![Homework Question 3
3. A case-control study was conducted to determine if Helicobacter pylori (H. pylori)
increased the risk of gastric cancer (stomach cancer). Vitamin C is a well-
established anti-oxidant and therefore may have anti-cancer properties. The
authors reported that the risk of gastric cancer was 1.71 times greater among
people with detectable H. pylori compared to people without detectable H pylori.
They then stratified by vitamin C use and observed an OR of 4.68 among low
vitamin C users, and an OR of 0.72 among high vitamin C users
a. In the results section the authors state, “The OR difference between the
two strata [of vitamin C use] was statistically significant (p-value=0.02).”
What does this p-value indicate?
b. Is vitamin C use an effect-modifier of the relation between H pylori and
gastric cancer? Why or why not?
c. Would you control for the use of vitamin C in your analysis, or would you
stratify by this variable?](https://image.slidesharecdn.com/biostatistics-slides-240528223054-d99987a9/85/Biostatistics-slides-considerations-for-reseaarch-31-320.jpg)
Biostatistics - slides considerations for reseaarch
- 1. Frankline M. Onchiri, Ph.D. Seattle Children’s Research Institute (SCRI) Statistical Considerations for Dental and Craniofacial Research
- 2. Classification of variable according to their intended use Outcome Y Variable that is primary focus of study. We estimate some summary measure of the distribution of Y within groups defined by exposure/POI Predictor of Interest (POI) X1 Variable that may influence size or occurrence of outcome. In RCT, this is intervention being studied. We divide population into subpopulations based on this variable Effect Modifier X2 Stratification variable: Effect modifiers define subgroups in which the association between the response and POI is different. Effect of an exposure differs among different subgroups of this variable. Confounder X3 • Variable that is associated with predictor and, which also is associated with outcome independent of predictor, and is NOT in causal pathway between predictor & outcome. • We also use these variables to divide the population into subpopulations. Each individual in given subpopulation will have the same value of each of the C Precision X4 Associated with outcome variable only but whose adjustment will provide precise estimates of association Others X5 variables to describe the study sample Measurements –Pre-specify covariates in protocol based on clinical and statistical reasoning
- 3. Statistical Role of Variables Statistical Role Response/outcome/ Disease Grouping variables Predictor/Exposure of interest Effect modifier / Stratifying variable Adjustment for covariates Confounders Precision variables
- 4. Statistical roles of variables 4 Outcome/dependent variable /effects /dependent/disease Confounders • Associated with outcome and exposure, NOT in causal pathway between exposure and outcome ? Association of interest TBD Primary predictors/ risk factors /Independent vars/Cofactors Precision variables • Associated with outcome only Intermediate variable Adjustment for covariates: Confounders, Precision variables
- 5. Statistical roles of variables 5 Outcome/dependent variable /effects /dependent/disease Cofounders • Associated with with outcome and exposure, NOT in causal pathway between exposure and outcome ? Association of interest TBD Primary predictors/ risk factors /Independent vars/Cofactors Precision variables • Associated with outcome only Variance Inflation variables • Associated with exposure only Intermediate variable Pathway (downstream effect of exposure) Adjustment for covariates: Confounders, Precision variables • Think about causal relationships between variables
- 6. Conditions for Confounding Exposure / Independent Variable Outcome / Dependent Variable Potential Confounder Every confounder must meet this criteria Pathway (downstream effect of exposure) Risk factor for exposure? (Yes) Risk factor for outcome? (Yes) In causal pathway? (No)
- 7. Statistical/Epidemiological roles of variables: Mediating variables Alcohol consumption Coronary Heart Disease Smoking Age HDL (good cholesterol) Risk factor for exposure? (Yes) Risk factor for outcome? (Yes) In causal pathway? (Yes) • Modest alcohol reduces CHD risk • Does so by raising HDL • High levels of HDL reduce risk of CHD • Mechanism: Modest alcohol consumption raises HDL levels, which in turn reduces risk of CHD • So, HDL is not confounder of association between alcohol and CHD
