# Comparing HRs

#### arkiaamu

##### New Member
I have study population with 900 patient, of whom 200 have had an adverse outcome. This outcome can be divided into two distinct entities.

I would be interested to study whether risk factor for outcome A differ from those of outcome B.

I know that difference between odds ratio can be calculated (http://stats.stackexchange.com/ques...l-test-for-difference-between-two-odds-ratios).

If I establish risk factors for both outcomes using cox multiple regression analysis, can I use the same the same methods to calculate for difference between HRs as I can do with ORs.

If not, is there a way to to this comparison?

UPDATE

I clarify. Lets women have adjusted HR (aHR) of 2.0 for the outcome A, and aHR of 2.4 for outome B. Is it possible statistically define that sex is more prevalanet rsk factor for outcome B.

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#### ledzep

##### Point Mass at Zero
I am afraid you can't use the same method for HR like for OR as mentioned in your link.
The computation of standard errors are going to be different.

Lets women have adjusted HR (aHR) of 2.0 for the outcome A, and aHR of 2.4 for outome B. Is it possible statistically define that sex is more prevalanet rsk factor for outcome B.
The hazard ratios are going to be affected by the other risk factors you adjust for. It is quite likely that the risk factors associated with outcome A might be slightly different to the risk factors associated with outcome B.

Apart from the fact that AHR associated with gender is bigger for outcome B than for A, If you want to show that sex is more significant risk factor for outcome A than for outcome B, then you can compute the Population Attributable Risks (PAR) associated with the risk factors. They are really simple to compute. Just take the AHR and the prevalence of the risk factor in your study sample (for. e.g 43% of the patients can be female in your data).

$$PAR_f = \frac {p_i(AHR-1)}{1+p_i(AHR-1)}$$
where pi is the porportion of female in the data and AHR is your AHR for your outcome from multivariable model.

Compute PAR associated with outcome A and outcome B. For example, for outcome A, the PAR for female might be 32% and for B this will be slightly higher (as the HR is bigger) 45%.
This will mean that 32% of the events for Outcome A was due to female gender, while 45% of the events for outcome B was due to being female which shows that gender accounted for more events for outcome B than for A.
You can compute the PAR for each of the other variables and see where gender stands in comparison to other for each of the outcome.

HTH

#### arkiaamu

##### New Member
Thank You very much ledzep! PAR seems as an excellent tool to assess differences in risk factors two different outcome variables.