Nonetheless, the patients in each cluster-period are from distinct distributions labelled as A, B, C, and D in Fig. In each cluster-period, we assume that the variability of the individual patient LOS is the same, and hence the yellow and blue curves have the same shape and are only shifted in location between the four cluster-periods. We have illustrated how the cluster randomisation aspect of the CRXO design leads to the formation of clusters of patients defined by ICU, while the crossover aspect of the design leads further to the formation of cluster-periods of patients within each cluster.
We have also illustrated how the cluster randomisation and crossover aspects of the CRXO design can lead to three sources or components of variation in the responses of patients in a CRXO trial: variation in the mean LOS between ICUs; variation in the mean LOS between cluster-periods; and variation between individual patient LOS within a cluster-period.
In this section we show how the three sources of variation outlined in the preceding section can be used to quantify the similarity in LOS between the groups of patients defined by ICU cluster and cluster-period. The within-cluster within-period correlation WPC quantifies the similarity of outcomes from patients in the same cluster-period.
The within-cluster between-period correlation BPC quantifies the similarity of outcomes from patients in the same cluster, but in different periods. Specification of these two correlations are required to perform sample size estimates for a CRXO trial. In practice, the LOS can only be measured on a sample of patients, and the true WPC and BPC will be estimated from this sample of patients, with some amount of random sampling error.
We now refer to Fig. For example, in Fig. In contrast, in Fig. Hence, the BPC is larger in Fig. As a result, the similarity between the LOS of two patients in cluster-period A is comparable to the similarity between the LOS of one patient from cluster-period A and one patient from cluster-period B or C or D.
As a result, the LOS of two patients in cluster-period A are more similar to each other than to one patient from cluster-period A cluster 1 and another patient from cluster-periods C or D cluster 2. Hence, the WPC is smaller in Fig. We note that the same comparison can be made between Fig. As a result, the similarity between the LOS of two patients in cluster-period A is comparable to the similarity between the LOS of one patient from cluster-period A and one patient from cluster-period B.
As a result, the LOS of two patients in cluster-period A are more similar to each other than to one patient from cluster-period A and another patient from cluster-period B and even more similar than one patient from cluster-period A and another patient from cluster-periods C or D. Hence the WPC is again smaller in Fig. In this section, we discuss how the WPC and BPC affect the precision of the estimate of the difference between interventions, and hence the sample size requirement, in a two-period, two-intervention, cross-sectional CRXO trial.
To illustrate the effect of the WPC and BPC on precision and equivalently the components of variation , we continue to assume that the true difference between interventions is zero. We consider a large sample of patients admitted to one cluster in a CRXO design, such that the sampling error in the estimated mean LOS for patients is assumed negligible.
Therefore, in the single cluster shown in Fig. In this section, we show which partitioning of the total variation in LOS into the components of variation leads to the most precision and to the least precision in the CRXO design.
The yellow blue curve indicates a normal distribution of patient LOS within each cluster or cluster-period where the patient or cluster was allocated to intervention S T. The true difference between intervention S and T is zero. The total variance in LOS remains constant.
In the CRXO design, the observed mean LOS of patients receiving each intervention can be compared within each cluster because each intervention is delivered in each cluster.
As an illustration, in Fig. As the variation in the true cluster-period mean LOS increases, and hence the separation between the green lines in Fig. Correspondingly, from Eqs. In conclusion, increasing variability in the cluster-period means leads to increasing uncertainty in the observed difference in the mean LOS between patients receiving each intervention.
In this scenario the separation between the green lines in Fig. Also, from Eqs. Figure 3b now approximates the diagram that one would expect from an IRCT with two ICUs with the mean LOS for each centre indicated by the green lines and half the patients within each cluster receiving each intervention.
This diagram arises in an IRCT because, for large sample sizes and under the assumption of no true differences between interventions, randomisation ensures that the distributions of LOS in each intervention yellow and blue curves are identical.
Conversely, the precision of the CRXO design decreases when the cluster-period variability increases. As the variability between periods within a cluster increases, the separation between the green lines , and correspondingly the yellow and blue curves , in Fig.
The increased separation results in greater variability in the comparison of patient LOS in each intervention within each cluster. For a fixed total variability in ICU LOS, as the variability between periods within a cluster increases, the variability between different clusters must reduce. In this case each cluster-period effectively resembles a separate cluster Fig.
The sample size required to detect a specified true difference between interventions with a given level of power decreases as the precision of the estimate of the intervention effect increases. However, even when the true difference is not zero, the effects of the WPC and BPC on precision described in the previous section continue to hold.
