Crossover Trials:

Design and Analysis

Peter T. Donnan

Professor of Epidemiology and Biostatistics

Objectives of sessionObjectives of session

• Understand what is meant by a Understand what is meant by a crossover trial designcrossover trial design

• Understand the correlated Understand the correlated nature of datanature of data

• Able to implement crossover Able to implement crossover analysis with continuous analysis with continuous outcome in SPSS and SASoutcome in SPSS and SAS

• Interpret the outputInterpret the output

• Understand what is meant by a Understand what is meant by a crossover trial designcrossover trial design

• Understand the correlated Understand the correlated nature of datanature of data

• Able to implement crossover Able to implement crossover analysis with continuous analysis with continuous outcome in SPSS and SASoutcome in SPSS and SAS

• Interpret the outputInterpret the output

Crossover designsCrossover designs

•In this design each patient In this design each patient receives ALL treatmentsreceives ALL treatments

•Comparison of treatments is Comparison of treatments is within-patient comparisonwithin-patient comparison

•Removes all fixed within-patient Removes all fixed within-patient factors e.g. genderfactors e.g. gender

•Essentially a matched designEssentially a matched design

RandomisationRandomisation

•OrderOrder of receipt is randomised of receipt is randomised

•With 2-period, 2-treatments – With 2-period, 2-treatments – AB or AB or BABA

•With 3-preriod, 3-treatments – With 3-preriod, 3-treatments –

•ABC, ACB, BAC, BCA, CAB, CBA ABC, ACB, BAC, BCA, CAB, CBA

•Note above are balanced in the sense Note above are balanced in the sense that every patient gets every that every patient gets every treatmenttreatment

•Requires a wash-out period between Requires a wash-out period between treatments – to prevent CARRY-OVERtreatments – to prevent CARRY-OVER

Crossover TrialCrossover Trial

RANDOMISED

Eligible subjects

Intervention

Control

Control Intervention

Wash-outWash-out Wash-outWash-out

Efficiency of Crossover Efficiency of Crossover designdesign

• To estimate efficiency we can compare the To estimate efficiency we can compare the variancesvariances

• For a similar parallel trial design:For a similar parallel trial design:

• Total number M = 2N / (1 – rho)Total number M = 2N / (1 – rho)• Where M is the total size of the parallel trial Where M is the total size of the parallel trial

and N is the number of subjects in the and N is the number of subjects in the crossover design and rho is the correlation crossover design and rho is the correlation between measurements in Period I and II between measurements in Period I and II between a random subjectbetween a random subject

• So a similar parallel trial design requires AT So a similar parallel trial design requires AT LEAST TWICE as many subjectsLEAST TWICE as many subjects

Strengths and Weaknesses Strengths and Weaknesses of crossover designof crossover design

• Within patient characteristics remain same Within patient characteristics remain same since matched analysissince matched analysis

• Smaller sample size needed compared with Smaller sample size needed compared with parallel design - Very efficient designparallel design - Very efficient design

• Not suitable for intervention that ‘cures’ Not suitable for intervention that ‘cures’ conditioncondition

• Used for treatments of symptoms / control Used for treatments of symptoms / control in chronic conditions; pain, asthma, COPD, in chronic conditions; pain, asthma, COPD, diabetes, MS, hypertension, etc.diabetes, MS, hypertension, etc.

• Fails if carry-over effect from previous Fails if carry-over effect from previous periodperiod

Senn S. (1993) Crossover trials in clinical research. Chichester, John Wiley

Simple AnalysisSimple Analysis

Simple analysis makes use Simple analysis makes use of the within-patient of the within-patient comparison:comparison:

• Paired t-test for Paired t-test for continuous outcomescontinuous outcomes

• McNemar’s Chi-squared McNemar’s Chi-squared test for categorical datatest for categorical data

Simple analysis makes use Simple analysis makes use of the within-patient of the within-patient comparison:comparison:

