ELIZA

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288503 occurrences (No.86 in the rank) during 5 years in the PubMed. [cache]

176) Maximum likelihood estimates for the population slope were acquired by direct maximisation of the marginal likelihood function and empirical Bayes estimates for the individual slopes were generated using Gaussian quadrature.

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PMID:22143404 DOI:10.1177/0962280211430681

2015 Statistical methods in medical research

* Slope estimation for informatively right censored longitudinal data modelling the number of observations using geometric and Poisson distributions: application to renal transplant cohort.

- Analysis of longitudinal data is often complicated by the presence of informative right censoring. This type of censoring should be accounted for in the analysis so that valid slope estimates are attained. In this study, we developed a new likelihood-based approach wherein the likelihood function is integrated over random effects to obtain a marginal likelihood function. Maximum likelihood estimates for the population slope were acquired by direct maximisation of the marginal likelihood function and empirical Bayes estimates for the individual slopes were generated using Gaussian quadrature. The performance of the model was assessed using the geometric and Poisson distributions to model the number of observations for every individual subject. Our model generated valid estimates for the slopes under both distributions with minimal bias and mean squared errors. Our sensitivity analysis confirmed the robustness of the model to assumptions pertaining to the underlying distribution and demonstrated its insensitivity to normality assumptions. Moreover, superiority of the model in terms of accuracy of slope estimates was consistently shown across the different levels of censoring in comparison to the naïve and bootstrap approaches. This model was illustrated using the cohort of renal transplant patients and estimates of the slopes that are adjusted for informative right censoring were acquired.

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(1)94 of	(10)7 with	(19)3 for	(28)2 leading
(2)74 null	(11)5 during	(20)3 has	(29)2 mutations
(3)53 and	(12)5 tests	(21)3 over	(30)2 on
(4)47 in	(13)5 that	(22)3 relationships	(31)2 or
(5)17 was	(14)4 among	(23)2 at	(32)2 physical
(6)12 as	(15)4 to	(24)2 but	(33)2 relationship
(7)12 is	(16)4 which	(25)2 can	(34)2 remains
(8)7 Index	(17)3 after	(26)2 could	(35)2 using
(9)7 were	(18)3 by	(27)2 grades

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--- WordNet output for function --- =>1.機能, 関数, 役割, 働き, 2.機能する, 作用する, 働く, 役目を果たす, 3.社交的会合, パーティー, 儀式 Overview of noun function The noun function has 7 senses (first 3 from tagged texts) 1. (43) function, mathematical function, single-valued function, map, mapping -- ((mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)) 2. (24) function, purpose, role, use -- (what something is used for; "the function of an auger is to bore holes"; "ballet is beautiful but what use is it?") 3. (7) function, office, part, role -- (the actions and activities assigned to or required or expected of a person or group; "the function of a teacher"; "the government must do its part"; "play its role") 4. function -- (a relation such that one thing is dependent on another; "height is a function of age"; "price is a function of supply and demand") 5. function -- (a formal or official social gathering or ceremony; "it was a black-tie function") 6. affair, occasion, social occasion, function, social function -- (a vaguely specified social event; "the party was quite an affair"; "an occasion arranged to honor the president"; "a seemingly endless round of social functions") 7. routine, subroutine, subprogram, procedure, function -- (a set sequence of steps, part of larger computer program) Overview of verb function The verb function has 3 senses (first 3 from tagged texts) 1. (9) function, work, operate, go, run -- (perform as expected when applied; "The washing machine won't go unless it's plugged in"; "Does this old car still run well?"; "This old radio doesn't work anymore") 2. (3) serve, function -- (serve a purpose, role, or function; "The tree stump serves as a table"; "The female students served as a control group"; "This table would serve very well"; "His freedom served him well"; "The table functions as a desk") 3. (1) officiate, function -- (perform duties attached to a particular office or place or function; "His wife officiated as his private secretary") --- WordNet end ---