Cox Regression, why can’t I just use logistic regression for survival data?

The Wise son:

Oh, how I love to talk about Cox Proportional Hazard (PH) regression versus Logistic Regression. So, you see, it depends on the study endpoint.  Does the outcome depend on the duration of  follow-up time? Logistic regression ignores the time to event all together. But everyone knows that the longer you follow someone, the higher the chance he/she will develop the outcome. Cox PH offers a regression framework to model the factors' effects on time to event while logistic regression will just model factors' effect on the event rate.

The Simple son:

Well, just remember that this is all about follow-up bias. You can use logistic regression as long as your outcome occurs instantaneously, or when all study participants have the same follow-up time. KIS - Just keep it simple.

The Wicked son:

And what about the proportionality assumption, that hazard ratio remains constant over time? One can test the assumption with R code:

cox.zph(model.coxph0)

With this code you will get the proportionality test for each variable in the model. Small p values indicate that proportionality assumption is violated. Oh, how I love to talk about violations.

The Simple son:

So what to do if the proportionality is rejected for a specific factor in the model?

The Wicked son:

Ha Ha! I knew you would ask this. For now it is beyond the scope of this cute little post. However, stratifying on the non-proportional factor may offer some remedy.  That is to say, that the hazard rate is estimated within in each stratum for all the other covariates.

He who couldn't ask:

Guys, with Cox PH  I’m in regression. What exactly Cox meant with the hazard parameter. At first I thought I understood what you're talking about, but now I’m helpless. When I feel like this, I make myself a healthy salad, with a bit of tahini on top, and it takes my worries go away.

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Tal has over 5 years of experience of consulting researchers on a variety of biomedical research including cardiology, internal medicine and infectious disease.  As a biostatistician, she is engaged in study life cycle from planning throughout the statistical analysis and up to publication.  She also took part in big-data analysis as part of evaluating Hospital databases.  Tal has served as a clinical trials’ statistician for number of studies.  She is an R programmer and has been teaching short courses of applied biostatistics with R in Tel-Aviv university and Ono Academic College.

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Her professional experience also includes: statistician at West Pennsylvania Psychiatric Institute; establishment of a statistical service at Wolfson Medical Center, Holon; lead biostatistician at a number of biotech startups.

Diklah is the author or coauthor of more than 50 scientific publications. Diklah has a B.Sc. in Statistics from University of Haifa; an M.Sc. in Biostatistics from the Graduate School of Public Health, University of Pittsburgh; a Master of Entrepreneurship and Innovation degree from ISEMI, Swinburne University of Technology; and Ph.D. in Biostatistics from Ben Gurion University of the Negev.