# [R] svy / weighted regression

David Winsemius dwinsemius at comcast.net
Tue Oct 13 17:21:11 CEST 2009

```On Oct 13, 2009, at 6:07 AM, Laust wrote:

> Dear David,
>
> Thanks again for your input! I realize that I did a bad job of
> explaining this in my first email, but the setup is that in Finland
> persons who die are sampled with a different probability (1) from
> those who live (.5). This was done by the Finnish data protection
> authorities to protect individuals against identification. In the rest
> of the countries everyone is sampled with a probability of 1. The data
> that I am supplying to R is summarized data for each country
> stratified by case status. Another way of organizing the data would
> be:
>
> # creating data
> listc <- c("Denmark","Finland","Norway","Sweden")
> listw <- c(1,2,1,1)
> listd <- c(1000,1000,1000,2000)
> listt <- c(755000,505000,905000,1910000)
> list.cwdt <- c(listc, listw, listd, listt)
> country2 <-
> data.frame(country=listc,weight=listw,deaths=listd,time=listt)
>
> I hope that it is clearer now that for no value of the independent
> variable 'country' is the rate going to be zero.

It is clearer now, and I think you were correct in believing that
should not have been the problem, so please accept my apologies. The
denominators and numerators should have been properly summed prior to
estimation.

> I think this was also
> not the case in my original example, but this was obscured by my poor
> communication- & R-skills. But if data is organized this way then
> sampling weight of 2 for Finland should only be applied to the
> time-variable that contains person years at risk and *not* to the
> number of deaths, which would complicate matters further. I would know
> how to get this to work in R or in any other statistical package.

> Perhaps it is - as Peter Dalgaard suggested - the estimation of the
> dispersion parameter by the survey package that is causing trouble,
> not the data example eo ipso. Or perhaps I am just using survey in a
> wrong way.

I think it is likely that we are now both using it incorrectly, but my
efforts are also creating nonsense. From the help page I thought that
the formula in svydesign might be need to be the country variable ...
wrong. Or that the weights might need to be the inverse of what you
had used ...wrong. Or that you ought to use quasipoisson for the
family ,,,, wrong again.

Lumley is preparing a book to accompany the package but that is still
several months away from release. He and Norm Breslow also published a
paper very recently in the American Journal of Epidemiology on the
using of survey sampling for analysis of case-cohort designs (of which
your problem seems to be an exceedingly simple example, albeit only in
one of the four strata.) I don't have access to the original paper at
the moment, but perhaps you are in an academic setting where such
access would be routine.

Or probably even more efficient would be to shoot a letter to Thomas
Lumley.

--
David

>
> Best
> Laust
>
> ****
> Post doc. Laust Mortensen, PhD
> Epidemiology Unit
> University of Southern Denmark
>
> On Mon, Oct 12, 2009 at 3:32 PM, David Winsemius <dwinsemius at comcast.net
> > wrote:
>> I think you are missing the point. You have 4 zero death counts
>> associated
>> with much higher person years of exposure followed by 4 death
>> counts in the
>> thousands associated with lower degrees of exposures. It seems
>> unlikely that
>> these are real data as there are not cohorts that would exhibit
>> such lower
>> death-rates. So it appears that in setting up your test case, you
>> have
>> created an impossibly unrealistic test problem.
>>
>> --
>> David
>>
>>
>> On Oct 12, 2009, at 9:12 AM, Laust wrote:
>>
>>> Dear Peter,
>>>
>>> Thanks for the input. The zero rates in some strata occurs because
>>> sampling depended on case status: In Finland only 50% of the non-
>>> cases
>>> were sampled, while all others were sampled with 100% probability.
>>>
>>> Best
>>> Laust
>>>
>>> On Sat, Oct 10, 2009 at 11:02 AM, Peter Dalgaard
>>> <p.dalgaard at biostat.ku.dk> wrote:
>>>>
>>>> Sorry, forgot to "reply all"...
