Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks
Traditionally, the regression analysis for competing risks survival time is based on the cause-specific hazard that treat failures from causes other than the cause of interest as censored observations. That includes technique such as the Cox proportional hazard model. The modelling of hazard rat...
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my-upm-ir.54182013-05-27T07:22:40Z Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks 2008 Kudus, Abdul Traditionally, the regression analysis for competing risks survival time is based on the cause-specific hazard that treat failures from causes other than the cause of interest as censored observations. That includes technique such as the Cox proportional hazard model. The modelling of hazard rate may or may not match the objective of investigator. It is often more desirable to investigate the subdistribution function, because cause-specific hazard doesn’t obviously give the information about proportion of individuals experiencing a cause of interest. Furthermore, the subdistribution and cause-specific hazard function are not interchangeable. Thus, if we intended to draw inference from subdistribution function, then we must model on subdistribution function directly or indirectly. Sometimes, we do not only intend to investigate the relationship between response and covariates through regression analysis, but also we want to identify the presence of subgroup of individuals in our data. We could then utilize tree-structured regression for this purpose. In this thesis, we developed statistical methods for competing risks data analysis through direct, indirect and parametric subdistribution modelling. Indirect model is employed via hazard of subdistribution. Evaluation of the performance of proposed methods is conducted through series of simulation studies as well as real data application. We developed four methods: 1) a method to categorize continuous covariate by considering the competing risks survival time outcome variables, called outcome-oriented categorization method, 2) a tree-structured competing risks regression to extract meaningful sub-groups of subjects determined by the value of covariates, 3) a hybrid model which boost the available subdistribution hazards regression by ugmenting it with tree-structured regression resulted from the previous step, 4) two kinds of parametric direct subdistribution model. These models are constructed based on non-mixture cure model. The first model is developed by taking into account the fraction of individuals who did not experience the event of interest in the long term. The second model is developed by reparameterizing the first model in order to mimic Gompertz distribution which allows no immune fraction. Research finding is as follows: 1) Method of outcome-oriented categorization based on deviance statistic is the best. The application of the method to contraceptive discontinuation data showed good result. 2) Regression tree for competing risks data can uncover the structure of data and yield the sub-group of individuals with a clear description based on their covariates. The application of the method to contraceptive discontinuation data showed good result. Extensive Monte Carlo simulation suggests the method has good performance in identifying the structure of data. 3) Application of the hybrid model to the contraceptive discontinuation data showed that the hybrid model is better than the available subdistribution regression in terms of AIC. 4) By using some well known kernel distribution, the parametric direct subdistribution models are developed. The maximum likelihood estimations are carried out simultaneously for all causes of event. In Bone Marrow Transplantation (BMT) data analysis, the first proposed model gave noticeably good fit to the nonparametric counterpart. The second proposed model is fitted to contraceptive discontinuation data and showed that Gompertz-like subdistribution with Gompertz kernel is the best fit. Mathematical analysis 2008 Thesis http://psasir.upm.edu.my/id/eprint/5418/ http://psasir.upm.edu.my/id/eprint/5418/1/IPM_2008_1.pdf application/pdf en public phd doctoral Universiti Putra Malaysia Mathematical analysis Institute Mathematical Research English |
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Mathematical analysis Kudus, Abdul Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| description |
Traditionally, the regression analysis for competing risks survival
time is based on the cause-specific hazard that treat failures from
causes other than the cause of interest as censored observations.
That includes technique such as the Cox proportional hazard
model. The modelling of hazard rate may or may not match the
objective of investigator. It is often more desirable to investigate
the subdistribution function, because cause-specific hazard
doesn’t obviously give the information about proportion of
individuals experiencing a cause of interest. Furthermore, the
subdistribution and cause-specific hazard function are not
interchangeable. Thus, if we intended to draw inference from subdistribution function, then we must model on subdistribution
function directly or indirectly.
Sometimes, we do not only intend to investigate the relationship
between response and covariates through regression analysis, but
also we want to identify the presence of subgroup of individuals in
our data. We could then utilize tree-structured regression for this
purpose.
In this thesis, we developed statistical methods for competing risks
data analysis through direct, indirect and parametric
subdistribution modelling. Indirect model is employed via hazard
of subdistribution. Evaluation of the performance of proposed
methods is conducted through series of simulation studies as well
as real data application.
We developed four methods: 1) a method to categorize
continuous covariate by considering the competing risks
survival time outcome variables, called outcome-oriented
categorization method, 2) a tree-structured competing risks
regression to extract meaningful sub-groups of subjects
determined by the value of covariates, 3) a hybrid model which
boost the available subdistribution hazards regression by ugmenting it with tree-structured regression resulted from the
previous step, 4) two kinds of parametric direct subdistribution
model. These models are constructed based on non-mixture
cure model. The first model is developed by taking into account
the fraction of individuals who did not experience the event of
interest in the long term. The second model is developed by
reparameterizing the first model in order to mimic Gompertz
distribution which allows no immune fraction.
Research finding is as follows: 1) Method of outcome-oriented
categorization based on deviance statistic is the best. The
application of the method to contraceptive discontinuation data
showed good result. 2) Regression tree for competing risks data
can uncover the structure of data and yield the sub-group of
individuals with a clear description based on their covariates.
The application of the method to contraceptive discontinuation
data showed good result. Extensive Monte Carlo simulation
suggests the method has good performance in identifying the
structure of data. 3) Application of the hybrid model to the
contraceptive discontinuation data showed that the hybrid
model is better than the available subdistribution regression in
terms of AIC. 4) By using some well known kernel distribution,
the parametric direct subdistribution models are developed. The maximum likelihood estimations are carried out simultaneously
for all causes of event. In Bone Marrow Transplantation (BMT)
data analysis, the first proposed model gave noticeably good fit
to the nonparametric counterpart. The second proposed model
is fitted to contraceptive discontinuation data and showed that
Gompertz-like subdistribution with Gompertz kernel is the best
fit. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Kudus, Abdul |
| author_facet |
Kudus, Abdul |
| author_sort |
Kudus, Abdul |
| title |
Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| title_short |
Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| title_full |
Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| title_fullStr |
Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| title_full_unstemmed |
Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks |
| title_sort |
tree-structured and direct parametric regression models for the subdistribution of competing risks |
| granting_institution |
Universiti Putra Malaysia |
| granting_department |
Institute Mathematical Research |
| publishDate |
2008 |
| url |
http://psasir.upm.edu.my/id/eprint/5418/1/IPM_2008_1.pdf |
| _version_ |
1747810420666662912 |