I was wondering if any of you have experience in fitting a Cox model to data with missing covariates. Do you know of any reference addressing the issues associated with Cox regression with missing covariates? I know of the approach using the Expectation Maximization (EM) algorithm, but I want to know if there is a publication comparing the different methods out there.
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3 Answers
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Flexible Imputation of Missing Data is an outstanding book by Stef van Buuren that covers this area wll.
answered Apr 11, 2013 at 12:48
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One approach as discussed by others is to multiply impute the missing covariates. Details for how this can be achieved are given in a recent paper I co-authored (free access here: http://smm.sagepub.com/content/early/2014/03/31/0962280214521348). The approach essentially works out what a compatible imputation model for the partially observed covariate is, given your assumed Cox model for the time to event outcome.
Software implementing the method is available in R and Stata, further details here: http://missingdata.lshtm.ac.uk/index.php?option=com_content&view=article&id=217&Itemid=139
answered Feb 16, 2015 at 17:57
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I just took a short course from Susanne May on survival analysis based on the book she coauthored with Hosmer and Lemeshow. The book gives good coverage to the Cox Model and its extensions (particularly to time varying covariates). There is also coverage of missing data and and imputation techniques. I haven't gotten the book yet but i think that in the case of a missing covariate there may be a way to use an alternative covariate or copvariates that is (are) correlated with the missing one to impute a value for the missing covariate. I think there is an excellent chance that you will find what you are looking for there. Here is the reference along with an excerpt from the publisher's review of the book. You can also go to amazon and find (currently 7 customer reviews of the book, many of which are excellent and unbiased).
Applied Survival Analysis: Regression Modeling of Time to Event Data (Wiley Series in Probability and Statistics) [Hardcover]
David W. Hosmer
David W. Hosmer (Author) Stanley Lemeshow (Author), Susanne May (Author)
This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. It offers a clear and accessible presentation of modern modeling techniques supplemented with real-world examples and case studies. Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data.
Features of the Second Edition include:
Expanded coverage of interactions and the covariate-adjusted survival functions The use of the Worchester Heart Attack Study as the main modeling data set for illustrating discussed concepts and techniques New discussion of variable selection with multivariable fractional polynomials Further exploration of time-varying covariates, complex with examples Additional treatment of the exponential, Weibull, and log-logistic parametric regression models Increased emphasis on interpreting and using results as well as utilizing multiple imputation methods to analyze data with missing values New examples and exercises at the end of each chapter
answered May 15, 2012 at 21:37