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Estimation of QT interval prolongation through model-averaging

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Abstract

The current method to analyze concentration-QT interval data, which is based on predictions conditional on a best model, fails to take into account the uncertainty of the model. Previous studies have suggested that failure to take into account model uncertainty using a best model approach can result in confidence intervals that are overly optimistic and may be too narrow. Theoretically, more realistic estimates are obtained using model-averaging where the overall point estimate and confidence interval are a weighted-average from a set of candidate models, the weights of which are equal to each model’s Akaike weight. Monte Carlo simulation was used to determine the degree of narrowness in the confidence interval for the degree of QT prolongation under a single ascending dose and thorough QT trial design. Results showed that model averaging performed as well as the best model approach under most conditions with no numeric advantage to using a model averaging approach. No difference was observed in the coverage of the confidence intervals when the best model and model averaging was done by AIC, AICc, or BIC, although in certain circumstances the coverage of the confidence interval themselves tended to be too narrow when using BIC. Modelers can continue to use the best model approach for concentration-QT modeling with confidence, although model averaging may offer more face validity, may be of value in cases where there is uncertainty or misspecification in the best model, and be more palatable to a non-technical reviewer than the best model approach.

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Authors and Affiliations

  1. Astellas, 1 Astellas Way, N2.184, Northbrook, IL, 60062, USA

    Peter L. Bonate

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Correspondence to Peter L. Bonate.

Electronic supplementary material

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10928_2017_9523_MOESM1_ESM.png

Supplemental Figure 1 Representative concentration-time profile for one simulation under the SAD study design. Each line is a single subject (PNG 1230 kb)

10928_2017_9523_MOESM2_ESM.png

Supplemental Figure 2 Representative concentration-time profile for one simulation under the TQT study design. Each line is a single subject (PNG 893 kb)

10928_2017_9523_MOESM3_ESM.png

Supplemental Figure 3 Representative concentration-ddQTcF profiles for five simulations under a SAD study design with a circadian baseline. Solid line is the linear regression fit to the data. Blue symbols were simulations where the slope of the concentration-ddQTcF interval was statistically significant (p<0.05) using standard Model 2 (PNG 1128 kb)

10928_2017_9523_MOESM4_ESM.png

Supplemental Figure 4 Representative concentration-ddQTcF profiles for five simulations under a TQT study design with a circadian baseline. Solid line is the linear regression fit to the data. Blue symbols were simulations where the slope of the concentration-ddQTcF interval was statistically significant (p<0.05) using standard Model 2 (PNG 1854 kb)

10928_2017_9523_MOESM5_ESM.png

Supplemental Figure 5 Stacked bar chart of best model selected for each level of slope stratified by information criterion used for model selection, study design, and baseline. For the TQT design, 9 sampling points were used in the chart (PNG 830 kb)

10928_2017_9523_MOESM6_ESM.png

Supplemental Figure 6 Shape of the drug effect profile as a function of concentration for Eq. (10) to (12) stratified by slope (PNG 641 kb)

10928_2017_9523_MOESM7_ESM.png

Supplemental Figure 7 Panel plot from Monte Carlo simulation of the ratio of the best model estimate to the MA approach for the TQT study design where the data generating model was noninclusive, the baseline was circadian, and using AICc as the selection metric. The median ratio in percent of the best model estimate to the model averaged estimate plotted as a function of the slope of the true slope parameter stratified by selection criteria, different levels of Cmax (200, 500, 1000, and 2000 ng/mL), and different sampling schemes (5, 9, and 13 data points). Plotted are the mean, upper 2-sided 90% CI, and CI range. A value of 100% implies no difference between estimates. Legend: open blue circle, point estimate; dark red plus, CI range; green cross, upper confidence interval (PNG 884 kb)

10928_2017_9523_MOESM8_ESM.png

Supplemental Figure 8 Panel plot from Monte Carlo simulation of the ratio of the best model estimate to the MA approach for the TQT study design where the data generating model was noninclusive, the baseline was circadian, and using BIC as the selection metric. The median ratio in percent of the best model estimate to the model averaged estimate plotted as a function of the slope of the true slope parameter stratified by selection criteria, different levels of Cmax (200, 500, 1000, and 2000 ng/mL), and different sampling schemes (5, 9, and 13 data points). Plotted are the mean, upper 2-sided 90% CI, and CI range. A value of 100% implies no difference between estimates. Legend: open blue circle, point estimate; dark red plus, CI range; green cross, upper confidence interval (PNG 881 kb)

10928_2017_9523_MOESM9_ESM.png

Supplemental Figure 9 Stacked bar chart of best model selected for each level of slope stratified by data generating equation, study design, baseline, and information criterion used for model selection when the data generating mechanism was non-inclusive. For the TQT design, 9 sampling points and a circadian baseline were used in the chart (PNG 681 kb)

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Bonate, P.L. Estimation of QT interval prolongation through model-averaging. J Pharmacokinet Pharmacodyn 44, 335–349 (2017). https://doi.org/10.1007/s10928-017-9523-3

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