Bhargava Kandala

Department of Pharmaceutics

College of Pharmacy , UF

Design and Analysis of Crossover Study Designs

Crossover StudyTreatments 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 DesignSingle center, double blind, randomized, 3

period, 3 treatment, 3 sequence crossover study

Randomization

Low

Medium

High

Low

Medium

High

Low

Medium

High

Washout Washout

Subjects = 10

Baseline 1

Period 1 (q.d.) 

 

Period 2 (q.d.) Period 3 (q.d.)

Baseline 2 Baseline 3

PD Measurements PD Measurements PD Measurements

1 Week 1 Week5 days 5 days 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 - CovariateAverage baseline

values not significantly different

Presence of significant carryover effects (p-value < 0.05)

No Covariate Analysis of Covariance (ANCOVA)

Baseline – Treatment

β = 0 β = Model Estimate β =1Baseline 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

β cannot be forced to be 1

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

ResultsParameter 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

Reduced impact of the baseline values while using ANCOVA can explain the absence of carryover effects

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

ConclusionsDay 5 data suitable for analysis

Maximum dose resolutionNo carryover effect

Baseline adjustmentSimple difference increases the variability

and introduces carryover effectsANCOVA is the preferred method

Crossover design model with baseline values as covariates will be used for future simulations

Patient Sequence Period 1 Period 2 Period 31 FSP 3500 3200 290010 FSP 3400 2800 220017 FSP 2300 2200 170021 FSP 2300 1300 140023 FSP 3000 2400 18004 SPF 2200 1100 26008 SPF 2800 2000 280016 SPF 2400 1700 34006 PFS 2200 2500 24009 PFS 2200 3200 330013 PFS 800 1400 100020 PFS 950 1320 148026 PFS 1700 2600 240031 PFS 1400 2500 22002 FPS 3100 1800 240011 FPS 2800 1600 220014 FPS 3100 1600 140019 FPS 2300 1500 220025 FPS 3000 1700 260028 FPS 3100 2100 28003 SFP 2100 3200 100012 SFP 1600 2300 160018 SFP 1600 1400 80024 SFP 3100 3200 100027 SFP 2800 3100 20005 PSF 900 1900 29007 PSF 1500 2600 200015 PSF 1200 2200 270022 PSF 2400 2600 380030 PSF 1900 2700 2800