CHL 5225 H Crossover Trials - PDF Document

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  1. CHL 5225 H Crossover Trials The Two-sequence, Two-Treatment, Two-period Crossover Trial Definition A trial in which patients are randomly allocated to one of two sequences of treatments (either 1 then 2, or 2 then 1) so that within-patient differences can be used to compare treatments (i.e. patients can be used as their own control) Patients must stop the first treatment and either start the second or enter a wash- out period at a predetermined point in time which is the same for all patients CHL 5225 H Crossover Trials Period 1 2 Patient receives Treatment 1 Patient receives Treatment 2 Patient receives Treatment 2 Patient receives Treatment 1 12 Sequence (order) 21

  2. CHL 5225 H Crossover Trials Blocking Blocking may be employed to ensure roughly the same number of patients in each sequence Stratification Blocking within strata to balance for prognostic factors is usually not necessary since patients are their own control CHL 5225 H Crossover Trials Appropriate Diseases and Conditions Chronic, relatively stable Manifest as patient symptoms or disability Cyclical conditions such as nausea/vomiting with chemotherapy Appropriate Treatments Transient, non-curative Provide symptom relief Short half-lives

  3. CHL 5225 H Crossover Trials Appropriate Measurements Subjective – symptom scores, ratings of pain, etc. Objective – strength Preference – which treatment period did the patient prefer CHL 5225 H Crossover Trials Blinding Whenever possible patients, clinicians and observers (research staff) should be Blinded (masked) to treatment sequence and, if possible, unaware of the time at which the crossover from one treatment to the other occurs Other Design Features Possible “wash-out” period between treatment periods Possible baseline measurements prior to both treatment periods

  4. CHL 5225 H Crossover Trials Advantages Treatments are compared within patients, thereby the influence of patient factors (age, sex, disease severity) are “subtracted out”; that is, the between-patient variance is removed, leading to: - smaller variances - increase power - smaller required sample sizes CHL 5225 H Crossover Trials Advantages 2     1 z  1 z       ( ) 2  N 4 N = number of patients required for a parallel groups trial, 2     1 z  1 z       ( ) 2   n 2 (1 ) where n = number of patients required for a crossover trial and = is the correlation between measurements made on the same patient

  5. CHL 5225 H Crossover Trials Advantages  2 n N 1 Typically  is between 0.3 and 0.6 n N 1 4  For  = 0.5 CHL 5225 H Crossover Trials Advantages Permits the use of preference data, which is particularly useful if a validated instrument for measuring outcome or disease status is not available

  6. CHL 5225 H Crossover Trials Disadvantages Short time frame does not permit the assessment of long term benefits and harms Crossover trial can be used because patients are more likely to consent Period effect – disease not a stable as expected CHL 5225 H Crossover Trials Disadvantages Bad press: 1977 report of the Biometric and Epidemiology Methodolgical Advisory Committee of the US FDA states that “the two-period crossover design is not the design of choice in clinical trials where unequivocal evidence of Trt effects is required.”

  7. CHL 5225 H Crossover Trials Disadvantages Treatment by period interaction - sequence (order) effect - residual carryover - partially confounds treatment effect i.e. produces biased estimates of Treatment effect More suitable for an early phase III trial CHL 5225 H Crossover Trials   i = 1: treat. 1 treat. 2 i = 2: treat. 2 treat. 1 Parametric model for continuous outcome Let Yijkbe the observed outcome on the jthpatient (j = 1, 2, . . . ni) randomized to the ithsequence (i = 1, 2) during the kthperiod (k = 1, 2)              i Y k ( 1) ijk k ( , ) v i k ij ijk where   overallmean th   k     k effect of period, 0 1 2 v(i,k)        1 i k i k * (mod3), effect of treatment v( , ) 0 2   the carryover effect of treatment from period1to period 2 i i   ij th th j i effect of patient in the order   the within patient deviation for period  k ijk

  8. CHL 5225 H Crossover Trials 2  2      ~N(0, ) and ~N(0, ),mutally independent ij ijk 2  2  k     k k : ' {    Y Y Cov , ijk ijk ' 2    k : ' 2        Y Y Corr , ij ij 1 2 2  2     Finally,let              (period effect) (treatment effect) (residual carryover)(a.k.a. treatment by period interaction a.k.a. sequence effect) 2 1 2 1 2 1 Means by Period and Trt 20        2 1 2 18        2 2 1 16      1 1 14 12      1 2 10 i = 2 k = 2 i = 1 k = 2 8 i = 1 k = 1 i = 2 k = 1 6 4 Trt 1 Trt 2 Trt 1 Trt 2 2 0 Period 2 Period 1

