Lecture 4. Confounding

Transcription

1 Lecture 4 Confounding

2 Learning Objectives In this set of lectures we will: - Formally define confounding and give explicit examples of it s impact - Define adjustment and adjusted estimates conceptually - Begin a discussion of the analytics of adjustment 2

3 Section A Confounding: A Formal Definition, and Some Examples

4 Learning Objectives Formally define confounding Establish conditions which can results in the confounding of an outcome/exposure relationship Demonstrate the potential effects of confounding via examples 4

5 Confounding (Lurking Variable) Consider results from the following (fictitious) study: - This study was done to investigate the association between smoking and a certain disease in male and female adults smokers and 240 non-smokers were recruited for the study Results for All Subjects Smokers Non Smokers TOTALS Disease No Disease TOTALS RR ˆ pˆ pˆ smokers non smokers / OR ˆ p non pˆ (1- pˆ smokers smokers ) smokers (1 pˆ non smokers )

6 What s Going On? Smoking is protective against disease? Most of the smokers are male and non-smokers are female All Subjects Smokers Non Smokers TOTALS Male Female TOTALS

7 What s Going On? Smoking is protective against disease? Further, most of the persons with disease are female All Subjects Disease No Disease TOTALS Male Female TOTALS

8 What s Going On? A picture? Disease Smoking Sex 8

9 What s Going On? The comparison of disease risk between smokers and non-smokers is potentially distorted or negated by the disproportionate percentage of males among the smokers 9

10 What s Going On? The original outcome of interest is DISEASE The original exposure of interest is SMOKING In this sample, SEX is related to both the outcome and exposure - This relationship is possible impacting overall relationship between DISEASE and SMOKING How can we look at relationship between DISEASE and SMOKING removing any possible interference from SEX? - On approach look at DISEASE and SMOKING relationship separately for males and females 10

11 Example Is smoking related to disease in males? Results for MALES Smokers Non Smokers TOTALS Disease No Disease TOTALS RR ˆ males pˆ pˆ male smokers male non smokers / OR ˆ males p pˆ male smokers male non smokers (1- pˆ (1 pˆ male smokers ) male non smokers )

12 Example Is smoking related to disease in females? Results for FEMALES Smokers Non Smokers TOTALS Disease No Disease TOTALS RR ˆ females pˆ pˆ female smokers female non smokers / OR ˆ females p pˆ female smokers female non smokers (1- (1 pˆ pˆ female smokers ) female non smokers )

13 Smoking, Disease and Sex A recap - The overall (sometimes called crude, unadjusted) relationship (RR) between smoking and disease was nearly 1 (risk difference nearly 0) ˆ ˆ ˆ RR 0.93; psmokers - p non- smokers The sex specific results showed similar positive associations between smoking and disease MALES: FEMALES: RR ˆ RR ˆ 1.8; pˆ pˆ malesmokers - male non-smokers 1.5; pˆ pˆ femalesmokers - female non-smokers (note, for the moment we are not considering statistical significance, just using estimates to illustrate point) 13

14 Simpson s Paradox The nature of an association can change (and even reverse direction) or disappear when data from several groups are combined to form a single group An association between an exposure X and an outcome Y can be confounded by another lurking (hidden) variable Z (or variables Z 1, Z 2, ) 14

15 Confounding (Lurking Variable) A confounder Z (or set of confounders Z 1 Z p ) distorts the true relation between X and Y This can happen if Z is related both to X and to Y X Y Z 15

16 What s Going On? A picture Y X Z 16

17 What is the Solution for Confounding? If you DON T KNOW what the potential confounders are, there s not much you can do after the study is over - Randomization is the best protection - Randomization eliminates the potential links between the exposure of interest and potential confounders Z 1, Z 2,..Z 3 If you can t randomize but KNOW what the potential confounders are there are statistical methods to help control (adjust for confounders) - Potential confounders must be measured as part of study 17

18 Randomization Minimizes Threat of Confounding How/Why does randomization minimize the threat of confounding? 18

19 Example 2: Arm Circumference and Height An observational study to estimate association between arm circumference and height in Nepali children randomly selected subjects, ages [0, 12) months, had arm circumference, weight and height measured - This study is observational it is not possible to randomize subjects to height groups! 19

20 Example 2: Arm Circumference and Height The data - Arm circumference range: cm - Height range: cm - Weight range: kg 20

21 Example 2: Arm Circumference and Height Scatterplot: arm circumference by height Arm Circumference versus Height Nepalese Children < 12 Months (n 150) yˆ x R Height (cm) With Regression Line 21

