sph.bu/otlt/lamorte/EP713/

1. Interactive learning modules and videos of abridged lectures can be accessed by smart phone as well. http://sph.bu.edu/otlt/lamorte/EP713/

2. Rounding errors When calculating ratios, don’t round off the numerator and denominator too much; it can cause the result to vary quite a bit. Keep 3-4 decimal places in the numerator & denominator. Round off the final result. 0.1199 rounded to 0.1449 0.1 = 1.0 0.1 0.1199 = 0.827 = 0.83 0.1449

3. Using a reference group for comparison: You can do this for both cohort studies and case-control studies.

4. Rate of MI per 100,000 P-Yrs (incidence) wgt kg hgt m2 # MIs (non-fatal) Person-years of observation Relative Risk BMI: 41 177,356 23.1 1.0 <21 57 194,243 29.3 1.3 21-23 56 155,717 36.0 1.6 23-25 67 148,541 45.1 2.0 25-29 85 99,573 85.4 3.7 >29

6. Using a Reference Group in a Case-Control Study Cancer Cancer Case Control Case Control some complete Tooth Loss Tooth Loss none none

7. Evaluating Random Error(Sampling Error)

8. Testing Whether a Factor Is Associated With Disease Target Population Inference Sample • Are the results valid? • Chance (Random Error) • Bias • Confounding Study population • Collect data • Make comparisons Is there an association?

9. What is a “random sample”? When selection of one subject doesn’t affect the chance of other subjects being chosen, i.e. selection is be independent (uninfluenced by other factors). To achieve this we should select by a process such that selection is independent of other factors… an independent selection process. In reality, we usually take convenience samples… we take the subjects that are available. Example: BWHS recruiting via subscribers to a magazine.

10. Types of Data • 1) Discrete Variables: Variables that assume only a finite number of values: • Dichotomous variables (male/female, alive/died) • Categorical variables (or nominal variables, e.g., race) • Ordinal variables: ordered categories (Excellent/Good/Fair/Poor) • 2) Continuous Variables: Can take on any value within a range of plausible values, e.g., serum cholesterol level, weight & systolic blood pressure. (Also called quantitative or measurement variables.)

11. Case fatality rate for H1N1? Is H1N1 vaccine effective? Suppose you were reading two studies: one that addressed the first question and another that addressed the second question… what would be the study design of each? What was being estimated in each?

12. Goals • One Group: • Estimating a prevalence, risk, or rate in one group • (e.g., case-fatality rate with bird flu) • Estimating mean (e.g. average body weight) • (How precise are the estimates?) • Comparing 2 or more groups: • Comparing risks, rates • Comparing means (body weigh in smokers versus non-smokers) • (Are differences just due to sampling error?) • (If we calculate a measure of association, • how precise is it?)

13. Measurements Frequencies Comparing two or more groups Do smokers weigh less than non-smokers? [measurement difference] Increased risk of wound infection? [relative risk] Estimates in one group. Case-fatality rate from bird flu (% of cases that die)? [proportion] Mean body weight of a population? [measurement] 1 2+ Are the groups different? How precise is measure of association?

14. Estimates in a Single Group: How Precise?

15. Measurements Frequencies Comparing two or more groups Do smokers weigh less than non-smokers? [measurement difference] Increased risk of wound infection? [relative risk] Estimates in one group. Case-fatality rate from bird flu (% of cases that die)? [proportion] Mean body weight of a population? [measurement] 1 2+ Are the groups different? How precise is measure of association?

16. True mean 100 120 140 160 180 200 220 240 260 280 300 320 Estimated Mean = 205

17. True mean 100 120 140 160 180 200 220 240 260 280 300 320 Estimated Mean = 140

18. True mean 100 120 140 160 180 200 220 240 260 280 300 320 Estimated Mean = 265

19. A sample provides an estimate of population mean weight. Distribution of Body Weights in a Population Total population (True Mean) Number of people with each body weight 100 120 140 160 180 200 220 240 260 280 300 320 Body Weight Estimates may vary from sample to sample. The estimates will be more precise with larger samples, i.e., more consistent, and they are more likely to be close to the true mean.

