# 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

3. Drag the cursor over the

4. Click on

5. Click on the "time" variable to highlight it.

6. Click on the

7. Click on the dichotomous categorical outcome variable to highlight it.

8. Click on the

9. Click on the

10. In the

11. Click

12. Click on any

13. Click on the

14. If researchers moved

15. Click on the categorical variable in the

16. Click on the

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

18. Click

19. Click on the

20. In the

21. Click

22. Click on the

23. Click on the

24. Click on a categorical variable in the

25. Click on the

26. Click

27. Click

2. Click

**.**__A__nalyze3. Drag the cursor over the

**drop-down menu.**__S__urvival4. Click on

**.**__C__ox Regression5. Click on the "time" variable to highlight it.

6. Click on the

**arrow**to move the variable into the**T**box.__i__me:7. Click on the dichotomous categorical outcome variable to highlight it.

8. Click on the

**arrow**to move the variable into the**Stat**box.__u__s:9. Click on the

**De**button.__f__ine Event10. In the

**box, enter the value or "**__S__ingle value:**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**Cov**box in the__a__riates:**Block 1 of 1**table.14. If researchers moved

**any categorical variables**into the**Cov**box, click on the__a__riates:**button.**__C__ategorical15. Click on the categorical variable in the

**box to highlight it.**__C__ovariates:16. Click on the

**arrow**to move the variable into the**Ca**box.__t__egorical Covariates: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

**button. Then click on the**__F__irst**C**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."__h__ange18. Click

**Continue**.19. Click on the

**button.**__O__ptions20. In the

**Model Statistics**table, click on the**box to select it.**__C__I for exp(B)21. Click

**Continue**.22. Click on the

**P**button.__l__ots23. Click on the

**box to select it.**__S__urvival24. Click on a categorical variable in the

**box to highlight it.**__C__ovariate Values Plotted at:25. Click on the

**arrow**to move the variable into the**Separate Lines**box.__f__or:26. Click

**Continue**.27. Click

**OK**.### The steps for interpreting the SPSS output for a Cox regression

1. In the

2. The

3. The

4. The values under the

5. Researchers will interpret the hazard ratio in the

If the confidence interval associated with the hazard ratio crosses over 1.0, then there is a non-significant association. The

If the hazard ratio is

If the hazard ratio if

If the variable is measured at the ordinal or continuous level, then the hazard ratio is interpreted as meaning

**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.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.## Hire A Statistician

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D., PStat** **will provide the following statistical consulting services for undergraduate and graduate students at $100/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics