints for bleeds at study start obtained from the case report forms, ratio of the number of bleeds in the 12-month pre-study period to the number of target joints for bleeds at study start and during the study. In the original PK model development,36 vWF was not available; this covariate was, therefore, tested for the first time in this analysis. Relevant parameter-covariate relationships were identified by the correlation coefficient (r), uncertainty of the effect size, and scientific plausibility.
The final analysis included 1,535 FVIII activity observations from 183 patients, 633 bleeds from 172 patients, and 11 covariates. The median bleeding observation period was approximately 12 months for LEOPOLD I and II, and six months for LEOPOLD kids. Eleven patients had PK observations available but did not contribute with bleeding information because either they only received on-demand treatment (n=5) or only participated in the PK part of the trial (n=6). The median patient was a 22-year old 60-kg white male, with a vWF level of 104%, one target joint at study start, and receiving prophylactic treatment before the study. In total, 116 patients (67% of total) had at least one bleed during the observation period (median 2, range 0-33), and the median time to first bleed was 48.2 days (range 14.5 hours-352 days). Descriptive statistics of study, patient characteristics and information on bleeding episodes are available in Table 1. (This information by age cohort is available in the Online Supplementary Appendix).
The PK component of the final model provided a good description of the PK data, similarly to the previously reported model.36 In addition to inter-individual variability on CL and V1, adding inter-individual variability on the residual error improved both model fit (ΔOFV=−199) and parameter precision. The median estimated individual CL was 1.80 dL/h (range 0.579-4.73 dL/h) and V1 was 29.5 dL (range 5.68-51.1 dL). The distribution of model-predicted plasma FVIII activity at the time of bleeding was strongly positively skewed with a median of 5.81 IU/dL (mean 11.6 IU/dL, range <1.50-140 IU/dL). The parameter estimates of the final model are available in Table 2.
A Gompertz hazard function with decreasing bleeding hazard over time provided an adequate description of the time-to-bleed data and was superior to the Weibull and exponential models. The effect of FVIII activity on the bleeding hazard was characterized by an Imax model (P<0.001; ΔOFV=−146), with full inhibition for high FVIII activity values. An exponential effect performed almost as well (ΔOFV=−133), while a linear relationship performed substantially worse (ΔOFV=−23). The final hazard equation was given by:
The observed Kaplan-Meier curves for the first three bleeding episodes and the 95% confidence interval (CI) of the model predictions, showing how well the model described the data, are presented in Figure 1, and the parameter estimates of the final model are available in Table 2. An additional model diagnostic plot is available in the Online Supplementary Appendix (Online Supplementary Figure S1).
The re-estimated model accounting for the spontaneous joint bleeding information only was found to describe the data well (Online Supplementary Figure S2 ), and the final parameter estimates are available in Table 3. As expected, when including only spontaneous joint bleeds, the bleeding hazard as well as the IF50 parameter decreased, reflecting less frequent events and higher potency for the replacement therapy, respectively.
The estimated correlations between the model parameters (CL, V1, PK residual error, bleeding hazard and bleeding severity including all bleeds) and the co-variates are illustrated in Figure 2. The strongest relationships found were: vWF on CL (r=−0.54; decreased unexplained inter-individual variability by 4.7%) and number of bleeds in the 12-month pre-study period on the bleeding hazard (r=0.45; decreased unexplained inter-individual variability by 15%). The effect of LBW on CL and V1 was included a priori in the PK structural model and the absence of a correlation between LBW on CL or V1 in the covariate analysis indicates that the relationship was well captured by the model. Other characteristics showed lower correlation coefficients, namely, Black race and Asian race decreasing and increasing CL (r=−0.25 and 0.17), respectively, and age and vWF being positively correlated to the severity of bleeding (r=0.23 and 0.28). In addition, correlations were identified between model parameters (e.g. CL and V1, r=0.45) and between covariates (e.g. treatment history and number of bleeds pre-study period, r=−0.71).
