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

 From Steven Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: right censoring of dependent and independent variable Date Fri, 30 May 2008 10:44:40 -0400

```Right.   I don't see how to use those cases.

On May 30, 2008, at 10:21 AM, Austin Nichols wrote:

```
```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/
-----------------------------------------

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