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The LIFEREG Procedure

MODEL Statement

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.

lower   upper   Comparison   Interpretation
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 flag takes 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.
Task   Option
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=
 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 tc = \frac{{g'}H^{-1}g}{| f|} 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.

By default, 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.

DISTRIBUTION= NOLOG specified? Resulting distribution
EXPONENTIALYesOne parameter extreme value
GAMMANoGeneralized gamma
GAMMAYesGeneralized gamma with untransformed responses
LOGISTICYesLogistic (NOLOG has no effect)
NORMALYesNormal (NOLOG has no effect)
WEIBULLYesExtreme value

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   Specification
list separated by blanks initial=3 4 5
list separated by commas initial=3,4,5
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" for details.
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.

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Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.