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Re: st: right censoring of dependent and independent variable


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: right censoring of dependent and independent variable
Date   Fri, 30 May 2008 09:56:03 -0400

Steven Samuels <sjhsamuels@earthlink.net>:

I'm afraid I don't understand this claim, since I don't agree with it.
 Are you saying that if you observe X=M (so X>=M but the true value is
not observed) and more than 50% of observations on Y are uncensored at
X=M, you can estimate the conditional median of Y given true
(unobserved) X?

On Fri, May 30, 2008 at 8:55 AM, Steven Samuels
<sjhsamuels@earthlink.net> wrote:
>
>  There is -some- information.  If for X > M (censoring value), P% of
> observations on Y are uncensored, you can estimate up to the P-th quantile
> of Y for X>M.  For anything more, you need very strong assumptions about the
> distribution of X for X>M, about E(Y|X) for X>M, or both.
>
>
> -Steve
>
> On May 30, 2008, at 4:52 AM, Garry Anderson wrote:
>
>> I was using fractional polynomials and so non-linearities are likely. It
>> seems unfortunate that observations of predictors with right censored
>> values need to be deleted from the analysis because I would think there
>> is at least some information in the censored value.
>>
>> Best wishes, Garry
>>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten buis
>> Sent: Thursday, May 29, 2008 10:44 PM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: right censoring of dependent and independent variable
>>
>> --- Garry Anderson <g.anderson@unimelb.edu.au> wrote:
>>>
>>> I have data where both the dependent and independent variable are
>>> right censored and continuous. Although intreg, cnreg or tobit can
>>> handle censoring of the dependent variable, they do not seem to allow
>>> censoring of the independent variable. Both the instruments can only
>>> measure to a maximum value, 30% of values are right censored on the Y
>>> variable and 15% on the X variable.
>>>
>>> I would welcome suggestions as to how to incorporate right censoring
>>> of the independent variable?
>>
>> In the graph below you can see that selection on the x variable is much
>> less of a problem than selection on the y variable. A part of the data
>> is turned into influential outliers, by selecting on the y. In the
>> example it is the upper right part of the observed values that pull the
>> regression line down. However, the same does not happen when you select
>> on x. With regression you model the mean of y conditional on x, the fact
>> that you don't observe all values of x, is unfortunate (loss of
>> power) but not disastrous. Things become obviously more complicated when
>> you are interested in any non-linearities in the effect of x.
>>
>> Hope this helps,
>> Maarten
>>
>> *----------------------- begin example ------------------------ clear
>> set seed 12345 matrix C = (1, .5 \ .5, 1) drawnorm x y, n(1000) corr(C)
>> twoway scatter y x if x < 1, aspect(1) xline(1) || ///
>>       scatter y x if x >= 1, msymbol(oh) mcolor(gs10) || ///
>>       lfit y x , lpattern(solid) lcolor(green) || ///
>>       lfit y x if x < 1, lpattern(solid) lcolor(red) ///
>>       title(selection on x) name(x, replace) ///
>>       legend(order( 1 "observed" ///
>>                     2 "censored" ///
>>                     3 "true"     ///
>>                     4 "estimated") ///
>>              rows(2))
>>
>>
>>
>> twoway scatter y x if y < 1, aspect(1) yline(1) || ///
>>       scatter y x if y >= 1, msymbol(oh) mcolor(gs10) || ///
>>       lfit y x , lpattern(solid) lcolor(green) || ///
>>       lfit y x if y < 1, lpattern(solid) lcolor(red) ///
>>       title(selection on y) name(y, replace) ///
>>       legend(order( 1 "observed" ///
>>                     2 "censored" ///
>>                     3 "true"     ///
>>                     4 "estimated") ///
>>              rows(2) colfirst)
>>
>>
>> grc1leg y x
>> *------------------------ end example --------------------------- (For
>> more on how to use examples I sent to the Statalist, see
>> http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html )
>>
>> For this example to run you need to download the -grc1leg- package,
>> see: -findit grc1leg-.
>>
>>
>> -----------------------------------------
>> Maarten L. Buis
>> Department of Social Research Methodology Vrije Universiteit Amsterdam
>> Boelelaan 1081
>> 1081 HV Amsterdam
>> The Netherlands
>>
>> visiting address:
>> Buitenveldertselaan 3 (Metropolitan), room Z434
>>
>> +31 20 5986715
>>
>> http://home.fsw.vu.nl/m.buis/
>> -----------------------------------------
>>
>>
>>      __________________________________________________________
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>>
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>
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