There are 37 tertiary ICUs in Australia and New Zealand, of which 25 to 30 might be expected to participate in a trial. We compare the sample size requirement for number of individuals and number of clusters ICUs from the CRXO design with the requirement from the stratified, multicentre, parallel-group, individually randomised design IRCT and the parallel-group cluster randomised design CRCT conducted over one period. Comparisons of the sample size requirements for these different designs can either be made by fixing the total number of clusters across all designs; or by treating the CRXO design as lasting twice as long, i.
We take the latter approach here so that the WPC is the same in each period. We include Stata do-files to estimate the required sample size for each trial design, for a chosen set of sample size parameters see Additional files 1 and 2.
The sample size formula for the total number of participants required for a normally distributed continuous outcome in a two-period, two-intervention CRXO trial, across all clusters and interventions, assuming a constant number of participants recruited to each cluster-period is [ 8 ]:. The formulae presented above include a correction for when the number of clusters small, as suggested in Eldridge and Kerry p.
No correction is necessary for the IRCT because the number of individual participants will be large in the example settings. We follow the methods of Turner et al. The overall mean LOS was 5. We follow the methods of Donner et al.
The overall mortality rate was 8. In practice, the choice of reduction in ICU LOS should be the minimally clinically important reduction, determined in consultation with subject matter experts. The standard deviation is estimated to be 1. As an illustration, we assume that in a month period, patients in each ICU will meet the inclusion criteria for the trial.
The CRCT design would require 7. Note that when the number of patients admitted in each cluster-period is relatively large, we would observe a similar increase in the sample size if we had underestimated the WPC by 0. The total number of patients and ICUs for each design are summarised in Table 3 see Appendix 2 for calculations.
In this example, the CRXO design required 2. This demonstrates that a small change in the assumed BPC can have a marked impact on the number of required ICUs and patients.
We have so far assumed that the cluster-period size is constant. In reality, it is likely that different ICUs will include a differing number of participants [ 17 , 18 ]. An extension to the sample size formula for this scenario is provided by [ 9 ].
When the analysis is based on unweighted cluster-period means, the arithmetic mean in the sample size formula given for the CRXO design can be replaced by the harmonic mean:. We assume that the cluster-period size is the same in each period within a cluster. For further extensions, see Forbes et al. You may have randomized someone to one treatment group but they decide they don't want to be in that treatment group. The rigorous methodology used allows avoid bias related to confounding factors through a control group , selection bias through randomisation and interpretation bias through double blinding.
The major limitation of randomized clinical trials is their restriction to interventions that are supposed to have a positive effect. Another limit is related to the difficulty to interpret or generalize the results because the studied population is very different from the population treated in normal life.
In clinical research terms, a cross-over design is adopted to rule out any possible 'period effect' the trial medications may have on the clinical outcome. It is also expected to reduce inter-subject variability. A "clean" comparison between two treatments simplifies the design and help to discriminate the results. A crossover trial has a repeated measures design in which each patient is assigned to a sequence of two or more treatments, of which one may be a standard treatment or a placebo.
A crossover design is a repeated measurements design such that each experimental unit patient receives different treatments during the different time periods, i. Every patient receives both treatment A and B. In fields such as epidemiology , social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concerns or logistical constraints.
A parallel design , also called a parallel group study, compares two or more treatments. Participants are randomly assigned to either group, treatments are administered, and then the results are compared. A key element of this design is randomization, which places participants randomly into a group. What is the purpose of randomization? Is a crossover trial an RCT? What type of study is a randomized controlled trial?
What level of evidence is an observational study? What is a washout period in clinical trials? What is randomization and what are its advantages? What is unplanned crossover?
What is the strength of a randomized trial? What are the limitations of clinical trials? How does a crossover study reduce experimental variability? What are the strengths and weaknesses of randomized controlled trials? What is a multiple crossover trial? What is a counterbalanced crossover design? What is observational epidemiology? Vaccine trials have to go through a rigorous testing process before being released for use.
This topic is particularly relevant as vaccine developers aim to deliver a SARS-CoV2 vaccine to the population in record time. COVID has highlighted the inefficiencies that exist in clinical research, as well as the frailties of the current publishing system. This blog examines two prominent examples from the pandemic. What are the key steps in EBM? Who are S4BE? Crossover trials: what are they and what are their advantages and limitations? I have a great interest in statistical methods for evidence-based healthcare and clinical epidemiology, especially meta-analyses and systematic reviews.
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