- 8. Statistical/Epidemiological roles of variables: Mediating variables Maternal smoking during pregnancy Infant Mortality Alcohol Age SES Birthweight Risk factor for exposure? (Yes) Risk factor for outcome? (Yes) In causal pathway? (Yes)
- 9. Statistical/Epidemiological roles of variables: Mediating variables Diet CHD Economic status Serum Cholesterol Diabetes, HPTN Risk factor for exposure? (Yes) Risk factor for outcome? (Yes) In causal pathway? (Yes)
- 10. DETOUR: Measures Of Disease-exposure Association • The chances (represented with letter p) of something happening can be expressed as a risk or as an odds: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = Number of persons with the disease Total Number of people in population = 𝑝𝑝 Odds= the chances of disease occurence the chances of disease NOT occuring = 𝑝𝑝 1−𝑝𝑝 • Thus a risk is a proportion, • But an odds is a ratio; in which the numerator and denominator sum to one
- 11. 11 Relationship between incidence of Lung-Cancer and drinking Status Have Lung cancer No Lung Cancer Total Heavy Drinker 33 1667 1700 No drinker 27 2273 2300 Total 60 3940 4000 • Overall: Risk of lung cancer=60/4000=0.015 • Among Heavy drinkers: Risk of lung cancer= 33/1700=0.0194 • Among Non-drinkers: Risk of lung cancer= 27/2300=0.0117 • Relative Risk (RR) is ratio of two risks • 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑜𝑜𝑜𝑜 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑖𝑖𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑜𝑜𝑜𝑜 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑖𝑖𝑖𝑖 𝑈𝑈𝑈𝑈𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 0.0194 0.0117 = 1.66 • RR of Lung cancer comparing Heavy Drinkers to Non-drinkers is 1.66
- 12. 13 Relationship between Smoking and CHD (Case-Control) CHD Cases Controls Total Smokers 112 176 288 Non-smokers 88 224 312 Total 200 400 600 • Among Cases: Proportion of Smokers=112/200=56% • Among Cases: Odds of smoking= 0.56 1−0.56 =1.273 • Among Controls: Proportion of Smokers= 176 400 = 0.44 • Among Controls: Odds of smoking= 0.44 1−0.44 = 0.785 • Odds Ratio (OR) comparing Cases and Controls • 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖𝑖𝑖 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑖𝑖𝑖𝑖 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = 1.273 0.785 = 1.623
- 13. Generally, Odds Ratio as a Cross-Product Exposed Have Disease Have no Disease Total Yes a b a+b No c d c+d Total a+c b+d a+b+c+d • Among Exposed: Odds of disease= 𝑎𝑎/(𝑎𝑎+𝑏𝑏) 1−𝑎𝑎/(𝑎𝑎+𝑏𝑏) = 𝑎𝑎 𝑏𝑏 • Among Unexposed: Odds of Disease = 𝑐𝑐/(𝑎𝑎+𝑏𝑏) 1−𝑐𝑐/(𝑐𝑐+𝑑𝑑) = 𝑐𝑐 𝑑𝑑 • Odds Ratio (OR)= 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑖𝑖𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑂𝑂𝑂𝑂𝑂𝑂𝑂𝑂 𝑜𝑜𝑜𝑜 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑖𝑖𝑖𝑖 𝑈𝑈𝑈𝑈𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑎𝑎/𝑏𝑏 c/d = 𝑎𝑎×𝑑𝑑 c×b
- 14. DETOUR BACK: Conditions for Confounding Exposure / Independent Variable Outcome / Dependent Variable Potential Confounder Every confounder must meet this criteria Pathway (downstream effect of exposure) Risk factor for exposure? (Yes) Risk factor for outcome? (Yes) In causal pathway? (No)
- 15. 16 Smoking as a Confounder of relationship between Lung-Cancer and drinking LC No LC Heavy Drinker 24 776 No Drinker 6 194 Smokers OR= 24×194 6×776 = 1.0 LC No LC Heavy Drinker 9 891 No Drinker 21 2079 Non-smokers OR= 9×2079 21×891 = 1.0 Have Lung cancer No Lung Cancer Heavy Drinker 33 1667 No drinker 27 2273 OR= 33×2273 27×1667 = 1.666 • Among SMOKERS and NON-SMOKERS: no relationship between LC and drinking since OR=1 • Observed distorted relationship between heavy drinking and LC was due to confounding by smoking Crude Analysis: Stratified Analysis:
- 16. For smoking to be a confounding factor, 3 conditions must be met Heavy Drinking vs. No Drinking Lung Cancer Potential Confounder: Smoking Pathway (downstream effect of exposure) Is smoking Risk factor for Heavy Drinking? Is smoking Risk factor for L. Cancer independent of Heavy Drinking? In causal pathway? (No) Smoking No Smoking Heavy Drinker a=? b=? No drinker c=? d=? Lung Ca No Lca Smoking a=? b=? No Smoking c=? d=?
- 17. 18 Smoking as a Confounder of relationship between Lung-Cancer and drinking LC No LC Total smokers Heavy Drinker 24 776 800 No Drinker 6 194 200 Smokers OR= 24×194 6×776 = 1.0 LC No LC Total NonSmokers Heavy Drinker 9 891 900 No Drinker 21 2079 2100 Non-smokers OR= 9×2079 21×891 = 1.0 Have Lung cancer No Lung Cancer Heavy Drinker 33 1667 No drinker 27 2273 OR= 33×2273 27×1667 = 1.666 • Among SMOKERS and NON-SMOKERS: no relationship between LC and drinking since OR=1 • Observed distorted relationship between heavy drinking and LC was due to confounding by smoking Crude Analysis: Stratified Analysis:
- 18. For smoking to be a confounding factor, 3 conditions must be met Heavy Drinking vs. No Drinking Lung Cancer Potential Confounder: Smoking Pathway (downstream effect of exposure) Is smoking Risk factor for Heavy Drinking? Is smoking Risk factor for L. Cancer independent of Heavy Drinking? In causal pathway? (No) Smoking No Smoking Heavy Drinker a=800 b=900 No drinker c=200 d=2100 Lung Ca No Lca Smoking a=6 b=194 No Smoking c=21 d=2079 OR= 800×2100 200×900 = 9.33 OR= 6×2079 21×194 = 3.06
- 19. Does smoking meet definition of Confounder? Heavy Drinking vs. No Drinking Lung Cancer Potential Confounder: Smoking Pathway (downstream effect of exposure) Is Smoking Risk factor for exposure? Yes: Drinking is associated with smoking: OR=9.33 Is Smoking Risk factor for outcome (Lca)? YES: Smoking is associated with Lung cancer: OR=3.06 In causal pathway? (No)
- 20. Effect Modification • Effect modification: variation relationship between exposure and outcome due to actions of another variable (called effect modifier) –stratum-specific measures of disease-exposure associations are appreciably different from each other • Strength of association between exposure and Disease depends on an effect modifier – association is MODIFIED by third factor.
- 21. Effect Modification CASES (D+) CONTROLS (D-) E+ 10 10 E- 5 20 CASES (D+) CONTROLS (D-) E+ 10 30 E- 15 20 CASES (D+) CONTROLS (D-) Exposed 20 40 Not Exposed 20 40 Crude/Un-adjusted OR= ad/bc=20*40/20*40=1.0 Stratum 2 OR=0.44 Stratum 1 OR=4.0 Crude Analysis: Stratified Analysis:
- 22. Conducting Analysis by Subgroups- Stratified analysis Disease No Disease Exposed 450 75 Unexposed 760 1975 Disease No Dis Exposed 370 10 Unexposed 400 280 Disease No Dis Exposed 80 65 Unexposed 360 1695 OR= 5.8 OR= 25.9 Overall OR=15.6 Stratum 1: Hep. B+ virus Stratum 2: No Hep. B Virus Crude Stratified Evaluating relationships between exposure and outcome in strata homogeneous with respect to a confounder.
- 23. Effect Modification • Effect modification is not bias or confounding and when found it provides information for the nature of an association • Effect modification does not violate internal validity of the study • It requires stratified analysis for different levels of the interacting factor (like sex or age group).
