Reference no: EM132376652

Design of Randomised Controlled Trials (DES) Assignment -

Question 1 -

a) Researchers would like to estimate the mean level of plasma creatine concentrations (mg/L) in adults. What would be the required sample size to estimate the mean with precision ±0.2 standard deviations (95% confidence intervals)?

b) Consider a trial to evaluate a new chemotherapeutic agent for the treatment of childhood leukaemia. The investigators anticipate that mean survival time for patients on this drug might increase by a factor of 1.5, with follow-up of all patients until death. State your null and alternative hypothesis for this trial and compute the required number of patients for the trial (per group). Assume the level of significance to be 0.05 and the power to be as sequence between 0.8-0.9.

Question 2 -

Herpetic gingivostomatitis is caused by the Herpes simplex virus and its clinical signs consist of mouth ulcers. It was known that the drug Aciclovar was useful in other Herpes infections and so researchers would like to trial its use in treating herpectic gingivostomatitis in children. The outcome measure is to be the duration of the ulcers. The duration of the ulcers has a population standard deviation of five (5) days. If 35 children are to be allocated to each treatment and the researchers are using a two sided test with significance level=0.05:

a) Calculate the power against the clinically significant alternative hypothesis H_A: δ = 3.

b) Find the value δ₁ > 0 for which we will have 80% power against the alternative H_A: δ = δ₁.

Question 3 -

The control regimen for a planned trial of treatment for hypertension consists of standard drug treatment, whereas the experimental intervention consists of a 'lifestyle modification package', including relaxation therapy and diet. The investigators anticipate that the cure rate is 80%.

a) What would be the required number of patients in the trial at α = 0.1 (one sided) and β = 0.2 to detect a difference in a cure rate between two groups of 10%?

b) If the anticipated proportion of patients in the intervention group whose blood pressure is under control is only 75 percent, then what would be the required number of patients in the trial. Compute the sample size assuming that the power is 80% and the level of significance takes a range of values in between 0.01-0.1.

Question 4 -

Assume that the survival time T (years) for a particular cancer follows an exponential distribution with parameter λ = 0.5.

a) What is the probability that a patient with this cancer will survive for at least two years.

b) What is the probability that a patient with this cancer will die in the first 4 years.

c) State the hazard rate for this cancer.

d) A new therapy protocol is to be considered to treat this cancer. It is believed that the hazard rate for this therapy is λ = 1/3. For a two sided test with α = 0.05 and β = 0.1, what sample size is needed if

i. All the patients are followed until death

ii. All the patients are recruited instantaneously and followed for 3 years

iii. All the patients are recruited over a two year period and followed for a further two years?

e) What is the expected number of deaths in scenario 4d (iii) for the new therapy protocol group?

Question 5 -

Consider a single-arm Phase II study into the treatment of a cancer. The endpoint of interest is the proportion of patients whose tumours shrink by at least 50% which we denote as p. A two stage design (see Module 4 reading number 3: Simon.R, 1989) is to be used. The researchers have decided that if the proportion p is less than 0.4, then the trial should stop, and if the proportion p is greater than 0.55 then the new treatment is to be researched further. As well, they require that the error probabilities are α = 0.05 and β = 0.2. For the Optimal design:

a) How many subjects are required in the first step?

b) How many subjects are required in total?

c) What is the expected sample size if the proportion p is 0.4?

d) What is the probability that the trial will be terminated at the first step if the proportion p is 0.4?

e) Write out a flow chart for the design protocol.

f) If the researchers decided to use the minimax design, does the total number of subjects needed increase or decrease?