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Background  Parallel intervention studies involving volunteers usually require a procedure to allocate the subjects to study-arms. Statistical models to evaluate the different outcomes of the study-arms will include study-arm as a factor along with any covariate that might affect the results. To ensure that the effects of the covariates are confounded to the least possible extent with the effects of the arms, stratified randomization can be applied. However, there is at present no clear-cut procedure when there are multiple covariates.    Methods  For parallel study designs with simultaneous enrollment of all subjects prior to intervention, we propose a D-optimal blocking procedure to allocate subjects with known values of the covariates to the study arms. We prove that the procedure minimizes the variances of the baseline differences between the arms corrected for the covariates. The procedure uses standard statistical software.    Results  We demonstrate the potential of the method by an application to a human parallel nutritional intervention trial with three arms and 162 healthy volunteers. The covariates were gender, age, body mass index, an initial composite health score, and a categorical indicator called first-visit group, defining groups of volunteers who visit the clinical centre on the same day (17 groups). Volunteers were allocated equally to the study-arms by the D-optimal blocking procedure. The D-efficiency of the model connecting an outcome with the study-arms and correcting for the covariates equals 99.2%. We simulated 10,000 random allocations of subjects to arms either unstratified or stratified by first-visit group. Intervals covering the middle 95% of the D-efficiencies for these allocations were [82.0, 92.0] and [93.2, 98.4], respectively.    Conclusions  Allocation of volunteers to study-arms with a D-optimal blocking procedure with the values of the covariates as inputs substantially improves the efficiency of the statistical model that connects the response with the study arms and corrects for the covariates.    Trial registration  Dutch Trial Register NL7054 ( NTR7259 ). Registered May 15, 2018.

bmc medical research methodology

A new randomization procedure based on multiple covariates and applicable to parallel studies with simultaneous enrollment of all subjects prior to intervention