Calculating the CACE

Calculating the CACE

by Jean Digitale -

It looks as though in the slides, CACE was calculated with:

Numerator: ARR = Control - Treatment (risk of eczema)

Denominator: Risk difference = Treatment - Control (risk of receiving treatment)


Then in the chapter, Box 9.1, CACE was defined and calculated as:

Numerator: Risk difference = Treatment - Control (risk of smoking cessation)

Denominator: Risk difference = Treatment - Control (risk of receiving treatment)

  • In both cases, the numerator and denominator were positive. Do we choose the numerator as (treatment - control) or (control - treatment) based on that?
  • I assume this again has to do with whether we define the outcome as a good thing (meaning we want an increase) or a bad thing (meaning we want a reduction)?
  • Is the denominator always (treatment - control)?

Re: Calculating the CACE

by Thomas Newman -

Thanks for the question, Jean, and sorry about the delayed response.  As you and your classmates may be noticing in some of this week's homework problems, the signs around risk differences (and their confidence intervals!) can be confusing.

 The risk difference (in general and as calculated by Stata) is Treatment - Control (or Exposed - unexposed).  If the treatment reduces the risk of the outcome, this will be negative.

The ARR is (generally) Control - Treatment.  So if treatment reduces the risk of the outcome, the ARR will be positive. This makes sense, because it is a risk reduction, not a risk difference.

 In the slides (slide 24) I only found "Excema risk difference/BF risk difference" (slide 24) for the CACE.  It's probably clearer to stick with risk differences so if you can tell me where I used ARR in the slides I will change it.

 My general advice (which may be helpful for the homework) is to first just look at the proportions with the outcome in each group and ask: which group did better?  When you compute the CACE, it should move the ITT estimate farther from zero.

I've found that 95% confidence intervals for risk differences confuse people mainly when they cross zero. In that case, the limit of the CI that is on the same side of zero as the point estimate will answer the question: "How good could treatment be?" if the point estimate was favorable and "How bad could treatment be?" if the point estimate was unfavorable. 

 Similarly, the limit of the confidence interval on the other side of zero will answer the opposite question: if treatment looked good, how bad could it be, and if it looked bad, how good could it be?

 Good luck on the HW and the final!

Tom

  

 


Re: Calculating the CACE

by Jean Digitale -

Following up on this - thanks for the response.

On slide 24:

the sentence above the calculation says: "it can be shown* that the absolute risk reduction for exclusive BF would need to be..."

Then, although this is labeled as a risk difference: "Eczema risk difference =  6.3% – 3.3%"

It appears to be control - treatment, or ARR. It then references the CACE of 8.6% as the ARR on slide 25.


Given this, if we use a risk difference, we would get a negative CACE. Is it possible to have a negative CACE as long as it moves the estimate farther from the null of 0?

Re: Calculating the CACE

by Thomas Newman -

Thank you for noticing this.  Yes, the CACE can be negative.  It's just a risk difference and the sign will depend on which group you subtract from the other.

I've changed Slide 24 to appropriately label the CACE on that slide as a risk REDUCTION and added that clarification to the derivation in the speaker notes. 

I've uploaded the new version of the slides with this correction and today's date as part of the filename to the CLE.

Best wishes,

Tom