  9. CHL 5225 H Crossover Trials in 1 12 (i = 1) 21 (i = 2) Period  j  Y Y i k . ijk n k = 1            k = 2        2       2  1 i E Y E Y ( ) ( ) Sequence (order) 1.1 1 1 1.2 2 1 E Y E Y ( ) ( ) 2.1 1 2 2.2 1 2 Treatment effect in Period 1: E Y Treatment effect in Period 2: E Y Therefore, Treatment X Period interaction exists    0 Effect of Sequence 1: 1.1 { ( ) E Y Effect of Sequence 2: 2.1 { ( ) E Y Sequence effect:     2 1 ( ) 2 Therefore, Sequence effect exists    0       2 E Y ( ( ) ) 2.1 1.1 1          2 1 1 E Y ( ( ) ) 1.2 2.2 2             1 2 (2 E Y ( )} 2 ) 2 1.2 1 2 1             1 2 (2 E Y ( )} 2 ) 2 2.2 1 2 2 2 CHL 5225 H Crossover Trials 12 (i = 1) 21 (i = 2) Period k = 1             k = 2         2         2 E Y E Y ( ) ( ) Sequence (order) 1.1 1 1 1.2 2 1 E Y E Y ( ) ( ) 2.1 1 2 2.2 1 2 Estimator of Treatment effect in Sequence 1: Estimator of Treatment effect in Sequence 2: Expected value of overall estimator of Treatment effect:                       2 Overall estimator of Treatment effect is biased    0  Y Y 1.2 1.1  Y Y 2.1 2.2   (   E Y     E Y Y Y Y 2 1.2 1.1 2.1 2.2      E Y E Y E Y ) ( ) ( ) ( ) 2 1.2 1.1 2.1 2.2 2 2 1 1 2 1 2

  10. sequence 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 patient 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 0 10 10 11 11 12 12 13 13 period 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 treatment 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 outcome 310 270 310 260 370 300 410 390 250 210 380 350 330 365 370 385 310 400 380 410 290 320 260 340 90 220 sex m m m m f f m m m m f f m m f f f f m m m m m m m m Sample means are rounded to whole numbers 400 346 337 350 306 283 300 250 200 150 i = 2 k = 2 i = 1 k = 2 i = 1 k = 1 i = 2 k = 1 100 50 Trt. 2 Trt. 1 Trt. 1 Trt. 2 0 Period 1 Period 2          ˆ     306 337 283 346 2 47             ˆ    346 337 306 283 2 16    ˆ2        283 337 306 346 2 7

  11. CHL 5225 H Crossover Trials SAS code for the analysis of the 2 X 2 X 2 crossover trial procMIXED data=sasf.xOverExampleData; class patient; model outcome = sequence period treatment / solution; repeated / subject=patient type=cs r rcorr; title 'All Patients'; run; Because of the coding (1, 2) we don’t need to declare as class variable. Will give means “2” minus “1” CHL 5225 H Crossover Trials Alternative SAS code for the analysis of the 2 X 2 X 2 crossover trial procMIXED data=sasf.xOverExampleData; class patient sequence period treatment; model outcome = sequence period treatment; repeated / subject=patient type=cs r rcorr; estimate 'PHI' treatment -12; estimate 'PI' period -12; estimate 'LAMBDA/2' sequence -12; title 'All Patients'; run;

  12. Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 375.06 65.8524 11 5.70 0.0001 sequence -7.2024 40.2026 11 -0.18 0.8611 period 15.8929 10.7766 11 1.47 0.1683 treatment -46.6071 10.7766 11 -4.32 0.0012 ˆ ( 2)  ( ) ˆ ˆ ( ) Estimated R Correlation Matrix for patient 1 Row Col1 Col2 1 1.0000 0.8659 2 0.8659 1.0000 Covariance Parameter Estimates Cov Parm Subject Estimate CS patient 4846.54 Residual 750.41  ˆ 2 ˆ  2 ˆ  2  ˆ      ˆ ˆ = 4846.54/(4846.54 + 750.42) = 0.8659 2 2 ˆ  

