Interpret the key results for Fit Cox Model in a Counting Process Form

Complete the following steps to interpret a Cox regression model in a counting process form. Key output includes the goodness-of-fit tests, the p-values, the relative risks, and graphical diagnostic tools.

In This Topic

Step 1: Determine how well the model fits your data
Step 2: Determine whether the association between the response and the term is statistically significant
Step 3: Determine the relative risks of the predictors
Step 4: Determine whether the model satisfies the proportional hazards assumption

Step 1: Determine how well the model fits your data

Use the goodness-of-fit tests to determine how well the model fits your data. The null hypothesis is that the model does not fit the data well. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the model fits the data well when it doesn't.

P-value ≤ α: The model fits the data well: If the p-value is less than or equal to the significance level, you can conclude that the model fits the data well. You should examine whether any of the terms are statistically significant and also ensure that the model satisfies the proportional hazards assumption.
P-value > α: There is not enough evidence to conclude that the model fits the data well: If the p-value is greater than the significance level, you cannot conclude that the model fits the data well. You may want to refit the model with different terms.

Goodness-of-Fit Tests

Test	DF	Chi-Square
Likelihood Ratio	4	29.39
Wald	4	32.47
Score	4	35.22

Key Results: P-Value

In these results, the p-values for all 3 tests are below 0.05, so you can conclude that the model fits the data well.

Step 2: Determine whether the association between the response and the term is statistically significant

To determine whether the association between the response and each term in the model is statistically significant, compare the p-value for the term to your significance level to assess the null hypothesis. The null hypothesis is that there is no association between the term and the response. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that an association exists when there is no actual association.

P-value ≤ α: The association is statistically significant: If the p-value is less than or equal to the significance level, you can conclude that there is a statistically significant association between the response variable and the term.
P-value > α: The association is not statistically significant: If the p-value is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. You may want to refit the model without the term.; If there are multiple predictors without a statistically significant association with the response, you can reduce the model by removing terms one at a time. For more information on removing terms from the model, go to Model reduction.

If a model term is statistically significant, the interpretation depends on the type of term. The interpretations are as follows:

If a categorical factor is significant, you can conclude the factor has an effect on the time to the event.
If a continuous predictor is significant, you can conclude that changes in the value of the predictor are associated with changes in the risk of the subject experiencing the event.
If an interaction term is significant, the relationship between a factor and the response depends on the levels of the other factors in the term. In this case, you should not interpret the main effects without considering the interaction effect.
If a polynomial term is significant, you can conclude that the data contain curvature.

Analysis of Variance

		Wald Test
Source	DF	Chi-Square	P-Value
Risk Category	2	9.77	0.008
Normal Platelets	1	9.13	0.003
Disease Stage	1	6.41	0.011

Key Results: P-Value

In these results, the p-value for Risk Category is significant at an α-level of 0.05. Therefore, you can conclude that the Risk Category has a statistically significant effect on the whether the patient is disease free. You can make the same conclusion about Normal Platelets and Disease Stage.

Step 3: Determine the relative risks of the predictors

Use the relative risk to assess the risk between different values of the predictor variables. Minitab displays a separate table of relative risks for categorical and continuous variables.

Categorical variable: In the Relative Risks for Categorical Predictors table, Minitab labels two levels of the categorical variable as Level A and Level B. The relative risk describes the occurrence rate of the event for level A relative to level B. For example, in the following results the risk of experiencing the event for patients with a High Risk for Disease Stage is 2 times higher than patients with a Disease Stage of Normal.
Continuous variable: In the Relative Risks for Continuous Predictors table, Minitab displays the unit of change and the relative risk. The relative risk describes the change in the hazard rate for every one unit of change in the predictor value. For example, if the relative risk is 1.02 for the variable age, a patient is 1.02 times more likely to experience the event for each increase of 1 year to their age.

You can use the confidence interval to determine whether the relative risk is statistically significant. Usually, if the confidence interval contains 1, you cannot conclude that the relative risk is statistically significant.

Relative Risks for Categorical Predictors

Level A	Level B	Relative Risk	95% CI
Risk Category
2	1	0.4524	(0.2409, 0.8495)
3	1	0.9673	(0.5116, 1.8290)
3	2	2.1383	(1.2487, 3.6616)
Normal Platelets
Yes	No	0.3666	(0.1912, 0.7029)
Disease Stage
Normal	High Risk	0.4986	(0.2909, 0.8547)

Key Results: Relative Risk, 95% CI

Step 4: Determine whether the model satisfies the proportional hazards assumption

Use the Tests for Proportional Hazards table, the Andersen plot, and the Arjas plot to determine whether the model meets the proportional hazards assumption. If the assumption is not met, the model may not fit the data well and you should use caution when you interpret the results.

Tests for Proportional Hazards table

Use the tests to determine whether the model meets the proportional hazards assumption. The null hypothesis is that the model meets the assumption for all the predictors. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that the model meets the assumption when it actually does not.

If the p-value is less than or equal to the significance level, you can conclude that the model does not meet the assumption of proportional hazards. If the p-value is greater than the significance level, you cannot conclude that the model does not meet the assumption.

Andersen plot

Use the Andersen plot to determine whether the model meets the proportional hazards assumption for different strata. Each combination of values of one or more stratification variables defines a stratum. The plot contains a curve for each stratum. If the model meets the assumption, the curves are straight lines through the point where X = 0 and Y = 0. If the baseline hazard rate for a stratum is the same as the baseline hazard rate for the stratum on the x-axis, then the curve follows the 45 degree reference line on the plot.

If the model does not meet the assumption, consider whether to divide the data by the stratification variable for which the model does not meet the proportional hazards assumption. Then perform a separate analysis on each subset of the data. The separate analyses provide different effects for the predictors in each subset.

Tests for Proportional Hazards

Term	DF	Correlation	Chi-Square	P-Value
Risk Category
2	1	0.0757	0.54	0.464
3	1	-0.1160	1.08	0.300
Normal Platelets
Yes	1	0.0296	0.09	0.769
Disease Stage
Normal	1	-0.1205	1.30	0.255
Overall	4	—	5.42	0.247

Key Results: P-value

In these results, the p-values for the test for proportional hazards are all greater than 0.05, so you cannot conclude that the model does not meet the proportional hazards assumption.