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enter image description here

Call:
survdiff(formula = Surv(time, DEATH_EVENT) ~ s_s, data = ss)

                              N Observed Expected (O-E)^2/E (O-E)^2/V
s_s=OverMedianSerumSodium   122       30     40.7      2.80      4.89
s_s=UnderMedian_SerumSodium 177       66     55.3      2.06      4.89

 Chisq= 4.9  on 1 degrees of freedom, p= 0.03 

I know that Log-Rank Tests are used to compare survival curves between groups in a similar way that the chi-squared test checks for independence.

In my project, I split at the median (to resist outliers). I'm going off of intuition. Do you think this is strange or am I fine with performing this?

Also, is there a way to check the strength of this independence much like Yule's Q?

Thank You.

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If you have a continuous measure associated with outcome, you typically don't want to dichotomize. See this page, among many others on this site. (You certainly don't want to try multiple cutoffs and choose the one that seems to work best on your data sample, but happily you're not proposing that.)

You are much better off fitting the predictor flexibly and continuously, for example with a regression spline. See this page or this page. That allows the data to tell you the form of the association with outcome, and will give an overall estimate of the association that doesn't depend on an arbitrary choice of cutoff.

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