Ted et.That solution is for (in "missing data language") MCAR
(Missing Completely At Random), i.e. the probability
of being missing does not depend on any of the variables
in the data.

For MAR (Missing At Random), the probability of being
missing may depend on the values of covariates but must
not depend on the value of the outcome variable.


-- Not quite right, I'm afraid. The Rubin-Little classification is that MAR
means the distribution of the observed outcomes does not depend on the
distribution of the missing values. In the common longitudinal setting, this
means the distribution of the current missing outcome CAN depend on the
distribution of past _observed_ outcomes but NOT on the (past or future)
missing outcomes. For example, when missingness is due to dropout triggered
 by threshholds of observed disease progression, the data are MAR (and
likelihood works, provided there are no shared parameters between the
missing data and observed data likelihoods).

Cheers,
Bert


So the way to generate MAR, for data where there are
covariates X1, X2, ... , Xk (and outcome Y) is to set
up a function P (could be anything) of some or all of
X1, X2, ... , Xk taking values in [0,1] (endpoints
included), and then set a "missing" variable Z to be
0 (not missing) or 1 (missing) with probability given
by the value of Z for that case.

So, if M is a data matrix with columns X1, ... , Xk , Y
where each row is a case, use apply() to evaluate the
function P() for each row in terms of (X1,X2,...,Xk).

You then get a vector p = c(p.1, p.2, ... , p.N) of
values of P for the N rows of M. At this point:

 Z <- 1*( runif(N) <= p )

creates a vectors of 0s and 1s which will be markers
of Missing At Random.

Ted.

--------------------------------------------------------------------
E-Mail: (Ted Harding) <ted.harding@wlandres.net>
Fax-to-email: +44 (0)870 094 0861
Date: 31-Jan-11                                       Time: 10:17:20
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-- 
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
http://devo.gene.com/groups/devo/depts/ncb/home.shtml

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