Minimisation is a method of adaptive

stratified sampling In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each s ...

that is used in

clinical trials Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments (such as novel vaccines, drugs, dietar ...

, as described by Pocock and Simon. The aim of minimisation is to minimise the imbalance between the number of patients in each

treatment group In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one tr ...

over a number of factors. Normally patients would be allocated to a treatment group

randomly In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...

and while this maintains a good overall balance, it can lead to imbalances within sub-groups. For example, if a majority of the patients who were receiving the active drug happened to be male, or smokers, the statistical usefulness of the study would be reduced. The traditional method to avoid this problem, known as blocked randomisation, is to stratify patients according to a number of factors (e.g. male and female, or smokers and non-smokers) and to use a separate randomisation list for each group. Each randomisation list would be created such that after every block of x patients, there would be an equal number in each treatment group. The problem with this method is that the number of lists increases

exponentially Exponential may refer to any of several mathematical topics related to exponentiation, including: *Exponential function, also: **Matrix exponential, the matrix analogue to the above * Exponential decay, decrease at a rate proportional to value *Exp ...

with the number of stratification factors. Minimisation addresses this problem by calculating the imbalance within each factor should the patient be allocated to a particular treatment group. The various imbalances are added together to give the overall imbalance in the study. The treatment group that would minimise the imbalance can be chosen directly, or a random element may be added (perhaps allocating a higher chance to the groups that will minimise the imbalance, or perhaps only allocating a chance to groups that will minimise the imbalance). The imbalances can be weighted if necessary to give some factors more importance than others. Similarly a ratio can be applied to the number of patients in each treatment group. In use, minimisation often maintains a better balance than traditional blocked randomisation, and its advantage rapidly increases with the number of stratification factors.

References

{{reflist Clinical research Design of experiments