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研究生:林佩伶
研究生(外文):Pei-LingLin
論文名稱:右設限資料下兩組醫療費用中位數比例之信賴區間
論文名稱(外文):Confidence intervals for the ratio of two median medical costs with right-censored data
指導教授:嵇允嬋嵇允嬋引用關係
指導教授(外文):Yun-Chan Chi
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:30
中文關鍵詞:醫療費用訊息設限中位數信賴區間
外文關鍵詞:Medical costsInformative censoringMedianConfidence interval
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估計醫療費用對於不同治療方式的成本評估,以及健康政策的制定至關重要。因為醫療費用通常為正偏態 (positively skewed) 分布,相對於平均醫療費用,醫療費用中位數 (median) 是較穩健 (robust) 的統計量,故其更適合用於估計中央趨勢。此外,由於右設限下的醫療費用資料含有訊息設限 (informative censoring),不適用傳統存活分析之估計方法。因此,Zhao et al. (2012) 提出以 Horvitz 和 Thompson (1952) 的機率倒數權重方法 (inverse probability weighting scheme) 來估計醫療費用之存活函數,進而建構單組醫療費用中位數和兩組醫療費用中位數比例之信賴區間 (confidence interval)。

然而,Zhao et al. (2012) 基於 Su 和 Wei (1993) 所建構的兩組醫療費用中位數比例之信賴區間,其信賴區間涵蓋率 (coverage rate) 在大樣本下仍過高。因此,本論文之目的為延伸 Tsai et al. (2016) 提出的 length-based 方法,估計樣本醫療費用中位數之變異數,進而建構兩組醫療費用中位數比例之 Wald 型式信賴區間,使信賴區間之涵蓋率能達到預設的信心水準。為了能建構 Wald 型式信賴區間,本論文需推導出樣本醫療費用中位數之漸近分布。

根據本論文的模擬結果,相較於 Su 和 Wei 型式信賴區間,依本論文方法建構的醫療費用中位數比例之 Wald 型式信賴區間,其信賴區間涵蓋率會較接近預設的信心水準,且其有較短的區間長度。因此,本論文建議研究者採用 length-based 估計方法,建構兩組醫療費用中位數比例之 Wald 型式信賴區間。
Estimating medical costs is a very important issue in making health policy. Since the distribution of medical costs is usually positively skewed, the median cost is more robust to describe the central tendency than the mean medical cost. Kaplan-Meier estimators can be biased for estimating the survival function of medical costs because medical cost data are often subject to informative right censoring. As a result, Zhao et al. (2012) proposed estimating the survival function for medical costs based on the inverse probability weighting scheme (Horvitz & Thompson, 1952). In addition, they constructed the confidence interval (CI) for the ratio of median medical costs from two treatments based on the idea of Su and Wei (1993). However, the coverage rate of the Su and Wei type CI is conservative even under large sample sizes. Therefore, it is important to construct a CI for the ratio of two median costs with desirable coverage rates for informative right-censored data.

This thesis constructs a Wald type CI for the ratio of two median medical costs based on the method derived for right-censored data in Tsai et al. (2016). A simulation study is conducted to compare the performance of two types of CIs. The simulation results indicate that the proposed Wald type CI for the ratio of two median medical costs yields desirable coverage rates. Furthermore, the Wald type CI has shorter interval lengths. Hence, the proposed method is recommended for establishing the CI for the ratio of two median costs with informative right-censored data, as well as ratios of other quantiles.
目錄
摘要 i
英文延伸摘要 ii
目錄 v
表目錄 vii
圖目錄 viii
第一章 緒論 1
第二章 文獻回顧 3
第一節 符號定義 3
第二節 醫療費用之存活函數估計量 4
2.2.1. 簡單權重估計量 5
2.2.2. 有效權重估計量 6
第三節 Su 和 Wei 型式的醫療費用中位數比例之信賴區間 9
2.3.1. 簡單權重估計量下的區間估計 9
2.3.2. 有效權重估計量下的區間估計 10
第四節 Wald 型式的中位數比例之信賴區間. . . . . . . . . . . . . . . . . . 10
第三章 樣本醫療費用中位數估計量之漸近分布 12
第一節 樣本醫療費用中位數估計量之漸近分布. . . . . . . . . . . . . . . . 12
第二節 Wald 型式的醫療費用中位數比例之信賴區間. . . . . . . . . . . . . 15
3.2.1. 簡單權重估計量下的區間估計. . . . . . . . . . . . . . . . . . . 15
3.2.2. 有效權重估計量下的區間估計. . . . . . . . . . . . . . . . . . . 16
第三節 醫療費用中位數之區間估計. . . . . . . . . . . . . . . . . . . . . . 16
3.3.1. 簡單權重估計量下的區間估計. . . . . . . . . . . . . . . . . . . 16
3.3.2. 有效權重估計量下的區間估計. . . . . . . . . . . . . . . . . . . 17
第四節 醫療費用分位數比例之信賴區間. . . . . . . . . . . . . . . . . . . . 18
第四章 模擬研究 19
第一節 模擬設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
第二節 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
第五章 結論與建議 29
參考文獻 30
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[2] Bang, H. (1999). Estimating medical costs with censored data and its efficiency study. Ph.D. dissertation, North Carolina State University, Raleigh, North Carolina.
[3] Bang, H., & Tsiatis, A. A. (2000). Estimating medical costs with censored data. Biometrika, 87(2), 329–343.
[4] Bang, H., & Tsiatis, A. A. (2002). Median regression with censored cost data. Biometrics, 58(3), 643649.
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[6] Chen, H.Y., Kuo, S., Su, P.F., Wu, J.S., & Ou, H.T. (2020). Health care costs associated with macrovascular, microvascular, and metabolic complications of type 2 diabetes across time: Estimates from a population-based cohort of more than 0.8 million individuals with up to 15 years of follow-up. Diabetes Care.
[7] Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American statistical Association, 47(260), 663–685.
[8] Huang, Y. (2009). Cost analysis with censored data. Medical care, 47(7 Suppl 1), S115.
[9] Huang, Y., & Louis, T. A. (1998). Nonparametric estimation of the joint distribution of survival time and mark variables. Biometrika, 85(4), 785–798.
[10] Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American statistical association, 53(282), 457–481.
[11] Lin, D., Feuer, E., Etzioni, R., & Wax, Y. (1997). Estimating medical costs from incomplete follow-up data. Biometrics, 419–434.
[12] Su, J. Q., & Wei, L. (1993). Nonparametric estimation for the difference or ratio of median failure times. Biometrics, 603-607.
[13] Tsai, T.H., Tsai, W.Y., Chi, Y., & Chang, S.M. (2016). Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data. Biometrics, 72(1), 232–241.
[14] Zhao, H., Zuo, C., Chen, S., & Bang, H. (2012). Nonparametric inference for median costs with censored data. Biometrics, 68(3), 717–725.
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