Clinical Trials Chapter 5

Question 1

What is a sequential trial?

Answer 1

A sequential trial provides interim analyses before completion of the trial, the final number of patients required is a random variable

Question 2

Disadvantages of fixed sample size

Answer 2

• requires all patients to complete the treatment and respond before the statistical analysis can be carried out which can take considerable time
• may become obvious relatively early that one treatment is better than the others, it is unethical to continue randomising patients to a treatment that is clearly inferior as well as costly and time consuming

Question 3

Naive group sequential test

Answer 3

The trial is divided into k stages, and the trial may be stopped according to the following naive ‘stopping rule’

At analysis j (1<=j,k0

• reject H0 if the test statistic is greater than the critical value
• otherwise enter the next group of 2n/k patients into the trial

A analysis k

• reject H0 as above
• do not reject H0 if the test statistic is less than the critical value
• the statistical tests are carried out at a 0.05 significance level
• the overall type 1 error is greater than 0.05 when k>1
• there are many opportunities to reject H_0

Question 4

Hybittle/Peto test

Answer 4

The trial is divided into k stages, each contains 2n/k patients
At the jth stage (1<=j=|z_(0.001/2)|
- otherwise continue to the next stage
At the final stage k, set significance level alpha = 0.05
- reject H0 if the test statistic Z>=|z_(0.05/2)|
- otherwise do not reject H0

The test gives an overall type 1 error rate slightly larger than 0.05

Question 5

The Pocock test

Answer 5

The trial is divided into k stages, each contains 2n/k patients. The critical value Cp(alpha, k) is chosen in order to give an overall type 1 error rate of alpha
- at all of the k stages, H0 is rejected if
Test statistic >= Cp(alpha, k)
- otherwise the next group of 2n/k patients is entered into the trial, or if it is the kth analysis, H0 is accepted

Question 6

Expected sample size

Answer 6

E(N|t) = sum from j=1 to k, 2jn/k p(N=2jn/k|t)

where t is the difference in treatment means

Question 7

Sequential trials for binary outcomes

Type 1 error

Answer 7

Probability of rejecting H0 given that H0 is true

=sum of probabilities that H0 is rejected in each stage

Question 8

Sequential trials for binary outcomes

Type 2 error

Answer 8

probability of not rejecting H0 given that H0 is false

= sum of probabilities that H0 is not rejected at each stage

Question 9

Expected sample size for binary outcomes

Answer 9

E(N|p) = sum from j=1 to k, 2jn/k p(N=2jn/k|p)

= sum of each N x P(N=N|p=…)

Question 10

Test statistics for sequential trials tests

Answer 10

Test statistic = (sum from i to n (x_i -y_i)/n)/(standard deviation for new ^2/n + standard deviation for old^2/n)

Question 11

Sequential trials for binary outcomes

Stopping rules

Answer 11

Stopping Rules
let n_j denote the total number of patients entered in the trials by stage j
S_nj=sum from i=1 to nj of Yi
S_nj denotes the total number of treatment successes by stage j

At stage j(j=bj

At final stage k, stop the trial in either of the following situations

• H0 is not rejected if S_nk < bk
• H0 is rejected if Snk>=bk