On using Lehmann alternatives with nonresponders
The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the kno...
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| Published in | Mathematical biosciences Vol. 109; no. 1; pp. 69 - 83 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
Elsevier Inc
01.04.1992
Elsevier Science |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0025-5564 1879-3134 |
| DOI | 10.1016/0025-5564(92)90052-X |
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| Abstract | The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness. |
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| AbstractList | The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness. The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness.The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of responses in the treatment group. It is shown that the locally most powerful test leads to a test statistic that, under the hypothesis of no treatment effect, is the sum of independent pareto random variables whereas under the alternative hypothesis it is the sum of independent random variables from a mixture of two pareto distributions. The limiting distribution of the test statistic under both hypotheses is in the domain of attraction of a stable distribution whose indices are derived. The power of the test is given, and its properties are discussed. A set of data from clinical research involving development of a new drug is used to show application of the procedure and demonstrate its usefulness. |
| Author | Razzaghi, Mehdi Nanthakumar, A. |
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| Cites_doi | 10.2307/2284101 10.2307/2532001 10.1137/0119017 10.2307/2531906 10.1017/S0305004100023987 10.6028/jres.077B.017 10.1007/BF03048130 10.2307/2525463 10.2307/2283875 10.1080/00949657408810066 10.2307/2531218 10.2307/2530351 10.2307/2333349 10.2307/2531256 10.1093/biomet/57.1.47 |
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| References | DuMouchel (BIB8) 1973; 68 Durairajan (BIB9) 1979; 19 Johnson, Verrill, Moore (BIB17) 1987; 43 Rao (BIB22) 1948; 44 Bartlet (BIB2) 1953; 40 Cross (BIB6) 1973; 3 Durairajan, Kale (BIB11) 1982; 44 Conover, Salsburg (BIB5) 1988; 44 DuMouchel (BIB7) 1971 Holt, Crow (BIB16) 1973; 77 Neyman (BIB20) 1959 Good (BIB14) 1979; 35 Arnold (BIB1) 1983 Moran (BIB19) 1970; 57 Prohorov, Rozanov (BIB21) 1969 Salsburg (BIB23) 1986; 42 Blum (BIB3) 1967; 19 Boos, Brownie (BIB4) 1986; 42 Durairajan, Kale (BIB10) 1981; 41 Feller (BIB13) 1971; Vol. II Fama, Roll (BIB12) 1968; 63 Govindarajulu (BIB15) 1973; 78 Mandelbrot (BIB18) 1963; 4 DuMouchel (10.1016/0025-5564(92)90052-X_BIB8) 1973; 68 Blum (10.1016/0025-5564(92)90052-X_BIB3) 1967; 19 Boos (10.1016/0025-5564(92)90052-X_BIB4) 1986; 42 Durairajan (10.1016/0025-5564(92)90052-X_BIB11) 1982; 44 Fama (10.1016/0025-5564(92)90052-X_BIB12) 1968; 63 Holt (10.1016/0025-5564(92)90052-X_BIB16) 1973; 77 Arnold (10.1016/0025-5564(92)90052-X_BIB1) 1983 Bartlet (10.1016/0025-5564(92)90052-X_BIB2) 1953; 40 Good (10.1016/0025-5564(92)90052-X_BIB14) 1979; 35 Conover (10.1016/0025-5564(92)90052-X_BIB5) 1988; 44 Feller (10.1016/0025-5564(92)90052-X_BIB13) 1971; Vol. II Rao (10.1016/0025-5564(92)90052-X_BIB22) 1948; 44 DuMouchel (10.1016/0025-5564(92)90052-X_BIB7) 1971 Govindarajulu (10.1016/0025-5564(92)90052-X_BIB15) 1973; 78 Cross (10.1016/0025-5564(92)90052-X_BIB6) 1973; 3 Durairajan (10.1016/0025-5564(92)90052-X_BIB9) 1979; 19 Neyman (10.1016/0025-5564(92)90052-X_BIB20) 1959 Johnson (10.1016/0025-5564(92)90052-X_BIB17) 1987; 43 Prohorov (10.1016/0025-5564(92)90052-X_BIB21) 1969 Salsburg (10.1016/0025-5564(92)90052-X_BIB23) 1986; 42 Durairajan (10.1016/0025-5564(92)90052-X_BIB10) 1981; 41 Moran (10.1016/0025-5564(92)90052-X_BIB19) 1970; 57 Mandelbrot (10.1016/0025-5564(92)90052-X_BIB18) 1963; 4 |
