Stratified randomisation

Israel E, ChinchUli VM, Ford JG, et al. (2004) Use of regularly scheduled albuterol treatment in asthma genotype-stratified, randomised, placebo-controlled cross-over trial. Lancet. 364, 1505-1512. 

In multicentre trials, it is usual to use a separate randomisation procedure within each centre to ensure that there is balance - or at least near balance within each centre. In such circumstances ICH E9 (Section 2.3.2) recommends that the randomisation be performed centrally, with several blocks allocated to each centre. This procedure is a simple form of stratified randomisation. 

A second, important, use of stratified randomisation is in those cases where it is known that... 

Dynamic randomisation - minimisation When there are a large number of prognostic variables to account for, it may be practically difficult to implement a fully stratified randomisation scheme. The reason being that with a large number of factors there are even more individual stratum combinations and therefore there will be very few patients in many of the combinations. In such circumstances the method of dynamic allocation, or minimisation, has been recommended. 

Now suppose that the mean survival times are observed to be 21.5 months in A and 27.8 months in group B. What conclusions can we draw It is very difficult the difference we have seen could be due to treatment differences or could be caused by the imbalance in terms of differential risk across the groups, or a mixture of the two. Statisticians talk in terms of confounding (just a fancy way of saying mixed up ) between the treatment effect and the effect of baseline risk. This situation is very difficult to unravel and we avoid it by stratified randomisation to ensure that the case mix in the treatment groups is comparable. 

Where the requirement is to have balance in terms of several factors, a stratified randomisation scheme using all combinations of these factors to define the strata would ensure balance. For example if balance is required for sex and age, then a scheme with four strata ... 

Earlier we discussed the use of stratified randomisation in multi-centre trials and where the centres are large this is appropriate. With small centres however, for example in GP trials, this does not make sense and a stratified randomisation with region defining the strata may be more appropriate. Central randomisation would be essential to manage such a scheme. 

Stratified randomisation with more than a small number of strata would be difficult to manage at the site level and the use of central randomisation is then almost mandatory. 

Dynamic aibcation is an alternative procedure in which the allocation of treatment to a subject is influenced by the current balance of allocated treatments and, in a stratified trial, by the stratum to which the subject belongs and the balance within that stratum. Deterministic dynamic allocation procedures should be avoided and an appropriate element of randomisation should be incorporated for each treatment allocation. ... 

When the number of patients within each centre is expected to be very small, it may not be practical to stratify the randomisation by centre. In that case it should be considered whether randomisation could be stratified by, for example, country or region. Such a choice might be driven by similarities in co-medication, palliative care or other factors that might make stratification advisable. ... 

Firstly, if the randomisation has been stratified for baseline variables then from a theoretical statistical point of view these variables should be taken into account in the analysis. Secondly, the efficiency of the statistical analysis can be improved in several ways if baseline prognostic factors (factors which influence outcome) are included in the analysis. Finally, it provides a framework for the investigation of the consistency of the treatment effect according to different values for those factors. 

As an example, suppose that the randomisation has been stratified on the basis of age and sex with four strata ... 

If we had not stratified the randomisation for age and sex, but nonetheless recognised that these were important prognostic factors, it would still have been advantageous to analyse the data in the same way using this adjusted methodology. 

This information can be useful for trial planning, for example choosing factors on which to stratify the randomisation, for the future. 

Remember however that variables used to stratify the randomisation should be included. It is also not usually appropriate to select covariates within ANCOVA models using stepwise (or indeed any other) techniques. The main purpose of the analysis is to compare the treatment groups not to select covariates. 

It is nonetheless appropriate to produce baseline tables of summary statistics for each of the treatment groups. These should be looked at from a clinical perspective and imbalances in variables that are potentially prognostic noted. Good practice hopefully will have ensured that the randomisation has been stratified for important baseline prognostic factors and/or the important prognostic factors... 

In Chapter 6 we covered methods for adjusted analyses and analysis of covariance in relation to continuous (ANOVA and ANCOVA) and binary and ordinal data (CMH tests and logistic regression). Similar methods exist for survival data. As with these earlier methods, particularly in relation to binary and ordinal data, there are numerous advantages in accounting for such factors in the analysis. If the randomisation has been stratified, then such factors should be incorporated into the analysis in order to preserve the properties of the resultant p-values. 

What are the key prognostic factors and how, if at all, should these be used to stratify the randomisation ... 

Should the randomisation be stratified by centre or by some higher-level factor, for example region or country ... 

Several variations on simple random allocation are often employed. For example, blocking is used to ensure that, in each block of a predetermined size, equal numbers of patients are allocated to the various treatments. For example, the random series can be designed so that five patients are allocated to each of the two treatments in every block of ten patients. Stratified randomisation means that separate random series (whether blocked or not) are used for different subgroups of patients. The subgroups may be determined by known or suspected prognostic factors (such as severity of illness) or by the source of the patients (particularly the individual centres or investigators in a multicentre trial). 

The study cohort was derived from 33,357 ALLHAT participants, who were aged 55 years or older, had hypertension and at least one additional cardiovascular disease risk factor. The participants who were normokalemic at baseline were randomised to chlorthalidone versus amlodipine or lisinopril and were stratified by level of potassium at year 1 into hypokalemia (<3.5 mmol/L) normokalemia (3.5-5.4 mmol/L) and hyperkalemia (>5.4 mmol/L). Incidence of hypokalemia in chlorthalidone was 12.9% and this differed significantly from amlodipine (2.1%, p < 0.001) and lisinopril (1.0%, p < 0.01). Incidence of hyperkalemia was greatest in lisinopril arm (3.6%) than in chlorthalidone arm (1.2%, p < 0.01) or amlodipine (1.9%, p < 0.01). Coronary heart disease occurred in 8.1%, 8.0% and 11% in patients with hypokalemia, normokalemia and hyperkalemia, respectively. 

MenACWY has been assessed in combination with licenced Hepatitis A/B vaccine (Twinriy ) a schedule that would potentially reduce the number cf vaccination clinic visits, and thereby increase uptake in travellers to endemic areas. An open-label, controlled study in Sweden and Denmark of 611 adolescents stratified by age, were randomised 3 1 1 to receive either both vaccines, MenACWY alone or Hepatitis A/B alone. Co-administration was demonstrated to be non-inferior to individual vaccine administration, with 99.4-100% showing seroprotection to all meningococcal serogroups, and 99.1% showing seropositivity for Hepatitis A and seroprotection for Hepatitis B.AE profile was comparable across all groups I95f. 

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