Appropriate model that considers both treatment and risk factors for outcome

Question

Consider a retrospective study to be planned with

• 200 patients with
• 5 risk factors (such as age, disease score = disease severity, hypertension etc.) which may affect (a) outcome as such (older patients may have a higher risk for unfavourable outcome even independent from intervention) and (b) success of an intervention (see next point)
• 2 interventions. One special thing in this retrospective analysis is that risk factors will have influenced the kind of intervention, because people think (albeit not know) that e.g. higher age should favour intervetion A vs B, i.e. there issome interaction between risk factors and intervention.
• 4 outcomes (success vs. treatment failure and adverse events) which, if necessary, can be taken together as one binary outcome (favourable/not favourable)

The aim of the study is to find guidance, which intervention is better, likely depending on an individual patient's risk factors.

I feel this should be a quite common study question, but somehow I am stuck. I'd like to do something beyond simply explorativly analysing each and any combination of the above variables. What way of analysis is appropriate? (as opposed to copy-paste code that technically can be executed)

I considered

• GLM: will analyse risk factors and outcome, but is it appropriate to simply add intervention as an additional independent variable to the GLM model (outcome.favourable ~ intervention + risk.factor.1 + risk.factor.2 ...)? Can this be modelled with interactions - if so, how to set them properly and to to avoid too many elements in the modele valuation?
• Cox proportional hazards model: would (as bonus) include follow-up time, but also here I am not sure how to incorporate treatment vs risk factor effets..., at least based on examples I found so far?
• I am happy for better suggestions

I prefer a solution that can be done in R.

Answer 1

Remember that the best you can get in this situation is guidance for designing a proper clinical trial. No treatment decisions should be made based on this type of analysis.

In general, you need to include the intervention as a predictor in your model to get an estimate of intervention effects.

There are several ways to try to take the associations between intervention choice and risk factors into account, discussed extensively on this page. One is to include both the risk factors and the intervention as predictors in the model, to "control for" the risk factors. Another is to weight each case by the inverse probability of its having received the intervention (inverse propensity of treatment weighting, IPTW). That tries to balance the net contributions of risk factors to outcome between the treatment groups, to minimize bias in the estimate of the effects of the intervention.

For those approaches to work, the way that the risk factors are associated either with outcome or with the probability of intervention, respectively, needs to be properly specified. As it's not generally possible to know that those specifications are correct, a "doubly robust" approach could use IPTW along with controlling for risk factors in the regression. That way, only one of the two needs to be specified correctly.

If you want to see whether results of interventions differ depending on particular risk factors, then you need to include interactions of the intervention with those risk factors in your model. A significant interaction term of that type shows that the effect of intervention differs depending on the risk factors. Note, however, that such analyses can become even more sensitive to situations in which, based on the risk factors, the intervention was unlikely.

The above principles apply regardless of whether you are using continuous, categorical, or survival measures for outcomes. Depending on how many predictor effects you want to model versus the number of cases, you might need to combine these approaches with some form of penalization to avoid overfitting. This paper shows some ways to deal with that type of situation.