- 24. Homework Questions: Q1 1. To measure the effect of exercise on heart disease, investigators in a 1961 study compared the incidence of the disease for two large groups of people who worked on the London bus system: drivers and conductors. Conductors get a lot more exercise than the drivers since they walk around all day collecting fares while the drivers just sit. The age distributions of the two groups were the same. The study found the incidence of heart disease was substantially lower among the conductors. a. How do you classify this study? (observational vs interventional? Cohort, case-control, cross-sectional or clinical trial?) a. The investigators seem to have been worried that age would be a confounding factor in their study. Was this the case? (i) Yes, age was a confounding factor. (ii) No, age was not a confounding factor. (iii)There is not enough information to determine whether age is a confounding factor
- 26. Homework Questions: Q1 1. To measure the effect of exercise on heart disease, investigators in a 1961 study compared the incidence of the disease for two large groups of people who worked on the London bus system: drivers and conductors. Conductors get a lot more exercise than the drivers since they walk around all day collecting fares while the drivers just sit. The age distributions of the two groups were the same. The study found the incidence of heart disease was substantially lower among the conductors. a. How do you classify this study? (observational vs interventional? Cohort, case-control, cross-sectional or clinical trial?) a. The investigators seem to have been worried that age would be a confounding factor in their study. Was this the case? (i) Yes, age was a confounding factor. (ii) No, age was not a confounding factor. (iii)There is not enough information to determine whether age is a confounding factor
- 27. Homework Question 2 In your opinion, is smoking status an effect modifier, confounder, neither, or both? Justify your answer in three sentences or less?
- 28. 30 Homework Question 2: Role of Smoking in relationship between Oral Cleft and drinking Oral Cleft Control Alcohol Drinker 46 14 Teetotaler 32 43 Smokers OR= 46×43 32×14 = 4.42 Oral Cleft Control Alcohol Drinker 18 18 Teetotaler 4 25 Non-smokers OR= 18×25 4×18 = 6.25 Oral Cleft Control Alcohol Drinker 64 32 Teetotaler 36 68 OR= 75×79 22×21 = 3.78
- 29. 31 Role of Smoking in relationship between Oral Cleft and drinking (Does smoking meet conditions for Confounding?) • Criteria 1: Be risk factor for exposure: Is smoking related to Drinking? Smoke Nonsmoker Alcohol drinkers 60 36 Teetotalers 75 29 Smoking status OR=0.644 • Criteria 2 : Be independent risk factor for disease: Is smoking related to Oral Cleft independent of drinking status? Among Alcohol Drinkers Oral Cleft Control Smoke 46 14 Not smoke 18 18 OR=3.29 Among teetotalers Oral Cleft Control Smoke 32 43 Not smoke 4 25 OR=4.65
- 30. For smoking to be a confounding factor, 3 conditions must be met Alcohol driking vs. No Drinking Oral Cleft Potential Confounder: Smoking Pathway (downstream effect of exposure) Is smoking Risk factor for Alcohol Drinking? Is smoking Risk factor for Oral cleft independent of Heavy Drinking? In causal pathway? (No) Smoking No Smoking Alcohol Drinker a=60 b=36 No drinker c=75 d=29 Oral Cleft No oral Cleft Smoking a=32 b=194 No Smoking c=4 d=25 OR= 60×29 75×36 = 0.644 OR= 32×25 4×194 = 4.65
- 31. Homework Question 3 3. A case-control study was conducted to determine if Helicobacter pylori (H. pylori) increased the risk of gastric cancer (stomach cancer). Vitamin C is a well- established anti-oxidant and therefore may have anti-cancer properties. The authors reported that the risk of gastric cancer was 1.71 times greater among people with detectable H. pylori compared to people without detectable H pylori. They then stratified by vitamin C use and observed an OR of 4.68 among low vitamin C users, and an OR of 0.72 among high vitamin C users a. In the results section the authors state, “The OR difference between the two strata [of vitamin C use] was statistically significant (p-value=0.02).” What does this p-value indicate? b. Is vitamin C use an effect-modifier of the relation between H pylori and gastric cancer? Why or why not? c. Would you control for the use of vitamin C in your analysis, or would you stratify by this variable?