The effect sizes of the most relevant parameter-covariate interactions are shown in Figure 3. The number of bleeds in the 12-month pre-study period correlating with the bleeding hazard was the most relevant interaction found. Compared to a mean patient with 8.2 bleeds in the pre-study period, a patient who had one bleed (5th percentile of the observed data) or 84 bleeds (95th percentile) pre-study was found to have a 54% lower (95%CI: 40-65) or 147% higher (95%CI: 79-226) hazard, respectively. These values translate into a bleeding hazard (λ0.5 IU/dL) of 1.30 year−1 (95%CI: 0.99-1.68) (1 pre-study bleed), and 6.97 year−1 (95%CI: 5.05-9.18) (84 pre-study bleeds). von Willebrand factor levels and race were found to correlate with CL. A patient with a vWF level of 64% (5th percentile) or 179% (95th percentile) had an estimated CL of 2.30 dL/h (95%CI: 2.17-2.45; terminal half-life 11.6 h) and 1.59 dL/h (95%CI: 1.47-1.69; terminal half-life 16.5 h), respectively. Patients of Black race had an estimated CL of 1.41 dL/h (95%CI: 1.16-1.71), Asian 2.21 dL/h (95%CI: 1.97-2.48), and Caucasian 1.93 dL/h (95%CI:1.80-2.07). A modest correlation was identified between vWF and bleeding severity, with a patient with a vWF level of 64% having a probability of having a moderate or severe bleed of 57% (95%CI: 55-59), while the corresponding probability for a patient with a vWF level of 179% was 68% (95%CI: 62-75); a similar trend was found for age.
An illustration of the observed plasma FVIII activity and time-to-bleed data for three patients, and the respective model-based predictions are available in Figure 4.
The inclusion of all available covariates in the model resulted in a decrease of 25% in the inter-individual variability on the bleeding hazard, with a final unexplained inter-individual variability value of 111%. Figure 5 shows how this variability translates into bleeding frequency by using the model to simulate the occurrence of bleeds during one year in a group of virtual patients with median characteristics, following doses leading to a given plasma FVIII activity trough value: 1, 3, 5 and 15 IU/dL. Plasma FVIII activity-time profiles with higher trough values were linked to lower bleeding hazards, leading to an expected lower simulated bleeding frequency. The median cumulative number of simulated bleeds for the given dosing scenarios ranged between 0.745 (FVIII activity trough 15 IU/dL) and 2.73 (FVIII activity trough 1 IU/dL) bleeds, and the 90th percentile, representing the inter-patient variability on the bleeding hazard (underlying bleeding tendency), ranged between 3.00 and 11.2 bleeds.
We developed a comprehensive mathematical model describing the relation between the dose of a recombinant FVIII product, plasma FVIII activity, the bleeding outcome as well as severity and the correlation with covariates, following prophylactic treatment in patients with severe hemophilia A. To our knowledge, this is the first reported model characterization including longitudinal bleeding events for a replacement FVIII product. The model was based on observed data of plasma FVIII activity (PK component), bleeding time and severity (RTTCE component) and covariates, collected during the LEOPOLD studies. The final model satisfactorily described plasma FVIII activity and time- and PK-related probability of bleeding. Besides LBW (included a priori influencing CL and V1), vWF and race correlated with CL, number of bleeds in the 12-month pre-study period correlated with the bleeding hazard, and age and vWF affected the severity of bleeding. However, even after identifying these covariate effects, the unexplained inter-individual variability on the bleeding hazard was high.
The covariate analysis allowed the exhaustive assessment of the clinical relevance of the correlation between the covariates available and the model parameters. For PK, higher vWF levels were associated with a decreased FVIII CL; an expected finding since the complex FVIII-vWF is known to protect FVIII from proteolytic degradation.41 The impact was, however, modest, with the typical value of CL being 2.30 and 1.59 dL/h at vWF levels of 64% and 179% (5th and 95th percentiles). The magnitude of the vWF effect on CL is in agreement with results of other population PK studies.42,43 Interestingly, Black race was associated with a 27% (95%CI: 12-40) lower CL compared to Caucasians. A similar trend was previously identified for a B-domain deleted recombinant FVIII product,6 and might be in part due to higher vWF levels in Black race patients or other unknown factors.44 Moreover, Asian race had a 14.2% (95%CI: 2.0-28) higher CL compared to Caucasians. Such a trend had been identified during the previous development of the population PK model, but the relation was not retained due to lack to statistical significance.36 Due to the modest effect sizes, and the high uncertainty associated with the low number of patients of these races (Asian 31, Black 10), these correlations should be interpreted with caution.