| References_xml | – volume: 41 start-page: 91 year: 1981 end-page: 100 ident: BIB10 article-title: Locally most powerful test for the mixing proportion publication-title: Sankhya B – volume: 63 start-page: 817 year: 1968 end-page: 836 ident: BIB12 article-title: Some properties of symmetric stable distributions publication-title: J. Am. Stat. Assoc. – volume: 44 start-page: 189 year: 1988 end-page: 196 ident: BIB5 article-title: Locally most powerful tests for detecting treatment effects when only a subset of patients can be expected to “respond to treatment” publication-title: Biometrics – volume: 3 start-page: 1 year: 1973 end-page: 27 ident: BIB6 article-title: Tables of finite-mean nonsymmetric stable distributions as computed from their convergent and asymptotic series publication-title: J. Stat. Comput. Simul. – volume: 44 start-page: 50 year: 1948 end-page: 57 ident: BIB22 article-title: Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation publication-title: Proc. Camb. Phil. Soc. – volume: 4 start-page: 111 year: 1963 end-page: 114 ident: BIB18 article-title: The stable paretian income distribution when the apparent exponent is near two publication-title: Int. Econ. Rev. – volume: 19 start-page: 191 year: 1967 end-page: 198 ident: BIB3 article-title: On the sums of independently distributed Pareto variables publication-title: SIAM, Appl. Math. – year: 1969 ident: BIB21 publication-title: Probability Theory: Basic Concepts, Limit Theorems, Random Processes – volume: 42 start-page: 671 year: 1986 end-page: 674 ident: BIB23 article-title: Alternative hypotheses for the effects of drugs in small-scale clinical studies publication-title: Biometrics – volume: 43 start-page: 641 year: 1987 end-page: 655 ident: BIB17 article-title: Two-sample rank tests for detecting changes that occur in a small proportion of the treated population publication-title: Biometrics – volume: 44 start-page: 153 year: 1982 end-page: 161 ident: BIB11 article-title: Locally most powerful similar test for the mixing proportion publication-title: Sankhya B – volume: 40 start-page: 306 year: 1953 end-page: 317 ident: BIB2 article-title: Approximate confidence intervals II. More than one unknown parameter publication-title: Biometrika – volume: 78 start-page: 89 year: 1973 end-page: 99 ident: BIB15 article-title: A central limit theorem for independent summands with infinite variances publication-title: Proc. Indian Acad. Sci. – volume: 35 start-page: 483 year: 1979 end-page: 489 ident: BIB14 article-title: Detection of a treatment effect when not all experimental subjects will respond to treatment publication-title: Biometrics – volume: Vol. II start-page: 312 year: 1971 end-page: 316 ident: BIB13 publication-title: An Introduction to Probability Theory and Its Applications – year: 1971 ident: BIB7 article-title: Stable distributions in statistical inference publication-title: Ph.D. Dissertation – start-page: 213 year: 1959 end-page: 234 ident: BIB20 article-title: Optimal asymptotic tests of composite statistical hypotheses publication-title: Probability and Statistics: The Harold Cramer Volume – volume: 42 start-page: 191 year: 1986 end-page: 197 ident: BIB4 article-title: Testing for a treatment effect in the presence of nonresponders publication-title: Biometrics – volume: 68 start-page: 469 year: 1973 end-page: 477 ident: BIB8 article-title: Stable distributions in statistical inference. 1. Symmetric stable distributions compared to other symmetric long-tailed distributions publication-title: J. Am. Stat. Assoc. – volume: 57 start-page: 47 year: 1970 end-page: 55 ident: BIB19 article-title: On asymptotically optimal tests for composite hypothesis publication-title: Biometrika – year: 1983 ident: BIB1 publication-title: Pareto Distributions – volume: 77 start-page: 143 year: 1973 end-page: 197 ident: BIB16 article-title: Tables and graphs of the stable probability density functions publication-title: J. Res. Natl. Bur. Std. USA – volume: 19 start-page: 15 year: 1979 end-page: 24 ident: BIB9 article-title: Invariant test for the mixture proportion publication-title: J. Indian Stat. Assoc. – volume: 68 start-page: 469 year: 1973 ident: 10.1016/0025-5564(92)90052-X_BIB8 article-title: Stable distributions in statistical inference. 