Question

CLRES 2020 Biostatistics: Statistical Approaches in Clinical Research Homework #10: Sample Size and Power Due: Friday, July 31, 2020 at the beginning of the class Please provide calculation details for each question. If you used Stata, please include commands used. In a patients with advanced Parkinson's disease, investigators were planning 5-year follow-up of bilateral stimulation of the subthalamic nucleus to assess changes in symptoms as measured by the Unified Parkinson's Disease Rating Scale (UPDRS). This scale ranges from 0 to 108 with higher value denoting more symptoms. Suppose it is known that the 5-year change in UPDRS follows a normal distribution with standard deviation of 15.3 based on historical data. Suppose the investigators hypothesize that there may be an increase or reduction in UPDRS after 5 years at a level of 0.05. a. State the null and alternative hypothesis for this problem. b. If they plan to enroll 49 patients, how much power will the study have to detect a mean difference of 5 units? C. What minimum sample size would be needed to detect a mean difference of 5 units with 80% power? The investigative team wanted to include a control group where patients do not receive stimulation. They believe that the mean change in UPDRS is 1 for this group, and the standard deviation is also 15.3. d. They would like to know whether the mean change in the stimulation group is different from the control group at a level of 0.05. State the null and alternative hypothesis for this problem. e. How many participants would be necessary to detect a mean difference in UPDRS change of 5 units between the stimulation group and the control group, assuming equal group sizes, with 80% power at a level of 0.05? f. If the investigators would like to recruit twice as many patients in the stimulation group relative to the control group, how many participants in stimulation and control groups would be necessary to detect a mean difference of 5 units size with 80% power at a level of 0.05? 8. Based on the above questions, we can conclude: 1. The sample size requirement is to achieve a higher power, and 2. Compared with a two-sample test with unequal size, an equal sized two-sample test will have _power for the same total sample size. A. Higher B. Lower

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Answer 1

(a) The hypothesis being tested is:

H₀: µ = 0

H_a: µ ≠ 0

(b) Power, 1 − β = Φ(z − z_1−α/2) + Φ(−z − z_1−α/2), z = μ−μ0/σ/√n = Φ(2.29 − 1.96) + Φ(−z − (-1.96) = 0.6295

(c) n = (σz_1−α/2 + z_1−β/μ−μ0)^2 = (15.3*1.96 + 1.645/5)^2 = 74

(d) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