Simple randomisation

Unrestricted (or simple) randomisation is simply a random list of, for example, As and Bs. In a moderately large trial, with say n = 200 subjects, such a process will likely produce approximately equal group sizes. There is no guarantee however that this will automatically happen and in small trials, in particular, this can cause problems. 

H. van der Voet, Comparing the predictive accuracy of models using a simple randomisation test, Chemom. Intell. Lab. Syst., 25, 1994, 313-323. 

When there are several prognostic factors that can be determined before treatment allocation, the treatment groups can be balanced for these factors using a method known as minimisation .This method is particularly valuable in relatively small trials (say, 100 or fewer patients per treatment group) where simple randomised allocation may give substantial differences between the groups purely by chance. 

VITATOPS Trial Study Group, 2002. The VITATOPS (Vitamins to Prevent Stroke) Trial rationale and design of an international, large, simple, randomised trial of homocysteine-lowering multivitamin therapy in patients with recent transient ischaemic attack or stroke. Cerebrovascular Diseases. 13. 120-126. 

Within the last 20 years or so, three major features of controlled clinical trials, in particular, have permitted significant advances in deciding whether treatments are of value or not randomisation, systematic review and metaanalysis, and the concept of the large-scale, simple (to understand and conduct) randomised trial in areas where only moderate benefits can be expected.All of these elements are likely to underpin future trials for purposes of regulation, pharmacoeconomics and healthcare policy. Yet there is no room for complacency or allowing standards to slip. Systematic reviews of some... 

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. 

However, there is a counter argument. In the ECMO trial, after the result of the nineth patient became known the RPW design requires that the patients be randomised to ECMO compared to the standard ventilator in the ratio 9 1. Clayton argues that if the one treatment is so much superior to the other that 90% of patients are allocated to it, it is unethical to withhold it from the remaining 10%. If we accept that argument, is it also true if the ratio is 8 1 or 7 1 How much information is sufficient to make us, ethically, refuse to randomise patients Such questions are not simple. 

Finally note that in our considerations we have worked with groups of equal size. It is straightforward to adapt the calculations for unequal randomisation schemes and the computer packages mentioned earlier can deal with these. Altman (1991), Section 15.3 provides a simple method for adapting the standard sample size calculation to unequal group sizes as follows. If N is the calculated sample size based in an equal randomisation and k represents the ratio of the number of patients in one group compared to the other group, then the required number of patients for a A to 1 randomisation is ... 

The randomisation test proposed by Wiklund et al. [34] assesses the statistical significance of each individual component that enters the model. This had been studied previously, e.g. using a t- or F-test (for instance, Wold s criterion seen above), but they are all based on unrealistic assumptions about the data, e.g. the absence of spectral noise see [34] for more advanced explanations and examples. A pragmatic data-driven approach is therefore called for and it has been studied in some detail recently [34,40]. We have included it here because it is simple, fairly intuitive and fast and it seems promising for many applications. 

Randomisation may be accomplished in simple or more complex ways such as ... 

The parallel group is a more simple design. A group of people is randomised to two treatments, e.g. active treatment and placebo or two different active treatments, and the primary variable is then compared between the groups. 

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). 

Randomised controlled trials have tested whether specific interventions are effective in reducing allergen exposure and whether this reduction leads to a reduction in sensitisation or disease. The second approach is only valid if the first is proven. Unfortunately, despite a huge amount of research, there is no simple allergen avoidance intervention designed to be prescribed or evaluated [214(NC)]. 

It is quite clear from an inspection of Figures 7.1 and 7.2 that the kind of agreement found between theory and experiment in Chapter 5 could not have occurred unless Pr was effectively infinite in these strong collision systems, because as soon as the randomisation processes become rate determining, there are severe departures from the simple strong collision, i.e. p, = oo, behaviour. We must then ask whether there are any known experimental results from which we can demonstrate a departure from infinitely rapid randomisation, and it appears that the well-studied thermal isomerisation of methyl isocyanide may be just such an example. 

On the theoretical front, it is possible to make a few simple assertions. We have already seen that a collisional component to the randomisation process may become faster the more dense are the states of the molecule. It is also obvious that the first order component will become slower as the states become further apart, but the molecular level density where this begins is not known a cut-off at about 1000 states per wavenumber has been suggested [82.S2] for intramolecular vibrational relaxation of isolated molecules in one kind of experiment. It is also obvious that there must be propensity rules for the occurrence of randomising transitions within any grain [81.P2] for example, transitions between states of... 

The Gaussian Approximation Potential scheme is not limited to simple semiconductors. We demonstrate this by applying the scheme to a metallic system, namely the body-centred cubic (bcc) phase of iron. We included configurations in the training set where the lattice vectors of the one-atom primitive cell were randomised and where the positions of the atoms in 8 and 16-atom supercells were also... 

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