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• W3148768688 abstract "This report contains two contributions to the update of the Encyclopedia of Statistical Sciences The contributions in this report are Nested case control sampling Sampling from the risk sets page Counter matched sampling page NESTED CASE CONTROL SAMPLING SAMPLING FROM THE RISK SETS Cox s regression model is one of the cornerstones in modern survival analysis and it is the method of choice when one wants to assess the in uence of risk factors and other covariates on mortality or morbidity Estimation in Cox s model is based on a partial likelihood which at each observed death or disease occurrence failure compares the covariate values of the failing individual to those of all individuals at risk at the time of the failure In large epidemiological cohort studies of a rare disease see EPIDEMIOLOGICAL STATISTICS and COHORT ANALYSIS Cox regression requires collection of covariate information on all individuals in the cohort even though only a small fraction of these actually get diseased This may be very expensive or even logistically impossible Cohort sampling techniques where covariate information is collected for all failing individuals cases but only for a sample of the non failing individuals controls then o er useful alternatives which may drastically reduce the resources that need to be allocated to a study Further as most of the statistical information is contained in the cases such studies may still be su cient to give reliable answers to the questions of interest The most common cohort sampling design is nested case control sampling Here one compares each case to a small number of controls selected at random from those at risk at the case s failure time and a new sample of controls is selected for each case A di erent type of cohort sampling design is case cohort sampling For this design one selects at the outset of the study a random sample of control individuals the subcohort and these individuals are used as controls throughout the study provided they are still at risk In this entry we focus on the nested case control design We rst indicate the relation between this form of case control sampling and the more classical case control designs see RETROSPECTIVE STUDIES INCLUDING CASE CONTROL and give a sketch of the development of the subject To x ideas we then describe in more details one particular nested case control study Further we review the Cox model describe precisely how the nested case control data are collected and present methods for statistical inference Finally a note on e ciency is given and we provide some remarks on extensions of the nested case control design as well as a brief comparison between nested case control sampling and case cohort sampling Nested case control studies and other case control designs The theory for case control studies for a binary response variable diseased not diseased dates back to the work of Corn eld in the early s see ODDS RATIO ESTIMATORS proceeds via the landmark paper by Mantel and Haenzel see MANTEL HAENSZEL STATISTIC to the implementation of the logistic regression model and the development of conditional logistic regression for matched case control data in the s The monograph by Breslow and Day gives an extensive exposition of this classical case control theory while provides a nice historical account Age or other time scales play no role in the statistical models on which the classical case control theory is based so this important aspect of a study has to be taken care of by strati cation or time matching This is di erent for a nested case control study where Cox s regression model is used to model the occurrence of failures and where the controls are sampled from the risk sets Further in a classical case control study the population from which the controls are sampled is often not well de ned while a nested case control study is performed within a well de ned cohort This makes the nested case control design intermediate between a classical case control study and a full cohort analysis The nested case control design was suggested in by Thomas as a tool to reduce error checking and the computational burden for the analysis of large cohorts He proposed to base inference on a modi cation of Cox s partial likelihood see below This suggestion was supported by the work of Prentice and Breslow who derived the same expression as a conditional likelihood for time matched case control sampling from an in nite population A more decisive but still heuristic argument was provided by Oakes who showed that is a partial likelihood when the sampling of controls is performed within the actual nite cohort It took more than ten years however before Goldstein and Langholz proved rigorously that the estimator of the regression coe cients based on Oakes partial likelihood enjoys similar large sample properties as ordinary maximum likelihood estimators Later Borgan Goldstein and Langholz gave a more direct proof along the lines of Andersen and Gill using a marked point process formulation It is indicated below how this marked point process approach also solves the problem of how to estimate the baseline hazard rate function from nested case control data" @default.
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• W3148768688 date "2006-01-01" @default.
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• W3148768688 title "Two contributions to the update of the Encyclopedia of Statistical Sciences Nested case control sampling and Counter matched sampling" @default.
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