### Article

## Parallel and cross-over studies in meta-analysis: a case study

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Published: | September 14, 2004 |
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### Outline

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#### Introduction

The objective of performing a meta-analysis of randomized trials in any disease is to increase the power to test the effect of a new treatment based on the sum experience of all clinical trials. Meta-analyses are usually based on trials of parallel group design. However, especially in chronic disease, some of the studies assess the treatment of interest using a cross-over design whereas other trials evaluate the treatment by parallel group design. In a systematic review we were investigating the effect of short acting insulin analogues versus structurally unchanged short acting insulin in patients with diabetes mellitus [Ref. 1]. Out of 27 included studies with type 1 diabetes patients, 18 were of cross-over design and 9 used the parallel group design. In the literature different approaches have been used to deal with the data of both designs in a meta-analysis [Ref. 2]. Our aim was to combine the results from both cross-over and parallel trials into one comprehensive meta-analysis. The practical problems encountered will be discussed.

#### Methods

In the individual studies included in the systematic review, the cross-over design used was the two-period, two-treatment design. In our further work we consider one main endpoint of the systematic review: the percentage of glycated haemoglobin. We assume no period effect and no carryover. The treatment effect in a cross-over trial can be estimated by the mean difference of the treatments or the difference between mean values as with parallel studies. In contrast to parallel trials the standard deviation, standard error or confidence interval for the within-person differences must be calculated. However, the results of cross-over trials are very often reported as though the data comes from a parallel trial, giving the mean values and standard deviations for treatment specific outcomes. In this case, at least the t-statistic or the p-value is needed in order to gather the necessary information for the meta-analysis, given that, in a general approach an estimate of the treatment effect and its standard error is required from each study. We tried to extract this information from all included studies. If no paired results were available these were approximated by assuming a certain degree of correlation between the two different treatment outcomes. For the meta-analysis we calculated the weighted mean difference (WMD) of the percentage of glycated haemoglobin using a random effects model. The robustness of the result was tested in sensitivity analyses by combining parallel studies and cross-over studies separately and treating the data from the cross-over design as if they had come from a parallel group design. Heterogeneity between trials was assessed by the χ^{2} test.

#### Results

In 20 studies of type 1 diabetic patients, data on post treatment HbA1c values could be extracted. There were 13 two-period, two-treatment cross-over trials and 7 studies with parallel group design. In 7 (54%) of the cross-over trials the necessary information was provided whereas in the remaining trials not enough detailed information was reported. In case that no standard error for the within-person differences could be extracted, the correlation between treatment outcomes was approximated using the lowest observed correlation among the other studies (r=0.69). For calculating the WMD using treatment effect and its standard error, for example the *meta* macro of Stata (StataCorp, College Station, TX, USA) or the generic inverse variance method of RevMan 4.2.3 (The Cochrane Collaboration) can be used. The weighted mean difference of HbA1c was estimated to be -0.12% (95% CI: -0.17% to -0.07%) in favour of insulin analogue as compared to structurally unchanged short acting insulin. The test of heterogeneity gave a p-value of 0.06. In the sensitivity analysis performed to assess the impact of the assumed correlation, the result was very similar to the main analysis (-0.13%; 95% CI: -0.18% to -0.07%). The result of the χ^{2} test showed no significant heterogeneity among trials (p=0.92). In the separate analysis of cross-over and parallel trials the results were -0.11% (95% CI: -0.19% to -0.03%) and -0.15% (95% CI: -0.22% to -0.08%), respectively. Cross-over trials showed heterogeneity whereas for parallel trials it was not significant. For parallel group trials, change-from-baseline results were also studied and revealed similar results (-0.11%; 95% CI: -0.20% to -0.03%).

#### Discussion

After the decision is reached that, in principle, cross-over trials should be included in a combined meta-analysis, practical problems arise, as shown in our review, in gathering the data needed for the analysis. These are quite often not available from the publication. Furthermore, as in our case, the cross-over trials had a simple design and it might be even more difficult getting the information if more complex designs are looked at. Comparing the pooled results of the meta-analysis, in which paired analyses were used to the one ignoring the cross-over design, revealed very similar answers. However, when looking at the individual cross-over studies, several confidence intervals are substantially larger when unpaired analysis is performed. This can also be seen in the analysis of heterogeneity. More emphasis has to be put on the fact that the relevant information needed for meta-analysis is included in the original publication of cross-over trials.

### References

- 1.
- Siebenhofer A, Plank J, Berghold A, Narath M, Gfrerer R, Pieber TR. Short acting short acting insulin analogues versus structurally unchanged short acting insulin in patients with diabetes mellitus (Cochrane Review). In: The Cochrane Library, Issue 2, 2004. Chichester, UK: John Wiley & Sons
- 2.
- Curtin F, Altman DG, Elbourne DR. Meta-analysis combining parallel and cross-over clinical trials. Stat in Med. 2002; 21: 2131-2144.