"Crossover experiment" redirects here. For the chemical reaction/mechanism analysis, see crossover experiment (chemistry).
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, education, 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 randomized clinical trial is a repeated measures design, the same measures are collected multiple times for each subject. A crossover clinical trial is a repeated measures design in which each patient is randomly assigned to a sequence of treatments, including at least two treatments (of which one "treatment" 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.
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.[1][2] However, the two-period design is often taught in non-statistical textbooks, partly because of its simplicity.
Contents
- 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[edit]
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 e.g. 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.
Advantages[edit]
A crossover study has two advantages over 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[edit]
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, the planning for sufficiently long wash-out periods does require expert knowledge of the dynamics of the treatment, which often is unknown, of course.
Also, there might be a "learning" effect. This is important where you have controls who are naive to the intended therapy. In such a case e.g. you cannot make a group (typically the group which learned the skill first) unlearn a skill such as yoga and then act as a control in the second phase of the study.
See also[edit]
- Chronic condition
- Clinical trial protocol
- Design of experiments
- Glossary of experimental design
- Longitudinal study
|
- Missing data
- Optimal design
- Parallel study
- Randomization
- Randomized controlled trial
|
- Repeated measures design
- Survival analysis
- Treatment effect
|
Notes[edit]
- ^ Vonesh & Chinchilli (1997)
- ^ Jones & Kenward (2003)
References[edit]
- Jones, Byron; Kenward, Michael G. (2003). Design and Analysis of Cross-Over Trials (Second ed.). London: Chapman and Hall. ISBN 0412606402.
- Najafi Mehdi, (2004). Statistical Questions in Evidence Based Medicine. New York: Oxford University Press. ISBN 0-19-262992-1
- 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. and 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.
|
Design of experiments
|
|
Scientific
Method |
- Scientific experiment
- Statistical design
- Control
- Internal & external validity
- Experimental unit
- Blinding
- Optimal design: Bayesian
- Random assignment
- Randomization
- Restricted randomization
- Replication versus subsampling
- Sample size
|
|
Treatment
& Blocking |
- Treatment
- Effect size
- Contrast
- Interaction
- Confounding
- Orthogonality
- Blocking
- Covariate
- Nuisance variable
|
|
Models
& Inference |
- Linear regression
- Ordinary least squares
- Bayesian
- Random effect
- Mixed model
- Hierarchical model: Bayesian
- Analysis of variance (Anova)
- Cochran's theorem
- Manova (multivariate)
- Ancova (covariance)
- Compare means
- Multiple comparison
|
|
Designs:
Completely
Randomized |
- Factorial
- Fractional factorial
- Plackett-Burman
- Taguchi
- Response surface methodology
- Polynomial & rational modeling
- Box-Behnken
- Central composite
- Block
- Generalized randomized block design (GRBD)
- Latin square
- Graeco-Latin square
- Orthogonal array
- Latin hypercube
Repeated measures design
- Crossover study
- Randomized controlled trial
- Sequential analysis
- Sequential probability ratio test
|
|
- Glossary
- Category
- Statistics portal
- Statistical outline
- Statistical topics
|
|
|
Statistics
|
|
|
Descriptive statistics
|
|
| Continuous data |
| Location |
- Mean (Arithmetic, Geometric, Harmonic)
- Median
- Mode
|
|
| Dispersion |
- Range
- Standard deviation
- Coefficient of variation
- Percentile
- Interquartile range
|
|
| Shape |
- Variance
- Skewness
- Kurtosis
- Moments
- L-moments
|
|
|
| Count data |
|
|
| Summary tables |
- Grouped data
- Frequency distribution
- Contingency table
|
|
| Dependence |
