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Usually the condition of the validity of a logistic regression is to have 10 events per predictor.

In our model the binary outcome variable (1 if Healthy aging ; 0 otherwise) has a frequency of healthy aging for around 1000 observations (37% of the sample).

Also there are 13 predictor variables, so the assumption of having 10 events per variable is widely satisfied.

But the question is the frequency of 37%.

Edited:

In this logistic regression model, we can't interpret odds-ratios as relative risks due to high event rate. What other regression methods can we use to model a binary outcome?

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    $\begingroup$ I often find that 20 events per predictor are required. But this is oversimplified because you need at least 96 observations just to estimate the intercept. I don't understand why you think a proportion of 0.37 for $Y=1$ could be a problem. And isn't healthy aging a continuous concept? If you used any dichotomization to arrive at $Y$ you'll get an inappropriate analysis. $\endgroup$ – Frank Harrell Apr 14 '16 at 11:49
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    $\begingroup$ Poisson models are for count data for $Y$. Your $Y$ dichotomized several continuous variables. Although it's challenging to put together multiple outcomes into one variable, it's worth doing because binary $Y$ has minimal information/minimum power. $\endgroup$ – Frank Harrell Apr 14 '16 at 12:24
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    $\begingroup$ Did all the subjects die already or do you have aome right- and/or left-censoring here? $\endgroup$ – Björn Apr 15 '16 at 6:08
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    $\begingroup$ My point was the selection bias of looking at it that way, when some may have becone unhealthy but you do not know (losses to follow-up) and some may yet do so (i.e. after the end of follow-up). Why only look at those alive? Presumably all will die eventually, what is the effect on your inference of looking at only those alive? $\endgroup$ – Björn Apr 15 '16 at 9:27
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    $\begingroup$ What do you mean by using Poisson regression? Is your outcome not just a yes/no, but rather a 0,1,2,3,4...? Or do you mean approximating the binomial distribution for extremely low rates and large risk sets by a Poisson distribution? Or do you mean using a Poisson regression likelihood with a follow-up offset to fit an exponential time-to-event model? $\endgroup$ – Björn Apr 15 '16 at 12:40
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In epidemiology, sometimes we are interested in calculating RRs than ORs. When the rare disease assumption is not valid (i.e. event rate is more than 10%) we cannot interprete odds-ratios as relative risks in logistic regression.

In order to calculate risks in this case, we used modified Poisson regression (cf. reference below) with robust error variance.

References:

  1. Guangyong Zou, A Modified Poisson Regression Approach to Prospective Studies with Binary Data, Am. J. Epidemiol. (2004) 159 (7): 702-706 doi:10.1093/aje/kwh090

  2. How can I estimate relative risk in SAS using proc genmod for common outcomes in cohort studies? Introduction to SAS. UCLA: Statistical Consulting Group. from http://www.ats.ucla.edu/stat/sas/notes2/.

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