HWI SIMONS TWO STAGE DESIGN FOR A SINGLE GROUP STUDY Cons

HWI - SIMON\'S TWO - STAGE DESIGN FOR A SINGLE - GROUP STUDY: Consider a single - group, phase II trial in oncology where the primary response variable is binary (responder, not responder). For example, a responder is a patient with at least 50% shrinkage of tumor. Let p denote the true response rate. Large values of p indicates efficacy of the treatment. Let p_0 denote some uninteresting level of the probability p and let p_1 (greaten than p_0) denote the desirable target level level of p. In Stage 1 of Simson\'s design, the null hypothesis H_0 p less than or equal to p_0 (that is the treatment is ineffective) is tested versus the alternative hypothesis H_1: p greater than or equal to p_1 (that is treatment is ineffective). The null hypothesis is not rejected if the number of responders is less than k_1 out of a total of n_1 patients evaluated, and the trial will be terminated. If the number of responders is at least k_1 out of n_1, then n_2 additional patients are enrolled in State 2. If the total number responders is less than k out n (= n_1 + n_2), again H_0 is not rejected; otherwise, H_1 is accepted. Derive the probability of not rejecting H_0 given the true value p, Simon (1989, p . 2, equation 1). Show all work. Derive the power function. Show that the derivative of the power function with respect to p is positive. State the property of the power function derived in 2) above.

Solution

1. To obtain the p value do as follows:

Start Minitab, Go to Stat> Basic statistics>1 proportion and select \'Summarized Data\'.

Enter 1, 2 and 0.5 corresponding to the text boxes. Click OK.

The exact p value is 1.