22 Example 2: Arm Circumference and Height Notice, perhaps not surprisingly: Arm Circumference versus Weight Nepalese Children < 12 Months (n 150) Height (cm) Height versus Weight Nepalese Children < 12 Months (n 150) Weight (kg) Weight (kg) R R

23 Example 2: Arm Circumference and Height Scatterplot: arm circumference by height, after adjusting for weight Arm Circumference versus Height Nepalese Children < 12 Months (n 150) β ( height) ˆ Height (cm) 23

24 Example 3: South African Study A longitudinal study from South Africa: birth cohort, followed up five years after birth 1 : Participation by medical aid status at birth, all baseline participants Follow-Up Participation No Follow-Up Participation All Subjects Medical Aid No Medical Aid TOTAL ,164 TOTAL 241 1,349 1,590 RR ˆ follow-up pˆ p ˆ medical aid no medical aid /1, Morell C. Simpson's Paradox: An Example From a Longitudinal Study in South Africa. Journal of Statistical Education (1999) 24

25 Example 3: South African Study A longitudinal study from South Africa: birth cohort, followed up five years after birth : Participation by medical aid status at birth, Black participants Black Subjects Follow-Up Participation No Follow-Up Participation Medical Aid No Medical Aid TOTAL ,048 TOTAL 127 1,325 1,452 Rˆ R follow-up Black pˆ pˆ medical aid Black no medical aid Black /1,

26 Example 3: South African Study A longitudinal study from South Africa: birth cohort, followed up five years after birth : Participation by medical aid status at birth, White participants Follow-Up Participation No Follow-Up Participation White Medical Aid No Medical Aid TOTAL TOTAL RR ˆ follow-up White pˆ p ˆ medical aid White no medical aid White /

27 Example 3: South African Study Whats going on? Race - Majority of sample Black subjects (91%) Race and follow-up participation - 26% of Black subjects completed follow-up as compared to 9% of White subjects Race and medical aid - 9% of Black subjects had medical aid compared to 83% of White subjects 27

28 Example 3: South African Study Recap 28

29 Example 4: Batch Effects In Lab Based Analyses Lab based results can be influenced by the technician, the laboratory used, the time of day, the temperature in the lab etc.. If the goal of a study is to ascertain differences in lab measures between groups (for example diseased and non-diseased), and the group is associated with at least some of the above characteristics, then there can be confounding 29

30 Summary In non-randomized studies, outcome/exposures relationships of interest may be confounded by other variables In order to confound an outcome/exposure relationship, a variable must be related to both the outcome and exposure 30

31 Section B Adjusted Estimates: Presentation, Interpretation and Utility for Assessing Confounding

32 Learning Objectives Understand how to interpret estimates of association that have been adjusted to control for a confounder Compare/contrast the comparisons being made by unadjusted and adjusted association estimates 32

33 Adjustment Adjustment is a method for making comparable comparisons between groups in the presence of a confounder/confounding variables We will discuss the basics of the mechanics behind adjustment in the next lecture section 33

34 Example 1: Fictitious Study Consider results from the following (fictitious) study: - This study was done to investigate the association between smoking and a certain disease in male and female adults smokers and 240 non-smokers were recruited for the study Results for All Subjects Smokers Non Smokers TOTALS Disease No Disease TOTALS RR ˆ pˆ pˆ smokers non smokers /

35 Example 1: Fictitious Study This relative risk is being influenced by the difference sex distributions among smokers and non-smokers This relative risk compares all smokers to all non-smokers in the sample without taking any other factors into account: this is called the unadjusted or crude estimated association between disease and smoking 35

36 Example 1: Fictitious Study Adjustment provides a mechanism for estimating an outcome/ exposure relationship after removing the potential distortion or negation that comes from a confounder or multiple confounders In the fictional example, for example, the relationship between disease and smoking can be adjusted for sex 36

37 Example 1: Fictitious Study Frequently, the presentation of results from non-randomized studies will include a table of unadjusted and adjusted measures of association Example: table of relative risks Table 2: Unadjusted and Adjusted Relative Risks of Disease Unadjusted Adjusted 1 Non- Smoker ref ref Smoker 0.93 (0.68, 1.27) 1.57 (1.12, 2.20) adjusted for sex 37

38 Example 1: Fictitious Study Unadjusted estimated relative risk, 0.93 Adjusted estimated relative risk,

39 Example 1: Fictitious Study Comparing unadjusted and adjusted associations to assess confounding Table 2: Unadjusted and Adjusted Relative Risks of Disease Unadjusted Adjusted 1 Non- Smoker ref ref Smoker 0.93 (0.68, 1.27) 1.57 (1.12, 2.20) adjusted for sex 39

40 Example 2: Arm Circumference and Height An observational study to estimate association between arm circumference and height in Nepali children randomly selected subjects, ages [0, 12) months, had arm circumference, weight and height measured - This study is observational it is not possible to randomize subjects to height groups! 40

