I received the following answers to my posting. The smrby.ado program for STATA 
was exactly what I needed. I had overlooked it.

Roland Andersson


> -----Original Message-----

> Subject:      Comparing SMR
> I have calculated SMR for a number of related diseases. I want to make 
> inferences on the difference. How? Are there softwares can I use? I have
> STATA and PEPI but have not found anything on this.  
 
> Regards
> 
> Roland Andersson, MD PhD
> Department of Surgery
> County Hospital Ryhov
> S-551 85 Jönköping
> SWEDEN
> 
> e-mail: [log in to unmask]
> phone:  +46-36-321344
> fax:    +46-36-321321
> ____________________________________________
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It is more usual to compare two SMRs using ratios tha differences. You will
find a worked example on page 69 of D. Altman's Statistics with confidence.
This book also contains a software disk which will do the calculation for
you.

Regards
Miland Joshi (Mr.)
Department of Epidemiology and Public Health
University of Leicester 


You cannot compare the differences of two (or more) separate SMR's to each
other, even if the same standard population is used for all calculated
SMR's.  Comparison can only be done between the study group and the
comparison population.  In order to compare the two study populations,
direct standardiazation must be used.

Hope this helps.

Tracy S. DuVernoy, DVM, MPH, Dipl. ACVPM
US Army Center for Health Promotion and Preventive Medicine
Directorate of Epidemiology and Disease Surveillance
Epidemiology Program
5158 Blackhawk Road, Attn:  MCHB-TS-EDE
E-1570, Room 141
Aberdeen Proving Ground, MD  21010-5403
410-436-1009/3534, FX:  410-436-5449 (DSN:  584)
[log in to unmask]


Because SMR's are ratios of the observed to the expected, differences
between such ratios are not usually calculated though ratios of SMR's may
be.  

You should realize that SMR's are functions of indirectly standardized
rates, which technically are not comparable (Ref:  Breslow NE, Day NE.
Statistical methods in cancer research.  Volume II.  The design and analysis
of cohort studies.  Lyon, France:  International Agency for Research on
Cancer, 1987:72-75).

Nonetheless, different SMR's are often compared, often by seeing whether
their confidence limits do or do not overlap or by other tests (op cit.,
91-103).

Matthew Zack


You might try using the SMRs as proportions and testing the difference
between two proportions, i.e., is the size of the difference greater than
what we would expect from chance, i.e., random real-world variation.

Another way, is to see if the confidence intervals for each point estimate,
i.e., SMR, "overlap" .  If so your null hypothesis can't be rejected (at say
alpha = 0.05). This is not the "best" way though, because it uses less
information when you're calculating degrees of freedom - the previous method
is supposed to be better..[using n1-n2-2] .although, I have seen this second
approach used. (So how "bad" can it be?)

I thought PEPI did this sort of thing. I have done it by hand using a
correction factor for the proportions recommended by Fleis in his famous
book...Rates, Ratios and Proportions. But, its a very long formula when
you're using proportions and hopefully a computer program is something
you'll find.


Deane

Vanderbrooke has a good approximation for calculating confidence intervals 
of SMT based on approximation of log(SMR)  to a normal distribution. I can't 
find ref immediately but it is around mid to late 1980's prob. in Am. J 
Epidemiology. If you trace the exact reference perhaps you could send it 
back to me.

Russell Ecob

Two PEPI programs, INDIRST and POISSON. calculate SMRs.

If SMRs are computed by INDIRST, standard errors are provided; see the PEPI
manual (ver. 3.00 or 3.01), pp 78-79.  The difference between two SMRs can
then be tested by an ordinary Z test, e.g. by using option 3 of the PEPI
program DIFFER.  SMRs should not be compared in this way if they relate to
different populations (see Kahn and Sempos, Statistical Methods in
Epidemiology, 2nd edn, 1989, pp. 96 and 102).

If SMRs are computed by entering observed and expected numbers of cases in
POISSON, confidence intervals (including Fisher and mid-P exact intervals)
are provided; see the PEPI manual (ver. 3.00 or 3.01), pp 139-141.

Joe Abramson


You could look at 'Confidence Interval Analysis' ('CIA')  produced by
the British Medical Association.  (Accompanying book 'Statistics with
Confidence.)  It does SMRs - and I think does differences with
confidence intervals.  I'm at home now, so can't really check.  Come
back to me by Monday if you would like to know.

Regards,

Michael Thrusfield
The Old Granary
Buxley
Ormiston
East Lothian
EH33 2NG
UK

+44 (0)1875 614609


Hi Roland
Use STATA Poisson regression, where the dependent variable is 
the observed count, and the 'offset' is the expected count in the 
SMR.
Mike
Professor Mike Campbell
Institute of Primary Care and General Practice
Community Sciences Centre
Northern General Hospital
Sheffield S5 7AU

Tel 0114 271 5919
Fax 0114 242 2136
e-mail [log in to unmask]

Stata has some user-supplied programs on their website for this.  
One is called smrby which is supposed to allow tabulation of observed to 
expected 
ratios and exact confidence limits, and tests for a linear trend across SMRs.  

Check their website at www.stata.com, and find STB-29, program sg29.1


Daniel Smith, Dr.P.H.
Environmental Health Investigations Branch
California Department of Health Services
1515 Clay Street, Suite 1700
Oakland, CA 94612-1404
Telephone 510.622.4500
Fax 510.622.4505
eMail to [log in to unmask]


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