Statistical methods for testing carryover effects: A mixed effects model approach

Figures

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  Fig. 1. One possible trajectory (of the many we simulated) of BP for a participant in the treatment arm of the TROPHY trial which concluded that the effect of treatment could be extended up to 2 years. Carryovers (Zitj) of lengths 0–2 years are plotted and randomisation occurs at time 0.

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  Fig. 2. The plot on the left is the long-term average blood pressure for participants in both control and treatment arms of the study. Unfortunately, blood pressure measurements vary so TROPHY investigators analysed the instantaneous measurements seen on the plot to the right. The light-grey line is the threshold used for TROPHY of 140 mm Hg.

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  Fig. 3. Q-Q Plots for both systolic and diastolic blood pressures. Besides terminal digit preference, there is not evidence against normality.

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  Fig. 4. The relative flatness of the variogram shows no autocorrelation. The red line indicates a 4 year lag, which is the length of our study.

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  Fig. 5. Schematic overview of simulations for this research. Adapted from [21].

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  Fig. 6. Boxplots of mean bias in estimates of carryover parameter for the mixed effects model (left panel) and the linear model (right panel) from our primary simulations. Bias in the mixed effects model is consistently smaller.

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  Fig. 7. The mixed effects model gives negligibly biased estimates of the carryover parameter for both systolic and diastolic measurements.

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  Fig. 8. Because the true risk ratio of hypertension is approximately 1 the first measurement after treatment ceases when carryover is 0, we can test the bootstrap confidence intervals for 1.

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  Fig. 9. Schematic overview of bootstrapping for relative risks. This method allows us to accurately test a carryover hypothesis. Adapted from [34].

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  Fig. 10. Proportion of bootstrap confidence intervals that contain 1 partitioned by length of carryover. When carryover is 0, 1 is the true value and is likely to be in the confidence intervals.