# 5.5.2 COX Model Estimator

## Summary

The Cox Model Estimation ,also called the proportional hazard model is a classical semi-parameter method in survival analysis. A Cox model provides an estimate of the effect on survival for variables and the hazard of death for an individual. Using Cox regression analysis, we will obtain an equation for the hazard as a function of several variables. A positive regression coefficient for an explanatory variable means that the hazard is higher with higher values of that variable. while for negative regression coefficient for an explanatory variable, the hazard is lower with higher values of that variable.

The proportional hazards assumption: Observations should be independent, and the hazard ratio should be constant across time; that is, the proportionality of hazards from one case to another should not vary over time.

## What you will learn

This tutorial will show you how to:

• Perform COX Model Estimator
• How to interpreting the results

## Perform COX Model Estimator

1. Click the Import Single ASCII button to import phm_Cox.dat located in the \Samples \Statistics subfolder.
2. Select Statistics: Survival Analysis: Cox Model Estimator to open the dialog.
3. Put the A(X):month column into Time Range. Similarly, put the B(Y):status column into Censor Range.
4. Click the interactive data selection button and choose the Charlson and tKt_v column into the Covariate Range edit box.
5. Select 0 as the censoring value form censoring value(s) drop-down list.
6. check Survival and Hazard box in Survival Plots group.
7. Click the OK button to perform the Cox Model Estimator analysis.

## Interpreting the Results

Go to worksheet CoxPHM1 for the analysis report.

1. From the "Summary of event and censored values" table, we can see that censored =112 and percent Censored =0.8.
2. The following table displays the result of test whether the model is significant or not. Note that the null hypothesis is $\beta 1= \beta 2=0$. In this example, Pr > ChiSq =4E(-4) <0.05, therefore we reject the null hypothesis; that is, either $\beta 1$ or $\beta 2$, or both, $\neq 0$.
3. In the "Analysis of parameter Estimates" table, the coefficient estimate of variable charlson is 0.2876 and Pr > ChiSq =5E-4<0.05 , so $\beta1=0.287$ and charlson is a significant variable. The Hazard ratio can be interpreted as the predicted change in the hazard for a unit increase in the predictor. For variable charlson , Hazard ratio=1.333, meaning that the hazard becomes 1.333 times when charlson increments one unit. Similarly, tKt_v is a significant variable .The coefficient estimates of tKt_v $\beta2= -0.837$ and hazard ratio=0.433. We know the hazard function:h(t,x)=h0(t)*exp(0.2876*charlson-0.837*tKt_v).
4. The Survival function plot shows the proportion of individuals surviving at each hour and is a visual display of the model-predicted. The horizontal axis shows the time to event. The vertical axis shows the probability of survival.
5. The Hazard function plot displays the instantaneous probability of the given event occurring at any point in time.