Randomisation blocked

Other problems pointed out by Box et al. [20] are serially correlated errors, dynamic relations and feedback. All the above problems can be overcome by the use of properly designed statistical experiments that employ features such as randomisation, blocking and other suitable controls. 

Let us start vrith one of the simplest conceptions in experimental design, the so-called Randomised. Block. ... 

Field trial designs differ somewhat from each other in details but follow the same general principles. The GM crop and its control are planted in randomised blocks within a plot, often with three or four rephcate blocks each. Recent studies of herbicide tolerant GM plants have included three treatment groups the control and transgenic plants are treated with conventional herbicides and in a separate block the transgenic plant is sprayed with the herbicide to which it is tolerant (Herman et al, 2004 Oberdoerfer et al,... 

Planting an experimental collection with clones coming from the plants selected in the previous cycle under a completely randomised block design (4—5 rephcates x four plants per genotype). For 3 years, data on yield, sugar, acidity and anthocyanins in the must... 

There was no correlation between the yield values for 52 individual plants of Antao Vaz from four vineyards and the values of the corresponding clones in a trial with a completely randomised block design (five replicates x five plants) (Figure 8.1). Given that this experimental design ensures a notorious reduction of environmental deviations and makes the observed values close to the true genetic values, the lack of relationship between the values of the clones and those of their mother individual plants proves that in practice these do not have a genetic basis. 

For a sample to be representative of a specific region where the variety is grown, it is first necessary to define the minimnm nnmber of mother plants (genotypes) required for the sample, which can be determined through simulation experiments (Martins et al., 1990 Gonsalves and Martins, 2012). Martins et al. (1990) collected an actual oversized sample of 198 mother plants of Touriga Nacional, which were then planted in the field as clones in a completely randomised block design with five replicates and three plants per plot. Yield and other traits were measured. Several subsamples were... 

Blocked randomisation If using blocked randomisation, we ensure balance between treatments within a block of patients. Suppose for example, we again wish to randomise the two treatments A and B to 12 patients in blocks of size four. Then within each block of four patients, treatments are randomly allocated to patients to ensure that two patients receive both A and B. For example ... 

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. 

To ensure balance in terms of numbers of subjects, we usually undertake block randomisation where a randomisation list is constructed by randomly choosing from the list of potential blocks. For example, there are six ways of allocating two As and two Bs in a block of size four ... 

In large trials it could be argued that block randomisation is unnecessary. In one sense this is true, overall balance will be achieved by chance with an unrestricted randomisation list. However, it is usually the case that large trials will be multicentre trials and not only is it important to have balance overall it is also important to have balance within each centre. In practice therefore we would allocate several blocks to each centre, for example five blocks of size four if we are planning to recruit 20 patients from each centre. This will ensure balance within each centre and also overall. 

For unequal randomisation we would choose the block size accordingly. For a 2 1 randomisation to A or P we could randomly choose from the blocks ... 

Block randomisation therefore forces the required balance in terms of the numbers of patients in the treatment groups, but things can still go wrong. For example, let s suppose in an oncology study with time to death as the primary endpoint that we can measure baseline risk (say in terms of the size of the primary tumour) and classify patients as either high risk (H) or low risk (L) and further suppose that the groups turn out as follows ... 

This simply means that we produce separate randomisation lists for the high risk and the low risk patients, the strata in this case. For example the following lists (which are block size four in each case) ... 

Method of randomisation (although block size will not be specified)... 

The experimental order of this study was also changed from the ideal randomised and blocked design. This was justified for reasons of automation where column changes needed to be minimised. As for the aspirin study the validity of this compromise depends on the fact that the repeatability of the method, over a time span such as that required for the ruggedness test, had previously been established. 

Berg H, Viby-Mogensen J, Roed J, et al. Residual neuromuscular block is a risk factor for postoperative pulmonary complications. A prospective, randomised and blinded study of postoperative pulmonary complications after atracurium, vecuronium and pancuronium. Acta Anaesthesiol Scandinavica 1997 41 1095-103. 

If we take the averages of the four results for each treatment tiiey wiB be statistic ly sound if the randomisation was properly carried out, but the error in each mean (average) will be inflated hecau it includes in itself the differences between blocks. The periment will thm not be as accurate as it m t be. 

It might, however, be more satisfactory if the order of carrying out the experiments were randomised (as they stand in Tablejf3 it is systematic, the order being A, B, C, D in each block). If there was any tendency for the firat experiment in each case to be high, then this would appear as a high result for A which would be Uacious. Randomisation, such as has been carried out in Table 1.4, would avoid this. 

Dasgupta D, Garasia M, Gupta KC, Satoskar RS. Randomised double-blind study of centbucridine and lignocaine for subarachnoid block. Indian J Med Res 1983 77 512-16. 

Sramek JJ, Leibowitz MT, Weinstein SP, Rowe ED, Mendel CM, Levy B, McMahon FG, Mullican WS, Toth PD, Cutler NR. Efficacy and safety of sibutramine for weight loss in obese patients with hypertension well controlled by beta-adrenergic blocking agents a placebo-controlled, double-blind, randomised trial J Hum Hypertens 2002 16(1) 13-19. 

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). 

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