Absolute and relative risk difference and number needed to treat

[Jadwiga Anna Konieczna]

Dear all,

I am working with data from RCT and trying to determine an effect of intervention versus control group (int_group) on binary outcome (0/1) after adjusting for some baseline covariables. I used logit and calculated odds ratio.

logit outcome i.int_group covariables

Since it is RCT, I would also like to calculate adjusted absolute risk difference (ARD), adjusted relative risk difference (RRD), and number needed to treat (NNT).

Do you have some useful hints ho to calculate these parameters?

BW

[Clyde Schechter]

Since this is an RCT, do you have a reason for doing adjusted analyses? Have you looked at the balance of the variables (other than outcome) in the study arms? If the arms are well balanced, you may have no need to adjust for anything. The other reason for adjusting can be to try to improve precision of estimates by reducing outcome variance--so if there are some putative covariates with strong associations to the outcome, you might consider adjusting for those. Or perhaps you wish to adjust the results to what you might find in some reference population which your study sample is not representative of? But in general, in an RCT there is no need to adjust the results unless the randomization produced an imbalance that left you with a confounding variable. And that rarely happens unless the trial was very small.

I have never heard of a "relative risk difference." A relative risk, by definition, is a ratio, not a difference. And the risk difference is absolute. Anyway, if you don't need to adjust for covariates, you can get the relative risk (aka risk ratio) and the risk difference by using the -cs- command. See -help cs-. The NNT is just the reciprocal of the risk difference.

If you do need to adjust for covariates, then you can get the relative risk by using Poisson regression instead of logistic. See -help poisson-. If you specify the -irr- option, the results will be shown as an "incidence rate ratio," which in this situation is the same thing as relative risk. The adjusted risk difference is estimated with a linear probability model, i.e. plain old -regress-.

Added: Note: You don't describe your study design beyond saying it is an RCT. In the above, because you say you used -logit- to analyze the trial results, I am inferring that it is a simple design involving some number of study arms (at least 2) and an outcome measured once at the end of the trial. If you have longitudinal data, then the adjusted analyses will be more complicated and other commands will be needed--but in that case, the -logit- analysis you have done would not be sufficient either.

[Bruce Weaver]

The 2013 Stata Journal article by Norton et al. may be of interest:

• https://journals.sagepub.com/doi/pdf...867X1301300304

. search adjrr, sj

Search of official help files, FAQs, Examples, and Stata Journals

SJ-13-3 st0306  . . . . .  Computing adjusted risk ratios and risk differences
        . . . . . . . . . . . . E. C. Norton, M. M. Miller, and L. C. Kleinman
        (help adjrr if installed)
        Q3/13   SJ 13(3):492--509
        calculates adjusted risk ratios and adjusted risk differences
        after running a logit or probit model with a binary, a
        multinomial, or an ordered outcome

(end of search)

[Leonardo Guizzetti]

One minor thing to add since Clyde addressed the main points: if it turns out that your risk difference is not statistically different from zero, do not report the NNT, as it no longer has a simple relationship with the risk difference and will not be easily interpretable.