參考曲線之比較

Abstract

參考曲線之比較包含兩個問題。一個是想知道一個或數個個體之成長是否跟由 某一群體所建立的成長曲線有相同的成長模式。另一個是想知道兩個群體之未知成 長模型是否相同。傳統上有母數參考曲線比較祇有做迴歸參數(斜率項或截距項)之 檢定，而無母數則做迴歸函數之比較。由於參考曲線是由條件迴歸分位函數來表示。 我們將提出一個研究方法，先找出由模型參數來表示參考曲線相等之關係。因此這 個參數關係之檢定就能真正去檢驗兩個群體之參考曲線是否相等。對於診斷個體成 長之問題我們將提出一個由概似函數建立之檢定，而且我們將嘗試發展此一檢定之 最佳化性質。另外，對於比較兩群體之未知參考曲線問題我們將提出概似比檢定法。 對於兩種檢定方法我們都將研究其檢定力之成效。

Problems of reference charts comparisons include screening some individuals (subjects) to see if they are drawn from a group of subjects with established (known) reference charts and screening unknown reference charts of two groups. Most parametric approaches of reference charts comparison are conducted through testing hypotheses of regression parameters (slope part and/or intercept term) and nonparametric approaches are through testing hypothesis of equality of regression functions. In both cases, the scale parameters involved in error variables are not considered in the hypotheses. While parametric reference charts are typically depicted as regression conditional quantiles, in this research, we will formulate the relationship between equality of reference charts of two group of subjects and equalities of model parameters. For problem of screening individuals (subjects), we will propose a likelihood based test that probably allow us to develop an optimal property in terms of volume of acceptance region and, for problem of screening two unknown reference charts that is interesting in public health study, we will propose the likelihood ratio test. In both cases, we will evaluate the power performance of these tests.