Population repeated time‐to‐event analysis of exacerbations in asthma patients: A novel approach for predicting asthma exacerbations based on biomarkers, spirometry, and diaries/questionnaires (2024)

Patient data and study design

The analysis dataset consisted of all subjects randomized in the Zenyatta study, a double‐blind, placebo‐controlled fixed‐dose phase IIb study of astegolimab in patients with uncontrolled severe asthma (GB39242, clinicaltrials.gov identifier: NCT02918019).16 Patients were on inhaled corticosteroid therapy (≥500µg fluticasone propionate or equivalent) plus greater than or equal to 1 additional controller medication. Patients were required to have a history of greater than or equal to 1 asthma exacerbation within 12months prior to screening. The study was approved by an ethics committee or institutional review board at each trial site and carried out in accordance with the International Conference on Harmonization Guideline for Good Clinical Practice. Informed consent was obtained from all subjects.

Data from 502 patients with asthma, randomized to subcutaneously administered placebo (n=127) or astegolimab as 70mg (n=127), 210mg (n=126) or 490mg (n=122) every 4weeks for 52weeks, were included in the analysis. Visits were scheduled on weeks 2, 4, and then every 4 weeks until week 52. Note that one single‐blind dose of placebo started at run‐in period (2 weeks prior to randomization). In this work, start of the randomized treatment period is used as the reference timepoint. The study recorded asthma exacerbations which could occur repeatedly, on any day, except that a new exacerbation could not occur until after the previous event had ended. Start of exacerbation events was the dependent variable for the present analysis, ignoring event duration. The data were censored at the end of the randomized treatment period at the individual patient level. An asthma exacerbation was defined as new or increased asthma symptoms that resulted in either hospitalization or an emergency department visit with administration of systemic corticosteroid treatment or treatment with systemic corticosteroids for greater than or equal to 3days or a long‐acting depot corticosteroid preparation with a therapeutic effectiveness of greater than or equal to 3days. Several biomarkers, spirometry, and diaries/questionnaires were measured throughout the study, of which 20 were explored as baseline covariates (Table1) and nine as time‐varying covariates (Table2). In addition to these covariates, astegolimab trough concentration (C_trough) was derived using the tabular output from a two‐compartment population pharmacokinetic model, developed on the same patients (data on file). If the time since the last dose greater than or equal to 56days, then C_trough was set to a half of lower limit of quantification (LLOQ/2; LLOQ = 0.15µg/ml), which was relevant after missing two consecutive planned doses (occurred for 2.9% of patients on active treatment). Because the tabular output did not include predictions for observations below LLOQ, imputation by LLOQ/2 required less effort than predicting actual values and was considered fit‐for‐purpose.

Graphical exploration

An exploratory graphical analysis was performed to guide model development, including Kaplan–Meier plots of time‐to‐first, second, and third exacerbations (data on file). Changes in time‐varying covariates versus time until next exacerbation were also plotted, in patients with greater than or equal to 1 exacerbation. Trends were assessed using smooths including 95% confidence intervals (CIs).

Model development

Model development started by exploring different baseline hazard parameterizations, including time‐varying Weibull and Gompertz distributions (based on time since randomization), and an exponential (constant hazard) distribution. These models were re‐investigated on the final model. Interindividual variability (IIV) was explored on the hazard as log‐normal and Box‐Cox distributions. Dropout modeling was not performed (dropout was <10%).

A baseline‐covariate analysis was performed using Full Random Effects Modeling (FREM),17, 18, 19 including 20 covariates (Table1). Baseline covariates were entered into the dataset as observed variables, and their distributions were modeled as random effects. A full covariance matrix between random effects for parameters and covariates was estimated together with the other model components.