• Paired t-test for Paired t-test for continuous outcomescontinuous outcomes

• McNemar’s Chi-squared McNemar’s Chi-squared test for categorical datatest for categorical data

Organisation of data Organisation of data

Trial of hypertension drug A vs Drug B, Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 109 randomised with n=55 AB and n = 54 BA 54 BA

Trial of hypertension drug A vs Drug B, Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 109 randomised with n=55 AB and n = 54 BA 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-testPaired t-test

Trial of hypertension drug A vs Drug B, Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 109 randomised with n=55 AB and n = 54 BA54 BA

Trial of hypertension drug A vs Drug B, Trial of hypertension drug A vs Drug B, 109 randomised with n=55 AB and n = 109 randomised with n=55 AB and n = 54 BA54 BAt = Mean difference / Se t = Mean difference / Se

(differences)(differences) = 3.94 / 1.67= 3.94 / 1.67 = 2.36= 2.36So with 108 df , p = 0.02So with 108 df , p = 0.02

•So a statistically significant effect with drug So a statistically significant effect with drug A generally lower BPA generally lower BP•Analysis assumes no PERIOD effect andAnalysis assumes no PERIOD effect and•No CARRY-OVER effectNo CARRY-OVER effect

Paired t-testPaired t-test

Then select two columns with the BP Then select two columns with the BP measurements for each drugmeasurements for each drug

Then select two columns with the BP Then select two columns with the BP measurements for each drugmeasurements for each drug

In SPSS:In SPSS:

AnalyzeAnalyzeCompare MeansCompare Means

Paired-Samples t-Paired-Samples t-testtest

Examining the Examining the assumptionsassumptions

We can test for a We can test for a PERIOD x PERIOD x TREATMENT TREATMENT interaction i.e. interaction i.e. Does the effect of the drug vary Does the effect of the drug vary depending on whether it is given in depending on whether it is given in the first period compared to the the first period compared to the second period?second period?

Common reason is Common reason is CARRY-OVERCARRY-OVERTest for interaction is independent t-Test for interaction is independent t-test for continuous outcometest for continuous outcome

We can test for a We can test for a PERIOD x PERIOD x TREATMENT TREATMENT interaction i.e. interaction i.e. Does the effect of the drug vary Does the effect of the drug vary depending on whether it is given in depending on whether it is given in the first period compared to the the first period compared to the second period?second period?

Common reason is Common reason is CARRY-OVERCARRY-OVERTest for interaction is independent t-Test for interaction is independent t-test for continuous outcometest for continuous outcome

Period X Treatment Period X Treatment interactioninteraction

Independent t-test Independent t-test

t = 0.77 which is not significantt = 0.77 which is not significant

Independent t-test Independent t-test

t = 0.77 which is not significantt = 0.77 which is not significant

AB BA

Num. 55 54

Mean of patient means

180.1 178.3

SD 26.3 26.6

Period X Treatment Period X Treatment interactioninteraction

Unfortunately the test is not very powerful Unfortunately the test is not very powerful and carry-over may not be detected with and carry-over may not be detected with small sample size even if presentsmall sample size even if present(Solution: design study to be powerful (Solution: design study to be powerful enough!)enough!)

If detected then the simple treatment If detected then the simple treatment analysis could be BIASED as the effect analysis could be BIASED as the effect depends on which period the patients got depends on which period the patients got which drugwhich drugThen only use comparison in FIRST period Then only use comparison in FIRST period for treatment effect (Grizzle two-step for treatment effect (Grizzle two-step analysis).analysis).

Unfortunately the test is not very powerful Unfortunately the test is not very powerful and carry-over may not be detected with and carry-over may not be detected with small sample size even if presentsmall sample size even if present(Solution: design study to be powerful (Solution: design study to be powerful enough!)enough!)

If detected then the simple treatment If detected then the simple treatment analysis could be BIASED as the effect analysis could be BIASED as the effect depends on which period the patients got depends on which period the patients got which drugwhich drugThen only use comparison in FIRST period Then only use comparison in FIRST period for treatment effect (Grizzle two-step for treatment effect (Grizzle two-step analysis).analysis).

