Indiana University-Purdue University Indianapolis (IUPUI) / It is generally of interest to explore if the risk of death would be modified by medical
conditions (e.g., illness) that have occurred prior. This situation gives rise to semicompeting
risks data, which are a mixture of competing risks and progressive state
data. This type of data occurs when a non-terminal event can be censored by a
well-defined terminal event, but not vice versa.
In the first part of this dissertation, the shared gamma-frailty conditional Markov
model (GFCMM) is adopted because it bridges the copula models and illness-death
models. Maximum likelihood estimation methodology has been proposed in the literature.
However, we found through numerical experiments that the unrestricted model
sometimes yields nonparametric biased estimation. Hence a practical guideline is
provided for using the GFCMM that includes (i) a score test to assess whether the
restricted model, which does not exhibit estimation problems, is reasonable under a
proportional hazards assumption, and (ii) a graphical illustration to evaluate whether
the unrestricted model yields nonparametric estimation with substantial bias for cases
where the test provides a statistical significant result against the restricted model.
However, the scientific question of interest that whether the status of non-terminal
event alters the risk to terminal event can only be partially addressed based on the
aforementioned approach. Therefore in the second part of this dissertation, we adopt
a Markov illness-death model, whose transition intensities are essentially equivalent
to the marginal hazards defined in GFCMM, but with different interpretations; we develop three nonparametric tests, including a linear test, a Kolmogorov-Smirnov-type
test, and a L2-distance-type test, to directly compare the two transition intensities
under consideration. The asymptotic properties of the proposed test statistics are
established using empirical process theory. The performance of these tests in nite
samples is numerically evaluated through extensive simulation studies. All three tests
provide similar power levels with non-crossing curves of cumulative transition intensities,
while the linear test is suboptimal when the curves cross. Eventually, the
proposed tests successfully address the scientific question of interest. This research is
applied to Indianapolis-Ibadan Dementia Project (IIDP) to explore whether dementia
occurrence changes mortality risk. / 2022-05-06
| Identifer | oai:union.ndltd.org:IUPUI/oai:scholarworks.iupui.edu:1805/22730 |
| Date | 04 1900 |
| Creators | Li, Jing |
| Contributors | Bakoyannis, Giorgos, Zhang, Ying, Gao, Sujuan, Song, Yiqing, Zhang, Chi |
| Source Sets | Indiana University-Purdue University Indianapolis |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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