  13. CHL 5225 H Crossover Trials Covariates—examining subgroups data temp; set sasf.xOverExampleData; m1f0 = 1; if sex eq 'f' then m1f0 = 0; m0f1 = 1; if sex eq 'm' then m0f1 = 0; run; procMIXED data=temp; class patient; model outcome = sequence period treatment m1f0 m1f0*treatment / solution; repeated / subject=patient type=cs r rcorr; title 'Effect in Female Patients'; run; procMIXED data=temp; class patient; model outcome = sequence period treatment m0f1 m0f1*treatment / solution; repeated / subject=patient type=cs r rcorr; title 'Effect in Male Patients'; run; Standard Effect Estimate Error DF t Value Pr > |t| Intercept 426.34 76.0138 10 5.61 0.0002 sequence -9.9569 38.6755 10 -0.26 0.8021 period 15.7328 11.2746 10 1.40 0.1931 treatment -51.2500 20.2386 10 -2.53 0.0298 m1f0 -67.9310 55.4962 10 -1.22 0.2490 treatment*m1f0 6.7241 24.3560 10 0.28 0.7881 Standard Effect Estimate Error DF t Value Pr > |t| Intercept 358.41 65.5131 10 5.47 0.0003 sequence -9.9569 38.6755 10 -0.26 0.8021 period 15.7328 11.2746 10 1.40 0.1931 treatment -44.5259 13.5504 10 -3.29 0.0082 m0f1 67.9310 55.4962 10 1.22 0.2490 treatment*m0f1 -6.7241 24.3560 10 -0.28 0.7881  Trt effect in males Trt effect in females Test for interaction→ i.e. Trt effect in females = Trt effect in males

  14. CHL 5225 H Crossover Trials   ) is valid       Test for treatment effect (i.e. H: When might this be true?  Placebo-controlled trial  Differential conditioning (nausea example)  Floor effect (caused by strong period effect)  “Unmasking” (leading to an over estimate of treatment effect in 2nd period) 0 0 0 Differential conditioning (nausea example) 20 18 18 16 16 14 14 12 10 10 8 i = 2 k = 2 i = 1 k = 2 i = 1 k = 1 i = 2 k = 1 6 4 Trt 1 Trt 2 Trt 1 Trt 2 2 0 Period 1 Period 2 Means by Period and Treatment

  15. Floor effect (caused by strong period effect) 100 84 90 80 70 70 60 50 40 30 i = 1 k = 1 i = 2 k = 1 25 30 i = 2 k = 2 i = 1 k = 2 20 Trt 1 Trt 2 Trt 1 Trt 2 10 0 Period 1 Period 2 Means by Period and Treatment “Unmasking” 100 90 80 80 70 60 60 50 50 40 30 i = 2 k = 2 i = 1 k = 1 i = 2 k = 1 30 i = 1 k = 2 20 10 Trt 1 Trt 2 Trt 1 Trt 2 0 Period 1 Period 2 Means by Period and Treatment

  16. CHL 5225 H Crossover Trials      / Gotta watch out for ˆ (0 5)/2    This implies physical carryover, and the analysis must be restricted to Period 1 data only (a two-sample t-test or comparable non-parametric test) 0 0  2.5 (favours treatment 1) 100 90 80 70 55 55 55 60 45 50 i = 2 k = 1 i = 2 k = 2 i = 1 k = 2 i = 1 k = 1 40 30 20 10 Trt 1 Trt 2 Trt 1 Trt 2 0 CHL 5225 H Crossover Trials      , and therefore test of null hypothesis is valid, But even if ˆ ( ) E    Only way to avoid bias is to use first period data only, that is ˆP Y Y        1 2 1 2 {( ) ( )} 2 0 0 2 and is therefore biased .1 2.1 1.1 2 ˆ ( ) V n n n n  ˆ (       2 2 V n n 1 2 n n ) {( ) ( )}( )   P .1 1 2    ˆ  ˆ   V V ( ) ( ) 1 2 P .1

  17. CHL 5225 H Crossover Trials The test of hypothesis based on ˆ has more power (i.e. has a greater probability of rejecting the null hypothesis when it is false) than the test based on .1  2 2(1 )       Willan and Pater Biometrics 1986; 42:593-599 Willan Biometrics 1988; 44:211-218  2 2(1 )   ˆP 0 0.586 0.816 1.00 0.3 0.5 CHL 5225 H Crossover Trials      hold????? When does Well ˆ ˆ P   2 2(1 ) ˆP   holds  |test statistic(ˆ)| > |test statistic(   ˆ )| 2 2(1 ) .1 .1  ˆ 2  is the estimate of      ˆ ˆ where 2 2 ˆ   Willan (1988) suggests basing analysis on the test statistic with the largest absolute value i.e. declare significance if either one is significant Introduces multiplicity Therefore must adjust level of significance to maintain type I error probability