20. Confidence Interval for a Mean The estimated mean was 202. With 95% confidence, the true mean lies in the range of 184-220. 184 202 220 The range within which the true value lies with a specified degree of confidence.

21. Measurements Frequencies Comparing two or more groups Do smokers weigh less than non-smokers? [measurement difference] Increased risk of wound infection? [relative risk] Estimates in one group. Case-fatality rate from bird flu (% of cases that die)? [proportion] Mean body weight of a population? [measurement] 1 2+ Are the groups different? How precise is measure of association?

22. Humans Who Got Bird Flu What is the case-fatality rate? No comparisons; just a single estimate in a group of cases. What type of measure of disease frequency are we estimating?

23. See Epi_Tools.XLS : Worksheet “CI – One Group” Interpretation: The estimated case-fatality rate was 50% (4/8). With 95% confidence the true CFR lies in the range 21.5-78.5%.

24. 95% Confidence Interval For A Proportion The range within which the true value lies, with 95% confidence. 95% Confidence Interval 0.22 0.78 0.0 1.0 4/8 = 0.5 = point estimate It is very unlikely (less than 5% probability) that the true value is outside this range.

25. Suppose it had been 32 deaths out of 64 cases, i.e., same proportion but larger sample? The confidence interval would be….? • Narrower • Wider • Same width • Can’t say

26. The greater the sample size… … the narrower the confidence interval (and the more precise the estimate). N N N N N Precision Depends on Sample Size

27. Weymouth, MA conducted an extensive health survey several years ago. One question asked, “Have you experienced violence because you or someone else was drinking alcohol?” What type of measure of disease frequency are we estimating?

28. Hypothesis Testing: Comparing Two or More Groups

29. Measurements Frequencies Estimates in one group. Mean body weight of a population? [measurement] Case-fatality rate from bird flu (% of cases that die)? [proportion] 1 2+ Comparing two or more groups Do smokers weigh less than non-smokers? [measurement difference] Increased risk of wound infection? [relative risk] Are the groups different? How precise is measure of association?

30. Null Hypothesis (H0): the groups are not different • H0: Mean Wgt. smokers = Mean Wgt. Non-smokers Alternative Hypothesis (HA): the groups are different HA: Mean Wgt. Smokers = Mean Wgt. Non-smokers

31. Null Hypothesis: Smokers & Non-Smokers Do Not Differ in Weight on Average True population distribution Note that, here, smokers & non-smokers have the same distribution of body weights and the mean weights are the same. Random Samples 100 120 140 160 180 200 220 240 260 280 300 320 Random sample of non-smokers Random sample of smokers The sample means may differ just by chance (random error).

32. Alternative Hypothesis: They Differ True means Population of non=smokers Population of smokers 100 120 140 160 180 200 220 240 260 280 300 320 sample of smokers sample of non-smokers Even if they are really different, there may be some overlap.

33. 190 lbs. 205 lbs. Smokers Non-smokers Statistical Testing How do we decide if they are really different or the differences were just due to chance? If the null hypothesis were true, what would be the probability of getting a difference this great (or greater) just by chance (random error)?

34. 190 lbs. 205 lbs. Smokers Non-smokers P– Values “p” is for probability. Definition of a p-value: The probability of seeing a difference this big or bigger, if the groups were not different, i.e. just by chance. P-values are generated by performing a statistical test. The particular statistical test used depends on study type, type of measurement, etc.

35. P-Values • Range between 0 and 1. • Small p-values(< 0.05) mean a low probability that the observed difference occurred just by chance (so they’re likely to be different). p-valueProbability of occurring by chance .55 55% .25 25% .12 12% .05 5% .01 1 in 100 (1% ) The differences may be due to chance. p < or = .05 Chance is an unlikely explanation

36. Statistical Significance If “p” < 0.05 it is unlikely that the difference is due to chance. If so, we reject the null hypothesis in favor of the alternative hypothesis, i.e. the groups probably are different. • This criterion for significance (< 0.05) is arbitrary. • The p-value is a probability, not a certainty. • P-values are influenced by: • The magnitude of difference between groups. • The sample size

37. If we wanted to compare two groups on measurement data (e.g. Is the mean weight of smokers less than that of non-smokers?), we might use a statistical test known as a “t-test” to determine whether there was a “statistically significant” difference. Epi_Tools.XLS Spreadsheet Describes T-Tests

38. Evaluating the Role of Chance With Categorical Data

39. Measurements Frequencies Estimates in one group. Mean body weight of a population? [measurement] Case-fatality rate from bird flu (% of cases that die)? [proportion] 1 2+ Comparing two or more groups Do smokers weigh less than non-smokers? [measurement] Increased risk of wound infection? [relative risk] Are the groups different? How precise is measure of association?

