Availability of code to fit accelerated failure model
Author Message Availability of code to fit accelerated failure model

ACCFLF
Fits the Accelerated Failure Model

ACCFLF fits  the  accelerated  failure  model with  the  log  F  error
structure  to   survival  data   with  or  without   covariates.   Its
capabilities include  fitting the general log-F model or any  submodel
with p  and q  fixed.  It  also can automatically fit  a set of models
specified by a rectangular grid in (p,q) coordinates or a set of named
models.  Several options are  provided for initial estimates in adding
covariates to an existing model.   ACCFLF will calculate time-to-event
probabilities for accelerated failure  models using either times  from
the current data or a  user-supplied list. (For those unfamiliar  with
the model, a brief introduction taken from the documentation of ACCFLF
is included at the bottom of this message.)

How to Get It

Source  code  to   ACCFLF  and  MSDOS  executable  modules,  all  with
documentation  are available by  anonymous ftp to odin.mda.uth.tmc.edu
(129.106.3.17) in  directory /pub/accflf.   Read file  INDEX  on  this
account for  an  explanation of  what is where.  Macintosh executables
should be available shortly, when our Mac expert returns.  We will ask
Mike Meyer to post ACCFLF to statlib after  receiving initial comments
from users on the net.

Those  who are {*filter*}ic  enough to read the code might notice  that
the formulae coded by  and large bear little obvious relation to those
in Kalbfleish and Prentice.   This is no accident.  A paper explaining
the rationale for the computational formulae is provided  in the  same
directory.  So are the data sets on which the code  was tested.   (The
code is not bullet proof but it seems robust enough to be useful.)

Brief Introduction to the Model

The parameters of  the accelerated failure model  are:  a  and b,  the
half-degrees of  freedom  of the  F distribution; mu  and  sigma,  the
constant and  scaling  term for the logarithm of survival time; and if
there are covariates, a coefficient beta(j)  for  each.  The model can
be summarized  as follows.  Let values of the  covariates  for the ith
subject be z(i,j), j=1,...,p and define

alpha(i) = mu + sum[j=1 to p] z(i,j) * beta(j).

If  Y(i)  is a  random variable distributed as  the  logarithm  of the
time-to-event for the ith subject, then

Y(i)  =  alpha(i)  +  sigma  *  W

where W is distributed as the logarithm of an F-variate with 2a and 2b
degrees of freedom.   If no covariates are modelled, then all alpha(i)
= mu and the Y(i) are identically distributed.

Since  covariates have an  additive effect on the  distribution of the
logarithm of  time, they have a multiplicative effect on time  itself.
The  term,  accelerated  failure,  expresses this consequence  of  the
model:   time  to  failure  is  traversed  at  a  rate  that   depends
multiplicatively on covariate values.

The appeal of this model is largely due to  the  diversity of forms of
the distribution of  survival times as  the degrees  of  freedom vary.
Many widely used parametric distributions are  obtained for particular
values  of a  and b; in several of these cases  the value of a or b is
infinite.   A  reparameterization  due  to  Prentice,  regularizes the
likelihood and eliminates testing problems associated with infinities.
The reparameterization from half degrees of freedom, (a,b) to (p,q) is
given by p = 2/(a+b) and q = (1/a -  1/b) / sqrt( 1/a + 1/b).  In this
parameterization, the  log likelihood has finite, not identically zero
derivatives everywhere on the boundary a = infinity or b = infinity as
well as on the interior of  the positive quadrant of the (a,b)  plane.
The   log-normal,  Weibull,  log-logistic,  reciprocal  Weibull,   and
generalized gamma model in  time,  not in the  logarithm  of time, are
given by  (p,q)  and  corresponding  (a,b)  values  shown  below.  The
regularity of the likelihood allows, for example, the  testing  of the
acceptability of a log-normal  model in comparison to a Weibull model.
Without this regular formulation, it  would not at all  be evident how
to perform such a test.

Model          (p,q)           (a,b)             Comment
-----          ----            -----             -------

Log-normal     (0,0)    (infinity,infinity)

Weibull        (0,1)    (1,infinity)

Exponential    (0,1)    (1,infinity)             sigma=1

Log-logistic   (1,0)    (1,1)

Reciprocal
Weibull     (0,-1)   (infinity,1)

Generalized
Gamma       p=0      a or b or both infinite

Reference:  Kalbfleish,  J.  D.  and  Prentice,  R.   L.  (1980),  The
Statistical  Analysis of  Failure  Time Data. New York: John Wiley and
Sons.

Barry W. Brown
Department of Biomathematics,
Box 237
University of Texas M. D.
Anderson Hospital
1515 Holcombe Blvd
Houston, TX 77030

internet address is (129.106.3.17)

--
Barry W. Brown
Department of Biomathematics,
Box 237
University of Texas M. D.

Sun, 22 Jan 1995 03:40:55 GMT

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