多階層Rasch模式於麻醉學筆試的應用

Hierarchical Rasch Model for Written Examinations in Anesthesiology

黃裕峰(Yu-Feng Huang)

指導教授 ： 陳秀熙

國立臺灣大學/公共衛生學院/流行病學與預防醫學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00081

摘要

背景：生物醫學研究領域中，預測變項與反應變項之間經常是存在非線性的函數呈現關係。其中一個典型的例子是利用羅吉斯迴歸(logistic regression)處理以二元反應變項的資料，例如Rasch模式，根據概似函數理論而來的傳統Rasch模式需符合局部獨立(local independence)，或稱為條件獨立(conditional independence)的假設，而且無法處理影響個人能力的共變量和階層的資料結構。因此如何對於Rasch模式發展新的統計方式，來避免局部獨立假設，並考慮因共變量造成的異質性，或是階層結構帶來的相關性影響，是值得關注研究的問題。

目的：我們提出非線性混合迴歸和貝氏多階層模式，來配適麻醉專科醫師甄審筆試中的實際數據，以表現此兩種創新Rasch模式的合適性。並且比較此兩種方式所得到的估計值與傳統最大概似法的差異。

研究材料與方法：首先在非線性混合迴歸的架構分析Rasch模式，將考生能力參數(θ)視為服從常態分配的隨機效應，來估計考生能力(θ)與試題難度(β)，再進一步將此模式擴展為納入多階層的結構，包含來不同訓練醫院的考生和不同出題者的試題；同理，並且對此問題發展貝氏多階層Rasch模式。所應用的資料來自參加2007至2010這四年測驗的考生，分別有34至37人，每一次筆試各有100道麻醉學方面的題目，同時考慮個人與醫院或不同出題者的試題，以及年齡、性別等共變量所帶來的多階層的資料結構，我們使用SAS (Statistical Analysis System)統計軟體中的NLIN和NLMIXED運算功能來估計Rasch模式中的參數；貝氏多階層Rasch模式是利用WinBUGS軟體來處理。

結果：我們的結果顯示使用最大概似法與非線性混合迴歸所得到關於考生能力(θ)與試題難度(β)的估計值與標準誤差非常接近。代表這份資料可能符合局部獨立的假設。然而，使用貝氏多階層模式來配適資料時，會使標準誤差有擴大的情況。

結論：非線性混合迴歸模式與貝氏多階層Rasch模式提供了另一種較具有彈性的估計參數方式，特別是對於多階層的資料結構，這項特性可藉由應用Rasch模式分析麻醉學筆試資料來表現。

關鍵字

非線性迴歸模型 ； 麻醉學 ； 多階層Rasch模式 ； 貝氏模型

並列摘要

Background: The relationship between the predictors and the response in biomedical field is often characterized by a non-linear function. One of classical examples is the application of the logistic regression model to dealing with the data on threshold-based response outcomes, such as the Rasch model. The conventional Rasch model based on likelihood-based theory requires the assumption of local independence (conditional independence) and cannot deal with covariate affecting ability and hierarchical data structure. It is therefore interesting to relax the assumption of local independence and consider the heterogeneity due to covariates or correlated property from hierarchical structure by developing new statistical methods for the Rasch model.

Aims: We proposed the nonlinear mixed and Bayesian hierarchical regression model to fit the empirical data on the written test of board certification examination for anesthesiologists to demonstrate the feasibility of using the two innovative Rasch models. Estimates obtained from both methods were compared with the conventional maximum likelihood method.

Material and Methods: The Rasch model was first framed by a non-linear mixed regression underpinning to analyze the examinee ability (θ) and item difficulty (β) by treating the parameters of θ as a random effect following a normal distribution. This non-linear mixed regression was further extended to accommodate the data with hierarchical structures on examinees from training hospitals and items developed by raters. We also developed Bayesian hierarchical Rasch model for the same purpose. The data used for applications are the numbers of examinees distributed from 34 to 37 in 4 consecutive years from 2007 to 2010. There were 100 questions related to anesthesiology in each test. Hierarchical data structured on individuals and hospitals or items under raters and also covariates on age and gender were considered in our illustration. We used Statistical Analysis System (SAS) to estimate the parameters of the Rasch model by using PROC NLIN and NLMIXED. WinBUGS software was used for Bayesian hierarchical Rasch model.

Results: Our results show the two sets of estimates (θ and β) and standard error from maximum likelihood method were very close to those from non-linear mixed regression model. This suggests the data may obey the assumption of local independence. However, the standard errors were inflated when Bayesian hierarchical Rasch model was fitted to data.

Conclusion: The nonlinear mixed regression model and Bayesian hierarchical Rasch model provides alternative ways of estimating parameters with flexibility, particularly for hierarchical data. The feasibility is demonstrated with the application of the Rasch model to written examinations in anesthesiology.

並列關鍵字

Nonlinear regression ； Anesthesiology ； Hierarchical Rasch model: Bayesian model

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