Details
| Original language | English |
|---|---|
| Pages (from-to) | 3325-3335 |
| Number of pages | 11 |
| Journal | Statistics in medicine |
| Volume | 21 |
| Issue number | 22 |
| Publication status | Published - 24 Oct 2002 |
Abstract
Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.
Keywords
- Asymptotic tests, Binomial data, Sample size determination, Trend test
ASJC Scopus subject areas
- Medicine(all)
- Epidemiology
- Mathematics(all)
- Statistics and Probability
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In: Statistics in medicine, Vol. 21, No. 22, 24.10.2002, p. 3325-3335.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Detecting dose-response using contrasts
T2 - Asymptotic power and sample size determination for binomial data
AU - Bretz, Frank
AU - Hothorn, Ludwig A.
PY - 2002/10/24
Y1 - 2002/10/24
N2 - Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.
AB - Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.
KW - Asymptotic tests
KW - Binomial data
KW - Sample size determination
KW - Trend test
UR - http://www.scopus.com/inward/record.url?scp=0037202572&partnerID=8YFLogxK
U2 - 10.1002/sim.1324
DO - 10.1002/sim.1324
M3 - Article
C2 - 12407675
AN - SCOPUS:0037202572
VL - 21
SP - 3325
EP - 3335
JO - Statistics in medicine
JF - Statistics in medicine
SN - 0277-6715
IS - 22
ER -