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Research Projects Supported by HKU's High Performance Computing Facilities |
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| Researcher: |
| Dr Kwok-fai Lam, Department of Statistics and Actuarial Science |
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Project Title: |
| State-space Modeling of Multivariate Grouped Survival Data |
| Project Description: |
| The main objectives in analyzing multivariate survival data are to assess the effects of potential risk factors on the failure times and study the level of dependence among the possibly correlated failure times. Research on the statistical analysis of various types of multivariate survival data has been active over the last two decades. In the analysis of grouped data, most of the semiparametric estimation procedures in the literature encounter at least one of the following four major problems. They are the inappropriate assumption of continuous time scale; presence of ties; the inappropriate assumption of constant hazard ratio or odds ratio for individuals with time independent covariates; and the presence of time-varying covariates, respectively. A state-space approach in modeling multivariate discrete survival data is considered in this research so that the above-mentioned problems can be addressed. This approach is highly flexible in that we can estimate the trend of the effect of the potential risk factors and the treatment effect (time-varying regression parameter), or indeed we can also assume a constant effect for the treatment effect (time independent regression parameter). The properties of the model, particularly in the correlation pattern of the failure times, will be studied and the estimation procedure using the EM-type algorithm will be suggested. Moreover, in the presence of long-term survivors, the proportion of long-term survivors can be estimated/predicted using this discrete model. |
| Project Duration: |
| December 2000-December 2003 |
| Project Significance: |
| A discrete model for grouped (multivariate) survival data is considered here. The model is able to handle ties and accommodate time varying covariates naturally, and the covariate effect is assumed to be constant only within each small interval, but possibly different among the time intervals (time varying regression parameter). With this approach we can estimate the trend of the treatment effect or we can also assume a constant treatment effect. The model is extremely flexible and is adequate to model a wide range of data. When the range of the intervals are short, the properties of the model should be very similar to the corresponding continuous model. The properties of the model, particularly in the correlation pattern of the survival times, will be studied and an efficient estimation procedure will be suggested. By introducing a random effect to the model, dependence among the failure times can be quantified in terms of the variance and covariance functions of the random effects and can be estimated by the method proposed here. The EM-type algorithm is suggested. The properties of the proposed estimator will be studied. Joint inference on the regression parameters can be made. Predictions of the survival probabilities up to certain time intervals can be made easily. Moreover, to analyze univariate survival data in the presence of long-term survivors, the proportion of long-term survivors (cured fraction) can be estimated/predicted using the discrete model considered here when the observation period is long enough. |
| Results Achieved: |
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Publications related to this
project: 1. ˇ§REML estimation for clustered grouped survival dataˇ¨. K.F. Lam & David Ip. Statistics in Medicine, 22, 2003, pp 2025-2034. Expected Publications related to this project: 1. ˇ§Bayesian approach in analyzing clustered interval-censored dataˇ¨. May C.M. Wong, K.F. Lam & Edward C.M. Lo. Submitted to Journal of Dental Research. 2. ˇ§Estimating the Proportion of Cured Patients in a Censored Sampleˇ¨. K.F. Lam, Daniel Y.T. Fong & O.Y. Tang. Revising for Statistics in Medicine for the second time 3. ˇ§State-space Modeling of Clustered Grouped Survival Dataˇ¨. K.F. Lam and O.Y. Tang. Submitted to Statistics in Medicine ˇ@ |
| Remarks on the Use of High Performance Computing Cluster: |
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The project is highly computational demanding and would not have been so smooth without the HPC Cluster in carrying out the simulations and computations. |