- 32. 34 Homework Question 3: Role of Smoking in relationship between Oral Cleft and drinking Oral Cleft Control H. Pylori a1 b1 No H. Pylori c1 d1 Low Vitamin C users OR= a1 ×d1 c1 ×b1 = 4.68 Gastric Ca Controls H. Pylori a2 b2 No H. Pylori c2 d2 OR= a2 ×d2 c2×b2 = 0.72 Gastric Ca Controls H. Pylori a b No H. Pylori c d OR= 𝑎𝑎×𝑑𝑑 c×b = 1.71 High Vitamin C users Statistical test comparing 4.68 vs. 0.72 resulted in p-value=0.02 Crude Analysis: Stratified Analysis:
- 33. Homework Question 4 4. Vitamin D has a well-known role in calcium regulation and bone metabolism. Significant sources of vitamin D include foods, endogenous vitamin D made by skin cells after sunlight exposure, and vitamin supplements. Recent laboratory studies suggest that vitamin D may also be involved in modulating cell growth and blood- vessel formation, both of which are important in cancer. In 1992–1998, a multi-national collaborative study in Europe recruited about 520,000 cancer-free adults from the general population or through screening programs. At recruitment, all participants donated a blood sample and completed a standardized dietary questionnaire. Occurrence of cancer was then monitored through population-based cancer registries and death certificates in each country. By 2003, 1,248 participants had developed oral cancer. Each of them was matched to a study participant of the same age, gender, and area of residence who was known to be alive and had not developed oral cancer. Stored blood samples and questionnaire data were then analyzed to compare the two groups. The results showed significantly lower blood vitamin D levels among those who developed oral cancer than among those who did not. However, essentially no differences were found with regard to dietary intake of foods high in vitamin D. a. Classify the study design. (1 point) b. The results for blood levels of vitamin D differed from the results for self-reported dietary intake of vitamin D. Could this difference be due to recall bias in the self-reported dietary data? Explain briefly. (1 point) c. The study results were considered encouraging by cancer control experts, because blood level of vitamin D may be a potentially modifiable risk factor for oral cancer. What type of study design might best establish whether raising a person’s blood level of vitamin D reduces his or her risk of oral cancer? (2 points)
- 34. Homework Question 5 5. Guillain-Barr´e syndrome (GBS) is a rare but potentially serious form of muscle paralysis that is known to be triggered by certain viral illnesses and some vaccines. In 2008, a group of Taiwanese investigators mounted a study to determine whether flare-ups of herpes zoster infection (“shingles”) can also trigger GBS. Taiwan’s national health insurance system covers almost all of the country’s population. From national health insurance data, researchers found that a total of 315,595 individuals had been diagnosed with herpes zoster infection on a medical visit during 2003–2005. For each herpes zoster victim, three comparison persons were chosen at random from among national health insurance enrollees who were of similar age and gender and who had made a medical visit on the same date for some other reason besides herpes zoster infection. During the two months following their index medical visit, 78 people in the herpes zoster group and 14 people in the comparison group were diagnosed with GBS, according to national health insurance records. Assume for present purposes that no participants died, disenrolled, or emigrated from Taiwan during those two months. How would you classify the basic study design?
- 35. Homework Question 6 6. (BONUS, OPTIONAL) The tables below show the association periodontitis and CVD according to a hypothetical susceptibility factor CVD+ CVD- Periodontitis (E+) 240 960 No Periodontitis (E-) 360 2440 Among patients without susceptibility factor: CVD+ CVD- Total Periodontitis (E+) 200 600 800 No Periodontitis (E-) 200 1000 1200 Among patients without susceptibility factor: CVD+ CVD- Total Periodontitis (E+) 40 360 400 No Periodontitis (E-) 160 1440 1600 Determine from the data if the susceptibility factor an Effect Modifier, Confounder, or both? Justify your answer by show of calculations (Hint: remember definition of confounder)
- 36. 38 Homework BONUS Question: Role of Susceptibility factor in relationship between Periodontitis and CVD CVD+ CVD- Periodontitis 200 600 No Periodontitis 200 1000 Stratum 1: Susceptibility factor OR= 200×1000 200×600 = 1.5 Oral Cleft Control Periodontitis 40 360 No Periodontitis 160 1440 Stratum 2: No Susceptibility factor OR= 40×1440 160×360 = 1.00 CVD+ CVD- Periodontitis 240 960 No Periodontitis 360 2440 Crude OR= 240×2440 360×960 = 1.56 Crude Analysis: Stratified Analysis:
- 37. Limitations of Stratified analysis • Inability to control simultaneously for multiple confounding variable • To adjust for multiple confounders, a regression model is used • Linear regression when outcome is continuous • Logistic regression when outcome is binary categorical