Cox regression with dependent error in covariates

Cox regression with dependent error in covariates IntroductionIn many survival studies, some covariates may be contaminated with error due to the lack of a gold standard of measurement, for example, CD4 count and viral load in HIV/AIDS research and nutritional intakes in cancer epidemiology. Just as with regression analyses in general (Carroll et al., ), accounting for the error is imperative in Cox regression since substantial bias may otherwise arise (Prentice, ; Hughes, ; Li and Ryan, ). Write survival time as S and censoring time as C. As a result of censoring, they are observed only through follow‐up time T=min(S,C) and censoring indicator Δ=I(S≤C), where I(·) is the indicator function. To focus on main ideas, we shall confine our attention to time‐independent covariates X∘≡(X,Z⊤)⊤ with scalar X being error‐prone and the rest Z accurately measured. The proportional hazards model (Cox, ) postulates dΛ(t∣X∘)=exp(β⊤X∘)dΛ0(t),S ╨ C∣X∘, where Λ(·∣X∘) is the cumulative hazard function of S given X∘, Λ0(·) is an unspecified baseline cumulative hazard function, β is an unknown regression coefficient, and  ╨  denotes statistical independence. While X is not directly observable, its error‐contaminated version W instead is observed, as well as so‐called replication data or instrumental data (cf. Carroll et al., , Section 2.3) but not validation http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Biometrics Wiley

Cox regression with dependent error in covariates

Loading next page...
 
/lp/wiley/cox-regression-with-dependent-error-in-covariates-UcFHevoOwl
Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018, The International Biometric Society
ISSN
0006-341X
eISSN
1541-0420
D.O.I.
10.1111/biom.12741
Publisher site
See Article on Publisher Site

Abstract

IntroductionIn many survival studies, some covariates may be contaminated with error due to the lack of a gold standard of measurement, for example, CD4 count and viral load in HIV/AIDS research and nutritional intakes in cancer epidemiology. Just as with regression analyses in general (Carroll et al., ), accounting for the error is imperative in Cox regression since substantial bias may otherwise arise (Prentice, ; Hughes, ; Li and Ryan, ). Write survival time as S and censoring time as C. As a result of censoring, they are observed only through follow‐up time T=min(S,C) and censoring indicator Δ=I(S≤C), where I(·) is the indicator function. To focus on main ideas, we shall confine our attention to time‐independent covariates X∘≡(X,Z⊤)⊤ with scalar X being error‐prone and the rest Z accurately measured. The proportional hazards model (Cox, ) postulates dΛ(t∣X∘)=exp(β⊤X∘)dΛ0(t),S ╨ C∣X∘, where Λ(·∣X∘) is the cumulative hazard function of S given X∘, Λ0(·) is an unspecified baseline cumulative hazard function, β is an unknown regression coefficient, and  ╨  denotes statistical independence. While X is not directly observable, its error‐contaminated version W instead is observed, as well as so‐called replication data or instrumental data (cf. Carroll et al., , Section 2.3) but not validation

Journal

BiometricsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ;

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off