Summary
Objectives: If in a clinical trial prognostic factors are known in advance, it is often recommended
that randomization of patients should be stratified. The best-known method is permuted-block
randomization within strata. But it suffers from the disadvantage that imbalance still
occurs in the trial as a whole if there are a large number of strata, or/and the block
sizes are too large for the number of patients. The results of Hallstrom and Davis
are appropriate for evaluating the risk of such a troubled situation by using two
special cases of their general variance formula. But it is merely generally argued
for whichever practical situations these special cases are valid. Consequently, additional
investigations are required to reveal the conditions for correct application.
Methods: We investigated the range of validity of special cases by performing computer simulations,
varying a number of trial characteristics, and discuss the application of results
for practical situations.
Results: The validity of special cases is not given in each situation. Depending on block
size, a binomial distribution model is valid for a permitted average maximum number
of patients per stratum between 36% and 57% of considered block sizes, whereas the
uniform distribution model works adequately from at least 70%. In an intermediate
range of invalidity, implementation of a simulation study is necessary to compute
the probability distribution of differences.
Conclusions: Our results are important if choosing the stratified permuted-block randomization
to estimate the risk for an intolerable overall imbalance when planning a trial.
Keywords
Stratified permuted-block randomization - balancing properties
