[Feature] Cox regression

[tombisho]

Currently, ACRO does not seem to include support for Cox proportional hazards regression. This creates a gap for users working with time-to-event data, particularly in epidemiology, public health, and clinical research, where survival analysis is a core analytical requirement. At the moment survival curves are offered but these only offer unadjusted survival for one grouping variable at a time.

We would like to see a disclosure-controlled implementation of Cox proportional hazards regression added to the package. Ideally, this would allow users to fit standard Cox models while ensuring that outputs are restricted to non-disclosive summary statistics (e.g. coefficient estimates, hazard ratios, confidence intervals, and model diagnostics that meet disclosure thresholds). Support for common options such as covariate adjustment, stratification, and robust standard errors—within the constraints of disclosure control—would make the feature broadly useful while maintaining privacy protections.

[jim-smith]

@tombisho should be very do-able as long as statsmodels would provide the underlying functionality you are looking for? (see point 1)

1. acro overloads statsmodels for this sort of analysis and it looks as if
   statsmodels supports cox regression according to this page of their user guide

2. Breaking this down into parts from an SDC perspective:

• we might want to adjust the way we 'bin' the plots (and attached equivalentfrequency tables) so each step represents a change of at least N people (our survival analysis code optionally does this for one curve already)
• we might want to restrict which descriptive statistics can be extracted, and ensure a minimum residual degree of freedom for each.

[tombisho]

That sounds promising, thanks @jim-smith . In future iterations it might be useful to look at some other Python packages like lifelines that offer more detailed functionality similar to the survival package in R. Real world analyses tend to require more complex options like robust standard errors and diagnostics that aren't available in statsmodels. I guess the idea is to keep the ACRO engine within Python and have other language use it, so having R provide Cox model functionality is possibly a non-starter. Perhaps R-ACRO could use the survival R package, though?

I agree that it would be sensible to enforce a minimum residual degree of freedom. I am not sure if any binning is needed, as I don't think fitting a Cox model generates a plot or frequency table (I might be wrong!)