```From:VPIOTROV@PRDBE.jnj.com
Subject: [NMusers] Imputation of missing sex covariate
Date:Thu, 22 Aug 2002 12:31:48 +0200

During the recent discussion about missing sex covariate (see 99jul302002 "Missing Gender (Categorical values)") someone suggested to use other
covariates like body size and serum creatinine (SCR) to predict sex. I explored very briefly
this opportunity and found that indeed sex can be predicted with a reasonable precision. I used
two data sets, one including Caucasians (N=401) and another one including Orientals (Japanese
to be exact, N=65). I fitted a logistic regression model using WT, BMI or BSA as predictors, and
additionally, WT+SCR, BMI+SCR and BSA+SCR. I used an S-PLUS function glm() which
is a convenient tool for this task. It turned out BSA (calculated as WT^0.538*HT^0.396*0.0243)
was the best predictor (sex was predicted correctly in 71 % of Caucasians and in 63 %
of Orientals. BSA+SCR gave better precision (74% Caucasians and 82% Orientals).

Fitted equations are as follows:
Caucasians:     logit = -9.184 + 4.754*BSA or
logit = -13.212 + 4.427*BSA + 4.541*SCR
Orientals:      logit = -15.254 + 10.666*BSA or
logit = -13.242 + 7.861*BSA + 3.033*SCR
BSA in m2, SCR in mg/dL

How to use these equations for imputation: introduce BSA or BSA and SCR and calculate the logit.
If it is positive sex is male otherwise sex is female.

It makes no sense to use this approach if sex is missing in a high proportion of individuals, however,
if the proportion is relatively low (say, <20 %) you can try to impute and test sex as a covariate
affecting PK parameters without omitting subjects with missing sex.

Best regards,

-----------------------------------------------------------------

Research Fellow, Advanced PK-PD Modeling & Simulation
Global Clinical Pharmacokinetics and Clinical Pharmacology (ext. 5463/151)
Johnson & Johnson Pharmaceutical Research &Development
Turnhoutseweg 30
B-2340 Beerse
Belgium

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From:"Lewis B. Sheiner"
Subject:Re: [NMusers] Imputation of missing sex covariate
Date:Thu, 22 Aug 2002 09:13:49 -0700

That's fine, but single imputaiton is not a good idea, so I would modify
as indicated below ...

Use multiple imputation:
Introduce BSA or BSA and SCR and calculate the anti-logit, p =
probability of being male.
Then for each of the 5-10 imputations, for each indivdual with missing sex
1. Draw a uniform random number r between 0 and 1, and assign sex = male
if r<p.
2. Analyze now-complete data

_/  _/  _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu)
_/  _/ _/    _/     _/      Professor: Lab. Med., Biophmct. Sci.
_/  _/ _/    _/_/_/ _/_/     Mail:      Box 0626, UCSF, SF,CA,94143
_/  _/ _/        _/ _/        Courier: Rm C255, 521 Parnassus,SF,CA,94122
_/_/   _/_/ _/_/_/ _/         415-476-1965 (v), 415-476-2796 (fax)

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From: "Kowalski, Ken"
Subject: RE: [NMusers] Imputation of missing sex covariate
Date:  Fri, 23 Aug 2002 10:49:29 -0400

How do you employ multiple imputation in the context of a model building
exercise where you might want to test the sex covariate as well as other
covariates on various parameters in the model?  It seems to me that multiple
imputation methods are geared towards a given model and the methodology
hasn't been worked out for model building.  Should we perform model building
for each imputation and then perform averaging across the final models for
the 5-10 imputations to obtain the final estimates even though the final
models may not include the same covariate parameters for each imputation?

Ken
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From:"Lewis B. Sheiner"
Subject:Re: [NMusers] Imputation of missing sex covariate
Date:Sun, 25 Aug 2002 15:28:01 -0700
Subject:

I didn't know we were talking about somehow trying to estimate 'model uncertainty' as well....
That's a much harder problem! I thought the goal was the simpler one of
'Given a model, but some missing (at random) covariates in our data, how do we estimate the model
from the data and get honest standard errors?"
If the model structure is regarded as uncertain, then what is the meaning of 'standard error' for
a parameter that may or may be part of that model?

LBS.

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From: "Kowalski, Ken"
Subject: RE: [NMusers] Imputation of missing sex covariate
Date:Mon, 26 Aug 2002 08:19:12 -0400

Lew,

I may have changed the thread of this discussion with my question/comment.  I'm not interested in a
standard error, per se, however, I may be interested in testing a covariate effect from two hierarchical
models using a likelihood ratio test when  the covariate requires substantial imputation.  In this model
building (model uncertainty) context, it is my understanding that multiple imputation methods have not
been worked out.  It is an issue as rarely are we 'given a model' as some form of model building is
typically required.

Ken

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