Multiple Imputation in mice/norm

On Apr 25, 2009, at 9:25 AM, Frank E Harrell Jr wrote:

Emmanuel Charpentier wrote:

Le vendredi 24 avril 2009 ? 14:11 -0700, ToddPW a ?crit :

I'm trying to use either mice or norm to perform multiple imputation 
to fill
in some missing values in my data.  The data has some missing values 
because
of a chemical detection limit (so they are left censored).  I'd like 
to use
MI because I have several variables that are highly correlated.  In 
SAS's
proc MI, there is an option with which you can limit the imputed 
values that
are returned to some range of specified values.  Is there a way to 
limit the
values in mice?

You may do that by writing your own imputation function and assign them
for the imputation of particular variable (see argument
"imputationMethod" and details in the man page for "mice").

                If not, is there another MI tool in R that will 
allow me to
specify a range of acceptable values for my imputed data?

In the function amelia (package "Amelia"), you might specify a "bounds"
argument, which allows for such a limitation. However, be aware that
this might destroy the basic assumption of Amelia, which is that your
data are multivariate normal. Maybe a change of variable is in order (e.
g. log(concentration) has usually much better statistical properties
than concentration).
Frank Harrell's aregImpute (package Hmisc) has the "curtail" argument
(TRUE by default) which limits imputations to the range of observed
values.
But if your left-censored variables are your dependent variables (not
covariates), may I suggest to analyze these data as censored data, as
allowed by Terry Therneau's "coxph" function (package "survival") ? code
your "missing" data as such a variable (use :
coxph(Surv(min(x,<yourlimit>,na.rm=TRUE),
          !is.na(x),type="left")~<Yourmodel>) to do this on-the-fly).
Another possible idea is to split your (supposedly x) variable in two :
observed (logical), and value (observed value if observed, <detection
limit> if not) and include these two data in your model. You probably
will run into numerical difficulties due to the (built-in total
separation...).
HTH,
                    Emmanuel Charpentier

Thanks for the help,
Todd

All see

@Article{zha09non,
 author =               {Zhang, Donghui and Fan, Chunpeng and Zhang, 
Juan and Zhang, {Cun-Hui}},
 title =                {Nonparametric methods for measurements below 
detection limit},
 journal =      Stat in Med,
 year =                 2009,
 volume =       28,
 pages =        {700-715},
 annote =       {lower limit of detection;left censoring;Tobit 
model;Gehan test;Peto-Peto test;log-rank test;Wilcoxon test;location 
shift model;superiority of nonparametric methods}
}


-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                    Department of Biostatistics   Vanderbilt University

It appears they were dealing with outcomes possibly censored at a limit 
of detection. At least that was the example they used to illustrate.

Is there a message that can be inferred about what to do with covariates 
with values below the limit of detection? And can someone translate to a 
non-statistician what the operational process was on the values below 
the limit of detection in the Wilcoxon approach that they endorsed? They 
transformed the right censored situation into a left censored one and 
then they do   ... what?

David Winsemius, MD
Heritage Laboratories
West Hartford, CT