Biases. Confounding Bias: Definition. OUTLINE Review Confounding bias Multiple linear regression In-class questions

Transcription

1 OUTLINE Review Confounding bias Multiple linear regression In-class questions Biases Selection bias Information bias Confounding bias Bias is an error in an epidemiologic study that results in an incorrect estimation of the association between exposure and outcome. Confounding Bias: Definition Is present when the association between an exposure and an outcome is distorted by an extraneous third variable (referred to a confounding variable).

2 Confounding Bias: Example Example : Study the association between coffee drinking and lung cancer LC Yes No Yes 80 5 No Coffee OR= (80x 85)/ (5 x 20)= 22 What would you conclude???? Confounding Bias: Minimize bias Research Design: Use of randomized clinical trial Restriction Data Analysis: Multivariate statistical techniques Bivariate Analysis Variable 2 LEVELS >2 LEVELS CONTINUOUS Variable 2 2 LEVELS X 2 chi square test >2 LEVELS X 2 chi square test CONTINUOUS T-test X 2 chi square test X 2 chi square test ANOVA (F-test) t-test ANOVA (F-test) -Correlation -Simple linear Regression

3 Multivariate analyses Logistic Regression (If outcome is 2 levels) Multiple Linear Regression (If outcome is continuous) Multivariate Analysis is used for adjusting for confounding variables. Multivariate Analysis WHY? To investigate the effect of more than one independent variable. Predict the outcome using various independent variables. Adjust for confounding variables Multivariate analyses Logistic Regression (If outcome is 2 levels) Multiple Linear Regression (If outcome is continuous)

4 Multiple Linear Regression: Ex Example : Research question: Does height and gender help to predict weight using a straight line model? SPSS Output: Summary R R Square R Square the Estimate.74 a a. Predictors: (Constant), gender, height a Unstandardized Standardized B Std. Error Beta t Sig. (Constant) height gender a. Dependent Variable: weight Multiple Linear Regression: Ex BEFORE Does height help to predict weight? Summary R R Square R Square the Estimate.65 a a. Predictors: (Constant), height Using a straight line model, Height is able to explain 42.4% of the variation in the observed weight. NOW Does height & gender help to predict weight? Summary R R Square R Square the Estimate.74 a a. Predictors: (Constant), gender, height Using a straight line model, height & gender are able to explain 54.8% of the observed variation in weight. Multiple Linear Regression: Ex Simple Linear Regression 42.4% Multiple Linear Regression 54.8% Variation in Weight Height Variation in Weight Height & Gender

5 Multiple Linear Regression: Ex a Unstandardized Standardized B Std. Error Beta t Sig. (Constant) height gender a. Dependent Variable: weight Weight = B 0 + B Height + B 2 Gender Weight = Height Gender Multiple Linear Regression: Ex Interpretation of the coefficients for Height and Gender Weight = Height Gender means: As Height increases by one unit the weight increases by Kg while adjusting for the gender of the study participants means: As gender increases by one unit the weight decreases by Kg while adjusting for the height of the participants. Does it make sense?? Multiple Linear Regression: Ex Interpretation of the coefficients for Height and Gender Weight = Height Gender Gender is coded in the SPSS database: = Male 2 = Female Therefore, Increasing gender by unit means that you are choosing the female gender!

6 Multiple Linear Regression: Ex HEIGHT Increase by unit cm Increase cm SEX Increase by unit Selecting females - Male 2- Female Multiple Linear Regression: Ex Interpretation of the coefficients for Height and Gender Weight = Height Gender means: As Height increases by one unit the weight increases by Kg while adjusting for the gender of the study participants means: Being a female decreases the weight by Kg while adjusting for the height of the participants. Example 2: SPSS Output: Summary R R Square R Square the Estimate.452 a a. Predictors: (Constant), Surgical intervention, ISS - injury severity measure Surgery is coded as: 0= No surgery = Surgery a Unstandardized Standardized B Std. Error Beta t Sig. (Constant) ISS - injury severity measure Surgical intervention a. Dependent Variable: Length of hospital stay

7 Summary R R Square R Square the Estimate.452 a a. Predictors: (Constant), Surgical intervention, ISS - injury severity measure The straight line model (including ISS and surgery) is able to explain 20.4% of the variation in the observed length of hospital stay values SPSS Output: a Unstandardized Standardized (Constant) ISS - injury severity measure Surgical intervention B Std. Error Beta t Sig a. Dependent Variable: Length of hospital stay LOS = ISS +.55 surgery Interpretation of the coefficients for ISS & Surgery LOS = ISS +.55 surgery means: As ISS increases by one unit the LOS increases by days while adjusting for whether the patient had a surgery performed or not..55means: patients who had a surgery spend.55 more days at the hospital than those who do not have a surgery while adjusting for the ISS.

8 Inference Does ISS score significantly help to predict length of hospital stay (LOS) after adjusting for surgical intervention? LOS= B 0 + B ISS + B 2 surgery a (Constant) ISS - injury severity measure Surgical intervention Unstandardized Standardized B Std. Error Beta t Sig a. Dependent Variable: Length of hospital stay LOS = ISS +.55 surgery H 0 : B ISS =0 while adjusting for surgery H a : B ISS 0 while adjusting for surgery Because the p value of the beta for the variable ISS is <0.05 then reject the null hypothesis and conclude that the ISS is significantly associated with length of hospital stay, while adjusting for surgical intervention. Inference Does surgical intervention help to predict length of hospital stay (LOS) after adjusting for ISS? LOS= B 0 + B ISS + B 2 surgery

9 a Unstandardized Standardized B Std. Error Beta t Sig. (Constant) ISS - injury severity measure Surgical intervention a. Dependent Variable: Length of hospital stay LOS = ISS +.55 surgery H 0 : B surg =0 while adjusting for ISS H a : B surg 0 while adjusting for ISS Because the p value of the beta for the variable surgery is >0.05 then do not reject the null hypothesis and conclude that surgical intervention is not significantly associated with length of hospital stay, while adjusting for ISS SPSS commands SLR Analyze Regression Linear LOS for dependent ISS for independent Statistics Select confidence interval for regression coefficients SPSS commands MLR Analyze Regression Linear LOS for dependent ISS for independent Surgical intervention for independent Statistics Select confidence interval for regression coefficients