interpretation of linear regression with confounders

[Kyra]

Hi,

I am running proc GLM and when I run it without confounders it is insignificant but after adding confounders it becomes significant. What does that mean?

Models and output pasted below. Exposure variable date has three categories.

proc glm data=red.clean16;
class date(ref='3') ;
model Hospital_Length_of_Stay =date;
run;

The GLM Procedure

Dependent Variable: Hospital_Length_of_Stay Hospital Length of Stay

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	2	139.79844	69.89922	1.77	0.1702
Error	876	34513.15947	39.39858
Corrected Total	878	34652.95791

R-Square	Coeff Var	Root MSE	Hospital_Length_of_Stay Mean
0.004034	87.43792	6.276829	7.178612

Source	DF	Type I SS	Mean Square	F Value	Pr > F
date	2	139.7984412	69.8992206	1.77	0.1702

Source	DF	Type III SS	Mean Square	F Value	Pr > F
date	2	139.7984412	69.8992206	1.77	0.1702

proc glm data=red.clean16;

class date(ref='3')   Gender steroiduse(ref='No') Wound_Classification _10__loss_of_body_weight_in_the_ Surgical_Wound_s__Closure  ;

model Hospital_Length_of_Stay =  Gender steroiduse Wound_Classification _10__loss_of_body_weight_in_the_ Surgical_Wound_s__Closure date  ;

run;

The GLM Procedure

Dependent Variable: Hospital_Length_of_Stay Hospital Length of Stay

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	10	1374.21056	137.42106	3.58	0.0001
Error	868	33278.74735	38.33957
Corrected Total	878	34652.95791

R-Square	Coeff Var	Root MSE	Hospital_Length_of_Stay Mean
0.039656	86.25477	6.191896	7.178612

Source	DF	Type I SS	Mean Square	F Value	Pr > F
Gender	1	24.6968228	24.6968228	0.64	0.4224
steroiduse	1	71.2541111	71.2541111	1.86	0.1732
Wound_Classification	3	608.3247122	202.7749041	5.29	0.0013
_10__loss_of_body_we	1	398.0304391	398.0304391	10.38	0.0013
Surgical_Wound_s__Cl	2	42.5667622	21.2833811	0.56	0.5742
date	2	229.3377091	114.6688546	2.99	0.0508

Source	DF	Type III SS	Mean Square	F Value	Pr > F
Gender	1	39.5736506	39.5736506	1.03	0.3099
steroiduse	1	27.0957154	27.0957154	0.71	0.4008
Wound_Classification	3	540.7447182	180.2482394	4.70	0.0029
_10__loss_of_body_we	1	442.3318647	442.3318647	11.54	0.0007
Surgical_Wound_s__Cl	2	32.1257351	16.0628676	0.42	0.6579
date	2	229.3377091	114.6688546	2.99	0.0508

[Reeza]

Just a friendly note, this is not logistic regression.

[Kyra]

sorry, linear regression!

[PaigeMiller]

---

@Kyra wrote:

Hi,

I am running proc GLM and when I run it without confounders it is insignificant but after adding confounders it becomes significant. What does that mean?

Models and output pasted below. Exposure variable date has three categories.

---

That's how regression works. It is seen by some people as a drawback when using regression that if you add in variables that are correlated with the original variable, the effect of the original variable changes from significant to not significant, or vice versa (sometimes even the sign of the regression coefficient changes). It is also seen as something that is non-intuitive.

Unfortunately, there really isn't a way around this using linear regression. Correlated predictor variables cause the model to become unstable (high variance of the coefficients). One potential solution that is much less affected by correlated predictor variables is Partial Least Squares (PROC PLS in SAS).

[Kyra]

Hi,

Is it statistically okay if i leave the analysis till univariate level saying the association was insignificant. and not getting into multivariable linear regression?

Thanks

[Reeza]

Your results show that length of stay is dependent on wound type and body weight loss, if I'm reading your variables correctly. Overall, if not considering the level there is no difference but if you consider the wound type and amount of weight loss you have different lengths of stays. That seems logically correct to me.
You should rename your variables so you don't have to type them out like that and so it's clear what you're working with.

[Kyra]

Hi,

For me outcome is length of stay, exposure is date( date variable is in three levels according to implementation of specifics treatment protocols in respective three time frames). All other variables are confounders.

How do i interpret in relation to date variable.

Thanks

[PaigeMiller]

---

@Kyra wrote:

Hi,

For me outcome is length of stay, exposure is date( date variable is in three levels according to implementation of specifics treatment protocols in respective three time frames). All other variables are confounders.

How do i interpret in relation to date variable.

Thanks

---

The combined effect of date and the other variables is statistically significant, and does predict. However, from your data, you cannot determine a unique effect (or contribution) of each of the variables.

[PGStats · Accepted solution]

The Model p-value tells you if your model explains something (i.e. reduces the error sum of squares more than by random association). It didn't with just time as a regressor, but it does when you add Wound_Classification and _10__loss_of_body_weight_in_the_ Surgical_Wound_s__Closure. So these two variables are important in explaining/predictng Hospital_Length_of_Stay.

[Kyra]

Thanks, I do understand this now.