28,491 research outputs found
Local partial likelihood estimation in proportional hazards regression
Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the
estimation of the risk function in the proportional hazards model.
Their proposed estimator is based on integrating the estimated derivative
function obtained through a local version of the partial likelihood. They
proved the large sample properties of the derivative function, but the large
sample properties of the estimator for the risk function itself were not
established. In this paper, we consider direct estimation of the relative risk
function for any location normalization point .
The main novelty in our approach is that we select observations in shrinking
neighborhoods of both and when constructing a local version of the
partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997)
1661--1690] only concentrated on a single neighborhood, resulting in the
cancellation of the risk function in the local likelihood function. The
asymptotic properties of our estimator are rigorously established and the
variance of the estimator is easily estimated. The idea behind our approach is
extended to estimate the differences between groups. A simulation study is
carried out.Comment: Published at http://dx.doi.org/10.1214/009053606000001299 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Most Likely Transformations
We propose and study properties of maximum likelihood estimators in the class
of conditional transformation models. Based on a suitable explicit
parameterisation of the unconditional or conditional transformation function,
we establish a cascade of increasingly complex transformation models that can
be estimated, compared and analysed in the maximum likelihood framework. Models
for the unconditional or conditional distribution function of any univariate
response variable can be set-up and estimated in the same theoretical and
computational framework simply by choosing an appropriate transformation
function and parameterisation thereof. The ability to evaluate the distribution
function directly allows us to estimate models based on the exact likelihood,
especially in the presence of random censoring or truncation. For discrete and
continuous responses, we establish the asymptotic normality of the proposed
estimators. A reference software implementation of maximum likelihood-based
estimation for conditional transformation models allowing the same flexibility
as the theory developed here was employed to illustrate the wide range of
possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics
2017-06-1
Systematically missing confounders in individual participant data meta-analysis of observational cohort studies.
One difficulty in performing meta-analyses of observational cohort studies is that the availability of confounders may vary between cohorts, so that some cohorts provide fully adjusted analyses while others only provide partially adjusted analyses. Commonly, analyses of the association between an exposure and disease either are restricted to cohorts with full confounder information, or use all cohorts but do not fully adjust for confounding. We propose using a bivariate random-effects meta-analysis model to use information from all available cohorts while still adjusting for all the potential confounders. Our method uses both the fully adjusted and the partially adjusted estimated effects in the cohorts with full confounder information, together with an estimate of their within-cohort correlation. The method is applied to estimate the association between fibrinogen level and coronary heart disease incidence using data from 154,012 participants in 31 cohort
Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration
Bayesian approaches for handling covariate measurement error are well
established, and yet arguably are still relatively little used by researchers.
For some this is likely due to unfamiliarity or disagreement with the Bayesian
inferential paradigm. For others a contributory factor is the inability of
standard statistical packages to perform such Bayesian analyses. In this paper
we first give an overview of the Bayesian approach to handling covariate
measurement error, and contrast it with regression calibration (RC), arguably
the most commonly adopted approach. We then argue why the Bayesian approach has
a number of statistical advantages compared to RC, and demonstrate that
implementing the Bayesian approach is usually quite feasible for the analyst.
Next we describe the closely related maximum likelihood and multiple imputation
approaches, and explain why we believe the Bayesian approach to generally be
preferable. We then empirically compare the frequentist properties of RC and
the Bayesian approach through simulation studies. The flexibility of the
Bayesian approach to handle both measurement error and missing data is then
illustrated through an analysis of data from the Third National Health and
Nutrition Examination Survey
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