| Proportions and Chi-Square Tests
Introduction
The power and sample size requirements of statistical tests involving
one or more proportions may be studied using PASS,
including
Chi-Square Test
The Chi-square test is often used to test whether sets of frequencies or
proportions follow certain patterns. The two most common cases are in
tests of goodness of fit and tests of independence in contingency
tables. The Chi-square goodness of fit test is used to test whether data
follow a particular distribution. The Chi-square test for independence
in a contingency table is the most popular use of this test. Here
individuals are classified by two classification variables into a
two-way table. This table contains the counts of the number of
individuals in each combination of the row categories and column
categories. The Chi-square test determines if there is any association
between the two classification variables. Power calculations are based
on the noncentral Chi-square distribution.
Confidence Interval for a Proportion
This module calculates the sample size necessary to estimate a
proportion at a specified precision.
One Proportion
Twelve procedures are available for testing the inequality,
non-inferiority, and equivalence of a single proportion compared to a
standard (reference) value. These include tests using the difference,
ratio, or odds ratio of the two proportions. Statistical tests whose
power may be compared include the exact binomial test, four editions of
the z test, and the t test.
Two Proportions
Sixteen procedures were added for testing the inequality,
non-inferiority, and equivalence of proportions from two independent
groups. These include tests using the difference, ratio, or odds ratio
of the proportions. Statistical tests whose power may be compared
include four editions of the z test, the t test, Fisher's Exact test,
and likelihood score tests by Miettinen & Nurminen, Farrington &
Manning, and Gart & Nam.
Correlated Proportions
Six procedures were added for testing the inequality, non-inferiority,
and equivalence of two correlated proportions using McNemar's test.
Mantel-Haenszel Test
The Mantel-Haenszel test procedure makes it possible to test proportions
from stratified designs.
Equivalence of Correlated Proportions
Use this module when you want to show that the proportion of patients
responding to a new treatment is equivalent to the proportion responding
to usual treatment. In this case, you want to show that one treatment is
as good as another treatment rather than showing that one is better than
the other. However, in this design, the proportions are
correlated--usually, because each subject responds twice. You might
think of this as McNemar’s test modified for equivalence.
Equivalence
Used to test whether one treatment is equivalent to another
treatment in terms of their means.
Non-Inferiority
Used to test whether one treatment is no worse than another treatment.
Group Sequential Tests of Proportions
Used in clinical trials when interim statistical tests will be conducted
before a trial is completed to determine if the trial should be stopped
early. The alpha spending functions described by Lan and DeMets are
implemented.
Matched Case-Control Designs
A 2-by-M matched case-control study investigares risk factors relevant
to the development of a disease. Each case patient with the disease is
matched with one or more control patients without the disease. The odds
ratio will be used to evaluate the risk factor.
McNemar’s Test
This module calculates power and sample size for McNemar’s test
which compares the proportions for two correlated dichotomous variables.
These two variables may be two responses on a single individual or two
responses from a matched pair (as in matched case-control studies).
One-, Two-, and Three-Stage Phase II Clinical Trials
Phase II clinical trials determine
whether a drug or regimen has sufficient activity against disease to
warrant more extensive study and development. In a two-stage design, the
patients are divided into two groups or stages. At the completion of the
first stage, an interim analysis is made to determine if the second
stage should be conducted. If the number of patients responding is
greater than a certain amount, the second stage is conducted. Otherwise,
it is not. This module finds designs that meet the error rate
(alpha and beta) criterion and minimize the expected sample size. The
algorithm is discussed by Simon. Extending Simon’s work, our algorithm
allows the investigation of near-optimal designs that may have other
useful properties. We have also added a module that analyzes a
three-stage design.
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