topic Puzzled: Hazard ratio is 0 when both arms have events in SAS Procedures

Puzzled: Hazard ratio is 0 when both arms have events

fengyuwuzu — Fri, 22 Sep 2023 16:48:12 GMT

I recently encountered a problem that the HR = 0 when both arms have events. One arm has 7 subjects with 2 events, and the other arm has 8 subjects with 3 events. How come HR is 0 from Proc PHREG?

I have posted my data and code below. Can anyone give me some clue how this happens?

Thank you!

data test;
input ID $ cnsr arm aval;
datalines;
01 0 2 2.9
01 1 1 0
03 0 1 14
04 1 2 0
05 0 1 9.6
06 1 2 5.6
07 0 2 1.1
08 1 1 0
09 0 2 2.8
10 1 2 3
11 1 2 0
12 1 1 0
13 1 1 8.5
14 1 2 0
15 1 1 0
;
run;
ods output ParameterEstimates = hazard; 
proc phreg data = test; 
class arm (ref="2"); 
model aval * cnsr(1) = arm / ties=breslow risklimits alpha=0.05 ; 
Run;

ods output quartiles=quartiles homtests=homtests_unstrat; 
proc lifetest data=test plots=survival method=km; 
time aval*cnsr(1); 
strata arm; 
run;

Re: Puzzled: Hazard ratio is 0 when both arms have events

FreelanceReinh — Fri, 22 Sep 2023 20:07:20 GMT

Hello @fengyuwuzu,

Thank you for posting complete code including usable sample data.

Note that the hazard ratio is not exactly zero. If you print your ODS output dataset HAZARD with more decimals,

proc print data=hazard;
format _numeric_ best16.;
run;

you'll see that both ChiSq and HazardRatio are small, but positive. The natural logarithm of the hazard ratio is the Estimate, which is -17.991..., and exp(-17.991...)=1.536...E-8. Without having checked more details I'd say that a very small hazard ratio of arm 1 vs. arm 2 is plausible, given that all uncensored patients in arm 1 were still "alive" after* all patients in arm 2 had "died" or had been censored -- a quite extreme situation. As soon as there is some overlap, e.g., change AVAL=14 of ID '03' to 5, the hazard ratio steps up (to 0.283).

* (of course not necessarily "after" in calendar time)

Re: Puzzled: Hazard ratio is 0 when both arms have events

fengyuwuzu — Fri, 22 Sep 2023 18:22:26 GMT

Thank you so much for the explanation. It makes sense.