Disease Association I Main points to be covered Fall 2010 Measures of association compare measures of disease between levels of a predictor variable Cross-sectional.

Disease Association I Main points to be covered Fall 2010 Measures of association compare measures of disease between levels of a predictor variable Cross-sectional study –Introducing: The 2 X 2 table –Prevalence ratio –Odds ratio Cohort study –Risk ratio (cumulative incidence) –Rate ratio (incidence rate) –Risk difference –Rate difference

Measures of Disease Association Measuring occurrence of new events can be an aim by itself, but usually we want to look at the relationship between an exposure (risk factor, predictor) and the outcome Measures of association compare measures of disease (incident or prevalent) between levels of a predictor variable The type of measure showing an association between an exposure and an outcome event is dictated by the study design

Cross-Sectional Study Design: A Prevalent Sample

Measures of Association in a Cross-Sectional Study Simplest case is to have a dichotomous outcome and dichotomous exposure variable Everyone in the sample is classified as diseased or not and having the exposure or not, making a 2 x 2 table The proportions with disease are compared among those with and without the exposure NB: Exposure=risk factor=predictor

2 x 2 table for association of disease and exposure Disease Yes No Exposure Yes No a b cd a + b c + d a + cb + d N = a+b+c+d Note: data may not always come to you arranged as above. STATA puts exposure across the top, disease on the side.

Prevalence ratio of disease in exposed and unexposed Disease Yes No Exposure Yes No a b cd a + b c + d c a PR =

Prevalence Ratio Text refers to Point Prevalence Rate Ratio in setting of cross-sectional studies We like to keep the concepts of rate and prevalence separate, and so prefer to use prevalence ratio

Sample data with prevalence ratio calculated CasesNoncasesTotalPrevalence Exposed1417310.45 Unexposed3882486360.61 Total667 Prevalence ratio = 0.45/0.61 = 0.74

Describing a PR < 1 Prevalence ratio = 0.45/0.61 = 0.74 In words: Those who are exposed are 0.74 times as likely to have the disease compared with those who are not exposed. OR There is a 0.74 fold lower prevalence of disease among exposed compared to unexposed.

Describing a PR > 1 For example, a prevalence ratio = 1.5 In words: Those who are exposed are 1.5 times as likely to have the disease compared with those who are not exposed. OR There is a 1.5 fold higher prevalence of disease among exposed compared to unexposed.

Exposed Unexposed | Total --------------------------------------------------- Cases | 14 388 | 402 Noncases | 17 248 | 265 --------------------------------------------------- Total | 31 636 | 667 | | Example of 2 x 2 Table Layout in STATA STATA puts exposure across the top, disease on the side.

Exposed Unexposed | Total --------------------------------------------------- Cases | 14 388 | 402 Noncases | 17 248 | 265 --------------------------------------------------- Total | 31 636 | 667 | | Risk |.4516129.6100629 |.6026987 Point estimate [95% Conf. Interval] --------------------------------------------- Risk ratio.7402727 |.4997794 1.096491 ----------------------------------------------- chi2(1) = 3.10 Pr>chi2 = 0.0783 Prevalence ratio (STATA output) STATA uses “risk” and “risk ratio” by default

Study Reporting Prevalence Ratios Prevalence of hip osteoarthritis among Chinese elderly in Beijing, China, compared with whites in the United States Abstract: The crude prevalence of radiographic hip OA in Chinese ages 60–89 years was 0.9% in women and 1.1% in men; it did not increase with age. Chinese women had a lower age-standardized prevalence of radiographic hip OA compared with white women in the SOF (age-standardized prevalence ratio 0.07) and the NHANES-I (prevalence ratio 0.22). Chinese men had a lower prevalence of radiographic hip OA compared with white men of the same age in the NHANES-I (prevalence ratio 0.19). Nevitt et al, 2002 Arthritis & Rheumatism

Summary: Prevalence ratio of disease in exp and unexp Disease Yes No Exposure Yes No a b cd a + b c + d c a Prevalence Ratio = a/(a+b) and c/(c+d) = probabilities of disease and PR is ratio of two probabilities

Probability and Odds Odds another way to express probability of an event Odds = # events # non-events Probability = # events # events + # non-events = # events # subjects

