Clinical Trials Chapter 3 Flashcards
Crossover trials
Examples of chronic diseases and acute diseases
Chronic
Health condition is not cured by treatment, symptoms may be reduced or disease progression slowed down
- it may be possible to compare treatments by giving them in sequence to every patient in a trial
- e.g heart disease, high blood pressure
Acute
- single course of treatment may cure some if not all patients
- it is not possible to give all treatments to the same patient
- head-ache, broken bone, flu
Crossover trials
AB/BA Crossover Trials
- Every patient receives both treatments, one treatment at a time
- There is usually a wash-out period between the two periods
- Patients are randomly allocated to two groups, one receiving A then B and the other receiving B then A
Crossover trials
Model
Period 1 Period 2 Group 1 (AB). y ̅_11=μ+τ_A+π_1. y ̅_12=μ+τ_B+π_2 Group 2 (BA).y ̅_21=μ+τ_B+π_1. y ̅_22=μ+τ_A+π_2
μ is the overall mean
τ_i represents the effect of treatment i
π_j represents the effect of period j
Estimating treatment effect
Suppose we have an AB/BA crossover trial with n1 and n2 subjects in groups 1 and 2
let (d_i ) ̅denote the difference between period 2 and period 1 for group i
then
τ_obs = (d ̅_1-d ̅_2)/2 is an unbiased estimator of treatment effect τ_A-τ_B
Variance of treatment effect
s^2/4(1/n1+1/n2) = 1/4(var(d1)/n1+var(d2)/n2)
where s^2=[(n1-1)var(d1)+(n2-1)var(d2)]/(n1+n2-2)
Hypothesis and test statistic for treatment effect
Null: τ_A=τ_B
versus
Alternative: τ_A≠τ_B
T=T hat/SE(T hat) = τ_obs/SE(τ_obs)
follows a t-distribution with n1+n2-2 degrees of freedom
T>T_critical then reject H_0
T
Estimating Period effect
d ̅_1+d ̅_2)/2 is an unbiased estimator of period effect π_1-π_2
Variance of period effect
Same as treatment effect
s^2/4(1/n1+1/n2) = 1/4(var(d1)/n1+var(d2)/n2)
where s^2=[(n1-1)var(d1)+(n2-1)var(d2)]/(n1+n2-2)
Hypothesis and test statistic for period effect
Null: π_1=π_2
versus
Alternative: π_1≠π_2
T=T hat/SE(T hat) = τ_obs/SE(τ_obs)
follows a t-distribution with n1+n2-2 degrees of freedom
T>T_critical then reject H_0
T
What is the carryover effect
The effect of the treatment from the previous time period on the response at the current time period.
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
Model with the carryover effect
Period 1 Period 2 Group 1 (AB). y ̅_11=μ+τ_A+π_1. y ̅_12=μ+τ_B+π_2+λ_A Group 2 (BA).y ̅_21=μ+τ_B+π_1. y ̅_22=μ+τ_A+π_2+λ_B
μ is the overall mean
τ_i represents the effect of treatment i
π_j represents the effect of period j
λ_i contamination of the effect of the treatment in period 2 by the treatment in period 1
Estimating carryover effect
λ_obs = S ̅_2-S ̅_1 is an unbiased estimator of λ_B-λ_A
S ̅_1 is the mean of the sum of responses in group 1 (AB),
y ̅_11+y ̅_12
Variance of carryover effect
[(n1-1)var(S1)+(n2-1)var(S2)]/[n1+n2-2] x [1/n1+1/n2]
=var(S1)/n1 +var(S2)/n2
Hypothesis and test statistic for carryover effect
Null: λ_A=λ_B
versus
Alternative: λ_A≠λ_B
T=T hat/SE(T hat) = λ_obs/SE(λ_obs)
follows a t-distribution with n1+n2-2 degrees of freedom
T>T_critical then reject H_0
T
Dealing with carryover effect
the treatment effect τ_A-τ_B is estimated by
(d ̅_1-d ̅_2)/2 - τ_A-τ_B/2
First, test the carryover effect. If the effect is significant, treatments are compared using the data on period 1 alone. Otherwise data on both periods are used.
To avoid the possibility of biased analysis pf treatment effects, the test of the carryover effect is usually carried out at the 10% level
If there is good scientific reason to believe a carryover effect may occur, the crossover design is not recommended and a parallel group design should be used instead
