Crossover study
Encyclopedia
A crossover study 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 health-care, especially 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 (Vonesh & Chinchilli; Jones & Kenward). However, the two-period design is often taught in non-statistical textbooks, partly because of its simplicity.
that was specified in the clinical trial protocol
, which needs to have been approved by the appropriate institutional review board
s and regulatory agencies before the trial could begin. Again, the clinical trial protocol
s specify the method of statistical analysis
. Most clinical trials are analyzed using repeated-measurements anova (analysis of variance
) or mixed linear model
s 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
.
. First, the influence of confounding covariate
s 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 covariate
s. 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 design
s).
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.
; 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.
Longitudinal study
A longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time — often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the...
in which subjects receive a sequence
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
of different treatments
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
(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
Education
Education in its broadest, general sense is the means through which the aims and habits of a group of people lives on from one generation to the next. Generally, it occurs through any experience that has a formative effect on the way one thinks, feels, or acts...
, pharmaceutical science, and health-care, especially medicine
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
.
Randomized
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
, controlled, crossover experiments are especially important in health-care. In a randomized clinical trial
Clinical trial
Clinical trials are a set of procedures in medical research and drug development that are conducted to allow safety and efficacy data to be collected for health interventions...
, the subjects are randomly assigned
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
to different arms of the study which receive different treatments. When the randomized
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
clinical trial
Clinical trial
Clinical trials are a set of procedures in medical research and drug development that are conducted to allow safety and efficacy data to be collected for health interventions...
is a repeated measures design
Repeated measures design
The repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
, the same measures are collected multiple times for each subject. A crossover clinical trial
Clinical trial
Clinical trials are a set of procedures in medical research and drug development that are conducted to allow safety and efficacy data to be collected for health interventions...
is a repeated measures design
Repeated measures design
The repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
in which each patient
Patient
A patient is any recipient of healthcare services. The patient is most often ill or injured and in need of treatment by a physician, advanced practice registered nurse, veterinarian, or other health care provider....
is randomly assigned to a sequence
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
of treatments, including at least two treatments (of which one "treatment" may be a standard treatment
Standard treatment
Standard treatment . The treatment that is normally provided to people with a given condition. In many studies, a control group receives the standard treatment while a treatment group receives the experimental treatment...
or a placebo
Placebo
A placebo is a simulated or otherwise medically ineffectual treatment for a disease or other medical condition intended to deceive the recipient...
).
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 (Vonesh & Chinchilli; Jones & Kenward). However, the two-period design is often taught in non-statistical textbooks, partly because of its simplicity.
The Clinical trial protocol specifies the statistical analysis
The data are analyzed using the statistical methodStatistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
that was specified in the clinical trial protocol
Clinical trial protocol
A clinical trial protocol is a document that describes the objective, design, methodology, statistical considerations, and organization of a clinical trial...
, which needs to have been approved by the appropriate institutional review board
Institutional review board
An institutional review board , also known as an independent ethics committee or ethical review board , is a committee that has been formally designated to approve, monitor, and review biomedical and behavioral research involving humans with the aim to protect the rights and welfare of the...
s and regulatory agencies before the trial could begin. Again, the clinical trial protocol
Clinical trial protocol
A clinical trial protocol is a document that describes the objective, design, methodology, statistical considerations, and organization of a clinical trial...
s specify the method of statistical analysis
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
. Most clinical trials are analyzed using repeated-measurements anova (analysis of variance
Analysis of variance
In statistics, analysis of variance is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation...
) or mixed linear model
Linear model
In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However the term is also used in time series analysis with a different...
s that include random effects.
In most longitudinal studies
Longitudinal study
A longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time — often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the...
of human subjects, patients may withdraw from the trial or become "lost to follow-up
Survival analysis
Survival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology...
" (due e.g. to moving abroad or to dying from another disease). There are statistical methods
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
for dealing with such missing-data and "censoring
Censoring (statistics)
In statistics, engineering, and medical research, censoring occurs when the value of a measurement or observation is only partially known.For example, suppose a study is conducted to measure the impact of a drug on mortality. In such a study, it may be known that an individual's age at death is at...
" problems. An important method analyzes the data according to the principle of the intention to treat
Intention to treat analysis
In epidemiology, an intention to treat analysis is an analysis based on the initial treatment intent, not on the treatment eventually administered. ITT analysis is intended to avoid various misleading artifacts that can arise in intervention research...
.
Advantages
A crossover study has two advantages over a non-crossover longitudinal studyLongitudinal study
A longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time — often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the...