Probability and Odds Probability = # events # subjects Odds = # events # subjects = probability # non-events (1 – probability) # subjects Odds = p / (1 - p) [ratio of two probabilities: unlike probability, can be greater than 1]

Probability and Odds If event occurs 1 of 5 times, probability = 1/5 = 0.2. Out of the 5 times, 1 time will be the event and 4 times will be the non-event, odds = 1 / 4 = 0.25 To calculate probability given the odds: probability = odds / 1+ odds

Understanding Odds To express odds in words, think of it as the frequency of the event compared to the frequency of the non-event “For every time the event occurs, there will be 3 times when the event does not occur” In words: “Odds are 1 to 3” Written as 1:3 or 1/3 or 0.33

Odds Less intuitive than probability (probably wouldn’t say “my odds of dying are 1 to 4”) No less legitimate mathematically, just not so easily understood

Odds (continued) Used in epidemiology because the measure of association available in case-control design is the odds ratio (more on this next week) Also important because the log odds of the outcome is given by the coefficient of a predictor in a logistic regression. Can use models to obtain multivariable adjustment in cross-sectional design. Less important now that adjusted models for prevalence ratio are possible.

Odds ratio As odds are just an alternative way of expressing the occurrence of an outcome, odds ratio (OR) is an alternative to the ratio of two probabilities (prevalence ratio) in cross-sectional studies Odds ratio = ratio of two odds

Probability and odds in a 2 x 2 table Disease Yes No Exposure Yes No 2 3 14 5 5 10 3 7 What is p of disease in exposed? What are odds of disease in exposed? And the same for the un-exposed?

Probability and odds ratios in a 2 x 2 table Disease Yes No Exposure Yes No 23 14 5 5 10 3 7 PR = 2/51/5 = 2 OR = 2/31/4 = 2.67

Odds ratio of disease in exposed and unexposed Disease YesNo Exposure Yes No ab c d a + b c + d c a OR = a a + b 1 - c c + d 1 - Formula of p / 1-p in exposed / p / 1-p in unexposed

Odds ratio of disease in exposed and unexposed a + b c + d c a OR = a a + b 1 - c c + d 1 - = a a + b b a + b c c + d d c + d a b c d == ad bc OR is the cross-product. However, calculating as odds of disease in exposed/ odds of disease in unexposed helps to keep track of what you are comparing.

Odds Ratio in Cross-Sectional Study The study design affects not just the measure of disease occurrence but also the measure of disease association Cross-sectional design uses prevalent cases of disease, so Odds Ratio in a cross- sectional study is a Prevalence Odds Ratio –Many authors do not use but we encourage –Promotes clarity of thought and presentation to be as accurate as possible about measures

OR compared to Prevalence Ratio 0 1∞ Stronger effect OR Prev Ratio Stronger effect Prev Ratio OR If Prevalence Ratio = 1.0, OR = 1.0; otherwise OR farther from 1.0

Prevalence ratio and Odds ratio If Prevalence Ratio > 1, then OR farther from 1 than Prevalence Ratio: PR = 0.4 = 2 0.2 OR = 0.4 0.6 = 0.67 = 2.7 0.2 0.25 0.8

Prevalence ratio and Odds ratio If Prevalence Ratio < 1, then OR farther from 1 than PR: PR = 0.2 = 0.67 0.3 OR = 0.2 0.8 = 0.25 = 0.58 0.3 0.43 0.7

Important property of odds ratio #1 OR approximates Prevalence Ratio only if disease prevalence is low in both the exposed and the unexposed group

Prevalence ratio and Odds ratio If risk of disease is low in both exposed and unexposed, PR and OR approximately equal. Text example: prevalence of MI in high bp group is 0.018 and in low bp group is 0.003: Prev Ratio = 0.018/0.003 = 6.0 OR = 0.01833/0.00301 = 6.09

Prevalence ratio and Odds ratio If prevalence of disease is high in either or both exposed and unexposed, Prevalence Ratio and OR differ. Example, if prevalence in exposed is 0.6 and 0.1 in unexposed: PR = 0.6/0.1 = 6.0 OR = 0.6/0.4 / 0.1/0.9 = 13.5 OR approximates Prevalence Ratio only if prevalence is low in both exposed and unexposed group

