It can, but the difference between Population Atributable Fractions (PAF) with OR vs HR varies with the distribution of the events, the presence of competing risks and the change on the prevalence of the risk factor along the time. Please see the work of Cindy Crownson and Therry Therneau, from the Mayo Clinic, on this subject: http://www.mayo.edu/research/documents/biostat-82pdf/DOC-10027843

Cheers,

Paulo

I think you can. When you say Risk Ratio, you usually mean Rate Ratio, traditionally obtained using life table techniques (number of cases divided by person years of observation). This is equivalent to HR obtained in survival analysis.

It can, but the difference between Population Atributable Fractions (PAF) with OR vs HR varies with the distribution of the events, the presence of competing risks and the change on the prevalence of the risk factor along the time. Please see the work of Cindy Crownson and Therry Therneau, from the Mayo Clinic, on this subject: http://www.mayo.edu/research/documents/biostat-82pdf/DOC-10027843

Cheers,

Paulo

Of course, you can describe the effect of covariates in your populations using the relative risks or Odds. the numerical results are slightly different but the meaning does not change.

Rare events, yes. Common events, no.

Risk belongs to the domain of risk (you still do not have the disease). hazard belongs to the domain of prognosis (you already have it). It all belongs to the question of the kind of causal relationship you are searching for. More about it in my textbooks. Best regards and good luck! Milos Jenicek

Yes, I have done this. See Natarajan S, Lipsitz SR, Rimm E. 2007. A simple method of determining confidence intervals for population attributable risk from complex surveys. Stat Med 26:3229–3239.

Thanks for all your helpful suggestions and references, everyone!

I think you can describe the strength of effect of several covariates in your populations using the (RR) or Odds .

You can conduct stratify analysis in PH model, and to examine the effect of diabetes on treatment groups separately. You can compare HRs and their 95% CIs between two groups. If the two CIs do not overlap to each other, you may conclude the effects of diabetes act differently between two groups.

You can also consider an advance interaction model that takes into account the interaction between diabetes and treatment groups in your PH model. You will include a product term (aka. interaction term) in the model instead of stratifying our samples. This model allows you to be more flexible to conduct detail tests. Caution needs to make for the interpretation because it can go wrong easily.

Hope this helps.

Thanks, Jason. I'd already built in interaction terms into my preferred/likely final model for the reasons implied in your answer. Given the widely different background prevalence of covariates between populations of interest (Indigenous and non-indigenous Australians), I was hoping to then use population attributable fractions to explain the different effects of these (different) risks/hazards on the different populations.

Hazard ratios are closer to the incidence density ratio than risk ratios incidence or prevalence ratios) and then would be even better. In fact the difference is usually tiny because prevalence of diseases are usually mathematically (not medically) small.

Clarification: The concept of rare events determine if Odds ratio are comparable with risk ratios or not. But here we are comparing risk ratios with hazard ratios not with the odds ratios. If the study outcome is sufficiently rare among exposed and unexposed study subjects, the odds ratio for the exposure–outcome association will closely approximate the risk ratio.

Hazard ratios differ from relative risk (or risk ratio not relative risk rations) in that risk ratios are cumulative over an entire study (you must use a defined endpoint which is pre-selected during design phase), while hazard ratios represent instantaneous risk at some particular time period during study, or a subset thereof. Hazard ratios suffer somewhat less from selection bias with respect to the endpoints chosen, and can indicate risks that happen before the endpoint. If risk ratios are calculated based on complete envelop of the study, they are comparable with the hazard ratios over the course of the study.

Incidense density is the true measure of risk (the unit is the inverse of time). The ratio of incidnece densities is the relative risk. Incidence and prevalence are % (cumulative over one year for incidence, over time of occurence for prevalence, usually the age). So, the hazard ratio is the true relative risk. Incidence ratios are closed if incidences are less, roughly, than 10% (mathematically small, not medically). Prevalence ratios are closed too with nearly the same condition (less than 10%)..The odds ratio is an indirect measure of relative risk with the same condition. The "rare disease" condition is a misleading wording of mathematically small, which is the case for most diseases. Exception would be diseases like COPD, antibodies prevalence for many diseases like measles or German measles.