Calculating incidence rate if I only have summary data

[Matt Price]

I have the number of cases (528 cases) and the person time (7613 person years of observation) and need to calculate an incidence rate per 1,000 PYO and 95% CI. It's easy to get a rate of 69.4 cases/1,000 PYO but harder (for me) to get the 95% CI.

I had thought Stata had an IR calculator, a little like iri (which is the Incidence-rate ratios calculator, and doesn't give me 95% CI of the incidence rates themselves), but I can no longer find it.

Am I misremembering this? Can Stata give me an incidence rate if I only have summary data?

Thank you

[Rich Goldstein]

your situation is not completely clear to me, but I suggesting starting here:

h immediate

[Matt Price]

I have taken a look at the Stata tables for epidemiologists, but I can't quite find what I'm looking for. They present ratios of rates (incident rate ratio, odds ratio) and things like the attributable / prevented risk fraction... But there is no 95% confidence interval around my incidence rate (just around the ratios).

But without running stptime (I have summary data, not the actual data) I can't figure out how to take this information:
528 cases
7613 person years of observation

and get this information:
6.94 cases per 100 person years of observation (95% CI: X-Y)

Is there a calculator on Stata that will get me X and Y? I suspect maybe not...

[Rich Goldstein]

can you treat this as a proportion and use -cii-? see

h cii

[Leonardo Guizzetti]

I wasn't able to find a Stata program that would do this for a single rate. The challenge is deciding which method of confidence interval construction is useful. Below I illustrate the Rothman and Greenland method, which is a refinement of the Normal approximation. Therefore it's an asymptotic method. Exact methods are more complicated and need iterative solutions.

scalar a = 528
scalar py = 7613 / 1000

scalar rate = a/py
scalar lower = exp( ln(rate) - invnormal(0.975)/sqrt(a) )
scalar upper = exp( ln(rate) + invnormal(0.975)/sqrt(a) )

di "Rate per 1,000 PY (95% CI): " strofreal(rate, "%8.2f") " (" strofreal(lower, "%8.2f") ", " strofreal(upper, "%8.2f") ")"

Result

Rate per 1,000 PY (95% CI): 69.36 (63.68, 75.53)

Rothman KJ, Greenland S. Modern Epidemiology, 2nd Edition. Lippincott-Raven Publishers, Philadelphia, 1998.

[Clyde Schechter]

-cii proportions- will do this for a single rate. It offers a variety of methods for calculating a confidence interval, which you can specify as options. The Rothman-Greenland method is not among them. But, as one would expect for relatively large numbers, the results from the different methods do not differ very much:

. foreach x in exact wald wilson agresti jeffreys {
  2. display "`x'"
  3. cii proportions 7613 528, `x'
  4. }
exact

                                                            Binomial exact   
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |      7,613    .0693551    .0029117        .0637482    .0752943
wald

                                                            Binomial Wald    
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |      7,613    .0693551    .0029117        .0636481     .075062
wilson

                                                                Wilson       
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |      7,613    .0693551    .0029117        .0638626    .0752818
agresti

                                                            Agresti–Coull    
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |      7,613    .0693551    .0029117        .0638585     .075286
jeffreys

                                                               Jeffreys      
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             |      7,613    .0693551    .0029117        .0638113    .0752261

Worth noting, -cii proportions- returns the estimate in -r(proportion)- and the confidence limits in -r(lb)- and -r(ub)-.