“Bias” in OR as estimate of PR Text refers to “bias” in OR as estimate of Prevalence Ratio (or Risk Ratio in a cohort study) Not “bias” in usual sense because both OR and PR are mathematically valid and use the same numbers Simply that OR cannot be thought of as a surrogate (“close approximation”) for the PR unless incidence is low

Table 2—Prevalence and odds of disability according to diabetes status (NHANES) – 60+ years old Gregg et al. Diabetes Care (2000) 23: 1272 DiabetesNo Diabetes Fell in previous year 36.3%24.9% Prevalence 36.3/10024.9/100PR= 36.3/24.9= 1.46 Odds 36.3/63.724.9/75.1OR= 36.3/63.7/24.9/75.1 = 1.72

Prevalence Ratio vs Odds Ratio Prevalence Ratio Zocchetti et al. 1997

Relative Measures and Strength of Association with a Risk Factor In practice many risk factors have a relative measure (prevalence ratio, risk ratio, rate ratio, or odds ratio) in the range of 2 to 5 Some very strong risk factors may have a relative measure in the range of 10 or more –Asbestos and lung cancer Relative measures < 2.0 may still be valid but are more likely to be the result of bias –Second-hand smoke risk ratio < 1.5 Underscores importance of interpretation of prevalence Odds Ratio in context of disease and exposure prevalences

Important property of odds ratio #2 Unlike Prevalence Ratio, OR is symmetrical: OR of event = 1 / OR of non-event

Symmetry of odds ratio versus non-symmetry of prevalence ratio OR of non-event is 1/OR of event PR of non-event = 1/PR of event

Example: Prevalence ratio not symmetrcial CasesNoncasesTotalPrevalence Exposed1417310.45 Unexposed3882486360.61 Total667 Prevalence ratio (of event) = 0.45/0.61 = 0.74 PR of non-event = (17/31)/(248/636) = 1.41 1/PR = 1 /0.74 = 1.35 NOT EQUAL to PR of non- event

Example: OR is symmetrical CasesNoncasesTotalPrevalence Exposed1417310.45 Unexposed3882486360.61 Total667 Odds ratio (of event) = (14/17)/(388/248)= 0.53 OR of non-event = (17/14)/(248/388) = 1.9 1/OR = 1/0.53 = 1.9 EQUAL to OR of non-event

Important property of odds ratio #3 Coefficient of a predictor variable in logistic regression is the log odds of the outcome e coefficient = OR Logistic regression. Method of multivariable analysis used most often in cross-sectional studies. Now possible to obtain adjusted models for prevalence ratio.

Smoking and Tooth loss – Example of prevalence odds ratio Methods. The authors collected information about tooth loss and other health- related characteristics from a questionnaire administered to 103,042 participants in the 45 and Up Study conducted in New South Wales, Australia. The authors used logistic regression analyses to determine associations of cigarette smoking history and ETS with edentulism (all teeth lost), and they adjusted for age, sex, income and education. Results. Current and former smokers had significantly higher odds of experiencing edentulism compared with never smokers (prevalence odds ratio [OR], 2.51; 95 percent confidence interval [CI], 2.31-2.73 and OR, 1.50; 95 percent CI, 1.43-1.58, respectively). Arora et al. JADA 2010

Vitamin D and PAD Objective – The purpose of this study was to determine the association between the 25-hydroxyvitamin D (25(OH)D) levels and the prevalence of peripheral arterial disease (PAD) in the general United States population. Methods and Results – We analyzed data from 4839 participants of the National Health and Nutrition Examination Survey. After multivariate adjustment for demographics, comorbidities, physical activity level, and laboratory measures, the prevalence ratio of PAD for the lower, compared to the highest, 25(OH)D quartile (<17.8 and ≥29.2 ng/mL, respectively) was 1.80 (95% CI: 1.19, 2.74) Melamed et. al. Arterioscler Throm Basc Biol 2010

