SUMMARY A unified estimation procedure is proposed for the analysis of censored data using linear transformation models, which include the proportional hazards model and the proportional odds model as special cases. This procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable. The estimator is the same as the Cox partial likelihood estimator in the case of the proportional hazards model. Moreover, the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug-in rules. The method is illustrated by simulation and is applied to the Veterans' Administration lung cancer data.

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Semiparametric analysis of transformation models with censored data

What motivated men to risk death in the most horrific war in U. S. history when pay was low and irregular and military punishment strategies were weak? In such a situation creating group loyalty by promoting social capital is of paramount importance and in the Civil War was the cement of both armies. We find that individual and company socioeconomic and demographic characteristics, ideology, and morale were important predictors of group loyalty in the Union Army. Company characteristics were more important than ideology or morale. Soldiers in companies that were more homogeneous in ethnicity, occupation, and age were less likely to shirk.

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Cowards and Heroes: Group Loyalty in the American Civil War

https://dukespace.lib.duke.edu/dspace/bitstream/handle/10161/1906/Khan_partial_%20rank_estimation.pdf;sequence=1

Partial rank estimation of duration models with general forms of censoring

The statistical literature on assessing the accuracy of risk factors or disease markers as diagnostic tests deals almost exclusively with settings where the test, Y, is measured concurrently with disease status D. In practice, however, disease status may vary over time and there is often a time lag between when the marker is measured and the occurrence of disease. One example concerns the Framingham risk score (FR-score) as a marker for the future risk of cardiovascular events, events that occur after the score is ascertained. To evaluate such a marker, one needs to take the time lag into account since the predictive accuracy may be higher when the marker is measured closer to the time of disease occurrence. We therefore consider inference for sensitivity and specificity functions that are defined as functions of time. Semiparametric regression models are proposed. Data from a cohort study are used to estimate model parameters. One issue that arises in practice is that event times may be censored. In this research, we extend in several respects the work by Leisenring et al. (1997) that dealt only with parametric models for binary tests and uncensored data. We propose semiparametric models that accommodate continuous tests and censoring. Asymptotic distribution theory for parameter estimates is developed and procedures for making statistical inference are evaluated with simulation studies. We illustrate our methods with data from the Cardiovascular Health Study, relating the FR-score measured at enrollment to subsequent risk of cardiovascular events.

/pdf/the-sensitivity-and-specificity-of-markers-for-event-times-2yovf9vtbz.pdf

The sensitivity and specificity of markers for event times.

SUMMARY In a case-cohort design introduced by Prentice (1986), covariates are assembled only for a subcohort randomly selected from the entire cohort, and any additional cases outside the subcohort. Semiparametric transformation models are considered here for failure time data from the case-cohort design. Weighted estimating equations are proposed for esti mation of the regression parameters. The estimation procedure of survival probability at given covariate levels is also provided. Asymptotic properties are derived for the estimators using finite population sampling theory, U-statistics theory and martingale convergence results. The finite-sample properties of the proposed estimators, as well as the efficiency relative to the full cohort estimators, are assessed via simulation studies. A case-cohort dataset from the Atherosclerosis Risk in Communities study is used to illustrate the estimating procedure.

Weighted estimating equations for semiparametric transformation models with censored data from a case‐cohort design

Inference procedures based on the partial likelihood function for the Cox proportional hazards model have been generalised to the case in which the data consist of a large number of independent small groups of correlated failure time observations (Lee, Wei & Amato, 1992; Liang, Self & Chang, 1993; Cai & Prentice, 1997). However, the Cox model may not fit the data well. A class of linear transformation models, which includes the proportional hazards and odds models as special cases, has been studied extensively for univariate event times. In this paper, statistical methods to analyse such correlated observations are proposed for these models. We use the data from a recent study of the genetic aetiology of alcoholism to illustrate the new procedures for estimation, prediction and model selection.

M. Wilcox

Papers

Semiparametric regression analysis for clustered failure time data