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Displayed Output

For each stratum, the LIFETEST procedure displays

the values of the stratum variables, if you specify the STRATA statement.

The following items are displayed when you request product-limit estimates:

• the observed event or censored times
• the estimate of the survival function
• the estimate of the cumulative distribution function of the failure time
• the standard error estimate of the estimated survival function
• the number of event times that have been observed
• the number of event or censored times which remain to be observed
• the frequency of the observed event or censored times if you specify the FREQ statement
• the values of the ID variables if you specify the ID statement
• the sample quartiles of the survival times
• the estimated mean survival time
• the estimated standard error of the estimated mean

The following items are displayed when you request life table estimates:

• time intervals into which the failure and censored times are distributed; each interval is from the lower limit, up to but not including the upper limit. If the upper limit is infinity, the missing value is printed.
• the number of events that occur in the interval
• the number of censored observations that fall into the interval
• the effective sample size for the interval
• the estimate of conditional probability of events (failures) in the interval
• the standard error of the estimated conditional probability of events
• the estimate of the survival function at the beginning of the interval
• the estimate of the cumulative distribution function of the failure time at the beginning of the interval
• the standard error estimate of the estimated survival function
• the estimate of the median residual lifetime which is the amount of time elapsed before reducing the number of at-risk units to one-half. This is also known as the it median future lifetime in Johnson and Johnson (1980).
• the estimated standard error of the estimated median residual lifetime
• the density function estimated at the midpoint of the interval
• the standard error estimate of the estimated density
• the hazard rate estimated at the midpoint of the interval
• the standard error estimate of the estimated hazard

The following results, summarized over all strata, are displayed:

• a summary of the number of censored and event times
• a table of rank statistics for testing homogeneity over strata. For each stratum, the log rank statistic can be interpreted as the difference between the observed number of failures and the expected numbers of failures under the null hypothesis of identical survival function.
• the covariance matrix for the log rank statistics for testing homogeneity over strata
• the covariance matrix for the Wilcoxon statistics for testing homogeneity over strata
• the approximate chi-square statistic for the log rank test, computed as a quadratic form of the log rank statistics (see Computational Formulas)
• the approximate chi-square statistic for the Wilcoxon test
• the likelihood ratio test for homogeneity over strata based on the exponential distribution

You can generate plots for

• the estimated SURVIVAL FUNCTION against FAILURE TIME
• the -log(estimated SURVIVAL FUNCTION) against FAILURE TIME
• the log(-log(estimated SURVIVAL FUNCTION)) against log(FAILURE TIME)
• censored observations for each stratum if the product-limit estimation method was used.

If you request the life table estimation method, you can also generate plots for the estimated HAZARD against FAILURE TIME and the estimated DENSITY against FAILURE TIME.

If you specify the TEST statement, the following statistics are printed:

• the univariate Wilcoxon statistics
• the standard deviations of the Wilcoxon statistics
• the corresponding approximate chi-square statistics
• the approximate probability values of the univariate chi-square statistics
• the covariance matrix for the Wilcoxon statistics
• the sequence of partial chi-square statistics for the Wilcoxon test in the order of the greatest increase to the overall test statistic
• the approximate probability values of the partial chi-square statistics
• the chi-square increments for including the given covariate
• the probability values of the chi-square increments. See Computational Formulas earlier in this chapter for a warning concerning these probabilities.
• the univariate log rank statistics
• the standard deviations of the log rank statistics
• the corresponding approximate chi-square statistics
• the approximate probability values of the univariate chi-square statistics
• the covariance matrix for the log rank statistics
• the sequence of partial chi-square statistics for the log rank test in the order of the greatest increase to the overall test statistic
• the approximate probability values of the partial chi-square statistics
• the chi-square increments for including the given covariate
• the probability values of the chi-square increments. See Computational Formulas earlier in this chapter for a warning concerning these probabilities

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