Fig. 1

Root mean square (RMS) of maximum absolute bias across the experimental scenarios. Within each experimental iteration, absolute bias was calculated as the absolute value of the difference between observed beta coefficient and the ‘true’ coefficient across the 10,000 most variable genes in the expression dataset. Maximum absolute bias represents the maximum absolute difference between the true beta (prior to adding batch effects) and the beta estimates from each of the experimental scenarios (Table 1). The root mean square or standard deviation of the maximum absolute bias estimates across the experimental simulations was estimated for \({\upbeta }_{1}\) (panel A, case vs control parameter that was set at 0 to represent the null hypothesis), \({\upbeta }_{2}\) (panel B, parameter estimate representing the association between age and gene expression), and \({\upbeta }_{3}\) (panel C, parameter estimate representing the association between HbA1c and gene expression. Opt = optimal allocation strategy, R = simple randomization strategy, SR = stratified randomization strategy