Biomedical Engineering Reference
In-Depth Information
ular, in addition to taking an SRS from the entire population, they decided
to oversample from the tails of the distributions about the children's health
development indices such as the Weschler Intelligence Scale(IQ), hearing
level, vision and birth defect, etc.
Likelihood based inference for data from an ODS scheme inevitably
involves the distribution of covariates. Parametric modeling of a covariate
distribution is not robust to model misspecication. Methods that do not
require parametric modeling of the underlying distribution of covariates are
desirable.
We discuss the recently developed methods that deal with various forms
of data sets from ODS schemes. In particular, we consider (i) an overall SRS
sample and several supplemental samples with continuous outcome (Section
2); (ii) an overall SRS sample, several supplemental samples and some infor-
mation for the underlying population with continuous outcome (Section 3);
(iii) an overall SRS sample, several supplemental samples with ordinal out-
come and auxiliary covariate (Section 4); and (iv) an overall SRS sample,
several supplemental samples and additional information for the underly-
ing population with ordinal outcome (Section 5). These methods are all
semiparametric in nature and include semiparametric empirical likelihood,
semiparametric estimated likelihood, and semiparametric penalized spline
estimated likelihood methods.
In Section 2, we discuss a semi-parametric approach for data from an
ODS design with a continuous outcome. In Section 3, we discuss an esti-
mated likelihood method when in addition to the ODS sample, information
on the underlying population is available. In Section 4, we discuss appli-
cation of ODS methods to an ordinal outcome. In Section 5, we review a
penalized spine methods to deal with nonlinear problems in ODS design.
2. Semiparametric Empirical Likelihood for ODS with a
Continuous Outcome Variable
This section considers semiparametric methods for dealing with ODS data
with X observed on an overall SRS sample and several supplemental sam-
ples, and the outcome being continuous. In the CPP data structure, com-
plete data are only available for 849 children from the SRS and for 189
children from the two supplemental samples. Specically, there are 81 chil-
dren with IQs less than or equal to 82 and 108 children with IQs greater
than 110.
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