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.

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