- MODEL response<*censor(list)>=independents
< / options > ;
- MODEL (lower,upper)=independents < / options >
- MODEL events/trials=independents < / options >
Multiple MODEL statements can be used with
one invocation of the LIFEREG procedure.
The optional label is used to label the
model estimates in the output SAS data set.
The first MODEL syntax allows for right censoring.
The variable response is possibly right censored.
If the response variable can be right censored, then
a second variable, denoted censor, must appear
after the response variable
with a list of parenthesized values,
separated by commas or blanks, to indicate censoring.
That is, if the censor variable takes on a value
given in the list, the response is a right-censored
value; otherwise, it is an observed value.
The second MODEL syntax specifies two variables,
lower and upper, that contain values
of the endpoints of the censoring interval.
If the two values are the same (and not missing),
it is assumed that there is no censoring
and the actual response value is observed.
If the lower value is missing, then the
upper value is used as a left-censored value.
If the upper value is missing, then the lower
value is taken as a right-censored value.
If both values are present and the lower value
is less than the upper value, it is assumed
that the values specify a censoring interval.
If the lower value is greater than the upper value or
both values are missing, then the observation is not
used in the analysis although predicted values can
still be obtained if none of the covariates are missing.
The following table summarizes the ways of specifying censoring.
|not missing|| ||not missing|| ||equal|| ||no censoring|
|not missing|| ||not missing|| ||lower < upper|| ||censoring interval-|
|missing|| ||not missing|| || || ||upper used as left-|
| || || || || || ||censoring value|
|not missing|| ||missing|| || || ||lower used as right-|
| || || || || || ||censoring value|
|not missing|| ||not missing|| ||lower > upper|| ||observation not used|
|missing|| ||missing|| || || ||observation not used|
The third MODEL syntax specifies two variables
that contain count data for a binary response.
The value of the first variable,
events, is the number of successes.
The value of the second variable,
trials, is the number of tries.
The values of both events and (trials-events)
must be nonnegative, and trials must
be positive for the response to be valid.
The values of the two variables do not need to
be integers and are not modified to be integers.
The variables following the equal
sign are the covariates in the model.
No higher order effects, such as interactions,
are allowed in the covariables list; only variable
names are allowed to appear in this list.
However, a class variable can be used as a main effect, and
indicator variables are generated for the class levels.
If you do not specify any covariates following the equal
sign, an intercept-only model is fit.
Examples of three valid MODEL statements are
a: model time*flag(1,3)=temp;
b: model (start, finish)=;
c: model r/n=dose;
Model statement a indicates that the response is contained
in a variable named time and that, if the variable
on the values 1 or 3, the observation is right censored.
The explanatory variable is
temp, which could be a class variable.
Model statement b indicates that the response is
known to be in the interval between the values of
the variables start and finish and that there are
no covariates except for a default intercept term.
Model statement c indicates a binary response, with
the variable r containing the number of responses
and the variable n containing the number of trials.
The following options can appear in the MODEL statement.
|Model specification|| || |
| ||specify distribution type for failure time|| ||DISTRIBUTION=|
| ||request no log transformation of response|| ||NOLOG|
| ||initial estimate for intercept term|| ||INTERCEPT=|
| ||hold intercept term fixed|| ||NOINT|
| ||initial estimates for regression parameters|| ||INITIAL=|
| ||initialize scale parameter|| ||SCALE=|
| ||hold scale parameter fixed|| ||NOSCALE|
| ||initialize first shape parameter|| ||SHAPE1=|
| ||hold first shape parameter fixed|| ||NOSHAPE1|
|Model fitting|| || |
| ||set convergence criterion|| ||CONVERGE=|
| ||set maximum iterations|| ||MAXITER=|
| ||set tolerance for testing singularity|| ||SINGULAR=|
|Output|| || |
| ||display estimated correlation matrix|| ||CORRB|
| ||display estimated covariance matrix|| ||COVB|
| ||display iteration history, final gradient,|| ||ITPRINT|
| || and second derivative matrix|| || |
sets the convergence criterion.
Convergence is declared when
the maximum change in the parameter estimates between
Newton-Raphson steps is less than the value specified.
The change is a relative change if the parameter is greater than
0.01 in absolute value; otherwise, it is an absolute change.
By default, CONVERGE=0.001.
sets the relative Hessian convergence criterion.
The value of number must be between 0 and 1.
After convergence is
determined with the change in parameter criterion
specified with the CONVERGE= option, the quantity
is computed and compared to
number, where g is the gradient vector, H is the
Hessian matrix for the model parameters, and f is the log-likelihood
function. If tc is greater than
number, a warning that the relative Hessian convergence criterion
has been exceeded is printed.
This criterion detects the occasional case where the change in parameter
convergence criterion is satisfied, but a maximum in the log-likelihood
function has not been attained.
