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StatsToDo : Cross Over Trials Explained

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Crossover study is an experimental designed where each subject received all the treatments, so that the different outcome caused by different treatments within the same subject can be observed

This research model are increasingly popular in clinical research. The two major advantages are firstly it exposes every subject to all of the alternative treatments, so reducing the overall sample size, and secondly by comparing the effects of the interventions against the very much smaller within subject variations, the model is much more powerful.

Crossover studies however are prone to two major areas of bias. These are period and carry over effects

  • The treatments are given at different times (periods), and the effect of time may contaminate the results. For example, different treatment for asthma may coincide with seasonal variations in pollen count and thus the frequency and severity of attacks. It is also possible that the progression of illness, the gaining of experience, and other time related effect on the individual subjects, may interfere with the effects of interventions.
  • It is also possible that carry over (residual) effects of the earlier treatment may affect observations related to current treatment, so careful design to include a "wash out" period is important. However this is often difficult to achieve, either because of time constraints, or in some studies (e.g. the effect of educational or social intervention) may have a more permanent effect on the subject, and carry over effects may persist.
There are therefore three basic models for the analysis of the crossover experimental design, each attempts to deal with the risks of bias and confounding in a different way.
  • Model 1 follow the arguments provided by Senn in his classic text on crossover trials (see references). He suggested that a complex mathematical approach is both unnecessary and does not necessarily identify carry over effects. From the statistical point of view, carry over effects are difficult to separate from the sequence (group) effect and the interaction between period and treatment. Senn's book suggested that researchers should design their studies to avoid carry over effects as much as possible, then use the period and interaction terms to check that these are not significant, thus ensure that no significant carry over effect exists. The approach is therefore to use the standard multiway Analysis of Variance, like that used in the Latin Square Model, with an initial check on the interaction between periods and treatment. If, as expected, there is no significant interaction, then the variance from interaction can be incorporated with that of error, and a final Analysis of Variance presented.
  • Model 2 is that presented in many statistical text book as the standard Multiway Analysis of Variance, suitable for the Latin Square model, where the variance is partitioned into rows (subjects), columns (periods), and treatment. In the standard Latin Square model, the rows and columns are partitioned to improve the efficiency of the model, and statistical significances are usually not tested. However when used in a crossover study, statistical significance are tested as a way of detecting bias.
  • Model 3, as developed by Williams and presented by Cochran and Cox (see references), argues that the carry over effects are sometimes unavoidable, because of time constraints, or the nature of intervention (such as education), and in some experimental situations, carry over effects may be relevant and need to be identified. The carry over effects should therefore be accepted as part of the information in the research model, identified, estimated, and used to adjust the conclusions of the analysis.