When the TREND option is specified in the STRATA statement, PROC LIFETEST displays p-values for two-sided trend tests in the column labeled Pr > |z| in the Trend Tests table. Beginning in SAS 9.2, the lower one-sided p-value, Pr < z, and the upper one-sided p-value, Pr > z for ordered alternatives are also displayed.

The null hypothesis for these tests is H₀: S₁(t) = S₂(t) = ... = S_k(t), for all t ≤ τ where τ is some upper bound and k is the number of survival functions being compared.

There are two ordered alternative hypotheses for the trend test:

H₁: S₁(t) ≥ S₂(t) ≥ ... ≥ S_k(t)

H₂: S₁(t) ≤ S₂(t) ≤ ... ≤ S_k(t)

for all t ≤ τ and with at least one inequality in each hypothesis, as shown in "Computational Formulas: Trend Tests" in the Details section of the LIFETEST documentation.

If you are not sure which of the two ordered alternatives are to be considered then a two-sided test is appropriate. Collett (2003, pg. 53) illustrates reporting a two-sided p-value for the trend test.

Tests for the ordered alternatives (H₁ or H₂ above) are provided automatically by the TREND option beginning in SAS 9.2. Prior to that release, p-values for these tests can be computed as discussed below.

Upper one-sided test of the H₁ alternative

The p-value for this test is obtained using either of the following. A small p-value indicates significance and rejects the null in favor of this ordered alternative.

• In a subsequent DATA step, compute p_value = 1-PROBNORM(z); where z is the value in the "Test Statistic" column of the Trend Tests table,

  or

• Compute p-value = p/2 if z ≥ 0 or 1-(p/2) if z < 0, where p is the Pr > |z| two-sided p-value displayed in the Trend Tests table and z is as above.

Lower one-sided test of the H₂ alternative

The p-value for this test is obtained using either of the following. A small p-value indicates significance and rejects the null in favor of this ordered alternative.

• In a subsequent DATA step, compute p_value = PROBNORM(z); where z is the value in the "Test Statistic" column of the Trend Tests table,

  or

• Compute p-value = p/2 if z ≤ 0 or 1-(p/2) if z > 0, where p is the Pr > |z| two-sided p-value displayed in the Trend Tests table and z is as above.

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References

Collett (2003)

Klein and Moeschberger (2003)