Re: st: 95% CI calculation

[Ronan Conroy <rconroy@rcsi.ie>]

On 2013 MFómh 16, at 21:20, Ubydul Haque wrote:

> Hello,
> In 2008 I had total 675 cases. In 2012 total cases were 168.
> Considering the base year 2008, 75% cases reduced in 2012. Please let
> me know how I can calculate 95% confidence interval on this estimate.
> Thank you.

Here are two suggestions. On the information given, it's as much as I can think of.

input year cases
0 675
1 168
end
poisson year [fw=cases], irr

Poisson regression                                Number of obs   =        843
                                                  LR chi2(0)      =       0.00
                                                  Prob > chi2     =          .
Log likelihood =  -438.9845                       Pseudo R2       =     0.0000

------------------------------------------------------------------------------
        year |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   .1992883   .0153754   -20.91   0.000     .1713208    .2318213
------------------------------------------------------------------------------



binreg year [fw=cases], rr

------------------------------------------------------------------------------
             |                 EIM
        year | Risk Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   .1992883   .0137583   -23.36   0.000     .1740673    .2281636
------------------------------------------------------------------------------


In both cases, the null hypothesis is really that there is a 50/50 split between years. The actual proportion in year 2 is given by the incidence rate ratio/relative risk. The confidence intervals are slightly different, and I prefer the Poisson because I think that you are observing a continuing process over a period of time rather than assessing a finite sample of trials. 

Note that -binreg- is an alternative to logistic regression that outputs relative risks but which, for this reason, is not guaranteed to yield results every time, since the estimates thus produced may be outside the range (0,1) that defines probabilities. 

Ronán Conroy
rconroy@rcsi.ie
Associate Professor
Division of Population Health Sciences
Royal College of Surgeons in Ireland
Beaux Lane House
Dublin 2


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