An investigation of minimisation criteria

Abstract

Background: Minimisation can be used within treatment trials to ensure that prognostic factors are evenly distributed between treatment groups. The technique is relatively straightforward to apply but does require running tallies of patient recruitments to be made and some simple calculations to be performed prior to each allocation. As computing facilities have become more widely available, minimisation has become a more feasible option for many. Although the technique has increased in popularity, the mode of application is often poorly reported and the choice of input parameters not justified in any logical way.

Methods: We developed an automated package for patient allocation which incorporated a simulation arm. We here demonstrate how simulation of data can help to determine the input parameters to be used in a subsequent application of minimisation.

Results: Several scenarios were simulated. Within the selected scenarios, increasing the number of factors did not substantially adversely affect the extent to which the treatment groups were balanced with respect to the prognostic factors. Weighting of the factors tended to improve the balance when factors had many categories with only a slight negative effect on the factors with fewer categories. When interactions between factors were included as minimisation factors, there was no major reduction in the balance overall.

Conclusion: With the advent of widely available computing facilities, researchers can be better equipped to implement minimisation as a means of patient allocation. Simulations prior to study commencement can assist in the choice of minimisation parameters and can be used to justify those selections.

Figure 1

Increasing the number of binary factors. 95^th centiles of the distributions of proportionate changes from expected for randomisation weights from 1 to 100 obtained from 5000 simulations and a simulated sample size of 500. The number of minimisation variables is increased from 1 (black line) to 5 (dark green), 20 (lime green) and to 30 (red).

Figure 2

Sample size 500, 5 prognostic factors (3 binary, 1 3-category, 1 4-category). 95^th centiles of the distributions of proportionate changes from expected for randomisation weights from 1 to 100 obtained from 5000 simulations. Dotted lines show results when prognostic factors are weighted according to the number of categories. Results for binary factors shown in black, 3-category in blue and 4-category in purple.

Figure 3

Sample size 40, 5 prognostic factors (3 binary, 1 3-category, 1 4-category). 95^th centiles of the distributions of proportionate changes from expected for randomisation weights from 1 to 100 obtained from 5000 simulations. Dotted lines show results when prognostic factors are weighted according to the number of categories. Results for binary factors shown in black, 3-category in blue and 4-category in purple.

Figure 4

Minimizing the difference of the interactions. 95^th centiles of the distributions of proportionate changes from expected for randomisation weights from 1 to 100 obtained from 5000 simulations. All 10 2-way interactions from 5 prognostic factors (3 binary, 1 3-category, 1 4-category) used as minimisation criteria. Dotted lines show results when prognostic factors are weighted according to the number of categories. Results for the 3 2 × 2 interaction terms shown in black, for the 3 2 × 3 interactions in dark green, the 3 2 × 4 in lime green and the 1 3 × 4 interaction in red.

Figure 5

Adding a 15-category factor. 95^th centiles of the distributions of proportionate change from expected for randomisation weights from 1 to 100 obtained from 5000 simulations. Dotted lines show results when prognostic factors are weighted according to the number of categories. Results for binary factors shown in black, 3-category in blue, 4-category in purple and 15-category in green.