Confounding, Effect modification, and Stratification

Transcription

1 Confounding, Effect modification, and Stratification Tunisia, 30th October 2014 Acknowledgment: Kostas Danis Takis Panagiotopoulos National Schoool of Public Health, Athens, Greece

2 Main points The concept of confounding and of effect modification How to check if confounding and if effect modification is present: stratification How to show results if confounding or if effect modification is present How to prevent confounding

3 Galaxy, Vol 11, Issue 2, Feb 1871 Mark Twain... Source:

4 Exposure Lying in bed The real player Disease (a third variable ), associated with the outcome, and also with the exposure (independently of the outcome) Outcome Q. 1 Is there a third variable risk factor for the Outcome which may be hidden behind the Exposure? Confounding The lying-in-bed association: a fallacy unmask the real player

5 Exposure Driving fast The co-player Outcome Q. 2 I s there a third variable risk factor for the Outcome which may be acting in combination with the Exposure? Effect modification The driving-fast association: a half-truth disentangle effects of co-players

6 Exposure Outcome Third variable Confounding: To eliminate (bias) Effect modification: To analyse (useful info)

7 Cohort studies marching towards outcomes

8 Cohort study Total Cases Non cases Risk % Exposed % Not exposed % Risk ratio: 50% / 10% = 5

9 Case-control studies

10 Source population Exposed Unexposed Sample Cases Controls: Sample of the source population Representative with regard to exposure Controls

11 Case-control study Exposed Not exposed Cases a c Controls b d Total a+c % exposed a/(a+c) % unexposed c/(a+c) Odds of exposure a/c b+d b/(b+d) d/(b+d) b/d Odds Ratio: = (a/c) / (b/d) = ad / bc

12 Cross-sectional (prevalence) studies

13 Cross-sectional study: Sampling Sampling Population Sample Target Population

14 Cross-sectional study Total Cases Non cases Prevalence % Exposed % Not exposed % Prevalence ratio (PR) 50% / 10% = 5

15 Should I believe my measurement? Exposure RR = 4 Outcome Chance? Bias? Confounding? True association - Causal? - Non-causal?

16 Exposure Outcome Third variable Confounding: To eliminate (bias) Effect modification: To analyse (useful info)

17 What should you do? In practice, we deal with: effect modification FIRST; confounding SECOND 1. Check for effect modification Analyse it. 2. Check for confounding Eliminate it. How? 1. Stratification 2. Stratified analysis Create strata according to levels of exposure to the third variable

18 Effect modification

19 Effect modification Variation in the magnitude of measure of effect across levels of a third variable Happens when RR or OR is different between strata (subgroups of population)

20 Why study effect modification To sort out (quantitatively) effect of the exposure under study and of a third variable (a potential effect modifier) To identify a subgroup with a lower or higher risk ratio To target public health action To study interaction between risk factors

21 Effect modification Factor A (asbestos) Factor B (smoking) Disease (lung cancer) Effect modifier / Interaction 21

22 Asbestos (As) and lung cancer (Ca) Case-control study, unstratified data As Ca Controls OR Yes No Ref. Total

23 Asbestos Lung cancer Smoking?

24 Smokers As Ca Controls OR Yes No Ref. Total Nonsmokers As Ca Controls OR Yes No Ref. Total Are stratum-specific RRs/ORs different between them?

25 Asbestos (As), smoking and lung cancer (Ca) Smoking As Cases Controls OR Yes Yes Yes No No Yes No No Ref. (Reference group is the same for all ORs)

26 Asbestos, smoking and lung cancer: interpretation In smokers, exposure to asbestos is 6 times higher among lung cancer cases than among controls In non-smokers, exposure to asbestos is 3 times higher among lung cancer cases than among controls Therefore, exposure to smoking modifies (increases by a factor of 2) the effect of exposure to asbestos Present data by stratum Public health implications?

27 Physical activity and myocardial infarction (MI) Physical activity MI Control s OR, 95%CI 2500 kcal/d ( ) < 2500 kcal/d Ref.

28 Physical activity Infarction Gender?

29 Men Physical activity MI Controls OR, 95%CI 2500 kcal/d ( ) < 2500 kcal/d Ref. Women Physical activity MI Controls OR, 95%CI 2500 kcal/d , ( ) < 2500 kcal/d Ref. Are stratum-specific RRs/ORs different between them?