1. Symmetric stable distributions compared to other symmetric long-tailed distributions publication-title: J. Am. Stat. Assoc. doi: 10.2307/2284101 – volume: 19 start-page: 15 year: 1979 ident: 10.1016/0025-5564(92)90052-X_BIB9 article-title: Invariant test for the mixture proportion publication-title: J. Indian Stat. Assoc. – year: 1983 ident: 10.1016/0025-5564(92)90052-X_BIB1 – volume: 43 start-page: 641 year: 1987 ident: 10.1016/0025-5564(92)90052-X_BIB17 article-title: Two-sample rank tests for detecting changes that occur in a small proportion of the treated population publication-title: Biometrics doi: 10.2307/2532001 – year: 1969 ident: 10.1016/0025-5564(92)90052-X_BIB21 – volume: 19 start-page: 191 year: 1967 ident: 10.1016/0025-5564(92)90052-X_BIB3 article-title: On the sums of independently distributed Pareto variables publication-title: SIAM, Appl. Math. doi: 10.1137/0119017 – volume: 44 start-page: 189 year: 1988 ident: 10.1016/0025-5564(92)90052-X_BIB5 article-title: Locally most powerful tests for detecting treatment effects when only a subset of patients can be expected to “respond to treatment” publication-title: Biometrics doi: 10.2307/2531906 – volume: Vol. II start-page: 312 year: 1971 ident: 10.1016/0025-5564(92)90052-X_BIB13 – volume: 44 start-page: 50 year: 1948 ident: 10.1016/0025-5564(92)90052-X_BIB22 article-title: Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation publication-title: Proc. Camb. Phil. Soc. doi: 10.1017/S0305004100023987 – volume: 77 start-page: 143 issue: B year: 1973 ident: 10.1016/0025-5564(92)90052-X_BIB16 article-title: Tables and graphs of the stable probability density functions publication-title: J. Res. Natl. Bur. Std. USA doi: 10.6028/jres.077B.017 – volume: 78 start-page: 89 year: 1973 ident: 10.1016/0025-5564(92)90052-X_BIB15 article-title: A central limit theorem for independent summands with infinite variances publication-title: Proc. Indian Acad. Sci. doi: 10.1007/BF03048130 – volume: 4 start-page: 111 year: 1963 ident: 10.1016/0025-5564(92)90052-X_BIB18 article-title: The stable paretian income distribution when the apparent exponent is near two publication-title: Int. Econ. Rev. doi: 10.2307/2525463 – start-page: 213 year: 1959 ident: 10.1016/0025-5564(92)90052-X_BIB20 article-title: Optimal asymptotic tests of composite statistical hypotheses – volume: 63 start-page: 817 year: 1968 ident: 10.1016/0025-5564(92)90052-X_BIB12 article-title: Some properties of symmetric stable distributions publication-title: J. Am. Stat. Assoc. doi: 10.2307/2283875 – volume: 3 start-page: 1 year: 1973 ident: 10.1016/0025-5564(92)90052-X_BIB6 article-title: Tables of finite-mean nonsymmetric stable distributions as computed from their convergent and asymptotic series publication-title: J. Stat. Comput. Simul. doi: 10.1080/00949657408810066 – volume: 42 start-page: 671 year: 1986 ident: 10.1016/0025-5564(92)90052-X_BIB23 article-title: Alternative hypotheses for the effects of drugs in small-scale clinical studies publication-title: Biometrics doi: 10.2307/2531218 – volume: 35 start-page: 483 year: 1979 ident: 10.1016/0025-5564(92)90052-X_BIB14 article-title: Detection of a treatment effect when not all experimental subjects will respond to treatment publication-title: Biometrics doi: 10.2307/2530351 – volume: 40 start-page: 306 year: 1953 ident: 10.1016/0025-5564(92)90052-X_BIB2 article-title: Approximate confidence intervals II. More than one unknown parameter publication-title: Biometrika doi: 10.2307/2333349 – volume: 42 start-page: 191 year: 1986 ident: 10.1016/0025-5564(92)90052-X_BIB4 article-title: Testing for a treatment effect in the presence of nonresponders publication-title: Biometrics doi: 10.2307/2531256 – volume: 44 start-page: 153 year: 1982 ident: 10.1016/0025-5564(92)90052-X_BIB11 article-title: Locally most powerful similar test for the mixing proportion publication-title: Sankhya B – volume: 57 start-page: 47 year: 1970 ident: 10.1016/0025-5564(92)90052-X_BIB19 article-title: On asymptotically optimal tests for composite hypothesis publication-title: Biometrika doi: 10.1093/biomet/57.1.47 – volume: 41 start-page: 91 year: 1981 ident: 10.1016/0025-5564(92)90052-X_BIB10 article-title: Locally most powerful test for the mixing proportion publication-title: Sankhya B – year: 1971 ident: 10.1016/0025-5564(92)90052-X_BIB7 article-title: Stable distributions in statistical inference |
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| SubjectTerms | Biological and medical sciences Biometry Data Interpretation, Statistical Drug Therapy - statistics & numerical data Fundamental and applied biological sciences. Psychology General aspects Humans |
| Title | On using Lehmann alternatives with nonresponders |
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