Design and Analysis of Crossover Study
Designs
Bhargava Kandala
Department of Pharmaceutics
College of Pharmacy , UF
Crossover Study
 Treatments




administered in a sequence to each
experimental unit over a set of time periods.
Comparison of treatments on a within-subject level.
Increased precision of treatment comparisons.
A treatment given in one period might influence the
response in the following treatment period –
residual/carryover effect
Baseline values – Can be included as covariates to increase
the precision
Study Design
 Single center, double blind, randomized, 3 period, 3
treatment, 3 sequence crossover study
Period 1 (q.d.)
Subjects = 10
Randomization
Washout
Period 2 (q.d.)
Washout
Period 3 (q.d.)
Low
Low
Low
Medium
Medium
Medium
High
High
High
Baseline 1
Baseline 2
PD Measurements
5 days
Baseline 3
PD Measurements
1 Week
5 days
PD Measurements
1 Week
5 days
Model for Crossover Design

Period 1
2
3
4
5
6
I
A
B
C
A
B
C
II
B
C
A
C
A
B
III
C
A
B
B
C
A
proc glm data = allperiodanaly;
class sequence subject period trt;
model fenoav = sequence
subject(sequence) period trt/solution;
random subject(sequence);
run;
proc mixed data = allperiodanaly;
class sequence subject period trt;
model fenoav = sequence period trt;
random subject(sequence);
lsmeans trt/ pdiff cl;
run;
Baseline
Baseline - Covariate
Baseline Average
80
Baseline Average by Period
75
70
1
2
3
 Average baseline values not
significantly different
 Presence of significant
carryover effects (p-value
< 0.05)
Period
No Covariate
Analysis of Covariance
(ANCOVA)
Baseline –Treatment
β=0
β = Model Estimate
β =1
Baseline is not used as a
covariate
Baseline values are treated as
a quantitative variable
By taking the simple
difference the value of β is
forced to be 1
Carryover Effect
* Covariates tested for carryover;
proc mixed data = allperiodanaly;
class sequence subject period trt;
model fenoav = sequence period fenob trt
carry1 carry2;
random subject(sequence);
lsmeans trt/ pdiff cl e;
run;
Results
Parameter
No Covariate
Analysis of
Covariance
(ANCOVA)
Baseline –
Treatment
β
0
0.38
1
Residual
Variability
85.39
67.02
180.02
Carryover Effect
Not significant
(p-value >0.05)
Not Significant
(p-value>0.05)
Significant
 β cannot be forced to be 1
Results

Parameter
No Covariate
Analysis of
Covariance
(ANCOVA)
Baseline –
Treatment
β
0
0.38
1
Residual
Variability
85.39
67.02
180.02
Carryover Effect
Not significant
(p-value >0.05)
Not Significant
(p-value>0.05)
Significant
Results
Parameter
No Covariate
Analysis of
Covariance
(ANCOVA)
Baseline –
Treatment
β
0
0.38
1
Residual
Variability
85.39
67.02
180.02
Carryover Effect
Not significant
(p-value >0.05)
Not Significant
(p-value>0.05)
Significant
 Reduced impact of the baseline values while using ANCOVA
can explain the absence of carryover effects
Conclusions
 Day 5 data suitable for analysis
 Maximum dose resolution
 No carryover effect
 Baseline adjustment
 Simple difference increases the variability and introduces
carryover effects
 ANCOVA is the preferred method
 Crossover design model with baseline values as covariates
will be used for future simulations