30 Interpretation Different effects (RR) in different strata (men-women) Therefore, effect of physical activity is modified by gender (more protective for men) Present data by stratum (gender)

31 Vaccine efficacy ARU ARV VE = ARU VE = 1 RR VE: vaccine efficacy ARU: Attack rate in unvaccinated ARV: Attack rate in vaccinated RR: risk ratio

32 Vaccine efficacy (VE) Status Pop. Cases Cases per 1000 RR V NV Ref. Total VE = 1 - RR = VE = 72%

33 Vaccine Disease Age?

34 Vaccine efficacy by age group Age Status Pop. Cases Cases /1000 <1y V % NV y V % NV y V % NV y V % NV > 24y V % NV RR VE Are stratum-specific RRs/ORs different between them?

35 Interpretation Different effects (RR) in different strata (age groups) Therefore, VE is modified by age Present data by age-stratum Public health implications?

36 Any statistical test to help us? Breslow-Day Woolf test Test for trends: Chi square

37 Comparison of strata-specific RRs/ORs Question: Are stratum-specific RRs/ORs different between them? Answer: 1. Do stratum-specific estimates look different? 2. 95% CI of OR/RR do NOT overlap? 3. Is the Test of Homogeneity significant?

38 Death from diarrhoea according to breast feeding, Brazil, 1980s (crude analysis) Diarrhoea Controls OR (95% CI) No breast feeding ( ) Breast feeding Ref

39 No breast feeding Diarrhoea Age?

40 Death from diarrhoea according to breast feeding, Brazil, 1980s Infants < 1 month of age Cases Controls OR (95% CI) No breast feeding (6-203) Breast feeding 7 68 Ref Infants 1 month of age Cases Controls OR (95% CI) No breast feeding ( ) Breast feeding Ref Woolf test (test of homogeneity): p=0.03 Are stratum-specific RRs/ORs different between them?

41 Interpretation Different effects (OR) in different strata (age groups) Therefore, protective effect of breast feeding is modified by age (more protective in neonates <1 mo of age compared to infants 1 mo by a factor of 12) Present data by age-stratum Public health implications?

42 Risk of gastroenteritis by exposure, outbreak X, place Y, time Z (crude analysis) Exposed Yes No Exposure n AR (%) * n AR(%) * RR (95% CI ) pasta (8.8-38) tuna ( ) * AR = Attack Rate RR = Risk Ratio 95% CI = 95% confidence interval of the RR

43 Tuna Gastroenteritis Pasta?

44 Pasta Yes Cases Total AR (%) RR (95% CI) Tuna ( ) No tuna Ref Pasta No Risk of gastroenteritis by exposure, Outbreak X, Place, time X Cases Total AR (%) RR (95% CI) Tuna (2.6-46) No tuna Ref Woolf s test (test of homogeneity): p= Are stratum-specific RRs/ORs different between them?

45 Interpretation Different effects (RR) in different strata Therefore, effect of exposure to tuna is modified by exposure to pasta Exposure to pasta reduces the effect of exposure to tuna (by a factor of 10) Present data by stratum Negative modification of effect is also possible

46 How to check for effect modification in stratified analysis Perform crude analysis Measure the strength of association (RR/OR with CIs) List potential effect modifiers Stratify data by level of exposure to potential modifier(s) Check for effect modification Are stratum-specific RRs/ORs different between them? [Yes = EM] Observe RRs/ORs CIs: overlapping? Woolf s test: statistical significance? If YES effect modification Show data by stratum If NO effect modification Check for confounding

47 Crazy findings!! Why?? A trial compared two treatments for kidney stones, Treatment A (surgery) and Treatment B (percutaneous nephrolithotomy). Successful outcome was defined as stones reduced to <2 mm in size. 350 patients were included in each treatment branch of the study. It was found that: Successful outcome, crude results Treatment A Treatment B 273/350 (78%) 289/350 (83%) Therefore, Treatment B is better (83% vs 78%). Successful outcome, stratified results by size of stones Treatment A Treatment B Small stones (<2 cm) 81/87 (93%) 234/270 (87%) Large stones ( 2 cm) 192/263 (73%) 55/80 (69%) TOTAL 273/ /350 Therefore, Treatment A is better (93% vs 87% and 73% vs 69%). Source: s_paradox, Charig CR et al, BMJ 29/03/1986.

