# Help with Binary logistics regression

#### victor horen

##### New Member

Trying to assess tumour size and response to treatment.
hypothesis is smaller tumours better response

Coding
TMR20 size less than 20 mm = "1"
TMR30 size less than 30 mm = "1"
TMR40 size less than 40 mm = "1"
RP2 , response where good = "1"

Why is it that when I run a binary logistic regression on each tumour size category, the test is not significant but when i cluster all three together, the TMR40 category becomes significant?

Variables in the Equation
B S.E. Wald df Sig. Exp(B) Lower Upper
Step 1a TMR40 .611 .435 1.973 1 .160 1.842 .785 4.320
Constant -.457 .293 2.427 1 .119 .633
a Variable(s) entered on step 1: TMR40.

Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B) Lower Upper
Step 1a TMR30(1) .288 .517 .310 1 .578 1.333 .484 3.673
Constant -.405 .456 .789 1 .374 .667
a Variable(s) entered on step 1: TMR30.

Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B) Lower Upper
Step 1a TMR20 .847 .936 .819 1 .365 2.333 .373 14.613
TMR30(1) 1.620 .848 3.648 1 .056 5.056 .959 26.664
TMR40 1.230 .574 4.590 1 .032 3.421 1.110 10.539
Constant -2.077 .898 5.355 1 .021 .125
a Variable(s) entered on step 1: TMR20, TMR30, TMR40.

Results are also significant when i run a binary regression using tumour size as a continuous variable.

Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B) Lower Upper
Step 1a TMRSZE -.022 .009 5.699 1 .017 .978 .960 .996
Constant .919 .493 3.471 1 .062 2.507

Many thanks .

Stats noob. Victor

#### hlsmith

##### Omega Contributor
You lose information when using categorical data. I would make sure there is a linear relationship (general additive model) between tumor size and outcome, then use it as a continuous variable. You can the create custom comparisons on continuous values (10 unit increase in tumor size and increase in odds of outcome, etc.) in logistic reg. If doing any of these (continuous or multiple categories) you may need to consider correcting your alpha for familywise error.

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#### victor horen

##### New Member
Hey thanks for getting back.

Ic Ic
Yes when I ran it as a continuous variable it did return a significant result as noted above.
I just wonder how I should interpret that result in light of the significant test. I get it that the smaller the tumour the more likely we get a good outcome. would it be accurate to say the odds of having a good outcome is increased by 22% with decreasing tumour size?

Variables in the Equation
B S.E. Wald df Sig. Exp(B) 95% C.I.for EXP(B) Lower Upper
Step 1a TMRSZE -.022 .009 5.699 1 .017 .978 .960 .996
Constant .919 .493 3.471 1 .062 2.507

I take on board your suggestion of custom comparisons. Will need to look into how I go about doing this. for us as clinicians its more helpful if we can get a cut off value of how small a tumour may be in order to decide on which patients are worth treating.

#### hlsmith

##### Omega Contributor
If you have the right group coded for the outcome in the model, it says for a one unit increase in tumor size there is a 0.02 times decrease in the odds of the outcome.

What do you plan to do with your results?