In a trial with 3 treatment groups, the method of minimisation (Pocock & Simon, 1975) was used to maintain balance between groups on the prognostic factors sex, age and disease severity. The table below shows the balance of these prognostic factors by treatment group after the first 20 patients had been entered into the trial. Factor Level Age 60yrs Disease severity Moderate Severe Total Treatment 1 2 3 2 3 3 6 4 6 2 6 6 8 4 2 2 10 8 10 1 1 Total 8 16 4 20 8 28 Suppose the next patient to enter the trial is 45 years old and has severe disease status. (a) Calculate the total amount of imbalance Gk that would arise following allocation of the patient to each of the 3 treatment groups (k = 1,2,3). Assume that imbalance within a factor level can be expressed using the range method and that balance on each of the two prognostic factors is equally important. [2 marks] (b)Calculate the total amount of imbalance Gk assuming an upper limit of acceptable treatment imbalance within each factor level of 1 and that balance on age is twice as important as balance on disease severity. [2 marks] (c) Using your answer to (b), calculate the probability of assignment of the 29th patient to each of the 3 treatment groups. Justify your choice of probabilities [2 marks] In a trial with 3 treatment groups, the method of minimisation (Pocock & Simon, 1975) was used to maintain balance between groups on the prognostic factors sex, age and disease severity. The table below shows the balance of these prognostic factors by treatment group after the first 20 patients had been entered into the trial. Factor Level Age 60yrs Disease severity Moderate Severe Total Treatment 1 2 3 2 3 3 6 4 6 2 6 6 8 4 2 2 10 8 10 1 1 Total 8 16 4 20 8 28 Suppose the next patient to enter the trial is 45 years old and has severe disease status. (a) Calculate the total amount of imbalance Gk that would arise following allocation of the patient to each of the 3 treatment groups (k = 1,2,3). Assume that imbalance within a factor level can be expressed using the range method and that balance on each of the two prognostic factors is equally important. [2 marks] (b)Calculate the total amount of imbalance Gk assuming an upper limit of acceptable treatment imbalance within each factor level of 1 and that balance on age is twice as important as balance on disease severity. [2 marks] (c) Using your answer to (b), calculate the probability of assignment of the 29th patient to each of the 3 treatment groups. Justify your choice of probabilities [2 marks]