# Re: st: right censoring of dependent and independent variable

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: right censoring of dependent and independent variable Date Fri, 30 May 2008 10:21:41 -0400

```Oh, okay.
Now it makes sense.  But if you were running a parametric model, you
would want to exclude topcoded cases (X=M observed), right?

On Fri, May 30, 2008 at 10:12 AM, Steven Samuels
> No, I meant that you can estimate the median of Y for that part of the X,Y
> population with X > M.  That's not much.
>
> On May 30, 2008, at 9:56 AM, Austin Nichols wrote:
>
>>
>> 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
>>>
>>>  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
>>>>
>>>> Buitenveldertselaan 3 (Metropolitan), room Z434
>>>>
>>>> +31 20 5986715
>>>>
>>>> http://home.fsw.vu.nl/m.buis/
>>>> -----------------------------------------
>>>>
>>>>
>>>>     __________________________________________________________
>>>> Sent from Yahoo! Mail.
>>>> A Smarter Email http://uk.docs.yahoo.com/nowyoucan.html
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>>>>
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>>>
>>> *
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>
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```