  18. CHL 5225 H Crossover Trials ˆ  0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Nominal level for 0.05 0.03037 0.02974 0.02917 0.02864 0.02814 0.02766 0.02721 0.02679 0.02637 0.02594 0.02532 Nominal level for 0.025 0.01469 0.01441 0.01414 0.01390 0.01368 0.01348 0.01329 0.01311 0.01295 0.01279 0.01258 CHL 5225 H Crossover Trials procMIXED data=sasf.xOverExampleData; class patient; model outcome = sequence period treatment / solution; repeated / subject=patient type=cs r rcorr; title 'All Patients'; run; procglm data=sasf.xOverExampleData; where period eq 1; model outcome = treatment / solution; title 'Period 1 Data Only'; run;

  19. Standard Effect Estimate Error DF t Value Pr > |t| Intercept 375.06 65.8524 11 5.70 0.0001 sequence -7.2024 40.2026 11 -0.18 0.8611 period 15.8929 10.7766 11 1.47 0.1683 treatment -46.6071 10.7766 11 -4.32 0.0012 Estimated R Correlation Row Col1 Col2 1 1.0000 0.8659 2 0.8659 1.0000 Standard Parameter Estimate Error t Value Pr > |t| Intercept 390.9523810 69.92825490 5.59 0.0002 treatment -53.8095238 45.28386839 -1.19 0.2597 CHL 5225 H Crossover Trials Reject null hypothesis: if the maximum of |-4.32| or |-1.19| exceeds cut-off point or equivalently if the smallest associated p-value is less than nominal value from the table for two-sided test, smallest associated p-value is min. of (0.0012, 0.257) for one-sided test, smallest associated p-value is min. of ( 0.0012 , 0.2597 ) 2 2 Use nominal level of 0.02594 to achieve a type I error probability of 0.05

  20. CHL 5225 H Crossover Trials Grizzle Procedure Grizzle JE. Biometrics 1965; 21: 467-480. Test H : 0 If H is rejected then use period 1 data only If H is not rejected then use data from both periods Not an issue of statistical inference (sample size being the biggest determinant of significance) The issue is the size of  and whether it is likely to be non-zero if   using a two-sided level of 0.1   0 Standard Effect Estimate Error DF t Value Pr > |t| Intercept 375.06 65.8524 11 5.70 0.0001 sequence -7.2024 40.2026 11 -0.18 0.8611 period 15.8929 10.7766 11 1.47 0.1683 treatment -46.6071 10.7766 11 -4.32 0.0012 Estimated R Correlation Row Col1 Col2 1 1.0000 0.8659 2 0.8659 1.0000 Standard Parameter Estimate Error t Value Pr > |t| Intercept 390.9523810 69.92825490 5.59 0.0002 treatment -53.8095238 45.28386839 -1.19 0.2597 Since p-value > 0.1, Use data from both periods

  21. CHL 5225 H Crossover Trials Missing Second Period Data Analyze complete data (i.e. patients with period 1 & 2 data) as before Yields: ˆC and ) ( )   C V SE dfC = mC – 2, where mC = # patients with complete data Analyze incomplete (i.e. patients with period 1 data only) data as 2-sample t-test Yields: ˆINC and ) ( )   INC V SE dfINC = mINC – 2, where mINC = # patients with missing period 2 data ˆ ( 2 ˆ ( 2 CHL 5225 H Crossover Trials Missing Second Period Data ˆ ˆ ˆ ( ) ˆ ( )   C V  C INC C df df m m t t Where ni = # of patients randomized to sequence i There fore   C INC m m  1 ˆ              1 ˆ  1 ˆ  ˆ ( )   V      V C INC , where ˆ  V V V ( ) ( ) ( ) INC C INC ˆ ˆ ( ) V     t      n n 4 4 INC 1 2  n n 1 2

