amsterdam rehabilitation research center | reade multiple regression analysis analysis of...

Amsterdam Rehabilitation Research Center | Reade

Multiple regression analysisAnalysis of confounding and effectmodificationMartin van de Esch, PhD


Literature

Fletcher & Fletcher (2005) Ch. 1, 2Guyatt et al (2008) Ch. A5, B9.1Andy Field Ch. 5 (143-217)

http://www.youtube.com/watch?v=TwwyyA3wIdw


Content

Checking assumptions (confounding and effect modification)


Definitions

Bias: A systematic error in the design, recruitment, data collection or analysis that results in a mistaken estimation of the true effect of the exposure and the outcome

Confounding: A situation in which the effect or association between an exposure and outcome is distorted by the presence of another variable. Positive confounding (when the observed association is biased away from the null) and negative confounding (when the observed association is biased toward the null) both occur

Effect modification : a variable that differentially (positively and negatively) modifies the observed effect of a risk factor on disease status. Different groups have different risk estimates when effect modification is present


Introduction

“Error” in research:•E

ffectmodification (interaction)•T

he combined effect of two or more independent variables on an outcome variable

•Confounding

•Influence on the association between determinant and outcome variable by an independant variable related to the determinant and the outcome variable

Amsterdam Rehabilitation Research Center | Reade6

Confounding

determinant(exposure)

confounder

outcome

Association (causal, marker), also in non-exposedAssociatio

n

Association

of our interest

Amsterdam Rehabilitation Research Center | Reade7

Effect modification

determinant(exposure)

Effect modifier

outcome

Association (causal, marker), also in non-exposed1

3

2Association

Association

of our interest


Three conditions for being a confounder of the association between determinant and outcome variable

Appearens of larynx cancer

Alcohol intake(determinant, expositionfactor)

Smoking(confounder, independent factor)

Positive association

Positive association

together

1

2 3

1 = independent determinant2 = association present3 = no causal relationship

Amsterdam Rehabilitation Research Center | Reademuscle strength Nm/kg

2,52,01,51,0,50,0

wa

lk-t

ime

(1

00

m)

se

c.

220

200

180

160

140

120

100

80

60

40

proprioception

poor

accurate

walktime100m (s)

Muscle strength (Nm/kg)

ProprioceptionO poor

▲ accurate

9

Muscle strengh, activity limitation and proprioception


Table 2. Results of the regression of functional ability (walking-time, GUG-time‡ and WOMAC-PF) on muscle strength and joint proprioception.

Walking- time GUG WOMAC-PF

Variables** b* (SE)† p-value

b* (SE)† p-value

b* (SE)† p-value

Intercept 91.73 11.91 29.19

Muscle strength -68.13 (8.90)

.000 -13.99 (1.70)

.000 -18.23 (4.37)

.000

Proprioception -1.56 (1.27)

.225 -0.513 (0.24)

.039 0.01 (0.62) .987

Muscle strength *

Proprioception-11.61(3.10)

.000 -3.05 (0.59)

.000 -0.94 (1.51)

.534

R2 =0.54 F=23.23 p<.001

R2 =0.57 F=25.76 p<.001

R2 =0.30 F=8.81 p<.001

•b = unstandardized regression coefficient•** Variables centered around the mean† SE = Standard Error of the Estimate‡ GUG = Get Up and Go test


Biomechanical model of activity limitations

Dekker et al 2013


Effectmodification and confounding with a crosstab


Example

Case-control study: assocation between alcohol-use and myocard infarction

OR = (71 48) / (52 29) = 2.26 (=‘ruwe OR’)

MI control total

alcohol 71 52 123

No alcohol 29 48 77

Total 100 100 200


95% CI of crude OR

95%-CI of OR:•E

XP(LN(2.26) ± 1.96 (1/71+1/52+1/29+1/48)) indicating 1.3 tot 4.1

Question: Is smoking an effectmodificator of the association between alcohol intake and MI?

Is the association between alcohol intake and MI different between smokers and non-smokers?


Example: effectmodification (interaction)

How to test?Stratification on variable smoking

Non-smoker smoker

MI control MI control

alcohol 8 17 63 35

no alcohol 22 44 7 4

total 30 61 70 39


Example: effectmodification

OR non-smoker = (8 44) / (17 22) = 0.94 95% CI = (0.4 - 2.5)

OR smoker = (63 4) / (35 7) = 1.03 95 % CI = (0.3 - 3.8)

No interaction, because OR1 OR2


Confounding

Question: Is smoking a confounder of the association between alcohol-intake and MI?

Is the effect of alcohol on MI (partly) caused (explained) by smoking?

How to testComparison between the crude association with the

corrected (pooled) association


Condition for confounding

Smoking is associated with alcoholSmoking is associated with MIOR for stata of the suspected confounder

Non smoker smoker


alcohol 8 17 63 35

No alcohol 22 44 7 4

total 30 61 70 39


How do we calculate the pooled association?

