Paper PO16 Estimate Carryover Effect in Clinical Trial Crossover Designs David Shen, WCI, Inc. Zaizai Lu, AstraZeneca Pharmaceuticals ABSTRACT The crossover design to study the differences in treatments yields a more efficient comparison of treatments than a parallel design. Subjects are on their own controls. The within-patient variation is less than between-patient variation. Crossover design requires a smaller sample size than a parallel design, but achieves same level of statistical power and precision. However, there might be a potential carryover effect in crossover design. The paper discusses how carryover effect may bias statistical results, and provides a method to test carryover effects. SAS procedures such as TTEST, GLM and MIXED are also included. INTRODUCTION A crossover trial is one in which individual subjects are given a sequence of treatments rather that one treatment at any time. The subjects cross over from one treatment to another treatment during the course of the trial. This is in contrast to a parallel design where subjects are randomized to a treatment and remain on that treatment throughout the whole trial. Crossover design is commonly used in the early phase trials such as: • Pharmacokinetic studies to establish concentration time profiles • Bioequivalence • Food interaction studies • Dose proportionality • Dose escalation studies for investigating maximum tolerated does (MTD) In clinical trials, the disease should be chronic and stable. Quickly reversible treatments are more suitable such as for asthma, arthritis, gastro-esophageal reflux and hypertension. The treatments should not be a complete cure but only alleviate the disease condition. If one treatment cures the patient disease in the first period, then the other treatment will have no chance to demonstrate its effectiveness in the second period. It’s not recommended for crossover design when either treatment is expected to be a cure or the condition disappears in a short period (e.g. common cold). The crossover design would increase the precision. Each patient serves his or her own control, so the comparisons are usually based on within-patient variability (which is usually less than the between-subject variability). The increased power with greater precision to estimate the treatment differences reduces the sample size. 1 MODEL AND DESIGN The order of drug treatment in a crossover study is called a sequence and the time of a treatment is called a period. The treatment are represented with capital letters, such as A, B, etc. The most common crossover design is AB/BA. Treatment A Treatment A Start Washout (Baseline) (Baseline) Treatment B Treatment B Subjects should be randomized to the sequence. If all subjects receive the two treatments in the same order, the difference between treatments would be confounded with any other changes, which may occur overtime. For example, in a study of treatment effect of cholesterol level, subjects may change their diet and exercise behavior for as a result of awareness of health issues. This would likely manifest itself as a decrease in cholesterol levels over the later portion of the study and might end up being attributed to the second treatment. In randomization, half of subjects are assigned to receive A/B while other half receive B/A. Any change that favors B over A in one sequence will favor A over B in the other sequence and cancel out of the treatment comparison. CARRYOVER EFFECTS Despite the appeal of having each subject serve as his own control, crossover studies have substantial weaknesses, as well. The potential problem in crossover design is that carryover effects may bias the direct treatment effects. Carryover (or residual) effect is defined as the effect of the treatment from the previous time period on the response at the current time period. It occurs when the effect of a treatment given in the first time period persists into the second period and distorts the effect of the second treatment. The incorporation of washout period in the design can diminish the impact of carryover effects. The washout period is defined as the time between treatment periods. In clinical trial studies, the length of the washout period usually id determined as some multiple of the half-life (t1/2) of the study medicine within the population of interest. Generally, a washout is at least 5 times of the t/12. If the carryover effects for A and B are equivalent in the AB|BA crossover design, then this carryover effect is not aliased with the treatment difference. While differential carryover effects may occur is in clinical trials where an active drug (A) is compared to placebo (B). The subjects in the AB sequence might experience a strong A carryover during the second period, whereas the subjects in BA sequence might experience a weak B carryover during the second period. A washout period should be long enough to minimize the carryover effects. Separate baseline is also helpful to eliminate the carryover effects. 