By default, CONVG=1E-4.
produces the estimated correlation matrix of the parameter estimates.
produces the estimated covariance matrix of the parameter estimates.
specifies the distribution type assumed for the failure time.
By default, PROC LIFEREG fits a type 1 extreme value
distribution to the log of the response.
This is equivalent to fitting the Weibull distribution, since
the scale parameter for the extreme value distribution
is related to a Weibull shape parameter and the
intercept is related to the Weibull scale parameter in this case.
When the NOLOG option is specified, PROC LIFEREG models the untransformed
response with a type 1 extreme value distribution as the default.
See the section "Supported Distributions"
for descriptions of the distributions.
The following are valid values for distribution-type:
- the exponential distribution, which is
treated as a restricted Weibull distribution
- a generalized gamma distribution (Lawless, 1982, p. 240).
The two parameter
gamma distribution is not available in PROC LIFEREG.
- a loglogistic distribution
- a lognormal distribution
- a logistic distribution (equivalent
to LLOGISTIC when the NOLOG option is specified)
- a normal distribution (equivalent
to LNORMAL when the NOLOG option is specified)
- a Weibull distribution.
If NOLOG is specified, it fits a type 1 extreme value
distribution to the raw, untransformed data.
PROC LIFEREG transforms the response with the natural logarithm
before fitting the specified model
when you specify the GAMMA, LLOGISTIC, LNORMAL, or WEIBULL option.
You can suppress the log transformation
with the NOLOG option.
The following table summarizes the resulting distributions when
the distribution options above are used in combination with
the NOLOG option.
|EXPONENTIAL||Yes||One parameter extreme value|
|GAMMA||Yes||Generalized gamma with untransformed responses|
|LOGISTIC||Yes||Logistic (NOLOG has no effect)|
|NORMAL||Yes||Normal (NOLOG has no effect)|
sets initial values for the regression parameters.
This option can be helpful in the case of convergence difficulty.
Specified values are used to initialize the regression
coefficients for the covariates specified in the MODEL statement.
The intercept parameter is initialized with
the INTERCEPT= option and is not included here.
The values are assigned to the variables in the MODEL statement
in the same order in which they are listed in the MODEL statement.
Note that a class variable requires k-1 values when
the class variable takes on k different levels.
The order of the class levels is determined by the ORDER= option.
If there is no intercept term, the first
class variable requires k initial values.
If a BY statement is used, all class variables must
take on the same number of levels in each BY group
or no meaningful initial values can be specified.
The INITIAL option can be specified as follows.
Type of List
|list separated by blanks|| |
initial=3 4 5
|list separated by commas|| |
|x to y|| |
initial=3 to 5
|x to y by z|| |
initial=3 to 5 by 1
|combination of methods|| |
initial=1,3 to 5,9
By default, PROC LIFEREG computes initial
estimates with ordinary least squares.
See the section "Computational Method"
initializes the intercept term to value.
By default, the intercept is initialized
by an ordinary least squares estimate.
displays the iteration history, the final evaluation of the
gradient, and the final evaluation of the negative of the
second derivative matrix, that is, the negative of the Hessian.
sets the maximum allowable number of
iterations during the model estimation.
By default, MAXITER=50.
holds the intercept term fixed.
Because of the usual log transformation of the
response, the intercept parameter is usually a
scale parameter for the untransformed response, or
a location parameter for a transformed response.
requests that no log transformation
of the response variable be performed.
By default, PROC LIFEREG models the log of the response variable for the GAMMA,
LLOGISTIC, LOGNORMAL, and WEIBULL distribution options.
holds the scale parameter fixed.
Note that if the log transformation has been applied
to the response, the effect of the scale parameter
is a power transformation of the original response.
If no SCALE= value is specified, the
scale parameter is fixed at the value 1.
holds the first shape parameter, SHAPE1, fixed.
If no SHAPE= value is specified, SHAPE1 is fixed
at a value that depends on the DISTRIBUTION type.
initializes the scale parameter to value.
If the Weibull distribution is specified, this scale parameter
is the scale parameter of the type 1 extreme value
distribution, not the Weibull scale parameter.
Note that, with a log transformation, the
exponential model is the same as a Weibull model
with the scale parameter fixed at the value 1.
initializes the first shape parameter to value.
If the specified distribution does not depend on
this parameter, then this option has no effect.
The only distribution that depends on this shape parameter is
the generalized gamma distribution.
See the "Supported Distributions" section
for descriptions of
the parameterizations of the distributions.
sets the tolerance for testing singularity of
the information matrix and the crossproducts
matrix for the initial least-squares estimates.
Roughly, the test requires that a pivot be at least
this number times the original diagonal value.
By default, SINGULAR=1E-12.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.