  22. CHL 5225 H Crossover Trials Binary Outcome Sequence 1 (1,2) 2 (2,1) Total Analyze “red” table using methods appropriate for testing for association in a 2 x 2 table Fisher Exact test Chi-squared tests Valid in the presence of period effect, but NOT in the presence of a physical residual carryover effect (1 = success; 0 = failure) (outcome period 1, outcome period 2) (0,0) (0,1) 12 41 10 23 22 64 (1,0) 18 38 56 (1,1) 9 11 20 Total 80 82 162 120 59 61 Use Fisher exact or continuity-corrected Chi-square for small cell frequencies CHL 5225 H Crossover Trials sequence y Frequency‚ Row Pct ‚ 1‚ 2‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 1 ‚ 41 ‚ 18 ‚ 59 ‚ 69.49 ‚ 30.51 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 2 ‚ 23 ‚ 38 ‚ 61 ‚ 37.70 ‚ 62.30 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 64 56 120 Statistics for Table of sequence by y Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 1 12.1754 0.0005 Likelihood Ratio Chi-Square 1 12.4011 0.0004 Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 41 Left-sided Pr <= F 0.9999 Right-sided Pr >= F 0.0004 Table Probability (P) 0.0003 Two-sided Pr <= P 0.0005

  23. CHL 5225 H Crossover Trials Alternatively, could use PROC GENMOD in SAS Patient Sequence Period Treatment Outcome 1 1 1 1 0 1 1 2 2 0 2 2 1 2 1 2 2 2 1 0 ect. proc genmod data=binaryXover; class patient; model outcome = sequence period treatment / dist=bin link=logit; repeated subject=patient / type=exch; run; CHL 5225 H Crossover Trials Exchangeable Working Correlation Correlation -0.456105135 GEE Fit Criteria QIC 437.9565 QICu 437.9565 Analysis Of GEE Parameter Estimates Empirical Standard Error Estimates Standard 95% Confidence Parameter Estimate Error Limits Z Pr > |Z| Intercept 1.9668 0.6594 0.6744 3.2592 2.98 0.0029 sequence -0.1071 0.1701 -0.4405 0.2264 -0.63 0.5292 period -0.2226 0.2760 -0.7635 0.3183 -0.81 0.4200 treatment -0.9627 0.2760 -1.5036 -0.4218 -3.49 0.0005 (-3.49)2= 12.18 Recall: square of normal = chi-squared(1)

  24. CHL 5225 H Crossover Trials Binary Outcome Sequence 1 (1,2) 2 (2,1) Total (   n n n n n (    c (outcome period 1, outcome period 2) (0,0) (0,1) n11 n12 n21 n22 n+2 (1,0) n13 n23 n+3 (1,1) n14 n24 Total n1+ n2+ n++ These are two-sided tests  2 n n n n ) 2 1 12 23 13 22     Reject at two-sided, level 0.05 if test statistic exceeds 3.84 1 2 2 3   2 n n n n n n 2)  12 23 n n n n 13 22 2 1 Reject at one-sided, level 0.05 if test statistic exceeds 2.72 and observe treatment effect in appropriate direction     1 2 2 3 2 3     i  2 LR n n n n n 2 log ( )    ij ij j 1   j 1 2 CHL 5225 H Crossover Trials 2x2 Cluster Crossover Trial Sequence Cluster Period 1 Period 2 Trt 1 (n11) Trt 1 (n21) Trt 1 (n31) Trt 1 (n41) Trt 1 (n51) Trt 1 (n61) Trt 2 (n71) Trt 2 (n81) Trt 2 (n91) Trt 2 (n10,1) Trt 2 (n11,1) Trt 2 (n12,1) Trt 2 (n12) Trt 2 (n22) Trt 2 (n32) Trt 2 (n42) Trt 2 (n52) Trt 2 (n62) Trt 1 (n72) Trt 1 (n82) Trt 1 (n92) Trt 1 (n10,2) Trt 1 (n11,2) Trt 1 (n12,2) 1 2 3 1 (Trt 1→Trt 2) 4 5 6 7 8 9 2 (Trt 2→Trt 1) 10 11 12 Assume that nij= m, and that within a cluster the patients in Period 1 are different from the patients in Period 2

