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Pseudoobservations (TG8) Andersen, Per Kragh
Description
<small>
Survival analysis is characterized by the need to deal with incomplete observation of outcome variables, most frequently caused by rightcensoring, and several  now standard  inference procedures have been developed to deal with this. Examples include the KaplanMeier estimator for the survival function and partial likelihood for estimating regression coefficients in the proportional hazards (Cox) regression model. During the past 15 years, methods based on pseudoobservations have been studied. Here, the idea is to apply a transformation of the incompletely observed survival data and, thereby, to create a more simple data set on which `standard' techniques (i.e., for complete data) may be applied, e.g., methods using generalized estimating equations (GEE).
As an example, we can consider the problem of relating the survival probability, $S(t_0)$ at a single time point, $t_0$, to covariates, $z$, based on rightcensored survival times $T_i$ and failure indicators $D_i$ for independent observations $i=1,...,n$. Here, $T_i=min(X_i,U_i)$ for potential complete failure times $X_i$ and rightcensoring times $U_i$ and $D_i=I(T_i=X_i)$. Let $\hat{S}(t)$ be the KaplanMeier estimator for $S(t)=P(X>t)$. Then the pseudoobservations for the incompletely observed survival indicators $I(X_i>t_0)$, $i=1,...,n$ are
$$S_i=n\hat{S}(t_0)(n1)\hat{S}^{(i)}(t_0),\;\;\;i = 1,...,n,$$
where $\hat{S}^{(i)}(t)$ is the KaplanMeier estimator applied to the sample of size $n1$ with observation $i$ taken out. Regression coefficients in a generalized linear model
$$g(S(t_0z)) =\beta_0 +\beta^{T}z$$
with link function $g$ are then estimated by solving the GEE
$$\sum_{i} A(\beta,z_i)\big(S_ig^{1}(\beta_0+\beta^{T}z)\big)=0$$
where, typically, $A(\beta,z)=\frac{\partial}{\partial \beta}g^{1}(\beta_0+\beta^{T}z)$.
An advantage of this approach is that it applies quite generally to parameters for which no other regression methods are directly available (including average time spent in a state of a multistate model), whereas disadvantages include that the method is not fully efficient and that it, in its most simple form, requires that the distribution of censoring times, $U$, is independent of the covariates, $z$. We will review the development in this field since the method was put forward by Andersen, Klein and Rosthoj (2003, Biometrika), with special emphasis on recent results by Overgaard, Parner and Pedersen (2017, Ann. Statist.) and Pavlic, Martinussen and Andersen (2019, Lifetime Data Anal.).
(Presentation 40 min. + Discussion 20 min.)</p>
Item Metadata
Title 
Pseudoobservations (TG8)

Creator  
Publisher 
Banff International Research Station for Mathematical Innovation and Discovery

Date Issued 
20190605T10:33

Description 
<small>
Survival analysis is characterized by the need to deal with incomplete observation of outcome variables, most frequently caused by rightcensoring, and several  now standard  inference procedures have been developed to deal with this. Examples include the KaplanMeier estimator for the survival function and partial likelihood for estimating regression coefficients in the proportional hazards (Cox) regression model. During the past 15 years, methods based on pseudoobservations have been studied. Here, the idea is to apply a transformation of the incompletely observed survival data and, thereby, to create a more simple data set on which `standard' techniques (i.e., for complete data) may be applied, e.g., methods using generalized estimating equations (GEE). 
Extent 
53.0 minutes

Subject  
Type  
File Format 
video/mp4

Language 
eng

Notes 
Author affiliation: University of Copenhagen

Series  
Date Available 
20191203

Provider 
Vancouver : University of British Columbia Library

Rights 
AttributionNonCommercialNoDerivatives 4.0 International

DOI 
10.14288/1.0386699

URI  
Affiliation  
Peer Review Status 
Unreviewed

Scholarly Level 
Faculty

Rights URI  
Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
Rights
AttributionNonCommercialNoDerivatives 4.0 International