Chapter 10--Hypothesis Testing--Categorical Data

# 52 where pd and pa are the projected proportion of

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Unformatted text preview: ess is deﬁned as ≤ 1 episode of OTM in the ﬁrst 12 months after treatment. How much power does such a study have of detecting a signiﬁcant diﬀerence if a two-sided test with an α level of .05 is used? Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Paired Samples: McNemar’s Test The sample size needed to conduct a two-sided test with signiﬁcance level α and power 1 − β is z1−α/2 + 2z1−β n= pA (1 − pA ) 2 4pD (pA − 0.5)2 where pD and pA are the projected proportion of discordant and type A discordant pairs. Power Achieved, Power = P Z ≤ 1 2 pA (1 − pA ) √ −z1−α/2 + 2|pA − 0.5| npD provided nD &gt; 20 and nD pA (1 − pA ) &gt; 5. Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction Two-Sample Test for Binomial Proportions McNemar’s Test Estimation of Sample Size and Power R × C Contingency Tables Chi-Square Goodness-of-Fit Test The Kappa Statistic Example:Cancer Suppose we want to compare two diﬀerent regimens of chemotherapy (A,B) for treatment of breast cancer where the outcome measure is recurrence of breast cancer or death over a 5-year period. A matched-pair design is used, in which patients are matched on age and clinical stage of disease, with one patient in a matched pair assigned to treatment A and the other to treatment B. Bases on previous work, it is estimated that patients in a matched pair will respond similarly to the treatments in 85% of matched pairs (i.e. both will either die or have a recurrence or both will be alive and not have a recurrence over 5 years). Furthermore, for matched pairs in which there is a diﬀerence in response, it is estimated that in two-thirds of the pairs the treatment A patient will either die or have a recurrence, and the treatment B patient will not; in one third of the pairs the treatment B patient will die or have a recurrence, and the treatment A patient will not. How many participants (or matched pairs) need to be enrolled in the study to have a 90% chance of ﬁnding a signiﬁcant diﬀerence using a two-sided test with type I error =...
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