現狀資料常見於人口統計調查研究，其中資料的觀測值包含調查時間及事件是否在調查時間時已經發生的狀態。在本論文中，我們聚焦現狀資料的正比例風險迴歸問題，其中狀態指標可能缺失但輔助訊息均可獲得。研究動機是來自骨質疏鬆的調查研究，其中骨質疏鬆的發病年齡均為現狀設限且大部分受訪者之骨質疏鬆狀態為缺失的。因此我們使用現狀資料可被完成觀測的確認子群來提出確認概似估計法分析此現狀資料。從實際的骨質疏鬆資料分析和模擬結果可知確認概似估計法不僅避免掉完整資料分析法所產生的偏誤而且來得比權重逆機率分析法更有效。

Current status data, which commonly arise from demographic studies, consist of a survey time and a status indicator representing whether the event time of interest has occurred by the survey time or not. In this work, our focus is on the proportional hazards regression for current status data where the status indicator may be missing but auxiliary information is always available. The motivation is a survey study of osteoporosis where the onset time of osteoporosis is current status censored and medical osteoporosis status is missing for most participants. For analyzing such data, we proposed the validation likelihood, which is derived from the likelihood function pertaining to the validation subsample where the current status data are fully observed. The real application to the osteoporosis survey data and simulation studies reveal that the validation likelihood method can avoid the bias resulted from the complete case analysis, and is more efficient than
the inverse probability weighting analysis.

1 Introduction 1
2 Validation likelihood estimator 4
3 Asymptotic theory and variance estimation 9
4 Simulation studies 12
5 Application to the osteoporosis survey data 17
6 Conclusion 20
References 32
Appendix 34

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