Dear Prof. Ratnayake:
You ought not be surprised that cost data are skewed. So are a number of
important variables in health economics, including expenditure.
Depending on the nature and degree of skew, there are approximate
distributions for modeling the response. But you may want to use a
'skew-correcting' Box-Cox family of transformations model. The 'classic'
type, in which only the response is power-transformed, can do the trick.
Additional benefit is that you apply a ML estimation in this case. If
that doesn't do the trick, you can use a 'Modulus' transformation model
that can transform any real-valued data, unlike the Box-Cox. The Box-Cox
can correct the skew but not pull in the tail of the distribution as it
should, but it is far better than your just applyinmg staright OLS to
skewed response data. If you did, this problem is bound to show up in
the shape of your residuals, and that itself has implications for the
quality of your slope estimates. So, applying standard method to skewed
cost data is highly UNlikely to give robust estimates.
ANOTHER advantage of the Box-Cox is that it can be used to generalize
the functional form for your model, so you are not stuck with the
log-log (for its convenience) or a straight linear specification - as
the world is not at all linear but we are too quick to impose,
unfortunately, simplicity of the linear form hypothesis without first
testing, .....
IF you are familiar with SHAZAM, The Econometric Program by Ken White
(at U. British Columbia, Econ Dept.) it contains a canned algorithm (so
you won't have to sweat much) to help you on this problem. But remember,
the estimates of the Box-Cox model are conditional on the estimated
lambda power of transformation naturally best for the input data
structure. there are many variants of the Box-Cox, and you will do best
to familiarize yourself with them. If you are interested in Box-Cox and
how used, I have a compendium of references and will send on request.
Better still, contact Prof. Ken White at UBC. He is a very helpful
colleague.
Good luck with your work.
Regards,
Albert Okunade
Suzanne Downs-Palmer Distinguished Research Professor of Economics, U.
of Memphis.
Prof. Albert A. Okunade
Department of Economics, Rm. 450BB
The FCBE
University of Memphis
Memphis, TN 38152
tel: (901) 678-2672; fax: (901) 678-2685
----- Original Message -----
From: Jay Ratnayake <[log in to unmask]>
Date: Tuesday, March 11, 2003 3:11 am
Subject: Statistical analysis - disease cost data
>
> >>Hi All,
> >>A patient survey has been conducted to collect individual
> disease related
> >>cost data (n=201). So that, overall disease costs per case
> could be
> >>worked out. The distribution of cost data is skewed. Can I
> apply usual
> >>statistical methods to this data? How robust and reliable are
> they? Any
> >>help (guidance/directions) greatly appreciated.
> >>
> >>
> >>Jay
>
|