Isotonic Inference

Hirotsu, Chihiro

doi:10.1002/0470011815.b2a15061

Cited by 4 publications

(3 citation statements)

References 55 publications

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“…A parametric solution to this problem is very difficult, especially when K > 2. These hypotheses define a problem of isotonic inference (see Hirotsu 1998).…”

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confidence: 99%

A permutation test for umbrella alternatives

Basso

Salmaso

2009

Stat Comput

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There is a wide variety of stochastic ordering problems where K groups (typically ordered with respect to time) are observed along with a (continuous) response. The interest of the study may be on finding the change-point group, i.e. the group where an inversion of trend of the variable under study is observed. A change point is not merely a maximum (or a minimum) of the time-series function, but a further requirement is that the trend of the time-series is monotonically increasing before that point, and monotonically decreasing afterwards. A suitable solution can be provided within a conditional approach, i.e. by considering some suitable nonparametric combination of dependent tests for simple stochastic ordering problems. The proposed procedure is very flexible and can be extended to trend and/or repeated measure problems. Some comparisons through simulations and examples with the well known Mack & Wolfe test for umbrella alternative and with Page's test for trend problems with correlated data are investigated

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“…A parametric solution to this problem is very difficult, especially when K > 2. These hypotheses define a problem of isotonic inference (see Hirotsu 1998).…”

mentioning

confidence: 99%

A permutation test for umbrella alternatives

Basso

Salmaso

2009

Stat Comput

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“…The half-life may vary with the concentration of the drug, and usually is longer for higher concentration levels. Table 6.2 shows data from Hirotsu (2005). It contains the half-lives in hours of an antibiotic at four different doses that is injected into rats.…”

Section: Examplementioning

confidence: 99%

Confidence intervals under order restrictions

Park

Kalbfleisch²,

Taylor³

2014

STAT SINICA

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In this paper, we consider the problem of constructing confidence intervals (CIs) for G independent normal population means subject to linear ordering constraints. For this problem, CIs based on asymptotic distributions, likelihood ratio tests and bootstraps do not have good properties particularly when some of the population means are close to each other. We propose a new method based on defining intermediate random variables that are related to the original observations and using the CIs of the means of these intermediate random variables to restrict the original CIs from the separate groups. The coverage rates of the intervals are shown to exceed, but be close to, the nominal level for two groups, when the ratio of the variances is assumed known. Simulation studies show that the proposed CIs have coverage rates close to nominal levels with reduced average widths. Data on half-lives of an antibiotic are analyzed to illustrate the method.

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“…Methods of isotonic regression have been developed specifically for situations where order constraints are imposed on dose-response relationships (Hirotsu, 1998) and would seem therefore particularly well-suited to the problem at hand. Two tests were considered.…”

Section: Tests Based On Isotonic Regressionmentioning

confidence: 99%

Tests for Monotonic Trend from Case‐Control Data: Cochran‐Armitage‐Mantel Trend Test, Isotonic Regression and Single and Multiple Contrast Tests

Leuraud

Bénichou

2004

Biometrical J

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SummaryTests for a monotonic trend between an ordered categorical exposure and disease status are routinely carried out from case-control data using the Mantel-extension trend test or the asymptotically equivalent Cochran-Armitage test. In this study, we considered two alternative tests based on isotonic regression, namely an order-restricted likelihood ratio test and an isotonic modification of the Mantel-extension test extending the recent proposal by Mancuso, Ahn and Chen (2001) to case-control data. Furthermore, we considered three tests based on contrasts, namely a single contrast (SC) test based on Schaafsma's coefficients, the Dosemeci and Benichou (DB) test, a multiple contrast (MC) test based on the Helmert, reverse-Helmert and linear contrasts and we derived their case-control versions. Using simulations, we compared the statistical properties of these five alternative tests to those of the Mantel-extension test under various patterns including no relationship, as well as monotonic and non-monotonic relationships between exposure and disease status. In the case of no relationship, all tests had close to nominal type I error except in situations combining a very unbalanced exposure distribution and small sample size, where the asymptotic versions of the three tests based on contrasts were highly anticonservative. The use of bootstrap instead of asymptotic versions corrected this anticonservatism. For monotonic patterns, all tests had close powers. For non monotonic patterns, the DB-test showed the most favourable results as it was the least powerful test. The two tests based on isotonic regression were the most powerful tests and the Mantel-extension test, the SC-and MC-tests had in-between powers. The six tests were applied to data from a case-control study investigating the relationship between alcohol consumption and risk of laryngeal cancer in Turkey. In situations with no evidence of a monotonic relationship between exposure and disease status, the three tests based on contrasts did not conclude in favour of a significant trend whereas all the other tests did.

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Isotonic Inference

Cited by 4 publications

References 55 publications

A permutation test for umbrella alternatives

A permutation test for umbrella alternatives

Confidence intervals under order restrictions

Tests for Monotonic Trend from Case‐Control Data: Cochran‐Armitage‐Mantel Trend Test, Isotonic Regression and Single and Multiple Contrast Tests

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