Date:         Fri, 16 Jan 2009 09:38:48 -0800
Reply-To:     Shawn Haskell <shawn.haskell@STATE.VT.US>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Shawn Haskell <shawn.haskell@STATE.VT.US>
Organization: http://groups.google.com
Subject:      Re: Modeling rate difference A little more detail
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=windows-1252

On Jan 16, 9:40 am, santoshkve...@HOTMAIL.COM (Santosh Verma) wrote:
> I am trying to model rate of slips and falls in restaurant workers.
> Generally we model rate using Poisson or negative binomial distribution and
> report rate ratios.  However, rate ratios do not say anything about
> absolute risk.  For example, a report that rate of slips and falls in
> restaurants with good floors was half of the rate in restaurants with not
> so good floors is like saying if you buy two lottery tickets instead of
> one, your chances of winning will be doubled.  Therefore, I also want to
> model rate difference.  By doing that I can tell decision makers that if
> you change your floor you can reduce your rate of slipping by ‘x’ slips per
> person work hours or for every person work hours you can prevent ‘x’ number
> of slips.  That is the motivation.
>
> Now the practical problem.  To get rate ratios we model E [ln(y/t] or E[ln
> (y) – ln(t)].
> To get rate difference we have to model E[y/t].  Now y/t has different
> variance based on what we choose as appropriate t, i.e. rate of slips and
> falls per hour has a lot less variance than rate of slips and falls per 40
> hours workweek.  This difference can lead to very different results.
>
> So my questions are:
>
> Has anyone tried this before or can point me to a reference for this?
> Am I missing something?
> What in you opinion would be an appropriate way to analyze this data?
>
> Thanks for your attention.
>
> Santosh

To start, "rate" implies a ratio of count:effort (or some similar
measure).  if this is the case then you can model counts with NegBin
or Poisson and use ln(time worked) as an offset term.  If you have the
"time worked" standardized, then you are just modeling counts (per
unit time) not "rates".  Your model will yield predictions given
certain covariates that should be interpretable as "If I change this
type of floor to that type of floor, we can expect X fewer falls
(perhaps in a 4-hr work week)".  If you want more formal hazard
ratios, then maybe consider Cox proportional hazards modeling - a
method that can be adapted for recurrent events.  Either way, I think
you should find similar results.  SH