Use of re-randomized data in meta-analysis

Abstract

Background: Outcomes collected in randomized clinical trials are observations of random variables that should be independent and identically distributed. However, in some trials, the patients are randomized more than once thus violating both of these assumptions. The probability of an event is not always the same when a patient is re-randomized; there is probably a non-zero covariance coming from observations on the same patient. This is of particular importance to the meta-analysts.

Methods: We developed a method to estimate the relative error in the risk differences with and without re-randomization of the patients. The relative error can be estimated by an expression depending on the percentage of the patients who were re-randomized, multipliers (how many times more likely it is to repeat an event) for the probability of reoccurrences, and the ratio of the total events reported and the initial number of patients entering the trial.

Results: We illustrate our methods using two randomized trials testing growth factors in febrile neutropenia. We showed that under some circumstances the relative error of taking into account re-randomized patients was sufficiently small to allow using the results in the meta-analysis. Our findings indicate that if the study in question is of similar size to other studies included in the meta-analysis, the error introduced by re-randomization will only minimally affect meta-analytic summary point estimate. We also show that in our model the risk ratio remains constant during the re-randomization, and therefore, if a meta-analyst is concerned about the effect of re-randomization on the meta-analysis, one way to sidestep the issue and still obtain reliable results is to use risk ratio as the measure of interest.

Conclusion: Our method should be helpful in the understanding of the results of clinical trials and particularly helpful to the meta-analysts to assess if re-randomized patient data can be used in their analyses.

Figure 1

Chouaid et al. study

Figure 2

Tree diagram showing the relationships between the variables in the re-randomization process

Figure 3

The 0.05 level curves for the relative difference between the risk difference before and after the re-randomization. We assume that c = 0.40 in this figure. The horizontal axis represents d – the multiplier for the probability of reoccurrence of the event after the re-randomization; The vertical axis represents x – the percentage of the patients who were re-randomized; The curves represent 0.05 relative error level curves for different values of the ratio of the total events reported and the initial number of patients entering the trial. The values of the ratio are indicated at the top of the graph. For a chosen value of the ratio : if a point (d, x) is between the two level curves with identical value (and color) – the relative error of the risk differences is less than 5%; otherwise – the relative error of the risk differences is more than 5%.

Figure 4

Meta-analysis conducted with Review Manager using the reported data from Anaissie et al. with re-randomized data included.

Figure 5

Meta-analysis conducted with Review Manager using our estimates for the data from Anaissie et al. without including the re-randomized data.