After FREM, a visit‐effect was investigated by exploring a difference in the hazard when approaching (or getting past) the planned time of a visit compared to in‐between visits. An “outpatient time ratio” (RATOUT, Equation 1) was derived, ranging between 0 and 1, and tested as a covariate. Zero signifies the beginning of an outpatient period (defined as 0.8days after finishing a planned visit) and 1means on‐going visit, or overdue for a visit. RATOUT was defined as:

where TSLV is the time since last visit and TUNV is the time until the next planned visit. RATOUT was set to 1 until 0.8days after a visit, ensuring that RATOUT = 1 for exacerbations occurring on the same date as an actual visit. The visit‐effect was included on the hazard through ROCOV, according to Equations 2 and 3:

where t_exac is the time since most recent exacerbation, θ_RO is the coefficient for the visit‐effect, and h(…) is a placeholder for other components of the model (e.g., baseline hazard and time‐varying covariates). This led to higher hazards when RATOUT > 0.9. This implementation converts the time between visits into a relative variable applicable regardless of the interval between visits (which varied throughout the study). The model included an 8‐day delay to implement a convention of phase III trials (e.g., refs. 8, 11) where exacerbations less than or equal to 7days apart are treated as a single exacerbation, and adding 1day which was considered the minimum duration between exacerbations. Note that for the Zenyatta study, there was no defined minimum duration between two exacerbations (but the shortest observed interval between exacerbation events were 10days).

Subsequently, a stepwise covariate model (SCM) building procedure20, 21, 22 was performed for the nine exploratory time‐varying covariates (Table2) included in the dataset as the difference from baseline, ratio versus (of) baseline or log‐ratio versus baseline, based on the observed data. The dataset was discretized into 3–4day intervals. The variables collected daily were explored as the average in each interval. If time‐varying covariates were unavailable at a given timepoint, last observation carry forward was applied. If the corresponding baseline value was missing (Table1 reports missingness), the time‐varying covariate was imputed with the median change for placebo. In the first stage, the nine potentially useful covariates were investigated (forward inclusion) and included into the model one‐by‐one, based on a significance level of p<0.01. In the second stage, included covariates were formally tested by removal from the model (backward elimination) where covariates were retained only if they were significant at p<0.001. The time‐varying covariate‐parameter relationships were implemented as linear models, according to Equation 4:

where Cov_m,ij is the individual change in covariate m, for subject i at time‐point t_j. Cov_m,ref is a reference covariate value for covariate m, around which the covariate was centered: the median change in placebo patients, at 6months. The θ_m is the coefficient for covariate m. The sum of the contribution of the selected time‐varying covariates (RESP_ij) was included on the hazard, h, on the log‐hazard scale according to Equation 5:

where h(…) is a placeholder for other functions on the hazard.

Following SCM, model finalizations were performed. This included exposure‐response evaluation based on time‐varying C_trough. This was performed after inclusion of significant covariates among the nine covariates tested in the SCM. Exposure was included through RESP_Exp on the log‐hazard ratio scale as in Equation 6:

where θ_Exp is the change in hazard for C_troughgreater than or equal to 0.15µg/ml (LLOQ). Linear and log‐linear exposure‐response models were also tested.

A Markov element was investigated to describe the lower hazard during the weeks/days after onset of an asthma exacerbation event, defined by a time‐dependent return to the baseline hazard according to Equation 7:

where t_{½, Markov} is a half‐life for the recovery of the hazard and t_lag is a lag‐time of 7days. Note that with t_lag set to 7days, the hazard starts well above zero as soon as the 8‐day delay period following an exacerbation has passed.

Sensitivity analyses

Sensitivity analyses were performed to assess the robustness of the final model. These included investigation of exposure‐response prior to performing an SCM, and performing an SCM only on the placebo subjects.

Model selection and evaluation

Models were selected based on differences in the objective function value (dOFV) where for a more complicated model to be retained it generally had to provide a significant improvement over the contending model (p<0.05 [dOFV=−3.84], whereas for the SCM for time‐varying covariates, a stricter value of p<0.001 [dOFV=−10.83] was used, to compensate for type I error inflation). The final model was evaluated using Kaplan–Meier visual predictive checks (VPCs) for time‐to‐first, second, and third exacerbations, and using posterior predictive checks (PPCs) for the weighted average exacerbation rate (total exacerbations/total duration of follow‐up in the randomized treatment period, per treatment arm). Parameter uncertainties were assessed using the covariance step in NONMEM (using MATRIX=R).

