Additional file 4 of Optimal target of LDL cholesterol level for statin treatment: challenges to monotonic relationship with cardiovascular events

Additional file 4: Figure S1. The cumulative martingale residuals (blue, thick line) plotted against 10-mg/dl LDL-C levels above the threshold value set by each model to check the linearity assumption in the Cox models, accompanied by 1000 resampled zero-mean random Gaussian processes (black, thin lines). If the relationship between LDL-C above the threshold and event hazards is actually linear in the Cox model (i.e., the linearity assumption holds), the cumulative sum of martingale residuals will approximately follow the zero-mean Gaussian process and fluctuate randomly. The supremum of the cumulative martingale residuals along the LDL-C levels can be tested against the suprema from randomly sampled zero-mean Gaussian processes. A small p-value from this resampling-based test would provide evidence against the linearity assumption.