ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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CHAPTER 3 ST 520, A. TSIATIS and D. Zhang � � πi(1 − πi) = E , this means that we can obtain an unbiased estimator for E � � πi(1−πi) by using N −1 N� i=1 Summarizing these results, we have shown that • s 2 p = � N (pi−¯p) 2 i=1 N−1 • We have also shown that N −1 � N i=1 ni pi(1 − pi) ni − 1 . is an unbiased estimator for var(pi) which by (3.4) equals E � � πi(1 − πi) ni + σ 2 π pi(1−pi) is an unbiased estimator for ni−1 � E � πi(1 − πi) Consequently, by subtraction, we get that the estimator ˆσ 2 π = ��Ni=1(pi − ¯p) 2 � � − N N − 1 −1 N� i=1 is an unbiased estimator for σ 2 π. ni ni � pi(1 − pi) ni − 1 Going back to the example given in Table 3.1, we obtain the following: • • • Hence N −1 � Ni=1(pi − ¯p) 2 N − 1 N� i=1 pi(1 − pi) ni − 1 = .0496 = .0061 ˆσ 2 π = .0496 − .0061 = .0435 Thus the estimate for study to study standard deviation in the probability of response is given by ˆσπ = √ .0435 = .21. This is an enormous variation clearly indicating substantial study to study variation. PAGE 48
CHAPTER 4 ST 520, A. TSIATIS and D. Zhang 4 Randomization In a randomized clinical trial, the allocation of treatment to patients is carried out using a chance mechanism so that neither the patient nor the physician knows in advance which treatment will be assigned. Each patient in the clinical trial has the same opportunity of receiving any of the treatments under study. Advantages of Randomization • Eliminates conscious bias – physician selection – patient self selection • Balances unconscious bias between treatment groups – supportive care – patient management – patient evaluation – unknown factors affecting outcome • Groups are alike on average • Provides a basis for standard methods of statistical analysis such as significance tests 4.1 Design-based Inference On this last point, randomization allows us to carry out design-based inference rather than model- based inference. That is, the distribution of test statistics are induced by the randomization itself rather than assumptions about a super-population and a probability model. Let me illustrate through a simple example. Suppose we start by wanting to test the sharp null hypothesis. Under the sharp null hypothesis, it will be assumed that all the treatments being compared would yield exactly the same response on all the patients in a study. To test this hypothesis, patients are randomly allocated to the different treatments and their responses are observed. PAGE 49
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ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

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