I am performing a univariate survival analysis (cox-ph regression) wherein I am trying to find the association of expression of some genes with patient survival in a specific cancer. For some gene 'X' I am getting a very good HR value (~5) but the p-value is insignificant (p=0.19). What does this imply?
I have many similar cases
It means that the data is still statistically compatible with hypotheses about HR < 1. The data does not provide sufficient information to conclude at which side of 1 (>1 or
A P-value is a ratio between the effect size (in this case, the hazard ratio) and the precision with which it has been measured. A small effect, measured precisely, is likely to be statistically significant, while a large effect measured imprecisely is likely not to be.
The trouble is that the P-value hides the size of your effect by dividing it by the measurement precision. So you can't tell the effect size or the precision from the P-value.
Ronán Michael Conroy Jochen Wilhelm So in terms of the risk estimation significance of the above gene, can I claim anything in a scientific publication?
If you look at the confidence interval, you might claim that the data you have is too incompatible with certain hazard ratios (you might, for instance, claim that the HR is unlikely to be greater than 20 or so). Just looking at the p-value leaves you only with the "conclusion" that the data is inconclusive w.r.t. to the direction of the effect (beneficial or even harmful).
Although your query is interpreted goodly by Jochen Wilhelm and Ronán Michael Conroy, however., for your future reference I would like to suggest you the links:
https://www.students4bestevidence.net/blog/2016/04/05/tutorial-hazard-ratios/
https://www.graphpad.com/guides/prism/7/statistics/index.htm?stat_the_hazard_ratio.htm
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