### SAS day 17: Proc Phreg

One day, my boss took a glance at a table with **Hazard Ratio** and **Median Survival Time** then he told me the program set the reference group in **Proc Phreg** flipped.

It turns out he was correct after validating the program. However, I was very curious about how did he figure it out by an Augenblick. Then he shared with us some knowledge about **Hazard Ratio** and **Proc Phreg**.

**Background knowledge**

*Hazard Rate*: Hazard Rate represents instantaneous risk at the given time for patients in one treatment group.

*Hazard Ratio*: the ratio between two **Hazard Rate**.

*Median Survival Time: *The time after which 50 percent of people with a particular condition are still living, and 50 percent have died.

**Median survival time and Hazard Rate
**

**if Median(A) > Median(B) then Hazard Rate(A) < Hazard Rate(B), vice versa.
**

Under the proportional hazards assumption, theoretically, if the median survival time of group A is significantly longer than group B, then the **Hazard Rate** of group A is smaller than Hazard Rate of group B at any given time, vice versa.

*Note: There were rare cases, this rule does not follow*

**Example **

Now we will demonstrate Proc Phreg with Hazard Ratio with **Sashelp.BMT** dataset.

Basic Proc Phreg Syntax

Proc phreg data=a; class x ; /*ref(x) only character value, the lowest character value is reference*/ model x*y= a/rl ; /*can input more than one variable on the RHS of the equation. rl:risk limit (eßt)*/ by z;/*optional*/ id m;/*optional*/ run;

- Read in the sashelp.BMT dataset and only consider AML Low Group and AML High Group

*Note: Hazard Ratio is usually designed for two-level comparison,*

*we will introduce*3-level*comparison next time.*

data aml; set sashelp.bmt; if group="AML-Low Risk" then ref="0"; if group="AML-High Risk" then ref="1"; if ref in("0","1"); run;

2. Apply Proc Phreg to generate the hazard ratio

proc phreg data=aml outest=est61 covout; class ref; model T*status(0)=ref/rl; run;

**Results:**

From the output, we have **Hazard Ratio=0.39**, which means the risk of death a patient in AML Low Group survives until today and will survive until tomorrow, compared with the AML High Group **Reduced by 0.61, (1-HR)*100%**.

Alternatively, we can say that in AML Low Group patients have a **156% (1/HR-1)*100% improvement** in the chance of surviving longer than AML High Patients.

**Validation:**

As we mentioned earlier, if Hazard Rate <1 then we expected a longer survival median time in AML Low Group. The following Kaplan Meier plot demonstrated the AML Low Group indeed has a larger survival median.

proc lifetest data=aml plots=survival; time T*status(0); strata Group; run;

Special thanks to Joe wang, not only sharing the Proc Phreg knowledge with us but also went over the Key points with me in a great level of details to make sure i truly understood the material. we will show the 3-level Hazard Ratio in Proc Phreg next time!

**Happy studying! 🐰**