Interpretation of the Hazard Ratio For this example with a single predictor variable, we have h(t) = h0(t)exp(1u1). Let Then the hazard ratio (HR) is given as follows: The estimated HR is 4.52 for this example. This means that at any given time, a patient who is still alive in treatment group 2 is 4.52 times more likely to die in the next very small time interval than a patient who is still alive in treatment group 1. That is, the instantaneous relative risk of death for a person in treatment group 2 compared to a person in treatment group 1 is 4.52. Note that this does NOT imply that the probability of surviving for a given time t is 4.52 times larger for group 1! Discussion of Hypothesis Tests For testing the significance of a term in our Cox PH model we test the following hypotheses: j Ho: = 0 j Ha: ≠ 0 Wald test statistic: However if we square this statistics we obtain a chi-square statistic which can then be converted to a p-value. Likelihood ratio test statistic: JMP uses likelihood ratio tests ( for individual model effects. The details of this test are not important but the results will similar to the Wald tests above. JMP reports the test statistic and p-value for each effect in the model.
Interpretation of the Hazard Ratio For this example with a single predictor variable, we have h(t) = h0(t)exp(1u1). Let Then the hazard ratio (HR) is given as follows: The estimated HR is 4.52 for this example. This means that at any given time, a patient who is still alive in treatment group 2 is 4.52 times more likely to die in the next very small time interval than a patient who is still alive in treatment group 1. That is, the instantaneous relative risk of death for a person in treatment group 2 compared to a person in treatment group 1 is 4.52. Note that this does NOT imply that the probability of surviving for a given time t is 4.52 times larger for group 1! Discussion of Hypothesis Tests For testing the significance of a term in our Cox PH model we test the following hypotheses: Ho: j = 0 Ha: j ≠ 0 Wald test statistic: However if we square this statistics we obtain a chi-square statistic which can then be converted to a p-value. Likelihood ratio test statistic: JMP uses likelihood ratio tests ( for individual model effects. The details of this test are not important but the results will similar to the Wald tests above. JMP reports the test statistic and p-value for each effect in the model.
HO19%20D%20(Cox%20Model%201%20-%20F14).docx