According to the Mantel-Haenszel method:Notation:

Stratum i Cases Non-cases Total

Exposure + ai bi m1i

Exposure - ci di m2i

Total n1i n2i ti


Mantel-Haenszel OR

Mantel-Haenszel Odds Ratio

i

ii

i

ii

MH

tc

b

td

a

OR


Example confounding

In our example:

ORMI = 0.97

1097

359122

17

1094

639144

8

MIOR


Example confounding

Summary

ORcrude = 2.26ORpooled= 0.97

Confounding, beacuse ORcrude ORpooled

We present the pooled ORAlmost 100(1-a)%-CI for ORMI (don’t remember the formula). In

the example:ORMI = 0.97 (0.4 - 2.1)


Summary effectmodification and confounding

•Effectmodification (interaction)

•The combined effect of two or more independent predictor variables on an outcome variable.

•Confounding

•Influence on the association between determinant and outcome variable by an independant variable related to the determinant and the outcome variable

Conclusion: there is no average association, crude association is not present for an individual subject within the study population.

In publication: present two associations (one OR for smokers and one OR for non-smokers)


Summary effectmodification and confounding

Confounding: The association between determinant and outcome is influenced, moderated by a third variable Confounder is related to determinant and outcome.

Non smoker smoker MI control MI control alcohol 8 17 63 35 non alcohol

22 44 7 4

total 30 61 70 39


summary effectmodification and confounding

Compare crude assocoation with corrected associationWhen these is a difference (>10%): confounding is assumed!


Example 2

Question: Is gender an interactor (moderator) of the association between alcohol inake and MI?

Is there a difference between male and female in the assocation between alcohol intake and MI?

male female


alcohol 38 34 33 18

No alcohol 20 43 9 5

total 58 77 42 23


Example 2

OR male = (38 43) / (34 20) = 2.40

95 % BI: (1.2 - 4.9)

OR female = (33 5) / (18 9) = 1.0295% BI: (0.3 - 3.5)

Modification because OR1 OR2Presentation of stratum specific OR's:“The" OR does not exist


Example 2

Question: is gender a confounder?


Summary examples

Smoking is a confounder which can be corrected by stratified analyses

Gender is an effect modificator (moderator): modification will be studied and the influence of the interactor will be presented in each stratum


Stratified analyses

Confounding and modification can be studied by splitting the data into strata: stratified analyses

Aim stratified analyses:

1. increasing “feeling” with data

2. studying effect modification

3. Reduction of confounding


General procedure

1. Calculation of "crude" association and ratio’s (OR/RR/RV)

2. Stratify always for one variable and calculate the specific measure

3. Compare the measure of each stratum with each other: Strong differences – moderationNo differences – no moderation


4. calculate the total/ composite measurecompare crude and composite measures

- When "crude" measure composite measure: no confoundingPresent "crude" measure and CI

- When "crude" measure composite measure: Confounding and present the composite measure + CI


"Beyond stratified analysis”

In case of more then one potential confounder or interactor; what to do?

Multipele regression analysis


Variables in the Equation

,767 ,326 5,529 1 ,019 2,154

-1,386 ,250 30,748 1 ,000 ,250

GROEP

Constant

Step1

a

B S.E. Wald df Sig. Exp(B)

Variable(s) entered on step 1: GROEP.a.


,531 ,340 2,442 1 ,118 1,701

-1,168 ,396 8,695 1 ,003 ,311

-,904 ,287 9,922 1 ,002 ,405

GROEP

LEEFTIJD

Constant

Step1

a


Variable(s) entered on step 1: GROEP, LEEFTIJD.a.

Confounding in (logistic) regression analysis


Confounding in case of (logistic) regression analysis

In regression analyses more than one confounder is possible: how to act?

•Step wise or other ways of input in the regression model: depending on type of analysis (association or prediction)

•Type of analysis is based on the hypothesis



,442 ,388 1,295 1 ,255 1,556

-1,350 ,563 5,740 1 ,017 ,259

,369 ,789 ,219 1 ,640 1,446

-,847 ,309 7,538 1 ,006 ,429

GROEP

LEEFTIJD

INTERACT

Constant

Step1

a


Variable(s) entered on step 1: GROEP, LEEFTIJD, INTERACT.a.

Effectmodification in case of logistic regression-analysis

Interact= group x age

Group is dichotomized or ordinal


Confounding in regression analysis

Confounding: adding a variable to the regression model – does B coefficient change with > 10%?

Statistical approach •

confoundes are known from literature, from correlation analses or confounder analyses


Confounding in regression analysis

•Present the model without and with confounders


Effectmodification and regression-analysis

Effect modification: adding the interaction variable to the regression model

Is the addition of the interaction significant? In the presence of a significant interaction: present

crude model and model with interaction. Explain what the interaction means (use graphs)


Coefficientsa

-7,200 ,550 -13,084 ,000

-2,800 ,778 -,248 -3,598 ,000

(Constant)

groep

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: VERSCHILa.

Coefficientsa

-6,300 1,292 -4,877 ,000

-2,800 ,779 -,248 -3,594 ,000

-,600 ,779 -,053 -,770 ,442

(Constant)

groep

geslacht

Model1

B Std. Error


Beta


t Sig.


Example: confounding by linear regression analysis


Coefficientsa

-10,200 1,696 -6,013 ,000

5,000 2,399 ,442 2,084 ,038

2,000 1,073 ,177 1,864 ,064

-5,200 1,517 -,763 -3,427 ,001

(Constant)

groep

geslacht

INTERACT

Model1

B Std. Error


Beta


t Sig.


Effecmodification by linear regression analysis: example


Questions?

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