4,597 research outputs found
Estimating medical costs from a transition model
Nonparametric estimators of the mean total cost have been proposed in a
variety of settings. In clinical trials it is generally impractical to follow
up patients until all have responded, and therefore censoring of patient
outcomes and total cost will occur in practice. We describe a general
longitudinal framework in which costs emanate from two streams, during sojourn
in health states and in transition from one health state to another. We
consider estimation of net present value for expenditures incurred over a
finite time horizon from medical cost data that might be incompletely
ascertained in some patients. Because patient specific demographic and clinical
characteristics would influence total cost, we use a regression model to
incorporate covariates. We discuss similarities and differences between our net
present value estimator and other widely used estimators of total medical
costs. Our model can accommodate heteroscedasticity, skewness and censoring in
cost data and provides a flexible approach to analyses of health care cost.Comment: Published in at http://dx.doi.org/10.1214/193940307000000266 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Bayesian semiparametric inference for multivariate doubly-interval-censored data
Based on a data set obtained in a dental longitudinal study, conducted in
Flanders (Belgium), the joint time to caries distribution of permanent first
molars was modeled as a function of covariates. This involves an analysis of
multivariate continuous doubly-interval-censored data since: (i) the emergence
time of a tooth and the time it experiences caries were recorded yearly, and
(ii) events on teeth of the same child are dependent. To model the joint
distribution of the emergence times and the times to caries, we propose a
dependent Bayesian semiparametric model. A major feature of the proposed
approach is that survival curves can be estimated without imposing assumptions
such as proportional hazards, additive hazards, proportional odds or
accelerated failure time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS368 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Hidden Markov Models and their Application for Predicting Failure Events
We show how Markov mixed membership models (MMMM) can be used to predict the
degradation of assets. We model the degradation path of individual assets, to
predict overall failure rates. Instead of a separate distribution for each
hidden state, we use hierarchical mixtures of distributions in the exponential
family. In our approach the observation distribution of the states is a finite
mixture distribution of a small set of (simpler) distributions shared across
all states. Using tied-mixture observation distributions offers several
advantages. The mixtures act as a regularization for typically very sparse
problems, and they reduce the computational effort for the learning algorithm
since there are fewer distributions to be found. Using shared mixtures enables
sharing of statistical strength between the Markov states and thus transfer
learning. We determine for individual assets the trade-off between the risk of
failure and extended operating hours by combining a MMMM with a partially
observable Markov decision process (POMDP) to dynamically optimize the policy
for when and how to maintain the asset.Comment: Will be published in the proceedings of ICCS 2020;
@Booklet{EasyChair:3183, author = {Paul Hofmann and Zaid Tashman}, title =
{Hidden Markov Models and their Application for Predicting Failure Events},
howpublished = {EasyChair Preprint no. 3183}, year = {EasyChair, 2020}
Modeling left-truncated and right-censored survival data with longitudinal covariates
There is a surge in medical follow-up studies that include longitudinal
covariates in the modeling of survival data. So far, the focus has been largely
on right-censored survival data. We consider survival data that are subject to
both left truncation and right censoring. Left truncation is well known to
produce biased sample. The sampling bias issue has been resolved in the
literature for the case which involves baseline or time-varying covariates that
are observable. The problem remains open, however, for the important case where
longitudinal covariates are present in survival models. A joint likelihood
approach has been shown in the literature to provide an effective way to
overcome those difficulties for right-censored data, but this approach faces
substantial additional challenges in the presence of left truncation. Here we
thus propose an alternative likelihood to overcome these difficulties and show
that the regression coefficient in the survival component can be estimated
unbiasedly and efficiently. Issues about the bias for the longitudinal
component are discussed. The new approach is illustrated numerically through
simulations and data from a multi-center AIDS cohort study.Comment: Published in at http://dx.doi.org/10.1214/12-AOS996 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary
Many researchers have investigated first hitting times as models for survival
data. First hitting times arise naturally in many types of stochastic
processes, ranging from Wiener processes to Markov chains. In a survival
context, the state of the underlying process represents the strength of an item
or the health of an individual. The item fails or the individual experiences a
clinical endpoint when the process reaches an adverse threshold state for the
first time. The time scale can be calendar time or some other operational
measure of degradation or disease progression. In many applications, the
process is latent (i.e., unobservable). Threshold regression refers to
first-hitting-time models with regression structures that accommodate covariate
data. The parameters of the process, threshold state and time scale may depend
on the covariates. This paper reviews aspects of this topic and discusses
fruitful avenues for future research.Comment: Published at http://dx.doi.org/10.1214/088342306000000330 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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