Calcite | Level 5

## Proc phreg / p-value for interaction (non-time covariates) by comparing two models

Hello,

I'm trying to calculate a p-value for non-time covariates interaction by comparing two models.

At first, I calculated the hazard ratio using this code:

```PROC PHREG DATA=PCA4;
CLASS FACTOR4_RANK(REF='0') AGE_CAT(REF='1') A00_SEX_N(REF='1');
MODEL F_TIME_Y*DYSLIPI_D(0)= FACTOR4_RANK AGE_CAT A00_SEX_N / RISKLIMITS;
STRATA AGE_CAT;
RUN;```

And then, I tried to calculate a p-value for interaction in sex and independent variable by comparing two models.

```PROC PHREG DATA=PCA4;
CLASS AGE_CAT(REF='1') A00_SEX_N(REF='1');
MODEL F_TIME_Y*DYSLIPI_D(0)= FACTOR4 AGE_CAT A00_SEX_N / RISKLIMITS;
STRATA AGE_CAT;
RUN; /*-2LogL with covariates = 17410.810*/

PROC PHREG DATA=PCA4;
CLASS AGE_CAT(REF='1') A00_SEX_N(REF='1');
MODEL F_TIME_Y*DYSLIPI_D(0)= FACTOR4 AGE_CAT A00_SEX_N A00_SEX_N*FACTOR4 / RISKLIMITS;
STRATA AGE_CAT;
RUN; /*-2LogL with covariates =17407.791*/

DATA _NULL_;
DIFF=17410.810-17407.791;
p=1-PROBCHI(DIFF,1);
PUT p; /*p=0.082*/
run;```

At this point, I have 2 questions as below.

(In the syntax for calculating a hazard ratio(first attached), the independent variable was "FACTOR4_RANK" which was categorizing "FACTOR4" continuous variable into tertiles)

1) I just want to check by all of you whether this syntax has any statistical problem.

2) When I calculate a hazard ratio, I used a categorical variable as an independent variable ("FACTOR4_RANK"),

but when I calculate a p-value for sex interaction with the independent variable, I used a continuous variable as an independent variable and interaction term ("FACTOR4" and "A00_SEX_N*FACTOR4").
My question is that if I used a categorical variable("FACTOR4_RANK") as an independent variable to find a hazard ratio,

should I use a categorical variable("FACTOR4_RANK") as an independent variable and interaction term in the syntax for calculating a p-value for interaction in the same way?

Or is there no statistical problem if I use the continuous variable("FACTOR4") to get a p-value for interaction and the categorical variable("FACTOR4_RANK") to get a hazard ratio?

Perhaps I lack the concept of finding the interaction between covariates(non-time dependent) and independent variables.

Thanks for your guidance.

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