Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Grammatica graeca, 1763

Bound volume containing a handwritten Greek grammar compiled by Joseph Drury beginning in 1763. The last sixteen pages contain a historical poem beginning, “Mason might once assert a Poets Claim. / But he must needs write.” The poem contains references to the “Great Patriot P—,“ the Roman conquest of Gall, Caeser, Versailles, and includes the verses, “How the King doth all his Cooks excel / Besides he longs to kiss his P / Saving your presence Louis keeps a whore.”

Norway and the Norwegians /

Disbound Original Held in Oak Street Library Facility

Spoken Chinese,

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Hans, the Eskimo; his story of Arctic adventure with Kane, Hayes, and Hall,

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Brush and pencil : an illustrated magazine of the arts of today.

Editors: Sept. 1897-Sept. 1900, Charles Francis Browne; Oct. 1900-May 1907, Frederick W. Morton.

Analysis of a power failure incident for the preliminary conceptual design of the small pressurized water reactor /

"Contract No. AT(40-1)-2589."

Texas and the Massachusetts resolutions.

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Source records of the great war : a comprehensive and readable source record of the world's great war, emphasizing the more important events, and presenting these as complete narratives in the actual words of the chief officials and most eminent leaders ... presenting documents from government archives and other authoritative sources, with outline narratives, indices, chronologies, and courses of reading on sociological movements and individual national activities /

"The war with Germany, a statistical summary by Leonard P. Ayres ... chief of the Statistics branch of the General staff": v. 7, 153 p. at end.

American literature 1607-1885 /

Photocopy. Ann Arbor, Mich. : University Microfilms, 1964. -- 20 cm.

Lee at Appomattox, and other papers,

Lee at Appomattox.--The treaty of Washington: before and after.--The British "change of heart".--An undeveloped function.--A plea for military history.--"Shall Cromwell have a statur?"

Cutter's guide to Mt. Clemens /

Description based on: 8th ed., 1900.

The dawn of history: an introduction to pre-historic study.

Keary, C.F. The earliest traces of man. The second stone age. The growth of language. Families of language. The nations of the old world.--Keary, H.M. Early social life. The village community.--Keary, A. Religion.--Keary, C.F. Aryan religions. The other world. Mythologies and folk tales.--Keary, A. Picture writing. Phonetic writing.--Keary, H. Conclusion.--Notes and authorities.

The inner life of George Eliot,

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