Algorithm for balancing both continuous and categorical covariates in randomized controlled trials

Minimization as proposed by Pocock and Simon for

balancing

categorical

covariates

in clinical trials with individual-level, consecutive randomization has been increasingly used. An extension of the method exists that uses the symmetric Kullback-Leibler divergence index to balance both

categorical

and

continuous

covariates

, albeit for two-arm

randomized controlled trials

only. To date, the

algorithm

has not been made widely available to researchers via publicly accessible software.

We adapted Endo et al.'s

algorithm

to randomized trials with two or more arms. In addition, our

algorithm

incorporates Efron's biased coin method to decrease the predictability of assignment even when a predefined threshold of difference in the numbers of subjects between treatment arms is reached, whereas Endo et al.'s

algorithm

assigns the next subject to the treatment of smaller size with certainty.

We developed code in the free statistical software R to make the

algorithm

readily available to trialists. While there are no definitive answers regarding the optimal choices for certain statistical parameters that must be defined prior to

algorithm

application (P(k), D(n), and p_D(n)), we provide guidance on these.

We conducted simulations with actual data from a three-arm randomized trial to compare the modified

algorithm

and R code to another published biased coin minimization method that can accommodate

continuous

and

categorical

covariates

in multi-arm trials. The three-arm trial used three

categorical

covariates

(sex, race/ethnicity, and online personal health record access) and four

continuous

covariates

(age, fasting blood glucose, body mass index, and waist circumference). All of the

continuous

and

categorical

covariates

were well balanced, and the results were comparable to the comparison method.