Crossover Trials:
Design and Analysis
Peter T. Donnan
Professor of Epidemiology and Biostatistics
Objectives of session
• Understand what is meant by a
crossover trial design
• Understand the correlated nature
of data
• Able to implement crossover
analysis with continuous outcome in
SPSS and SAS
• Interpret the output
Crossover designs
•In this design each patient receives
ALL treatments
•Comparison of treatments is withinpatient comparison
•Removes all fixed within-patient
factors e.g. gender
•Essentially a matched design
Randomisation
•Order of receipt is randomised
•With 2-period, 2-treatments – AB or BA
•With 3-preriod, 3-treatments –
•ABC, ACB, BAC, BCA, CAB, CBA
•Note above are balanced in the sense that
every patient gets every treatment
•Requires a wash-out period between
treatments – to prevent CARRY-OVER
Crossover Trial
Eligible subjects
RANDOMISED
Intervention
Wash-out
Control
Wash-out
Control
Intervention
Efficiency of Crossover
design
•
To estimate efficiency we can compare the variances
•
For a similar parallel trial design:
• Total number M = 2N / (1 – rho)
•
Where M is the total size of the parallel trial and N
is the number of subjects in the crossover design
and rho is the correlation between measurements in
Period I and II between a random subject
•
So a similar parallel trial design requires AT LEAST
TWICE as many subjects
Strengths and Weaknesses of
crossover design
•
Within patient characteristics remain same since
matched analysis
•
Smaller sample size needed compared with parallel
design - Very efficient design
•
Not suitable for intervention that ‘cures’ condition
•
Used for treatments of symptoms / control in
chronic conditions; pain, asthma, COPD, diabetes,
MS, hypertension, etc.
•
Fails if carry-over effect from previous period
Senn S. (1993) Crossover trials in clinical research. Chichester, John Wiley
Simple Analysis
Simple analysis makes use of the
within-patient comparison:
• Paired t-test for continuous
outcomes
• McNemar’s Chi-squared test
for categorical data
Organisation of data
Trial of hypertension drug A vs Drug B, 109
randomised with n=55 AB and n = 54 BA
ID
Systolic after
A
Systolic B
after B
Diff (A-B)
1
174
180
-6
2
162
173
-11
3
182
179
3
4
167
168
-1
5
…
Paired t-test
Trial of hypertension drug A vs Drug B, 109
randomised with n=55 AB and n = 54 BA
t = Mean difference / Se (differences)
= 3.94 / 1.67
= 2.36
So with 108 df , p = 0.02
• So a statistically significant effect with drug A
generally lower BP
• Analysis assumes no PERIOD effect and
• No CARRY-OVER effect
Paired t-test
In SPSS:
Analyze
Compare Means
Paired-Samples t-test
Then select two columns with the BP
measurements for each drug
Examining the
assumptions
We can test for a PERIOD x TREATMENT
interaction i.e.
Does the effect of the drug vary
depending on whether it is given in the
first period compared to the second
period?
Common reason is CARRY-OVER
Test for interaction is independent ttest for continuous outcome
Period X Treatment
interaction
Independent t-test
AB
BA
Num.
55
54
Mean of patient
means
180.1
178.3
SD
26.3
26.6
t = 0.77 which is not significant
Period X Treatment
interaction
Unfortunately the test is not very powerful
and carry-over may not be detected with
small sample size even if present
(Solution: design study to be powerful enough!)
If detected then the simple treatment
analysis could be BIASED as the effect
depends on which period the patients got
which drug
Then only use comparison in FIRST period for
treatment effect (Grizzle two-step analysis).
Grizzle Two-stage
analysis not recommended
Senn (1994) says:
•Two-step approach does not remove
potential bias and carry-over test is
usually underpowered
•Test on period 1 is also underpowered
•Best approach is to make sure there is
NO carry-over with an efficient washout!
•FDA recommend Washout ≥ 3 x halflife of drug
Senn’s advice
Senn (1994) offers this advice:
…my advice to the trialist is
under no circumstances must the
two-stage procedure be used.”
Senn’s proposed
analysis
Make use of the two baseline measures
in a two period design so we have four
measurements
ID
Order Baseline
BP
Baseline
BP
(1=AB,
A
after A
B
after B
2=BA)
Diff
Baseline
(A–B)
Diff
Outcome
(A-B)
1
1
172
174
180
180
-8
-6
2
2
160
162
176
173
-4
-11
3
2
182
182
178
179
2
3
4
1
170
167
180
168
-10
-1
….
Senn’s proposed
analysis
Use Generalised Linear Models (GLM)
Fit simple SAS model as below:
proc glm;
class ORDER;
model OUTCOME = ORDER BASELINE;
Estimate ‘TREATMENT’ intercept 1;
run;
Intercept value is the TREATMENT effect and p-value
Baseline can be removed to assess the effect of
baseline in results
Senn’s proposed
analysis
Generalized Linear Models (GLM) include both
continuous and categorical data and can be
fitted in SPSS
Analyze
Generalized Linear Model
etc…
n.b. SPSS offers Generalized Estimating Equations
(GEE) for binary outcomes
Other pitfalls
• Patient drop-out in the first period can mean
•
•
•
there are fewer in the second period and
potentially with different characteristics
Analysis of only complete data or ‘Per
Protocol’ is likely to be BIASED and breaks
the Intention-To-Treat (ITT) principle
Consider Multiple Imputation but assumes
data is Missing-At-Random (MAR)
Alternatively use Mixed Models (also assumes
MAR)
Summary
•
•
•
•
Design is powerful and efficient
Eliminates within-patient confounding
Opportunity for head-to-head trials
Problem of carry-over effect; test
often underpowered
• Drop-outs break ITT principle and per
protocol analysis could bias results
References
Senn S. (2002) Crossover trials in clinical research. Chichester,
John Wiley
Mills JM, Chan A-W, Wu P, Vail A, Guyatt GH, Altman DG.
Design, analysis and presentation of crossover trials. BMC
Trials 2009; 10: 27
Schouten H and Kester A. A simple analysis of a simp[le
crossover trial with a dichotomous outcome measure. Statist
Med 2010; 29: 193-198
Senn S. The AB/BA crossover: past, present and future?
Statistical Methods in Medical Research 1994; 3:303-324.
Thank you
for
listening!