The PHREG Procedure
- Overview
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Getting Started
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Syntax
PROC PHREG Statement ASSESS Statement BASELINE Statement BAYES Statement BY Statement CLASS Statement CONTRAST Statement EFFECT Statement ESTIMATE Statement FREQ Statement HAZARDRATIO Statement ID Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement OUTPUT Statement Programming Statements RANDOM Statement STRATA Statement SLICE Statement STORE Statement TEST Statement WEIGHT Statement
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Details
Failure Time Distribution Time and CLASS Variables Usage Partial Likelihood Function for the Cox Model Counting Process Style of Input Left-Truncation of Failure Times The Multiplicative Hazards Model The Frailty Model Hazard Ratios Specifics for Classical Analysis Specifics for Bayesian Analysis Computational Resources Input and Output Data Sets Displayed Output ODS Table Names ODS Graphics
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Examples
Stepwise Regression Best Subset Selection Modeling with Categorical Predictors Firth’s Correction for Monotone Likelihood Conditional Logistic Regression for m:n Matching Model Using Time-Dependent Explanatory Variables Time-Dependent Repeated Measurements of a Covariate Survivor Function Estimates for Specific Covariate Values Analysis of Residuals Analysis of Recurrent Events Data Analysis of Clustered Data Model Assessment Using Cumulative Sums of Martingale Residuals Bayesian Analysis of the Cox Model Bayesian Analysis of Piecewise Exponential Model
- References
| Failure Time Distribution |
Let 
be a nonnegative random variable representing the failure time of an individual from a homogeneous population. The survival distribution function (also known as the survivor function) of is written as
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A mathematically equivalent way of specifying the distribution of is through its hazard function. The hazard function 
specifies the instantaneous failure rate at 
. If is a continuous random variable, is expressed as
 |
where 
is the probability density function of . If is discrete with masses at 
, then survivor function is given by
 |
where 
=0 if 
< 0 and 
=1 otherwise. The discrete hazards are given by
 |