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Crossover study

crossover study, crossover study in clinical trials
A crossover study, also referred to as a crossover trial, is a longitudinal study in which subjects receive a sequence of different treatments or exposures While crossover studies can be observational studies, many important crossover studies are controlled experiments, which are discussed in this article Crossover designs are common for experiments in many scientific disciplines, for example psychology, pharmaceutical science, and medicine

Randomized, controlled crossover experiments are especially important in health care In a randomized clinical trial, the subjects are randomly assigned to different arms of the study which receive different treatments When the trial has a repeated measures design, the same measures are collected multiple times for each subject A crossover trial has a repeated measures design in which each patient is assigned to a sequence of treatments, including at least two treatments of which one may be a standard treatment or a placebo

Nearly all crossover designs have "balance", which means that all subjects should receive the same number of treatments and that all subjects participate for the same number of periods In most crossover trials, in fact, each subject receives all treatments, usually in a random order

Statisticians suggest that designs have four periods, a design which allows studies to be truncated to three periods while still enjoying greater efficiency than the two-period design However, the two-period design is often taught in non-statistical textbooks, partly because of its simplicity


  • 1 Clinical trial protocol specifies the statistical analysis
  • 2 Advantages
  • 3 Limitations and disadvantages
  • 4 See also
  • 5 Notes
  • 6 References

Clinical trial protocol specifies the statistical analysis

The data are analyzed using the statistical method that was specified in the clinical trial protocol, which needs to have been approved by the appropriate institutional review boards and regulatory agencies before the trial could begin Again, the clinical trial protocols specify the method of statistical analysis Most clinical trials are analyzed using repeated-measurements anova analysis of variance or mixed models that include random effects

In most longitudinal studies of human subjects, patients may withdraw from the trial or become "lost to follow-up" due eg to moving abroad or to dying from another disease There are statistical methods for dealing with such missing-data and "censoring" problems An important method analyzes the data according to the principle of the intention to treat


A crossover study has two advantages over both a parallel study and a non-crossover longitudinal study First, the influence of confounding covariates is reduced because each crossover patient serves as his or her own control In a non-crossover study, even randomized, it is often the case that different treatment-groups are found to be unbalanced on some covariates In a controlled, randomized crossover designs, such imbalances are implausible unless covariates were to change systematically during the study

Second, optimal crossover designs are statistically efficient and so require fewer subjects than do non-crossover designs even other repeated measures designs

Optimal crossover designs are discussed in the graduate textbook by Jones and Kenward and in the review article by Stufken Crossover designs are discussed along with more general repeated-measurements designs in the graduate textbook by Vonesh and Chinchilli

Limitations and disadvantages

These studies are often done to improve the symptoms of patients with chronic conditions For curative treatments or rapidly changing conditions, cross-over trials may be infeasible or unethical

Crossover studies often have two problems:

First is the issue of "order" effects, because it is possible that the order in which treatments are administered may affect the outcome An example might be a drug with many adverse effects given first, making patients taking a second, less harmful medicine, more sensitive to any adverse effect

Second is the issue of "carry-over" between treatments, which confounds the estimates of the treatment effects In practice, "carry-over" effects can be avoided with a sufficiently long "wash-out" period between treatments However, planning for sufficiently long wash-out periods requires expert knowledge of the dynamics of the treatment, which is often unknown

See also


  1. ^ Vonesh & Chinchilli 1997
  2. ^ Jones & Kenward 2003
  3. ^ Jones, B, & Kenward, M G 2003 Design and analysis of cross-over trials 2nd ed Boca Raton, Fla: Chapman & Hall/CRC


  • M Bose and A Dey 2009 Optimal Crossover Designs World Scientific ISBN 978-9812818423
  • D E Johnson 2010 Crossover experiments WIREs Comp Stat, 2: 620-625
  • Jones, Byron; Kenward, Michael G 2014 Design and Analysis of Cross-Over Trials Third ed London: Chapman and Hall ISBN 0412606402 
  • K-J Lui, 2016 Crossover Designs: Testing, Estimation, and Sample Size Wiley
  • Najafi Mehdi, 2004 Statistical Questions in Evidence Based Medicine New York: Oxford University Press ISBN 0-19-262992-1
  • D Raghavarao and L Padgett 2014 Repeated Measurements and Cross-Over Designs Wiley ISBN 978-1-118-70925-2
  • D A Ratkowsky, M A Evans, and J R Alldredge 1992 Cross-Over Experiments: Design, Analysis, and Application Marcel Dekker ISBN 978-0824788926
  • Senn, S 2002 Cross-Over Trials in Clinical Research, Second edition Wiley ISBN 978-0-471-49653-3
  • Stufken, J 1996 "Optimal Crossover Designs" In Ghosh, S; Rao, C R Design and Analysis of Experiments Handbook of Statistics 13 North-Holland pp 63–90 ISBN 0-444-82061-2 
  • Vonesh, Edward F; Chinchilli, Vernon G 1997 "Crossover Experiments" Linear and Nonlinear Models for the Analysis of Repeated Measurements London: Chapman and Hall pp 111–202 ISBN 0824782488 

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