48 Crazy findings!! Why?? A trial compared two treatments for kidney stones, Treatment A (surgery) and Treatment B (percutaneous nephrolithotomy). Successful outcome was defined as stones reduced to <2 mm in size. 350 patients were included in each treatment branch of the study. It was found that: Successful outcome, stratified results by size of stones Treatment A Treatment B Small stones (<2 cm) 81/87 (93%) 234/270 (87%) Large stones ( 2 cm) 192/263 (73%) 55/80 (69%) TOTAL 273/350 (78%) 289/350 (83%) Simpson s paradox or reversal paradox Treatment A dominated by large stones: 263/350 (75%) Treatment B dominated by small stones: 270/350 (77%) AND Less successful outcome for large stone SOS: crude rates can be misleading in some circumstances!! Source: s_paradox, Charig CR et al, BMJ 29/03/1986.

49 Confounding

50 Exposure Outcome Third factor (potential confounding factor) Distortion of measure of effect because of a third (confounding) factor, which must be related to the exposure must be a risk factor itself must not be in the causal chain of exposure-outcome Confounding should be prevented or controlled for

51 Example: third factor in the causal chain Smoking Heart attack NO + Atherosclerosis NOT a confounding

52 Example 1 Skateboarding Chlamydia infections Age not evenly distributed between the two exposure groups: 90% of Skate-boarders are young 20% of Non skate-boarders are young Age? In conclusion (1) Age is a possible CF (2) Thus, the effect of skateboarding on chlamydia infections likely close to 1 Chlamydia infection

53 Example 2 Coffee drinking NOTE: New study says that coffee drinkers are more likely to get lung cancer Lung cancer Smoking? Smoking not evenly distributed between coffee drinkers/non-drinkers: - Drinkers: 70% smokers - Non-drinkers: 10% smokers In conclusion (1) Effect of coffee drinking on lung cancer likely confounded by smoking. Smoking is a likely CF (2) Effect of coffee drinking on lung cancer likely close to 1

54 Example 3 Birth order Down syndrome Age of mother?

55 Example 3 (ii) Incidence Cases of Down syndroms syndrome by birth order Cases per live births Birth order

56 Example 3 (iii) Incidence of Cases Down of syndrome Down Syndrom babies by by age mothers groups age group Cases per live births < Age groups

57 Incidence of Down syndrome Cases of Down syndrom by birth order and mother's age babies by birth order AND age of mother Cases per XXXXXXXXXXXXXXXXXXXXX Birth order < Age groups

58 Example 3 (v) Birth order Down syndrome Age of mother? In conclusion (1) Effect of birth order on Down syndrome babies confounded by age of mothers (possible CF). (2) Effect of birth order on down syndrome will be likely close to 1

59 So, remember! A confounding factor always.. Confounding factors must met the two following conditions: Exposure Outcome Third variable Be associated with outcome - independently of exposure Be associated with exposure - without being the consequence of exposure

60 The distortion introduced by confounding factors May simulate an association May hide an association that does exist

61 How to prevent/control confounding? Prevention of confounding (in study design) Randomization (experiment) Restriction to one stratum Matching Control of confounding (in analysis) Stratified analysis Multivariable analysis

62 Example: Are Mercedes more dangerous than Porsche? A paper looking at 1000 Mercedes and 1000 Porsche drivers who were followed for one year (cohort study) Type Total Accidents AR % RR Porsche Mercedes Ref. Total % CI =

63 Distribution by age of driver Proportion of < 25 yo among Porsche drivers: 55 %... among Mercedes drivers: 30 %

64 Car type=porsche Accidents Confounding factor: Age of driver?

65 < 25 years Type Total Accidents AR % RR, 95% CI Porsche ( ) Mercedes years Type Total Accidents AR % RR, 95% CI Porsche ( ) Mercedes Crude RR = 1.5 Adjusted RR = 1.1 ( ) Is adjusted RR/OR different from crude?

66 Incidence of malaria according to the presence of a radio set, Kahinbhi Pradesh Crude data Malaria Total AR% RR Radio set No radio Ref 95% CI =

67 Radio Malaria Confounding factor: Mosquito net?

68 Sleeping under mosquito net Malaria Total AR% RR Radio No radio Ref No mosquito net Malaria Total AR % RR Radio No radio Ref Crude RR = 0.7 Adjusted RR = 1.01 Is adjusted RR/OR different from crude?