  25. CHL 5225 H Crossover Trials 2x2 Cluster Crossover Trial – sample size for continuous outcome 2     1 z  1 z       2( )   2     1)  N m m 1 ( N = total number of patients required  = between patient variance, within a cluster  = smallest clinically important difference  = ICC for 2 patients from the same cluster in the same period  = ICC for 2 patients from the same cluster in different periods   c N pm N (2 ) m ( ) c = total number of clusters m = number of patients per period, per cluster p = number of periods CHL 5225 H Crossover Trials 2x2 Cluster Crossover Trial – sample size for binary outcome 2        z  1 z ( )   ) 1 (      1 1 2       1 )      1)  N m m 2 (1 (1 1 2 2 2 1and 2are the probabilities of the outcome on Treatment 1 and Treatment 2, respectively, under the alternative hypothesis That is, 1– 2is the smallest clinically important difference Giraudeau et al. Statist Med 2008; 27(27):5578–5585 Rietbergen C. J of Educ and Behav Statistics 2011; 36(4):472-490

  26. CHL 5225 H Crossover Trials PADIT Cluster Crossover Design High risk patients undergoing arrhythmia device procedures Treatment 1 (Control): single dose of preoperative cefazolin Treatment 2 (Intervention): single dose of preoperative cefazolin plus: single dose preoperative of vancomycin plus: intraoperative wound pocket wash plus: postoperative oral cephalexin or cephadroxil The primary outcome of the trial is admission to hospital for proven device or pocket infection Six-month periods Connolly J. et al Canadian J of Cardiology 2013; 29(6):652-658 CHL 5225 H Crossover Trials PADIT Cluster Crossover Design 1= 0.02 2= 0.013 2– 1=0.007  = 0.05 m = 100  = 0.2  = 0.015  = 0.015 2        z  1 z ( )   ) 1 (      1 1 2       1 )      1)  N m m 2 (1 (1 1 2 2 2 2        (1.960 0.8416) 0.007       N 2 0.02(0.98) 0.013(0.987) 1 0.015  10,661   c N (2 ) m x 10661 (2 100) 54,  assuming 2x2 design

  27. CHL 5225 H Crossover Trials PADIT Cluster Crossover Design Sequence Period 1 Period 2 Trt 1 Clusters 1 to 28 2800 patients Trt 2 Clusters 1 to 28 2800 patients 1→2 Trt 2 Clusters 29 to 56 2800 patients Trt 1 Clusters 29 to 56 2800 patients 2→1 CHL 5225 H Crossover Trials PADIT Cluster Crossover Design Consider 4-sequence→ 4-period design 1→2→1→2 2→1→2→1 1→2→2→1 2→1→1→2   c N pm x ( ) 10661 (4 100) 27, 

  28. CHL 5225 H Crossover Trials PADIT Cluster Crossover Design Sequence Period 1 Period 2 Period 3 Period 4 Trt 2 Clusters 1 to 7 700 patients Trt 1 Clusters 1 to 7 700 patients Trt 2 Clusters 1 to 7 700 patients Trt 1 Clusters 1 to 7 700 patients 1→2→1→2 Trt 2 Clusters 8 to 14 700 patients Trt 1 Clusters 8 to 14 700 patients Trt 2 Clusters 8 to 14 700 patients Trt 1 Clusters 8 to 14 700 patients 2→1→2→1 Trt 1 Clusters 15 to 21 700 patients Trt 1 Clusters 15 to 21 700 patients Trt 2 Clusters 15 to 21 700 patients Trt 2 Clusters 15 to 21 700 patients 1→2→2→1 Trt 2 Clusters 22 to 28 700 patients Trt 1 Clusters 22 to 28 700 patients Trt 1 Clusters 22 to 28 700 patients Trt 2 Clusters 22 to 28 700 patients 2→1→1→2 CHL 5225 H Crossover Trials Cluster Crossover Trial – analysis for continuous outcome    j     i y x e ijk ij ij ijk    i c p 1,... #clusters ( ) 1,... #periods ( ) 1,... # patients j k      2 2 2 N N e N (0, ); (0, ); (0, )      i ij ijk   ijx 1if cluster receives treatment 2 duringpeiod i i j j 0 if cluster receives treatment1duringpeiod

  29. CHL 5225 H Crossover Trials Cluster Crossover Trial – analysis for binary outcome     j    i x logit( ) ij ij ij   i c p 1,... #clusters ( ) 1,... #periods ( ) prob.ofoutcom from cluster j e fora patient   ij i j duringperiod     2 2 N N (0, ); (0, );     i ij   ijx 1if cluster receives treatment 2 duringpeiod i i j j 0 if cluster receives treatment1duringpeiod CHL 5225 H Crossover Trials Assignment: First line of data: 1, 82.715348081, 67.856553121, 1, 1, 1, 1