The aims of this proposal are to develop new efficient statistical inference procedures for generalized varying-coefficient partially linear models (GVCPLM) when there are measurement errors and missing data, and to apply these methods to analyze AIDS data. The proposal consists of two aims. The first specific aim is to study GVCPLM with measurement errors or missing data: (a) to develop goodness-of-fit tests for the generalized partially linear models (GPLM); (b) to develop model selection methods for the GVCPLM; (c) to develop flexible estimation methods for the GPLM when the linear covariates are measured with errors; (d) to develop flexible statistical methods for the partially linear models when the independent variables are missing at random and when the data are longitudinal; (e) to develop appropriate statistical methods for the GPLM when the covariates or independent variable are missing at random, and when the data are longitudinal; and (f) to develop computer packages to implement the proposed methods.
The second aim i s (a) to apply the developed methods in studies of HIV dynamics by using data from AIDS clinical trials conducted by the AIDS Clinical Trials Group (ACTG); (b) to characterize long-term HIV/T-cell dynamics in HIV-1 -infected patients treated with the highly active antiretroviral therapy (HAART) by using the GPLM and the methods developed to study the relationship between long-term HIV dynamics and T-lymphocyte kinetics in the environment of long-term antiretroviral drug exposure; (c) to determine the effects of pharmacologic, clinical, and host-specific factors on the long-term dynamics of HIV and T lymphocytes when there are missing data or measurement errors; (d) to study the relation between clinical endpoints and the long-term patterns of HIV and T-lymphocyte dynamics when there are missing data or measurement errors; (e) to explore ways in which the long-term HIV and T-cell dynamic patterns can be used to assess long-term effectiveness of antiretroviral therapies. The proposed research is expected to benefit semiparametric modeling as well as AIDS research.
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