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Purpose
This function
fits Cox's proportional hazards model for survival-time (time-to-event) outcomes
on one or more predictors.
Survival analysis refers to the analysis of elapsed time. The
response variable is the time between a time origin and an end point. The end
point is either the occurrence of the event of interest, referred to as a death
or failure, or the end of the subject’s participation in the study. These
elapsed times have two properties that invalidate standard statistical
techniques, such as t-tests, analysis of variance, and multiple regression.
First of all, the time values are often positively skewed. Standard statistical
techniques require that the data be normally distributed. Although this skewness
could be corrected with a transformation, it is easier to adopt a more realistic
data distribution.
The second problem with survival data is that part of the
data are censored. An observation is censored when the end point has not been
reached when the subject is removed from study. This may be because the study
ended before the subject’s response occurred, or because the subject withdrew
from active participation. This may be because the subject died for another
reason, because the subject moved, or because the subject quit following the
study protocol. All that is known is that the response of interest did not occur
while the subject was being studied.
Preparations
Run Statistics→Survival
Analysis→Cox Regression....
command.
Survival time
- variable containing the time to reach the event of interest, or
the time of follow-up.
Status (sometimes called "endpoint") - variable containing
codes 1 for the cases that reached the endpoint, or code 0 for the cases that
have not reached the endpoint, either because they withdrew from the study, or
the end of study was reached.
Independent variables - variables that you expect to
predict survival time. These must be continuous, or dichotomous, or ordered
categorical variables. The Cox proportional regression model assumes that the
effects
Results
Overall Model Fit
The Chi-square
statistic tests the relationship between time and all the covariates in the
model.
Coefficients and Standard Errors
Beta - this is the estimate of the regression
coefficient. Thus the quantity is the amount that the log of the hazard rate
changes when Xi is increased by one unit. Note that
a positive coefficient implies that as the value of the covariate is increased,
the hazard increases and the prognosis gets worse. A negative coefficient
indicates that as the variable is increased, the hazard decreases and the
prognosis gets better.
Standard Error - this is, the large-sample estimate of
the standard error of the regression coefficient. This is an estimate of the
precision of the regression coefficient. It is provided by the square root of
the corresponding diagonal element of the covariance matrix.
Risk Ratio
- Exp(Beta). This value is often called the risk ratio since it is the ratio of
two hazards whose only difference is that is increased by one unit.
Prob Level - This is the two-sided probability level.
This is the probability of obtaining a z-value larger in absolute value than the
one obtained. If this probability is less than the specified significance level
(say 0.05), the regression coefficient is significantly different from zero.
Baseline cumulative hazard function
Finally, the program lists the baseline cumulative hazard.
The baseline cumulative hazard can be used to calculate the survival probability
S(t) for any case at time t.
Graph
The graph displays the survival curves for all categories of
the categorical variable.
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