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- One group is assessed before and after the experimental intervention, whereas two other groups provide respective, independent treatment comparisons in each period. We call this a dog-leg design because of the pattern of assessments in the three groups.
pubmed.ncbi.nlm.nih.gov/24453236/
One group is assessed before and after the experimental intervention, whereas two other groups provide respective, independent treatment comparisons in each period. We call this a dog-leg design because of the pattern of assessments in the three groups.
- Richard Hooper, Liam Bourke
- 2014
- Introduction
- Methods
- Results
- Discussion
- Conclusions
- Funding
- Acknowledgements
Cross-over trials—clinical trials in which participants act as their own controls and are randomized to the order in which they get the experimental and control treatments—are contraindicated when the effects of treatment could carry over from one period of the trial to the next.1 They can work well for pharmacokinetic trials,2but are problematic f...
Design
Figure 1 illustrates the design. Figure 1a shows the timing of the intervention and assessments post-randomization. Routine care is assumed to be given up to the point where any intervention is indicated. Figure 1b is a schema for the schedule of assessments, distinguishing between assessments conducted before and after the intervention. Participants are randomized into three arms: in the central arm (group 2), participants act as their own controls, being assessed both before and after the e...
Statistical model
The standard error of the treatment effect could be derived using the theory of generalized least squares estimators, whereby the variance-covariance matrix of the estimator is given by , but for the model specified above the standard error can be derived without recourse to matrix inversion by directly determining the minimum variance unbiased estimator (see Appendix, available as Supplementary data at IJE online). By comparing this standard error with the standard error from an ANCOVA in a...
Correlation between baseline and follow-up—a systematic review
The relative advantages of different trial designs depend on the correlation between assessments before and after intervention in the same individual. Sample size calculations for trials have tended to assume this correlation is moderate.3 To provide information for this article on typical correlations, we systematically reviewed clinical trials published in the Lancet or New England Journal of Medicine between 01 January 2012 and 31 March 2013. Details of methods and results are given in the...
Relative efficiency
Figure 2(a) shows the relative efficiency of the dog-leg design compared with a parallel groups design analysed with ANCOVA, plotted against p for various values of r. The best choice of p depends on r, but close-to-optimal performance can be achieved over a wide range of r-values by choosing p= 1/3, that is by allocating participants to arms in the ratio 1:1:1. Figure 2(b) shows the relative efficiency plotted against r for allocation ratios 1:1:1 (p = 1/3), 1:2:1 (p = 0·25) and 2:1:2 (p = 0...
Sample size
Using the above expression for the standard error of the treatment effect, we constructed a table of the sample size per group needed to achieve 80% or 90% power at the 5% significance level with a dog-leg design, assuming a variety of effect sizes and correlations between baseline and follow-up, and with a 1:1:1 allocation ratio to the three arms (Table 1). Sample size tables for parallel groups trials with and without baseline assessments are widely available.7 For example, an investigator...
Correlation between baseline and follow-up
Of 250 clinical trials published in the Lancet and New England Journal of Medicine between 01 January 2012 and 31 March 2013, 36 met the criteria specified in our systematic review. We were able to calculate 30 correlations from 23 of these trials (see online supplement, available as Supplementary data at IJEonline): these correlations had a median of 0·71, with interquartile range 0·59 to 0·80.
Adding further assessments
As with any design, the power of the dog-leg could potentially be increased by adding assessments. Not all such augmentations are helpful, however. A second assessment in group 1 (period 2) could not be used to estimate the treatment effect because we are assuming nothing about the carry-over effect of the experimental intervention. A baseline assessment (at the time of randomization) in group 1 is also of little help by itself if no other group is assessed at randomization for comparison, si...
Practicalities of running a dog-leg trial
The dog-leg design is unconventional in having a different schedule of assessments in each randomized arm. Group 1 participants are not assessed in the second period of the trial, nor is the analysis affected by the treatment they receive in this period. The trial protocol should specify how participants in group 1 are to be treated in the second period: a choice that can be made according to ethical and scientific considerations. Group 3 participants, meanwhile, are not assessed until the se...
Dependence on the correlation
A curious feature of the dog-leg design is that its efficiency relative to a parallel groups design analysed with ANCOVA first increases, and then decreases with increasing correlation between baseline and follow-up assessments. This is because for small r, the ANCOVA is able to take relatively little advantage of the baseline assessment, whereas the dog-leg design is able to benefit from some participants being their own controls (a benefit which increases as the correlation increases). For...
The dog-leg design requires fewer participants for the same power than a parallel groups design with a baseline assessment if the correlation between baseline and follow-up is not too high. From our review we conclude that correlations below 0·7 are not uncommon in studies of chronic diseases. The dog-leg design also requires even fewer assessments...
R.H. is partially supported by the UK National Institute for Health Research through its funding for Research Design Service London. L.B. is supported by the Higher Education Funding Council for England.
We thank three reviewers of an earlier draft for their very valuable input. Conflict of interest:None declared.
- Richard Hooper, Liam Bourke
- 2014
Nov 29, 2013 · We describe a simple but novel alternative design and its performance characteristics. One group is assessed before and after the experimental intervention, while two further, independent groups provide treatment comparisons at each time point. We call this a dog-leg design because of the pattern of assessments in the three groups.
Mar 17, 2014 · We’ve called it the dog-leg trial. Dog-leg and stepped wedge. The design, which we published in the International Journal of Epidemiology, took its inspiration from another variant of the...
Nov 29, 2013 · The dog-leg design is reminiscent of a stepped wedge design, but with a reduced schedule of assessments and with the notable difference that not all groups receive the intervention.
Jan 22, 2014 · The dog-leg design is reminiscent of a stepped wedge design, but with a reduced schedule of assessments and with the notable difference that not all groups receive the intervention.
Jun 26, 2021 · The Interrupted Time Series (ITS) is a quasi-experimental design commonly used in public health to evaluate the impact of interventions or exposures. Multiple statistical methods are available to analyse data from ITS studies, but no empirical investigation has examined how the different methods compare when applied to real-world datasets.