69 To identify confounding Compare crude measure of effect (RR or OR) to adjusted (weighted) measure of effect Mantel-Haenszel RR or OR

70 Any statistical test to help us? When is OR MH different from crude OR? Adjusted Crude Crude > 10-20%

71 Mantel-Haenszel summary measure Adjusted or weighted RR or OR S (a i d i ) / n i ORMH = S (b i c i ) / n i Advantages of MH Zeroes allowed

72 Mantel-Haenszel summary measure Mantel-Haenszel (adjusted or weighted) OR Exp+ For each stratum Cases Controls a 1 b 1 SUM (a i d i / n i ) OR MH = Exp- c 1 d 1 SUM (b i c i / n i ) n 1 Cases Controls (a 1 x d 1 ) / n 1 + (a 2 x d 2 ) / n OR MH = (b 1 x c 1 ) / n 1 + (b 2 x c 2 ) / n Exp+ Exp- a 2 b 2 c 2 d 2 n 2

73 How to check for confounding in stratified analysis Perform crude analysis Measure the strength of association (RR/OR with CIs) List potential confounders Stratify data by level of exposure to potential confounder(s) Check for effect modification If NO effect modification Check for confounding Is adjusted RR/OR different from crude? [Yes = CF] adjusted RR/OR: Mantel-Haenszel (Adjusted-Crude)/Crude > 10 20%? If YES confounding Show adjusted data If NO confounding Show crude data

74 How to define the strata? Strata defined according to third variable: Usual confounders (e.g. age, sex, socio-economic status) Any other suspected confounder, effect modifier or additional risk factor Strata of public health interest For two risk factors: stratify on one to study the effect of the second on outcome Two or more exposure categories: each is a stratum Residual confounding? 74

75 How to deal with multiple risk factors Logical order of data analysis 1) Crude analysis 2) Stratified analysis 3) Multivariate analysis (mathematical model) - linear regression - logistic regression - Simultaneous adjustment for multiple risk factors/confounders - Can address effect modification

76 Stratified Analysis: an example. csinter case pesto, by(pasta) Pasta = Exposed Pesto Total Cases Risk % Exposed Unexposed Risk difference [ ] Risk Ratio 0.98 [ ] Attrib.risk.exp 0.02 [ ] Attrib.risk.pop 0.01 [..] Pasta = Unexposed Pesto Total Cases Risk % Exposed Unexposed Risk difference 0.01 [ ] Risk Ratio 1.21 [ ] Attrib.risk.exp 1.17 [ ] Attrib.risk.pop 0.02 [..] Test of Homogeneity (M-H) : pvalue : Crude RR for pesto : 2.08 [ ] MH RR for pesto adjusted for pasta : 0.99 [ ] Adjusted/crude relative change : % > 10-20%

77 Examples of stratified analysis Examples Stratum 1 Stratum 2 Crude RR ) Are RRs/ORs different between strata? EM 2) Is adjusted RR/OR different from crude? CF

78 Summary: effect modification and confounding Effect modification Belongs to nature Modifies effect of exposure under study Need to disentangle effect of risk factors Useful: increases knowledge of biological mechanism Allows targeting of public health action Confounding Belongs to study Distorts effect of exposure under study Need to unmask effect of third variable Prevent (study design) Control (analysis)

79 Exposure Effect modification The co-player Outcome The driving-fast association: a half-truth disentangle effects of co-players

80 Exposure Confounding The real player Outcome The lying-in-bed association: a fallacy unmask the real player

81 Summary: how to conduct a stratified analysis Perform crude analysis Measure the strength of association (RR/OR with CIs) List potential effect modifiers and/or confounders Stratify data by level of exposure to potential modifiers or confounders Check for effect modification (Are stratum-specific RRs/ORs different between them? CIs / Woolf s test) If YES effect modification Show data by stratum If NO effect modification Check for confounding (Is adjusted RR/OR different from crude? >10-20%) If YES confounding Show adjusted data If NO confounding Show crude data

82 A train can mask a second train A variable can mask another variable!

83 Thank you Takis Panagiotopoulos National Schoool of Public Health, Athens, Greece