Example: Adjusted prevalence ratio

3 Useful Properties of Odds Ratios Odds ratio of non-event is the reciprocal of the odds ratio of the event (symmetrical) Regression coefficient in logistic regression equals the log of the odds ratio Odds ratio of disease equals odds ratio of exposure –Important in case-control studies (Discussed next week)

Measures of Association in a Cohort Study With cross-sectional data we can calculate a ratio of the probability or of the odds of prevalent disease in two groups, but we cannot measure incidence A cohort study allows us to calculate the incidence of disease in two or more groups

Measuring Association in a Cohort Following two groups by exposure status within a cohort: Equivalent to following two cohorts defined by exposure

Analysis of Disease Incidence in a Cohort Measure occurrence of new disease separately in a sub-cohort of exposed and a sub-cohort of unexposed individuals Compare incidence in each sub-cohort –How?

Two Measures Recall from previous lectures the 2 measures of incidence: cumulative incidence and incidence rate Corresponding measures of disease association are risk ratio for comparing cumulative incidences and rate ratio for comparing incidence rates

Risk Ratio and Rate Ratio Risk is based on proportion of persons with disease = cumulative incidence –Risk ratio = ratio of 2 cumulative incidence estimates = cumulative incidence ratio = also called relative risk Rate is based on events per person-time = “average” incidence rate or hazard rate –Rate ratio = ratio of 2 incidence rates = incidence rate ratio = also called relative rate –Hazard ratio = ratio of 2 hazard rates We prefer risk ratio, rate ratio in cohort studies (just as we prefer prevalence ratio and odds ratio in cross-sectional study)

A Note on RR or “Relative Risk” Relative risk or RR is very common in the literature, but is used loosely and may refer to a risk ratio, a rate ratio, a prevalence ratio, or even an odds ratio Best to avoid this non-specific term. Be explicit about the different types of ratios.

What is that “Relative Risk”? Determine if prevalent or incident disease was measured. There can be substantial difference in the association of a risk factor with prevalent versus incident disease If incident disease, determine if cumulative incidence (at what time?) or a person-time incidence rate (average or hazard rate) was used to calculate ratio Any measure of association labeled “relative” should be a ratio, not a difference

Risk Ratio (No Censoring) Diarrheal Disease (w/in 3 days) Yes No Total Ate potato salad 54 16 70 Did not eat potato salad 2 26 28 Total 56 42 98 Probability of disease, ate salad = 54/70 = 0.77 Probability of disease, no salad = 2/28 = 0.07 Risk ratio = 0.77/0.07 = 11 Illustrates risk ratio in cohort with complete follow-up

Risk Ratio in a Cohort with Censoring Choose a time point for comparing two cumulative incidences: At 6 years, % dead in low CD4 group = 0.70 and in high CD4 group = 0.26. Risk ratio at 6 years = 0.70/0.26 = 2.69

Clinical trial originally designed for 3 years, extended by DSMB to 5 years Risk Ratio: 1yr= 0.95 2yr=0.86 3yr=0.80 5yr=0.78

NB: If displayed as survival curves, take 1-survival probability to get risk: Risk Ratio = 0.3/0.5=0.6

Subarachnoid hemorrhage (SAH): Risk ratio Background –…examine ethnic and gender difference in …subarachnoid hemorrhage (SAH). Methods – All patients with nontraumatic SAH older than 44 years were prospectively identified from January 1, 200 to December 31, 2006, as part of the Brain Attack Surveillance In Corpus Christi project, and urban population-based study in southeast Texas. Risk ratios for cumulative SAH incidence comparing MAs with non Hispanic whites (NHWs) and women with men were calculated. Results – A total of 107 patients had a SAH during the time period (7-year cumulative incidence: 11/10,000). The overall age-adjusted risk ratio for SAH in MAs compared with NHWs was 1.67 (95%CI: 1.13, 2.47), and in women compared to men was 1.74 (95% CI 1.16, 2.62). Eden et al. Neurology 2008

SAH: Example of risk ratio

Rate ratio: Comparison of “average” incidence rates Ratio of two person-time rates –NB: denominators of two person-time rates must be in the same units Outcome: CHD death or MI Rate NANSAID use = 12.02 per 1000 person-yrs Rate for non use = 11.86 per 1000 person-years Rate ratio = 12.02/11.86 = 1.01 Ray, Lancet, 2002