>>>>
>>>> Laust wrote:
>>>>>
>>>>> Dear list,
>>>>>
>>>>> I am trying to set up a propensity-weighted regression using the
>>>>> survey package. Most of my population is sampled with a sampling
>>>>> probability of one (that is, I have the full population).
>>>>> However, for
>>>>> a subset of the data I have only a 50% sample of the full
>>>>> population.
>>>>> In previous work on the data, I analyzed these data using SAS and
>>>>> STATA. In those packages I used a propensity weight of 1/[sampling
>>>>> probability] in various generalized linear regression-
>>>>> procedures, but
>>>>> I am having trouble setting this up. I bet the solution is
>>>>> simple, but
>>>>> I’m a R newbie. Code to illustrate my problem below.
>>>>
>>>> Hi Laust,
>>>>
>>>> You probably need the package author to explain fully, but as far
>>>> as I
>>>> can see, the crux is that a dispersion parameter is being used,
>>>> based on
>>>> Pearson residuals, even in the Poisson case (i.e. you effectively
>>>> get
>>>> the same result as with quasipoisson()).
>>>>
>>>> I don't know what the rationale is for this, but it is clear that
>>>> with
>>>> your data, an estimated dispersion parameter is going to be
>>>> large. E.g.
>>>> the data has both 0 cases in 750000 person-years and 1000 cases
>>>> in 5000
>>>> person-years for Denmark, and in your model they are supposed to
>>>> have
>>>> the same Poisson rate.
>>>>
>>>> summary.svyglm starts off with
>>>>
>>>>   est.disp <- TRUE
>>>>
>>>> and AFAICS there is no way it can get set to FALSE.  Knowing
>>>> Thomas,
>>>> there is probably a perfectly good reason not to just set the
>>>> dispersion
>>>> to 1, but I don't get it either...
>>>>
>>>>>
>>>>> Thanks
>>>>> Laust
>>>>>
>>>>> library(survey)
>>>>>
>>>>> # creating data
>>>>> listc <-
>>>>>
>>>>> c
>>>>> ("Denmark
>>>>> ","Finland
>>>>> ","Norway","Sweden","Denmark","Finland","Norway","Sweden")
>>>>> listw <- c(1,2,1,1,1,1,1,1)
>>>>> listd <- c(0,0,0,0,1000,1000,1000,2000)
>>>>> listt <- c(750000,500000,900000,1900000,5000,5000,5000,10000)
>>>>> list.cwdt <- c(listc, listw, listd, listt)
>>>>> country <-
>>>>> data
>>>>> .frame(country=listc,weight=listw,deaths=listd,yrs_at_risk=listt)
>>>>>
>>>>> # running a frequency weighted regression to get the correct point
>>>>> estimates for comparison
>>>>> glm <- glm(deaths ~ country + offset(log(yrs_at_risk)),
>>>>> weights=weight, data=country, family=poisson())
>>>>> summary(glm)
>>>>> regTermTest(glm, ~ country)
>>>>>
>>>>> # running survey weighted regression
>>>>> svy <- svydesign(~0,,data=country, weight=~weight)
>>>>> svyglm <- svyglm(deaths ~ country + offset(log(yrs_at_risk)),
>>>>> design=svy, data=country, family=poisson())
>>>>> summary(svyglm)
>>>>> # point estimates are correct, but standard error is way too large
>>>>> regTermTest(svyglm, ~ country)
>>>>> # test indicates no country differences
>>>>>
>>>>> ______________________________________________
>>>>> R-help at r-project.org mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide
>>>>> http://www.R-project.org/posting-guide.html
>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>>
>>>> --
>>>>  O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>>>>  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>>>>  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45)
>>>> 35327918
>>>> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45)
>>>> 35327907
>>>>
>>>>
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>> David Winsemius, MD
>> Heritage Laboratories
>> West Hartford, CT
>>
>>

David Winsemius, MD
Heritage Laboratories
West Hartford, CT

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