2 Carryover effects will cause the difference between the two treatments to be different in the two time periods, resulting in a significant TREATMENT*PERIOD interaction. Thus, TREATMENT*PERIOD interactions label carryover effect. When the interaction is significant, indicating the presence of carryover, a usual practice is to set aside the results of the second time period and analyze the first period only, because the first period is free of carryover effects. If the preliminary test for carryover is not significant, then the data from both periods are analyzed in the usual manner. STATISTICAL DETAILS Analysis is more complex than parallel group designs, possibility of carryover effects poses added concern in the analysis which is not present in the randomized parallel group design. The two-stage model Grizzle proposed is shown below. Yijk = µ + bij + πk + φm + λm + εijk where i = sequence, j = patient, k = period and m = treatment µ : overall mean th th 2 bij : effect of j patient with i sequence and is ~N(0, σb ) th πk : effect of k period th φm : direct effect of m drug treatment th λm : residual effect of m drug treatment 2 εijk : random error and is ~N(0, σb ) The table 1 lists al the effects in period 1 and period 2. Note this is no carryover effect in period 1. Table 1. Effects of AB| in both Period BA Period 1 Period 2 Sum Difference Sequence AB µ + π1 + φ1 µ + π2 + φ2 + λ1 Y1.1+ Y2.1 Y1.1 - Y2.1 (Y1.1) (Y2.1) Sequence BA µ + π1 + φ2 µ + π2 + φ1 + λ2 Y1.2+ Y2.2 Y1.2 - Y2.2 (Y1.2) (Y2.2) Step 1. Estimate the carryover effect H0: λ1 = λ2 The effect sum for each sequence can be used for the hypothesis test. H0 Y1.1+ Y2.1 = Y1.2+ Y2.2 that is µ + π1 + φ1 + µ + π2 + φ2 + λ1 = µ + π1 + φ2 + µ + π2 + φ1 + λ2 finally λ1 = λ2 If the null hypothesis can not be rejected, then go to step 2, otherwise go to step 3. Step 2. Estimate the treatment effect of 2 periods 3 H0: φ1 = φ2 The effect crossover difference for each sequence can be used for the hypothesis test. H0 ½ ( Y1.1- Y2.1 ) = ½( Y1.2 - Y2.2 ) that is ½ ( µ + π1 + φ1 - µ - π2 - φ2 - λ1 ) = ½( µ + π1 + φ2 - µ - π2 - φ1 - λ2) φ1 - ½ λ1 = φ2 - ½ λ2 assume λ1 = λ2 then φ1 = φ2 Step 3. Estimate the treatment effect of period 1 H0: φ1 = φ2 If carryover effect is significant, then data from period 1 only is used. H0: Y1.1 = Y2.1 µ + π1 + φ1 = µ + π1 + φ2 that is φ1 = φ2 DATA ANALYSIS The analysis of crossover studies is more complex than parallel group designs. The following is an example of AB/BA crossover study. data a; input subject sequence $ period regimen $ result ; cards; 1 AB 1 A 15 1 AB 2 B 10 2 AB 1 A 14 2 AB 2 B 11 3 AB 1 A 16 3 AB 2 B 10 4 AB 1 A 15 4 AB 2 B 9 5 AB 1 A 16 5 AB 2 B 9 6 BA 1 B 11 6 BA 2 A 15 7 BA 1 B 10 7 BA 2 A 14 8 BA 1 B 9 8 BA 2 A 16 9 BA 1 B 12 9 BA 2 A 15 10 BA 1 B 11 10 BA 2 A 14 ; run; PROC MEANS is used to calculate the descriptive statistics by SEQUENCE, PERIOD or REGIMEN PERIOD, then show the mean values graphically by PROC GPLOT. 4 Calculate the sum and difference of AB/BA sequences cross two periods. data b; set a; by subject; retain sum dif ; if first.subject then do; sum = result; dif = result; end; else do; sum = sum + result; dif = dif - result; end; if last.subject then output; run; Estimate the carryover effect using sum values by T-Test, proc ttest data= b; class sequence; var sum; run; T-Tests Variable Method Variances DF t Value Pr > |t| sum Pooled Equal 8 -0.67 0.5237 The p-value of 0.5237 shows the possible carryover effect is no significantly different between AB/BA sequences. Now estimate the effect of two treatments in 2 periods, proc ttest data= b; class sequence; var dif; run; 5 T-Tests Variable Method Variances DF t Value Pr > |t| dif Pooled Equal 8 9.60 <.0001 The result from T-test shows that effect of treatment A is significantly better than that of treatment B at <0.001 level. The statistical analysis can also be done by linear models. title “Grizzles Model by PROC GLM”; proc glm data=a; class subject sequence period regimen; model result = sequence subject(sequence) period regimen / ss3; lsmeans sequence regimen /pdiff stderr; estimate 'Regimen' regimen 1 -1; test h=sequence e=subject(sequence); run; quit; title “Grizzles Model Using PROC MIXED with a Random Effcet”; proc mixed data=a; class sequence subject regimen period; model result = sequence period regimen ; random subject (sequence); lsmeans sequence regimen /pdiff cl; run; quit; CONCLUSION The feature of crossover seems to make the design preferable to parallel group study.