6,628 research outputs found
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
Estimation of Conditional Power for Cluster-Randomized Trials with Interval-Censored Endpoints
Cluster-randomized trials (CRTs) of infectious disease preventions often yield correlated, interval-censored data: dependencies may exist between observations from the same cluster, and event occurrence may be assessed only at intermittent clinic visits. This data structure must be accounted for when conducting interim monitoring and futility assessment for CRTs. In this article, we propose a flexible framework for conditional power estimation when outcomes are correlated and interval-censored. Under the assumption that the survival times follow a shared frailty model, we first characterize the correspondence between the marginal and cluster-conditional survival functions, and then use this relationship to semiparametrically estimate the cluster-specific survival distributions from the available interim data. We incorporate assumptions about changes to the event process over the remainder of the trial---as well as estimates of the dependency among observations in the same cluster---to extend these survival curves through the end of the study. Based on these projected survival functions we generate correlated interval-censored observations, and then calculate the conditional power as the proportion of times (across multiple full-data generation steps) that the null hypothesis of no treatment effect is rejected. We evaluate the performance of the proposed method through extensive simulation studies, and illustrate its use on a large cluster-randomized HIV prevention trial
Penalized log-likelihood estimation for partly linear transformation models with current status data
We consider partly linear transformation models applied to current status
data. The unknown quantities are the transformation function, a linear
regression parameter and a nonparametric regression effect. It is shown that
the penalized MLE for the regression parameter is asymptotically normal and
efficient and converges at the parametric rate, although the penalized MLE for
the transformation function and nonparametric regression effect are only
consistent. Inference for the regression parameter based on a block
jackknife is investigated. We also study computational issues and demonstrate
the proposed methodology with a simulation study. The transformation models and
partly linear regression terms, coupled with new estimation and inference
techniques, provide flexible alternatives to the Cox model for current status
data analysis.Comment: Published at http://dx.doi.org/10.1214/009053605000000444 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A sieve M-theorem for bundled parameters in semiparametric models, with application to the efficient estimation in a linear model for censored data
In many semiparametric models that are parameterized by two types of
parameters---a Euclidean parameter of interest and an infinite-dimensional
nuisance parameter---the two parameters are bundled together, that is, the
nuisance parameter is an unknown function that contains the parameter of
interest as part of its argument. For example, in a linear regression model for
censored survival data, the unspecified error distribution function involves
the regression coefficients. Motivated by developing an efficient estimating
method for the regression parameters, we propose a general sieve M-theorem for
bundled parameters and apply the theorem to deriving the asymptotic theory for
the sieve maximum likelihood estimation in the linear regression model for
censored survival data. The numerical implementation of the proposed estimating
method can be achieved through the conventional gradient-based search
algorithms such as the Newton--Raphson algorithm. We show that the proposed
estimator is consistent and asymptotically normal and achieves the
semiparametric efficiency bound. Simulation studies demonstrate that the
proposed method performs well in practical settings and yields more efficient
estimates than existing estimating equation based methods. Illustration with a
real data example is also provided.Comment: Published in at http://dx.doi.org/10.1214/11-AOS934 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
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