NANSAID use and CHD Background We did an observational study to measure the effects of NANSAIDs, including naproxen, on risk of serious coronary heart disease. Methods We used data from the Tennessee Medicaid programme obtained between Jan 1, 1987, and Dec 31, 1998, to identify a cohort of new NANSAID users (n=181 441) and an equal number of non- users, matched for age, sex, and date NANSAID use began. The study endpoint was hospital admission for acute myocardial infarction or death from coronary heart disease. Findings During 532 634 person-years of follow-up, 6362 cases of serious coronary heart disease occurred, or 11·9 per 1000 person-years. Multivariate-adjusted rate ratios for current and former use of NANSAIDs were 1·05 (95% CI 0·97–1·14) and 1·02 (0·97–1·08), respectively. Described as “rate ratio.” “Incidence rate ratio” (IRR) also acceptable

Radiation exposure and cancer incidence. Nuclear power workers in Korea. This study examines for the first time cancer incidence between radiation and non-radiation workers in nuclear power facilities in the Republic of Korea… Statistical analyses were carried out using the standardized incidence ratio (SIR), to compare the cancer risks of radiation and non-radiation workers with those of the general population. Poisson regression was also used to estimate the rate ratio (RR)… The RR for radiation workers compared with non- radiation workers was 1.18 (95% CI 0.89-1.58) for all cancers combined. Jeong et al. Radiat Environ Biophys 2010

Example: Rate ratio and standardized incidence ratio

Proportional hazards model Proportional hazards model compares hazards in the exposed and unexposed Result is a type of rate ratio and is often reported as a “hazard ratio” A type of regression model that can adjust for factors simultaneously

Example: Mortality after pediatric kidney transplant, stratified by donor type Vittinghoff et al. Regression Methods in Biostatistics 2005 Survival curves Hazard functions

From proportional hazards model: Hazard ratio = 2.06

Example: Risk ratio and Hazard ratio in clinical trial

Risk Ratio for Vertebral Fracture – identified by x-ray

Hazard ratio (Rate ratio) for nonvertebral fx

Rate Ratio vs. Relative Risk Example: What was reported comparing death in two BMI groups: “the relative risk of death was 1.52” (Calle, NEJM, April 2003) What was calculated (from Methods): “Relative risks (the age-adjusted death rates in specific body mass index category divided by the corresponding rate in the reference category) were calculated.” The ratio of two person-time rates was calculated but reported as a relative risk.

Rate ratio vs. Risk ratio Risk must be between 0 and 1 –Thus in comparing 2 groups high risk in unexposed group limits how large ratio can be –Eg, risk in unexposed group = 0.7 means maximum risk ratio = 1.0/0.7 = 1.42 Rates are not restricted between 0 and 1 –If exposed rate = 10/100 person-years and unexposed rate = 5/100 person-years, risk (cumulative incidence) in 2 groups after 20 years = 0.88 and 0.64. –Risk ratio would be 0.88/0.64 = 1.38 –but rate ratio = 10/5 = 2.0.

Risk Ratio vs. Rate Ratio In preceding example of risk ratio = 1.38 and rate ratio = 2.0, which would you report? Are the two ratios telling you something different?

Risk Ratio and Rate Ratio with constant incidence rate Exp = 0.50 per pers-yr; Unexp = 0.25 per pers-yr

Risk Ratio and Rate Ratio with lower incidence rate Exp = 0.050 per pers-yr; Unexp = 0.025 per pers-yr

Risk Ratio vs. Rate Ratio Use depends on data available and desired emphasis. Go back two slides - Risk ratio –How probability of disease differs by exposure Rate ratio –Exposure as a risk factor for the disease. –Preserves the relative “force” of exposure on disease outcome. –More fundamental measure of disease occurrence.

