## Should I consider the correlation when calculate Odds ratio and Relative Risk in Crossover design?

Frequent Contributor
Posts: 88

# Should I consider the correlation when calculate Odds ratio and Relative Risk in Crossover design?

[ Edited ]

Dear ALL,

Just a 2 by 2 crosser design with two treatments at each period;

Sequence 1: Period 1 --Treatment A; Period 2--Treatment B;

Sequence 2: Period 1 --Treatment B;  Period 2-- Treatment A;

Subject will be randomized to sequence 1 or 2;

Each sequence will have 5 subjects;

The variable we want to analyze is a Response binary variable ( with values 0 (No) or 1 (Yes));

The pupose is to check whether the response between two Treatments are same.

Perperty of this design: Each subject will be assessed two times (each for one treatment).

Result have below two cases:

Case I:

Treatment A: Response=Yes (10 subjects, i.e. all response to Yes for treatment A); Response=No (0 subjects);

Treatment B: Response=Yes (10 subjects, ie. all response to Yes for Treatment B as well); Response=NO (0 Subjects);

Per the posts I raised earlier, the odds ratio for this case is not defined as the cells under Response=0 for both treatments are 0;

Question: I can't calculate the relative risk under this case, right?

Case II:

Treatment A: Response=Yes (9 subjects, i.e. 9 response to Yes for treatment A); Response=No (1 subjects);

Treatment B: Response=Yes (9 subjects, ie. 9 response to Yes for Treatment B as well); Response=NO (1 Subjects);

Wired thing came out:

When I use below code with the consideration of each subject as stratum, both the odds ratio and relative risk can't be produced.

``````proc freq data=dar_s(where=(group=5));
tables drgdsc1a*swaevl2C;
run;

proc freq data=dar_s (where=(group=5)) order=data;
BY Group;
table SBJ1N*drgdsc1a*SWAEVL2C /alpha=0.1 cmh noprint;
output out=ODDS CMH;/*This table is used to calculate the p-value so as to make a commparison with the value produced from PROC LOGISTIC**/
run;``````

What is your suggestion? Should I not to consider the dependence?

Only use McNemar Test to assess whether the resposne results to two treatments are consistent and test whether the proportion between two treatment for Response=yes is equal?

Highly appreciated for your help .

Best,

JACK

Super User
Posts: 10,214

## Re: Should I consider the correlation when calculate Odds ratio and Relative Risk in Crossover desig

```"Question: I can't calculate the relative risk under this case, right?"
You can get that as long as it is 2x2 contingency table.
tables drgdsc1a*swaevl2C/relrisk(col=2) ;

If it was square table , why not use AGREE ?

tables drgdsc1a*swaevl2C/agree ;

```
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