. First, the influence of confounding covariate
Covariate
In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable....
s is reduced because each crossover patient serves as his or her own control
Scientific control
Scientific control allows for comparisons of concepts. It is a part of the scientific method. Scientific control is often used in discussion of natural experiments. For instance, during drug testing, scientists will try to control two groups to keep them as identical and normal as possible, then...
. In a non-crossover study, even randomized
Randomization
Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
, it is often the case that different treatment-groups are found to be unbalanced on some covariate
Covariate
In statistics, a covariate is a variable that is possibly predictive of the outcome under study. A covariate may be of direct interest or it may be a confounding or interacting variable....
s. In a controlled, randomized crossover designs, such imbalances are implausible (unless covariates
Time-varying covariate
A time-varying covariate is a term used in statistics, particularly in survival analyses. It reflects the phenomenon that a covariate is not necessarily constant through the whole study...
were to change systematically during the study).
Second, optimal
Optimal design
Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
crossover designs are statistically efficient
Efficiency (statistics)
In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors...
and so require fewer subjects than do non-crossover designs (even other repeated measures design
Repeated measures design
The repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
s).
Optimal
Optimal design
Optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
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
Repeated measures design
The repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
in the graduate textbook by Vonesh and Chinchilli.
Limitations and disadvantages
These studies are often done to improve the symptoms of patients with chronic conditionsChronic (medicine)
A chronic disease is a disease or other human health condition that is persistent or long-lasting in nature. The term chronic is usually applied when the course of the disease lasts for more than three months. Common chronic diseases include asthma, cancer, diabetes and HIV/AIDS.In medicine, the...
; 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
Confounding
In statistics, a confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable...
the estimates
Estimates
In countries using the Westminster system the Estimates are a series of legislative proposals to parliament outlining how the government will spend its money....
of the treatment effects
Effect size
In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity...
. 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
Psychodynamics
Psychodynamics is the theory and systematic study of the psychological forces that underlie human behavior, especially the dynamic relations between conscious motivation and unconscious motivation...
of the treatment
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
, 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
- Chronic conditionChronic (medicine)A chronic disease is a disease or other human health condition that is persistent or long-lasting in nature. The term chronic is usually applied when the course of the disease lasts for more than three months. Common chronic diseases include asthma, cancer, diabetes and HIV/AIDS.In medicine, the...
- Clinical trial protocolClinical trial protocolA clinical trial protocol is a document that describes the objective, design, methodology, statistical considerations, and organization of a clinical trial...
- Design of experimentsDesign of experimentsIn general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
- Glossary of experimental designGlossary of experimental design- Glossary :* Alias: When the estimate of an effect also includes the influence of one or more other effects the effects are said to be aliased . For example, if the estimate of effect D in a four factor experiment actually estimates , then the main effect D is aliased with the 3-way interaction ABC...
- Intention to treat analysisIntention to treat analysisIn epidemiology, an intention to treat analysis is an analysis based on the initial treatment intent, not on the treatment eventually administered. ITT analysis is intended to avoid various misleading artifacts that can arise in intervention research...
- Longitudinal studyLongitudinal studyA longitudinal study is a correlational research study that involves repeated observations of the same variables over long periods of time — often many decades. It is a type of observational study. Longitudinal studies are often used in psychology to study developmental trends across the...
- Missing data
- Observational studyObservational studyIn epidemiology and statistics, an observational study draws inferences about the possible effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator...
- Optimal designOptimal designOptimal designs are a class of experimental designs that are optimal with respect to some statistical criterion.In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance...
- Parallel studyParallel studyA Parallel study is a type of clinical study where two groups of treatments, A and B, are given so that one group receives only A while another group receives only B...
- RandomizationRandomizationRandomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....
- Randomized controlled trialRandomized controlled trialA randomized controlled trial is a type of scientific experiment - a form of clinical trial - most commonly used in testing the safety and efficacy or effectiveness of healthcare services or health technologies A randomized controlled trial (RCT) is a type of scientific experiment - a form of...
- Repeated measures designRepeated measures designThe repeated measures design uses the same subjects with every condition of the research, including the control. For instance, repeated measures are collected in a longitudinal study in which change over time is assessed. Other studies compare the same measure under two or more different conditions...
- SequenceTupleIn mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
- Statistical inferenceStatistical inferenceIn statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
- Survival analysisSurvival analysisSurvival analysis is a branch of statistics which deals with death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, and duration analysis or duration modeling in economics or sociology...
- Treatment effectEffect sizeIn statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity...