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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Accelerated failure time model ： ウィキペディア英語版 Accelerated failure time model In the statistical area of survival analysis, an accelerated failure time model (AFT model) is a parametric model that provides an alternative to the commonly used proportional hazards models. Whereas a proportional hazards model assumes that the effect of a covariate is to multiply the hazard by some constant, an AFT model assumes that the effect of a covariate is to accelerate or decelerate the life course of a disease by some constant. This is especially appealing in a technical context where the 'disease' is a result of some mechanical process with a known sequence of intermediary stages. ==Model specification== In full generality, the accelerated failure time model can be specified as ::$$ \lambda(t|\theta)=\theta\lambda_0(\theta t) where $\backslash theta$ denotes the joint effect of covariates, typically $\backslash theta=\backslash exp(-(+\; \backslash cdots\; +\; \backslash beta\_pX\_p))$. (Specifying the regression coefficients with a negative sign implies that high values of the covariates ''increase'' the survival time, but this is merely a sign convention; without a negative sign, they increase the hazard.) This is satisfied, if the probability density function of the event is taken to be $f(t|\backslash theta)=\backslash theta\; f\_0(\backslash theta\; t)$, from which is follows for the survival function that $S(t|\backslash theta)=S\_0(\backslash theta\; t)$. From this it is easy to see that the moderated life time $T$ is distributed such that $T\backslash theta$ and the unmoderated life time $T\_0$ have the same distribution. Consequently, $log(T)$ can be written as ::$$ log(T)=-log(\theta)+log(T\theta):=-log(\theta)+\epsilon where the last term is distributed as $log(T\_0)$, i.e. independently of $\backslash theta$. This reduces the accelerated failure time model into regression analysis (typically a linear model) where $-log(\backslash theta)$ represents the fixed effects, and $\backslash epsilon$ represents the noise. Different distributional forms of $\backslash epsilon$ imply different distributional forms of $T\_0$, i.e. different baseline distributions of the survival time. It is typical of survival-analytic contexts, that many of the observations are censored, i.e. we only know that $T\_i>t\_i$, not $T\_i=t\_i$. In fact, the former case represents survival, while the later case represents an event/death/censoring during the follow-up. These right-censored observations can pose technical challenges for estimating the model, if the distribution of $T\_0$ is unusual. The interpretation of $\backslash theta$ in accelerated failure time models is straight forward: E.g. $\backslash theta=2$ means that everything in the relevant life history of an individual happens twice as fast. For example, if the model concerns the development of a tumor, it means that all of the pre-stages progress twice as fast as for the unexposed individual, implying that the expected time until a clinical disease is 0.5 of the baseline time. However, this does not mean that the hazard function $\backslash lambda(t|\backslash theta)$ is always twice as high - that would be the proportional hazards model. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Accelerated failure time model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.