- Pearson product-moment correlation
- Rank correlation (Spearman's rho, Kendall's tau)
- Partial correlation
- Scatter plot
|
|
| Statistical graphics |
- Bar chart
- Biplot
- Box plot
- Control chart
- Correlogram
- Forest plot
- Histogram
- Pie chart
- Q–Q plot
- Run chart
- Scatter plot
- Stemplot
- Radar chart
|
|
|
|
|
Data collection
|
|
| Designing studies |
- Effect size
- Standard error
- Statistical power
- Sample size determination
|
|
| Survey methodology |
- Sampling
- Stratified sampling
- Opinion poll
- Questionnaire
|
|
| Controlled experiment |
- Design of experiments
- Randomized experiment
- Random assignment
- Replication
- Blocking
- Factorial experiment
- Optimal design
|
|
| Uncontrolled studies |
- Natural experiment
- Quasi-experiment
- Observational study
|
|
|
|
|
Statistical inference
|
|
| Statistical theory |
- Sampling distribution
- Order statistics
- Sufficiency
- Completeness
- Exponential family
- Permutation test (Randomization test)
- Empirical distribution
- Bootstrap
- U statistic
- Efficiency
- Asymptotics
- Robustness
|
|
| Frequentist inference |
- Unbiased estimator (Mean unbiased minimum variance, Median unbiased)
- Biased estimators (Maximum likelihood, Method of moments, Minimum distance, Density estimation)
- Confidence interval
- Testing hypotheses
- Power
- Parametric tests (Likelihood-ratio, Wald, Score)
|
|
| Specific tests |
- Z (normal)
- Student's t-test
- F
- Goodness of fit (Chi-squared, G, Sample source, sample normality, Skewness & kurtosis Normality, Model comparison, Model quality)
- Signed-rank (1-sample, 2-sample, 1-way anova)
- Shapiro–Wilk
- Kolmogorov–Smirnov
|
|
| Bayesian inference |
- Bayesian probability
- Prior
- Posterior
- Credible interval
- Bayes factor
- Bayesian estimator
- Maximum posterior estimator
|
|
|
|
|
Correlation and regression analysis
|
|
| Correlation |
- Pearson product–moment correlation
- Partial correlation
- Confounding variable
- Coefficient of determination
|
|
| Regression analysis |
- Errors and residuals
- Regression model validation
- Mixed effects models
- Simultaneous equations models
- MARS
|
|
| Linear regression |
- Simple linear regression
- Ordinary least squares
- General linear model
- Bayesian regression
|
|
| Non-standard predictors |
- Nonlinear regression
- Nonparametric
- Semiparametric
- Isotonic
- Robust
- Heteroscedasticity
- Homoscedasticity
|
|
| Generalized linear model |
- Exponential families
- Logistic (Bernoulli)
- Binomial
- Poisson
|
|
| Partition of variance |
- Analysis of variance (ANOVA)
- Analysis of covariance
- Multivariate ANOVA
- Degrees of freedom
|
|
|
|
|
Categorical, multivariate, time-series, or survival analysis
|
|
| Categorical data |
- Cohen's kappa
- Contingency table
- Graphical model
- Log-linear model
- McNemar's test
|
|
| Multivariate statistics |
- Multivariate regression
- Principal components
- Factor analysis
- Cluster analysis
- Classification
- Copulas
|
|
| Time series analysis |
| General |
- Decomposition
- Trend
- Stationarity
- Seasonal adjustment
- Exponential smoothing
- Cointegration
|
|
| Specific tests |
- Granger causality
- Q-Statistic
- Durbin–Watson
|
|
| Time domain |
- ACF
- PACF
- XCF
- ARMA model
- ARIMA model
- ARCH
- Vector autoregression
|
|
| Frequency domain |
- Spectral density estimation
- Fourier analysis
|
|
|
| Survival analysis |
- Survival function
- Kaplan–Meier
- Logrank test
- Failure rate
- Proportional hazards models
- Accelerated failure time model
|
|
|
|
|
Applications
|
|
| Biostatistics |
- Bioinformatics
- Clinical trials & studies
- Epidemiology
- Medical statistics
|
|
| Engineering statistics |
- Chemometrics
- Methods engineering
- Probabilistic design
- Process & Quality control
- Reliability
- System identification
|
|
| Social statistics |
- Actuarial science
- Census
- Crime statistics
- Demography
- Econometrics
- National accounts
- Official statistics
- Population
- Psychometrics
|
|
| Spatial statistics |
- Cartography
- Environmental statistics
- Geographic information system
- Geostatistics
- Kriging
|
|
|
|
- Category
- Portal
- Outline
- Index
|
|