Grizzle Two-stage Grizzle Two-stage analysis analysis notnot

recommendedrecommendedSenn (1994) says:Senn (1994) says:

•Two-step approach does not remove Two-step approach does not remove potential bias and carry-over test is potential bias and carry-over test is usually underpoweredusually underpowered•Test on period 1 is also underpoweredTest on period 1 is also underpowered•Best approach is to make sure there Best approach is to make sure there is NO carry-over with an efficient wash-is NO carry-over with an efficient wash-out!out!•FDA recommend Washout FDA recommend Washout ≥ ≥ 3 x half-3 x half-life of druglife of drug

Senn (1994) says:Senn (1994) says:

•Two-step approach does not remove Two-step approach does not remove potential bias and carry-over test is potential bias and carry-over test is usually underpoweredusually underpowered•Test on period 1 is also underpoweredTest on period 1 is also underpowered•Best approach is to make sure there Best approach is to make sure there is NO carry-over with an efficient wash-is NO carry-over with an efficient wash-out!out!•FDA recommend Washout FDA recommend Washout ≥ ≥ 3 x half-3 x half-life of druglife of drug

Senn’s adviceSenn’s advice

Senn (1994) offers this Senn (1994) offers this advice:advice:

……my advice to the trialist is my advice to the trialist is under no circumstances under no circumstances must the two-stage must the two-stage procedure be used.”procedure be used.”

Senn (1994) offers this Senn (1994) offers this advice:advice:

……my advice to the trialist is my advice to the trialist is under no circumstances under no circumstances must the two-stage must the two-stage procedure be used.”procedure be used.”

Senn’s proposed Senn’s proposed analysisanalysis

Make use of the two baseline Make use of the two baseline measures in a two period design measures in a two period design so we have four measurementsso we have four measurements

Make use of the two baseline Make use of the two baseline measures in a two period design measures in a two period design so we have four measurementsso we have four measurements

ID Order(1=AB,2=BA

)

Baseline A

BP after

A

Baseline B

BP after

B

Diff Baseline

(A–B)

Diff Outcom

e(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 Senn’s proposed analysisanalysis

Use Generalised Linear Models (GLM)Use Generalised Linear Models (GLM)Fit simple SAS model as below:Fit simple SAS model as below: proc glm;proc glm;

class ORDER;class ORDER;model OUTCOME = ORDER BASELINE;model OUTCOME = ORDER BASELINE;Estimate ‘TREATMENT’ intercept 1;Estimate ‘TREATMENT’ intercept 1;

run;run;

Intercept value is the TREATMENT effect and p-Intercept value is the TREATMENT effect and p-valuevalueBaseline can be removed to assess the effect of Baseline can be removed to assess the effect of baseline in resultsbaseline in results

Use Generalised Linear Models (GLM)Use Generalised Linear Models (GLM)Fit simple SAS model as below:Fit simple SAS model as below: proc glm;proc glm;

class ORDER;class ORDER;model OUTCOME = ORDER BASELINE;model OUTCOME = ORDER BASELINE;Estimate ‘TREATMENT’ intercept 1;Estimate ‘TREATMENT’ intercept 1;

run;run;

Intercept value is the TREATMENT effect and p-Intercept value is the TREATMENT effect and p-valuevalueBaseline can be removed to assess the effect of Baseline can be removed to assess the effect of baseline in resultsbaseline in results

Senn’s proposed Senn’s proposed analysisanalysis

Generalized Linear Models (GLM) include Generalized Linear Models (GLM) include both continuous and categorical data both continuous and categorical data and can be fitted in SPSSand can be fitted in SPSS

AnalyzeAnalyzeGeneralized Linear ModelGeneralized Linear Model

etc…etc… n.b. SPSS offers Generalized Estimating n.b. SPSS offers Generalized Estimating Equations (GEE) for binary outcomesEquations (GEE) for binary outcomes

