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Modeling of FVIII activity, bleeds and covariates
the estimated individual PK parameters and recorded dose infor- mation 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 sponta- neous bleeds from the studies LEOPOLD I and II to characterize the joint bleeding patterns in patients aged 12 years or older.
Covariate analysis
The correlation between covariates (patient and study charac- teristics), 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 impu- tation 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 avail- able; this covariate was, therefore, tested for the first time in this analysis. Relevant parameter-covariate relationships were identi- fied by the correlation coefficient (r), uncertainty of the effect size, and scientific plausibility.
Results
Patients and data
The final analysis included 1,535 FVIII activity observa- tions 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 bleed- ing 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 tar- get joint at study start, and receiving prophylactic treat- ment 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 infor- mation by age cohort is available in the Online Supplementary Appendix).
Population pharmacokinetic model
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 (DOFV=-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.
Repeated time-to-categorical bleed model
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; DOFV=-146), with full inhibition for high FVIII activity values. An exponential effect performed almost as well (DOFV=-133), while a linear relationship performed substantially worse (DOFV=-23). The final hazard equa- tion was given by:
where h(t) is the time-varying bleeding hazard, λ and γ
are the scale and shape factors of the Gompertz distribu-
tion, FVIII(t) is the individual PK model-predicted FVIII
activity at time t, IF50 is the FVIII activity resulting in half-
maximum inhibition of the hazard, and η is a log-normal-
ly distributed random effect describing the unexplained
inter-individual variability of the bleeding hazard in the
population. Instead of representing the bleeding hazard
when FVIII activity in plasma is zero, λ and IF50 were re-
parametrized to represent the bleeding hazard when plas-
mλ a FVIII activity was 0.5 IU/dL and 20 IU/dL (λ
0.5IU/dL and
20IU/dL, respectively) one year after study start. The assess- ment of a time dependency between consecutive bleeds, given by a transient effect where the occurrence of a bleed changed the bleeding hazard of a new bleed, could not be identified (P>0.05 for Markov component). The estimated probability of a bleed during the study to be mild, moder- ate or severe was 39.6, 55.7 and 4.72%, respectively.
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 bleed- ing hazard as well as the IF50 parameter decreased, reflecting less frequent events and higher potency for the replacement therapy, respectively.
Covariate analysis
The estimated correlations between the model parame- ters (CL, V1, PK residual error, bleeding hazard and bleed- ing 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
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