🚀 go-pugleaf

     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 masochistic  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

    bwb@odin.mda.uth.tmc.edu
    internet address is (129.106.3.17)


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