40. Is the risk of wound infection really different, or were the observed differences just due to “the luck of the draw”? Wound Infection Cumulative Incidence Yes No 5.3% Yes 7 124 131 (7/131) Had Incidental Appendectomy 1.3% No 1 78 79 (1/79) 8 202 210 Subjects Do incidental appendectomy? RR = 7/131 = 5.3 = 4.2 1/79 1.3

41. What would the null hypothesis be for the study on wound infections after incidental appendectomy?

42. How confident are we that the groups are different? How accurate is this estimate? The “null” value; i.e., no difference. Estimated RR = 4.2 0 1.0 10 Possible values of RR or OR

43. Null Hypothesis (H0): the groups are not different • H0: Incid. Infectionexposed = Incid. infection not exposed • or H0: RR = 1.0 (or OR = 1) • or H0: RD = 0 • or H0: Attrib. fraction = 0 Alternative Hypothesis (HA): the groups are different • HA: RR or OR = 1.0 • or HA: RD = 0 • or HA: Attrib. fraction = 0

44. 1.3% 5.3% No appy. Appendectomy Statistical Testing How do we decide if they are really different or the differences were just due to chance? If the null hypothesis were true, what would be the probability of getting a difference this great (or greater) just by chance (random error)?

45. 5 (62% of 8) 126 3 (38% of 8) 76 If the Null Hypothesis Were True, What Would You Have Expected? Expected if no association (Null Hypothesis) Observed Data: Infection No Inf. Infection No Inf. Appy Appy 7 124 131 (62%) No Appy No Appy 1 78 79 (38%) 8 202 210 total • How big a difference was there between what you expected under the null hypothesis and what was observed? • If the null hypothesis were true, what is the probability of seeming a difference this big just due to sampling variability (the luck of the draw)?

46. 5 (62% of 8) 126 3 (38% of 8) 76 If the Null Hypothesis Were True, What Would You Have Expected? Expected if no association: Observed Data: Infection No Inf. Infection No Inf. Appy Appy 7 124 131 (62%) No Appy No Appy 1 78 79 (38%) 8 202 210 total Expected with null hypothesis c2 = S (O-E)2 E = 2.24 If the null hypothesis were true, there would be a 13% probability of obtaining a difference this big (or bigger) just by chance (“luck of the draw”). p = 0.13 (“p-value”)

47. Observed Data: Person-Years of Observation Death Yes No + 30 - 699 - 36 - 1,399 66 2,098 total Chi Squared Test with Person-Years of Observation c2 = S (O-E)2 E

48. Death Yes No - + 30 - - - 36 - c2 = 82 + 82 =2.91 + 1.45 = 4.36 22 44 (p < 0.05) Chi Squared Test with Person-Years of Observation Data Expected by Chance: Observed Data: 33% of 66 = 22 Death Yes No Expected with null hypothesis 22 + 699 (33%) - 44 1,399 (67%) 67% of 66 = 44 66 2,098 total c2 = S (O-E)2 E

49. c2 = S (O-E)2 E = 2.24 p = 0.13 Caution: c2 Test Exaggerates Significance with Small Samples Expected with null hypothesis: Infection No Inf. Appy 5 126 No Appy 3 76 Fisher’s Exact Test (for small samples, i.e. if expected number in any cell is <5): Here, p = 0.26 with Fisher’s. Fisher’s requires an iterative calculation that is tough for a spreadsheet. See http://www.langsrud.com/fisher.htm for a 2x2 table that performs Fisher’s Exact Test.

50. P = 0.26