Software details

The analysis was performed using NONMEM 7.3.0,23 using Monte Carlo importance sampling for estimation. Plotting and processing of NONMEM output were performed using R 3.5.3.24 VPCs, FREM, and SCM were run using PsN 4.9.0.20, 21 Xpose 4.6.0 was used as an aid in model assessment.25

Graphical exploration

The graphical exploration for changes in time‐varying covariates versus time until next exacerbation suggests that peak expiratory flow (PEF), diary‐based symptom score, rescue medication use, nighttime awakenings, and FEV1 had relevant trends 10–20days prior to an exacerbation event (Figure1). However, note that the CIs should be interpreted with caution because some subjects contributed several data points.

Model development

The final model included a Weibull parameterization for the baseline hazard. The shape parameter was positive, indicating an increase in hazard over time (on top of changes from time‐varying covariates). A Markovian element of lower hazard following an exacerbation was included, with a time‐dependent return to the baseline hazard. A visit‐effect predicted higher hazard just prior to and during visits or when overdue for a visit. The influence on the hazard from the baseline covariates are visualized in Figure2; baseline symptom score and history of asthma exacerbations were most influential. Symptom score, short‐acting rescue medication use, and FEV1 were selected as time‐varying covariates. Exposure was included as a step function, although not significant at p<0.05 but was included given the limited size of the dataset and the magnitude of the point estimate of reduction in hazard (28%).

A visit‐effect in the hazard was significant (dOFV=−13.2), predicting 90% higher hazard just prior to and during visits and when overdue for a visit. The predicted increase in hazard was similar both before and after including time‐varying covariates, and was present also in subjects randomized to placebo (FigureS1). The cutoff‐value 0.9 in Equation 3 was motivated by the graphical exploration, showing that exacerbations occurred more frequently at RATOUT>0.9 (FigureS1).

In the SCM, the diary‐based symptom score (dOFV=−83.7) and short‐acting rescue medication use (dOFV=−33.5) were selected. Both coefficients were positive, yielding higher hazard when these variables increased (i.e., worsening of asthma). Finally, FEV1 was selected (dOFV=−14.9) with a negative coefficient, predicting reduced hazard following FEV1 improvement. PEF met forward inclusion criteria (p=0.0087) but was eliminated in the backward step (i.e., 0.001<p<0.01).

Because time‐varying covariates captured majority of the drug‐exposure effect, after the time‐varying covariates were included, exposure was not statistically significant (p>0.05, dOFV=−2.1) but was included anyway. This conservative measure made the model specific for astegolimab treatment, which should be considered when using this model to predict asthma exacerbations for other treatments. Exposure could not be determined as clinically irrelevant, given the effect size of 28% reduction in hazard. A step function described the data better than linear or log‐linear exposure‐response relationships. The Markovian element was significant (dOFV=−13.7) and improved VPCs for time‐to‐second and third exacerbations (Figures S2andS3, respectively). The final model included a log‐normally distributed IIV in the hazard. A Box‐Cox transformation was not statistically significant (p>0.05, dOFV=−3.47). Example NONMEM code for the final model (ExampleNONMEMCode) is provided as a supplementary material.

Sensitivity analyses

Including exposure prior to inclusion of time‐varying covariates was statistically significant (p<0.01, dOFV=−7.84, performed as a sensitivity analysis), which is consistent with the treatment effect of asthma exacerbation rate reduction in the Zenyatta study.16 An SCM performed on placebo subjects only (sensitivity analysis) selected the same three time‐varying covariates (at p<0.05), as in the SCM described above (based on all subjects in Zenyatta). The time‐varying covariate coefficients were comparable to those of the final model (TableS1).

Model evaluation

The final model described the observed data well according to a VPC for time‐to‐first exacerbation (Figure3), as well as the time‐to‐second and third exacerbations (Figures S2andS3, respectively). A PPC showed that the difference in exacerbation rates for active treatment arms versus placebo were well predicted (Figure4). Importantly, the model correctly predicted the ranking among the treatment arms (i.e., the model captured the observed trend of higher exacerbation rate for the 210‐mg arm than for both the 70‐mg and 490‐mg arms).

The parameters were estimated with reasonable precision (Table3), however, the exposure‐response step effect parameter (θ_E‐R,step) had a quite large RSE of 59%, which is not surprising because it was not statistically significant after inclusion of time‐varying covariates.

Figures S1‐S3

Table S1

ExampleNONMEMCode

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Supplementary Materials