Cox regression
Multivariate comparison of groups on the temporal aspects of a dichotomous categorical outcome
Cox regression is the most powerful type of survival or time-to-event analysis. Cox regression is the multivariate extension of the bivariate Kaplan-Meier curve and allows for the association between a primary predictor and dichotomous categorical outcome variable to be controlled for by various demographic, prognostic, clinical, or confounding variables. Cox regression generates hazard ratios, which are interpreted the same as odds ratios with 95% confidence intervals.
The figure below depicts the use of Cox regression. Independent groups are being compared on the time it takes for an outcome to occur when controlling for clinical, confounding, and demographic variables. Cox regression is a multivariate survival analysis test that yields hazard ratios with 95% confidence intervals.
The steps for conducting a Cox regression in SPSS
1. The data is entered in a multivariate fashion.
2. Click Analyze.
3. Drag the cursor over the Survival drop-down menu.
4. Click on Cox Regression.
5. Click on the "time" variable to highlight it.
6. Click on the arrow to move the variable into the Time: box.
7. Click on the dichotomous categorical outcome variable to highlight it.
8. Click on the arrow to move the variable into the Status: box.
9. Click on the Define Event button.
10. In the Single value: box, enter the value or "level" of the dichotomous categorical outcome variable that denotes the event has occurred. Example: "1"
11. Click Continue.
12. Click on any demographic, predictor, or confounding variables that are to be included in the model to highlight them.
13. Click on the arrow to move them into the Covariates: box in the Block 1 of 1 table.
14. If researchers moved any categorical variables into the Covariates: box, click on the Categorical button.
15. Click on the categorical variable in the Covariates: box to highlight it.
16. Click on the arrow to move the variable into the Categorical Covariates: box.
17. Here is where researchers set the reference category for interpreting the statistical results. Most times it is just easier to set the reference category to the other level of the outcome that denotes the event has NOT occurred. So, when researchers do this, they can say that the predictor or exposure is so many times more or less likely to cause the event versus not cause the event. Click on the First button. Then click on the Change button to use the lowest level of the categorical variable as the reference category. Always codify NOT having a characteristic or outcome or reference category as "0."
18. Click Continue.
19. Click on the Options button.
20. In the Model Statistics table, click on the CI for exp(B) box to select it.
21. Click Continue.
22. Click on the Plots button.
23. Click on the Survival box to select it.
24. Click on a categorical variable in the Covariate Values Plotted at: box to highlight it.
25. Click on the arrow to move the variable into the Separate Lines for: box.
26. Click Continue.
27. Click OK.
2. Click Analyze.
3. Drag the cursor over the Survival drop-down menu.
4. Click on Cox Regression.
5. Click on the "time" variable to highlight it.
6. Click on the arrow to move the variable into the Time: box.
7. Click on the dichotomous categorical outcome variable to highlight it.
8. Click on the arrow to move the variable into the Status: box.
9. Click on the Define Event button.
10. In the Single value: box, enter the value or "level" of the dichotomous categorical outcome variable that denotes the event has occurred. Example: "1"
11. Click Continue.
12. Click on any demographic, predictor, or confounding variables that are to be included in the model to highlight them.
13. Click on the arrow to move them into the Covariates: box in the Block 1 of 1 table.
14. If researchers moved any categorical variables into the Covariates: box, click on the Categorical button.
15. Click on the categorical variable in the Covariates: box to highlight it.
16. Click on the arrow to move the variable into the Categorical Covariates: box.
17. Here is where researchers set the reference category for interpreting the statistical results. Most times it is just easier to set the reference category to the other level of the outcome that denotes the event has NOT occurred. So, when researchers do this, they can say that the predictor or exposure is so many times more or less likely to cause the event versus not cause the event. Click on the First button. Then click on the Change button to use the lowest level of the categorical variable as the reference category. Always codify NOT having a characteristic or outcome or reference category as "0."
18. Click Continue.
19. Click on the Options button.
20. In the Model Statistics table, click on the CI for exp(B) box to select it.
21. Click Continue.
22. Click on the Plots button.
23. Click on the Survival box to select it.
24. Click on a categorical variable in the Covariate Values Plotted at: box to highlight it.
25. Click on the arrow to move the variable into the Separate Lines for: box.
26. Click Continue.
27. Click OK.
The steps for interpreting the SPSS output for a Cox regression
1. In the Variables in the Equation table, look at the Sig. column, the Exp(B) column, and the two values under 95.0% CI for Exp(B) column heading.
2. The Sig. column shows the p-value associated with that variable in the model.
3. The Exp(B) column shows the hazard ratio associated with that variable in the model.
4. The values under the 95.0% CI for Exp(B) are the lower and upper limits of the confidence interval for the hazard ratio.
5. Researchers will interpret the hazard ratio in the Exp(B) column and the confidence interval.
If the confidence interval associated with the hazard ratio crosses over 1.0, then there is a non-significant association. The p-value associated with these variables will also be HIGHER than .05.
If the hazard ratio is ABOVE 1.0 and the confidence interval is entirely above 1.0, then exposure to the predictor increases the risk of the outcome.
If the hazard ratio if BELOW 1.0 and the confidence interval is entirely below 1.0, then exposure to the predictor decreases the risk of the outcome.
If the variable is measured at the ordinal or continuous level, then the hazard ratio is interpreted as meaning for every one unit increase in the ordinal or continuous variable, the risk of the outcome increases at the rate specified in the hazard ratio.
2. The Sig. column shows the p-value associated with that variable in the model.
3. The Exp(B) column shows the hazard ratio associated with that variable in the model.
4. The values under the 95.0% CI for Exp(B) are the lower and upper limits of the confidence interval for the hazard ratio.
5. Researchers will interpret the hazard ratio in the Exp(B) column and the confidence interval.
If the confidence interval associated with the hazard ratio crosses over 1.0, then there is a non-significant association. The p-value associated with these variables will also be HIGHER than .05.
If the hazard ratio is ABOVE 1.0 and the confidence interval is entirely above 1.0, then exposure to the predictor increases the risk of the outcome.
If the hazard ratio if BELOW 1.0 and the confidence interval is entirely below 1.0, then exposure to the predictor decreases the risk of the outcome.
If the variable is measured at the ordinal or continuous level, then the hazard ratio is interpreted as meaning for every one unit increase in the ordinal or continuous variable, the risk of the outcome increases at the rate specified in the hazard ratio.
Click on the Download Database and Download Data Dictionary buttons for a configured database and data dictionary for Cox Regression. Click on the Validation of Statistical Findings button to learn more about bootstrap, split-group, and jack-knife validation methods.
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