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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
twosided test with an α level of .05 is used? Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
TwoSample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
ChiSquare GoodnessofFit Test
The Kappa Statistic Paired Samples: McNemar’s Test
The sample size needed to conduct a twosided 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 + 2pA − 0.5 npD provided nD > 20 and nD pA (1 − pA ) > 5.
Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
TwoSample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
ChiSquare GoodnessofFit 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 5year period. A matchedpair 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 twothirds 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 twosided test with type I error =...
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 Fall '12
 SolomonHarrar
 Statistics, Biostatistics

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