Evaluation of model of Heart Rate during Exercise Tolerance Test with missing at random dropouts
Lemenuel-Diot A., Laffont C.M. , Jochemsen R., Foos-Gilbert E.
Servier Research Group, Courbevoie, France
Introduction: Exercise Tolerance Tests (ETT) are commonly used in clinical trials to assess the effect of heart rate (HR) lowering agents during effort. These tests consist of bicycle or treadmill exercise, increasing effort intensity at successive steps (workload). Usually, for safety and ethical reasons, each subject can stop the exercise at his own convenience. Therefore missing data due to dropout can be generated, especially when high values of heart rate are reached, and may lead to a possible misinterpretation in model evaluation.
Purpose: To illustrate that simple model evaluation can be misleading when missing at random dropout occurs, and to propose two approaches that take into account dropout in order to correctly evaluate the model.
Method: HR data were obtained following ETT with bicycle performed in twelve healthy male volunteers before treatment administration. During ETT, the workload was increased every 3 minutes from 50 to 180 watts. Subjects who stopped the exercise before reaching 180 watts were considered as dropout. HR was measured at rest and every minute during ETT. The relationship between HR and workload during ETT was first modelled using the available data. Goodness-of-fit (GOF) plots and visual predictive checks (VPC) were performed for model evaluation. Assuming that data were Missing At Random (MAR) (i.e. missing data are predictable based on previous individual observations), dropout was then considered in the model evaluation using two different approaches. In a first approach, VPC and GOF were performed again after imputing missing HR data with individual predictions obtained with the previous model. In a second approach, a dropout model was developed using the estimated individual parameters (under constraint that the risk for dropout at the beginning of ETT is null) and model evaluation (VPC) was performed using this new model by simulating a probability of dropout at each workload for each subject among the replicates. All these analyses were performed using NONMEM V. In both approaches, the HR model was not re-estimated.
Results: Six subjects out of twelve dropped out before reaching 180 watts. The increase of HR during ETT was found to be linearly related to the workload. However, simple GOF plots and VPC showed that HR was overpredicted at high workload values, wrongly suggesting a misspecification of the structural model. When missing HR were imputed with the individual predictions of the model (approach 1), VPC and GOF were satisfactory and no misspecification of the model was observed. Further estimation of the dropout model (approach 2) provided VPC fully consistent with the observed HR.
Conclusion: Two different approaches were used to take into account dropout for evaluation of the HR model during ETT. Approach 1 did not require to model dropout and is a very simple way to evaluate a model when MAR dropout occurs. Approach 2 required the development of a dropout model, which was specific of ETT. If dropout had been not MAR, approach 2 would have been more appropriate than approach 1. In our example involving MAR dropout, both approaches allowed us to properly evaluate the estimated model of HR without treatment. Then, by adding the HR measured after treatment administration, treatment effect would be better characterized.