Preferred ratio measures of association by study design Cross-sectional study –Prevalence ratio** –(Prevalence) odds ratio Cohort Study –Risk ratio –Rate ratio Case-control study (next week) –Odds ratio (only possible)

Difference vs. Ratio Measures Two basic ways to compare measures: –difference: subtract one from the other –ratio: form a ratio of one over the other Can take the difference of either an incidence or a prevalence measure (but rarely done with prevalence) Example using incidence: cumulative incidence 26% in exposed and 15% in unexposed, –risk difference = 26% - 15% = 11% –risk ratio = 0.26 / 0.15 = 1.7

Example: Long-Term Use of Statins and Risk of Colorectal Cancer (Manitoba) VariablePerson years of follow-up CRC cases Incidence Rate* IRR95% CI No statin use 3,250,2666,2352.161.0Reference Regular statin users 134,7344022.291.030.93-1.14 *per 1,000 person-years Singh et al, Amer Jour of Gastroenterology 2009 Rate difference = 2.29-2.16 = 0.13 per 1,000 person-yrs

Primary biliary cirrhosis and death – STATA example from last week sts graph, hazard K-M survival curve for same data Average incidence rate = 0.13 deaths per person-year 10 yr cum incidence = 0.2375 More information in the plot

KM plots by treatment

Risk ratio – Tmt and death TimeFailure Function Risk Ratio Placebo 30.282 60.552 100.772 Active 30.2990.299/0.282 = 1.06 (3 yrs) 60.4860.486/0.552 = 0.88 (6 yrs) 100.6970.697/0.772 = 0.90 (10 yrs)

Calculating Rates in STATA Example: Biliary cirrhosis time to death data.use biliary cirrhosis data, clear.stset time, fail(d).strate D Y Rate Lower Upper 96 747.04 0.1285 0.1052 0.1570.strate treat Treat D Y Rate Lower Upper Placebo 49 355.0 0.138 0.104 0.183 Active 47 392.0 0.120 0.090 0.160 Rate ratio (active vs pbo) = 0.120/0.138 = 0.87

Hazard functions by treatment

Hazard ratio Calculate in STATA Hazard ratio = 0.86 (95% CI 0.57, 1.28) ------------------------------------------------ That gives us 3 measures of association. From previous slides: Average incidence rate ratio = 0.87 Risk ratio (9 yrs) = 0.90

Summary of Measures of Association RatioDifference Cross-sectional prevalence ratio(prevalence difference) odds ratio(odds difference) Cohortrisk ratiorisk difference rate ratiorate difference (odds ratio)(odds difference) (rarely used)

Why use difference vs. ratio? Risk/rate difference gives an absolute measure of the association between exposure and disease occurrence –public health implication is clearer with absolute measure: how much disease might eliminating the exposure prevent? Risk/rate ratio gives a relative measure –relative measure gives better sense of strength of an association between exposure and disease for inferences about causes of disease

Example of Absolute vs. Relative Measure of Risk TB recurrence over 1 yr No TB recurrence over 1 yr Total Treated: > 6 mos 14 986 1000 < 3 mos 40 960 1000 Risk ratio = 0.040/0.014 = 2.9 Risk difference = 0.040 – 0.014 = 2.6% If incidence is very low, relative measure can be large but difference measure small

Reciprocal of Absolute Difference ( 1/difference) Depending on scenario: –Number needed to treat to prevent one case of disease –Number needed to treat to harm one person –Number needed to protect from exposure to prevent one case of disease TB rifampin example: 1/0.026 = 38.5, means that you have to treat 38.5 persons for 6 mos vs. 3 mos. to prevent one case of TB recurrence

Table 2. Return of spontaneous circulation according to intervention Intervention Return of Spontaneous Circulation Risk Difference (95% CI) p-value Rapid Defibrillation ( N=1391) 12.9% -- Advanced Life Support (N=4247) 18.0% 5.1% (3.0-7.2) <0.001 Stiel et al., NEJM, 2004 Example of study reporting risk difference Risk difference = 0.051; number needed to treat = 1/0.051 = 20

Summary points Cross-sectional study –Prevalence ratio –Odds ratio Cohort study: –Risk ratio –Rate ratio –Risk/rate difference Ratio measures of association –Strength of association –For etiologic research Difference measures of association –Public health/clinical importance

Disease Association I Main points to be covered Fall 2010 Measures of association compare measures of disease between levels of a predictor variable Cross-sectional.

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Disease Association I Main points to be covered Fall 2010 Measures of association compare measures of disease between levels of a predictor variable Cross-sectional.

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