Indiana University-Purdue University Indianapolis (IUPUI) / In many longitudinal studies, the time scales upon which we assess the primary outcomes
are anchored by pre-specified events. However, these anchoring events are
often not observable and they are randomly distributed with unknown distribution.
Without direct observations of the anchoring events, the time scale used for analysis
are not available, and analysts will not be able to use the traditional longitudinal
models to describe the temporal changes as desired. Existing methods often make
either ad hoc or strong assumptions on the anchoring events, which are unveri able
and prone to biased estimation and invalid inference.
Although not able to directly observe, researchers can often ascertain an interval
that includes the unobserved anchoring events, i.e., the anchoring events are
interval censored. In this research, we proposed a two-stage method to fit commonly
used longitudinal models with interval censored anchoring events. In the first stage,
we obtain an estimate of the anchoring events distribution by nonparametric method
using the interval censored data; in the second stage, we obtain the parameter estimates
as stochastic functionals of the estimated distribution. The construction of the
stochastic functional depends on model settings. In this research, we considered two
types of models. The first model was a distribution-free model, in which no parametric
assumption was made on the distribution of the error term. The second model was
likelihood based, which extended the classic mixed-effects models to the situation that the origin of the time scale for analysis was interval censored. For the purpose
of large-sample statistical inference in both models, we studied the asymptotic
properties of the proposed functional estimator using empirical process theory. Theoretically,
our method provided a general approach to study semiparametric maximum
pseudo-likelihood estimators in similar data situations. Finite sample performance of
the proposed method were examined through simulation study. Algorithmically eff-
cient algorithms for computing the parameter estimates were provided. We applied
the proposed method to a real data analysis and obtained new findings that were
incapable using traditional mixed-effects models. / 2 years
| Identifer | oai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/16278 |
| Date | 01 March 2018 |
| Creators | Chu, Chenghao |
| Contributors | Zhang, Ying, Tu, Wanzhu |
| Source Sets | Indiana University-Purdue University Indianapolis |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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