41 Example 2: Arm Circumference and Height The data - Arm circumference range: cm - Height range: cm - Weight range: kg 41

42 Example 2: Arm Circumference and Height Frequently, the presentation of results from non-randomized studies will include a table of unadjusted and adjusted measures of association Example: table of linear regression slopes Table 2: Regression Slopes for Arm Circumference Unadjusted Adjusted Height (cm) 0.16 (0.13, 0.19) (- 0.21, ) Weight (kg) 0.80 (0.72, 0.89) 1.40 (1.21, 1.60) 42

43 Example 2: Arm Circumference and Height Unadjusted linear regression slope estimate for height, ˆ 0.16 β height Adjusted linear regression slope estimated for height, ˆ 0.16 β height 43

44 Example 2: Arm Circumference and Height Comparing unadjusted and adjusted associations to assess confounding Table 2: Regression Slopes for Arm Circumference Unadjusted Adjusted Height (cm) 0.16 (0.13, 0.19) (- 0.21, ) Weight (kg) 0.80 (0.72, 0.89) 1.40 (1.21, 1.60) 44

45 Example 3: Academic Physician Salaries 1 From abstract 1 Jagsi R, et al. Gender Differences in the Salaries of Physician Researchers. Journal of the American Medical Association (2012); 307(22);

46 Example 3: Academic Physician Salaries Unadjusted linear regression slope estimate for sex (1M, 0 F) ˆ $32,764 β sex Adjusted linear regression slope estimated for sex (1M, 0 F) ˆ $13,399 β sex ( after adjustment for specialty, academic rank, leadership positions, publications, and research time) 46

47 Example 3: Academic Physician Salaries Unadjusted linear regression slope estimate for sex (1M, 0 F) ˆ $32,764 β sex Adjusted linear regression slope estimated for sex (1M, 0 F) ˆ $13,399 β sex ( after adjustment for specialty, academic rank, leadership positions, publications, and research time) 47

48 Summary Adjustment is a method for making comparable comparisons between groups in the presence of a confounder/confounding variables The group comparisons made by adjusted associations are more specific than those made by unadjusted (crude) associations Contrasting crude and adjusted association estimates is useful for identifying confounding 48

49 Section C Adjusted Estimates: The General Idea Behind the Computations

50 Learning Objectives Gain some insight conceptually as to how adjusted estimates are computed 50

51 Example 1: Fictitious Study Consider results from the following (fictitious) study: - This study was done to investigate the association between smoking and a certain disease in male and female adults smokers and 240 non-smokers were recruited for the study Results for All Subjects Smokers Non Smokers TOTALS Disease No Disease TOTALS RR ˆ pˆ pˆ smokers non smokers /

52 Example 1 :Smoking, Disease and Sex A recap - The overall (sometimes called crude, unadjusted) relationship (RR) between smoking and disease was nearly 1 (risk difference nearly 0) Rˆ R 0.93; - The sex specific results showed similar positive associations between smoking and disease MALES: FEMALES: Rˆ R 1.8; Rˆ R 1.5; (note, for the moment we are not considering statistical significance, just using estimates to illustrate point) 52

53 Example 1: How to Adjust for Confounding? Stratify when Z is categorical - Look at tables separately - For our example, separate tables for males and females - Take weighted average of stratum specific estimates Ex: To get a sex adjusted relative risk for the smoking disease relationship we could weight the sex-specific relative risks by numbers of males and females RRˆ sex adjusted n males RRˆ n males males + n + n females females RRˆ females RRˆ sex adjusted

54 Example 1: How to Adjust for Confounding? There are better ways than this to take such a weighted average (weighting by standard error, for example), but this just illustrates the concept Confidence intervals can be computed for these adjusted measures of association Multiple regression (in this case, logistic) will be a very useful tool for performing adjustment 54

55 Example 2: Arm Circumference and Height Scatterplot: arm circumference by height Arm Circumference versus Height Nepalese Children < 12 Months (n 150) yˆ x R Height (cm) With Regression Line 55

56 Example 2: Arm Circumference and Height IDEA Scatterplots: arm circumference by height, stratified by weight values 56

57 Summary The adjusted association between Y and X, adjusted for a single potential confounder Z can be estimated by: - Stratifying on Z (hard to operationalize is Z is continous) - Estimate the Y/X relationship for each strata of Z - Take a weighted estimate of all Z strata specific Y/X associations Idea can be generalized to estimating the adjusted association between Y and X, adjusted for a multiple potential confounders Z 1, Z 2,.Z c 57

58 Summary Multiple regression methods will make the adjustment process easy and straightforward 58