Generalized Linear Models (GLM) include Generalized Linear Models (GLM) include both continuous and categorical data both continuous and categorical data and can be fitted in SPSSand can be fitted in SPSS

AnalyzeAnalyzeGeneralized Linear ModelGeneralized Linear Model

etc…etc… n.b. SPSS offers Generalized Estimating n.b. SPSS offers Generalized Estimating Equations (GEE) for binary outcomesEquations (GEE) for binary outcomes

Other pitfalls Other pitfalls

• Patient drop-out in the first period can Patient drop-out in the first period can mean there are fewer in the second period mean there are fewer in the second period and potentially with different characteristicsand potentially with different characteristics

• Analysis of only complete data or ‘Per Analysis of only complete data or ‘Per Protocol’ is likely to be BIASED and breaks Protocol’ is likely to be BIASED and breaks the Intention-To-Treat (ITT) principlethe Intention-To-Treat (ITT) principle

• Consider Multiple Imputation but assumes Consider Multiple Imputation but assumes data is Missing-At-Random (MAR)data is Missing-At-Random (MAR)

• Alternatively use Mixed Models (also Alternatively use Mixed Models (also assumes MAR)assumes MAR)

• Patient drop-out in the first period can Patient drop-out in the first period can mean there are fewer in the second period mean there are fewer in the second period and potentially with different characteristicsand potentially with different characteristics

• Analysis of only complete data or ‘Per Analysis of only complete data or ‘Per Protocol’ is likely to be BIASED and breaks Protocol’ is likely to be BIASED and breaks the Intention-To-Treat (ITT) principlethe Intention-To-Treat (ITT) principle

• Consider Multiple Imputation but assumes Consider Multiple Imputation but assumes data is Missing-At-Random (MAR)data is Missing-At-Random (MAR)

• Alternatively use Mixed Models (also Alternatively use Mixed Models (also assumes MAR)assumes MAR)

SummarySummary

• Design is powerful and efficient Design is powerful and efficient • Eliminates within-patient confoundingEliminates within-patient confounding• Opportunity for head-to-head trialsOpportunity for head-to-head trials• Problem of carry-over effect; test Problem of carry-over effect; test

often underpoweredoften underpowered• Drop-outs break ITT principle and per Drop-outs break ITT principle and per

protocol analysis could bias resultsprotocol analysis could bias results

• Design is powerful and efficient Design is powerful and efficient • Eliminates within-patient confoundingEliminates within-patient confounding• Opportunity for head-to-head trialsOpportunity for head-to-head trials• Problem of carry-over effect; test Problem of carry-over effect; test

often underpoweredoften underpowered• Drop-outs break ITT principle and per Drop-outs break ITT principle and per

protocol analysis could bias resultsprotocol analysis could bias results

ReferencesReferences

Senn S. (2002) Crossover trials in clinical research. Senn S. (2002) Crossover trials in clinical research. Chichester, John WileyChichester, John Wiley

Mills JM, Chan A-W, Wu P, Vail A, Guyatt GH, Altman Mills JM, Chan A-W, Wu P, Vail A, Guyatt GH, Altman DG. Design, analysis and presentation of crossover DG. Design, analysis and presentation of crossover trials. BMC Trials 2009; 10: 27trials. BMC Trials 2009; 10: 27

Schouten H and Kester A. A simple analysis of a Schouten H and Kester A. A simple analysis of a simp[le crossover trial with a dichotomous outcome simp[le crossover trial with a dichotomous outcome measure. Statist Med 2010; 29: 193-198measure. Statist Med 2010; 29: 193-198  Senn S. The AB/BA crossover: past, present and future? Senn S. The AB/BA crossover: past, present and future? Statistical Methods in Medical Research 1994; 3:303-Statistical Methods in Medical Research 1994; 3:303-324. 324. 

Thank youThank youforfor

listening!listening!