The RTTCE component of the model describes the bleeding probability throughout the study period and the likelihood of that bleed to be mild, moderate or severe. The hazard function describes the distribution of bleeds in time, and represents the instantaneous risk of having a bleed per unit of time. Thus, the cumulative hazard gives the likely number of events in a given time interval. In this analysis, the hazard described a declining bleeding probability with time. The estimated lambda parameter (λ) represents the bleeding hazard at the end of the LEOPOLD I and II studies (1 year), and the shape parameter (γ) describes whether the hazard decreases, remains stable or increases with time. The bleeding hazard estimates for a typical patient at the end of the study were 2.7, 2.0 and 1.2 year-1 for the thresholds of 1, 5 and 15 IU/mL, reflecting the model-predicted annual bleeding rates of patients constantly at a trough value. For instance, a typical patient with a permanent level of 1 IU/dL would be expected to have approximately three bleeds per year, if he remained at the same hazard that was estimated at the end of the study. This numerical summary ignores protective effects against bleeds provided by higher levels and overall exposure, and therefore less bleeds would be expected in a real-world scenario. No additional correlations between PK and the bleeding hazard were found, besides the time-varying FVIII activity.
A time trend was identified in the hazard with a typical patient having 5.0 bleeds/year at the start of the study and 2.8 bleeds/year at the end (assuming a constant plasma FVIII activity of 0.5 IU/dL). The lower bleeding rate at the end of the study most likely captures a treatment effect, not explained by plasma FVIII activity, and can be a consequence of a normalization of the clotting system due to prophylactic treatment or a better adherence to treatment in a clinical trial setting. The number of bleeds in the 12-month pre-study period was found to be a strong predictor of the bleeding frequency. This finding can be explained by the individual-specific bleeding risk given, for example, by pre-existing joint disease and extent of joint damage, comorbidities or level of physical exercise.
The estimated unexplained inter-individual variability on the bleeding hazard was high (111%), representing the variability in the bleeding tendency not being explained by the time-varying plasma FVIII activity or other covariates. Figure 5 shows that even when virtual patients with identical characteristics had a plasma FVIII activity trough of 5 IU/dL, i.e. moderately above the common target of 1 IU/dL, the cumulative number of simulated bleeds was still highly variable at one year, with a median 1.53 bleeds, and 40% of the patients having 1.53 - 6.17 bleeds, and 10% having more than 6.17 bleeds. Such high variability agrees with the clinical observation that patients may respond differently to identical plasma FVIII activity values, thus requiring also individual FVIII trough target levels. Part of this variability may be explained by factors that are known to influence the bleeding tendency in severe hemophilia A patients but that were not available to our study, such as FVIII gene mutation type, or physical activity patterns.45,46 However, even though the magnitude of inter-patient variability potentially explained by missing co-variates is unknown, variability in a real-world scenario is still expected to be high due, for example, to lack of adherence to treatment, or unidentified hemostatic factors playing a role in the occurrence of bleeds.
This study has limitations. First, the LEOPOLD trials were not designed for the aims of this post-hoc analysis or to characterize the individual bleeding pattern. Information, for example, on pre-existing joint disease, comorbidities or level of physical exercise before and during the trials could have been useful to better characterize the bleeding patterns. Second, bleeds (occurrence and severity) and doses were self-reported, which may result in uncertainty of timing and occurrence of bleeds (although the data were reviewed and validated by study staff in an effort to reduce uncertainty). Third, patients without any bleeds (33% of those enrolled in the bleeding observation period) contributed with PK and co-variate information, but with little information to the characterization of the FVIII activity-bleeding hazard relationship. Finally, in the absence of data from on-demand treatment or placebo, we are not able to estimate a bleeding hazard corresponding to untreated patients. Thus, our results cannot be applied to treatment strategies other than prophylaxis.
The individual bleeding hazard estimated by the presented mathematical model is a numerical translation of the individual bleeding phenotype and may be used to further optimize the individualization of dosing regimens of replacement FVIII products. Using this model for dose individualization, a pre-defined FVIII activity target would not be required, in contrast to the current implementation of PK-based dosing. Instead, the full model would be employed using a Bayesian approach, with the estimation of the individual bleeding hazard in addition to the individual PK parameters. Thus, the individualized dose and dosing interval would be selected not only based on the individual pharmacokinetics, but also the individual bleeding risk. This implementation warrants further study; namely, to understand which information is required to allow a precise estimation of the individual bleeding risk and which target to aim for in the dose calculation.47
In conclusion, we have developed an integrated population PK and repeated time-to-categorical bleed model based on data from patients with severe hemophilia A following prophylactic treatment. This combined model characterizes the relationship between the dose of a recombinant FVIII product, plasma FVIII activity, the bleeding outcome, as well as severity and the correlation with covariates. In the future, this model may be used for dose-tailoring using covariate, PK and/or bleeding information. Such an application requires a detailed theoretical assessment as well as robust data on bleeding and other factors, such as lifestyle or comorbidities, with the final goal of suggesting a more effective individualized FVIII dose.
The authors would like to thank Gunnar Yngman for skillful assistance during the implementation of the full random effects modeling approach.