risks & ratios

calculating relative risk

*RR = (risk among exposed) / (risk among unexposed)* using a 2X2 table: RR = (a/a+b) / (c/c+d) people that have disease out of total exposed DIVIDED BY people that have the disease out of total unexposed

relative risk RR = 1 RR > 1 RR < 1

*RR = 1* - the exposed have the same risk for a disease as the unexposed - no association *RR > 1* - the exposed have a GREATER risk of a disk than the unexposed - positive (possibly causal) association *RR < 1* - the exposed have a LOWER risk of disease than he unexposed - negative (possible protective) association

example calculations: AR for exposed group AR as proportion

1) *AR for exposed group* (31-18.1)/1000 = 12.9/1000 *interpretation* = 12.9 of the 31 per 1000 cases of lung cancer among smokers are attributable to smoking 2) *AR as proportion* (31-18.1)/31 = 12.9/31 = .416 = 41.6% *interpretation* = 41.6% of the lung cancer cases among smokers are attributable to smoking, and can be prevented by eliminating smoking

point estimate

= the level of association measured in confidence intervals can be variable - the width of the variation around the point estimate expresses the *statistical precision* of the estimate the width of the CI indicates the amount of sample variability in the data

p-value

= the probability that the difference observed could have occurred by chance alone (basically that there is no difference between study groups) indicates how likely it is that the observed result would occur if they null hypothesis (RR=1, OR=1) is actually true if p < 0.05 - results are likely NOT due to chance - reject the null p-values are useful for accepting/rejecting the null hypothesis, BUT they provide *no info about the precision of the estimate* edidemiologists prefer confidence intervals

calculating odds ratio EXAMPLE

A jar contains 10 marbles, each a different color. What are the odds of selecting a blue marble? probability P = 1/10 = .1 *odd ratio = P / (1-P)* ODDS = .1 / (1-.1) = .1/.9 = .11

attributable risk

AR *determines what proportion of the risk in exposed people is ACTUALLY due to the exposure* the incidence due to exposure - must subtract out "background risk" indicates the proportion of the disease occurrence that potentially would be eliminated if the exposure to risk was prevent AR is key component of policy decisions

calculating attributable risk AR % in exposed group

AR % = proportion of the total incidence AR = *[(incidence in exposed) - (incidence in unexposed)] / incidence in exposed* EX: Incidence of MI in those with hypertension is .2. Incidence of MI in normal BP is .05. AR % = (.2-.05)/.2 = 75% *interpretation* = 75% of the total risk of MI in those with hypertension is attributable to hypertension

calculating attributable risk AR in exposed group

AR = *(incidence in exposed) - (incidence in unexposed)* EX: Incidence of MI in those with hypertension is .2. Incidence of MI in normal BP is .05. AR = .2-.05 = 15% *interpretation* = the elimination of hypertension would lower the risk of MI in the exposed group by 15%

attributable vs. relative risk

ATTRIBUTABLE RISK - determines how much risk is due to a specific exposure - *preferred* - important in intervention, policy, etc. - quantities how much a certain outcome can be preventing by addressing specific exposure RELATIVE RISK (and OR) - measure the strength of associations between exposures and outcomes - important in *causality*

The odds ratio always approximates the relative risk if the disease is frequent. T/F

False OR can predict RR when the disease is *rare*

odds ratio calculations MATCHED vs. UNMATCHED

MATCHED - only use discordant pairs = b/c OR = 9/2 UNMATCHED - uses normal calculations = (ad)/(bc) OR = (13X14) / (6x7)

when to use relative risk? when to use odds ratio?

ODDS RATIO - can be used in both *cohort and case-control* studies RELATIVE RISK - can be calculated directly in cohort studies only ***RR is a preferred measure

risk vs. odds

RISK - the probability of a certain event occurring ODDS - the ratio of the probability of an event occur VS the probability of the event not occurring

causation

a change in the frequency or quality of an independent (predictor) variable triggers a corresponding change in the dependent (outcome) variable EX: long-term chronic smoking can cause lung cancer

association

a statistical relationship between two variables, events, etc. may or may not be causal EX: smoking and drinking are associated, but one does not cause the other

RR = 1.4 95% CI = 0.7 - 2.6 p-value = .10 What does the p-value suggest (α=0.05)? a) Do not reject the null since p-value is greater than 0.05 b) Reject the null since p-value is greater than 0.05

a) Do not reject the null since p-value is greater than 0.05

The study always assumes that the ______ is true. a) Null hypothesis b) Alternate hypothesis

a) Null hypothesis

RR = 1.4 95% CI = 0.7 - 2.6 p-value = .10 What would be a good summary statement about these data? "Although there seems to be a 40% risk of developing breast cancer among those exposed to pesticides compared to those not exposed, the result is however not statistically significant based on the 95% CI and p-value." a.True b.False

a.True

relative risk

aka *risk ratio* compares the risk of disease in an exposed group VS. the risk of disease in a non-exposed group *measure of strength of an association* cumulative incidence & incidence density can both/either be used to compute RR *RR = (risk among exposed) / (risk among unexposed)* can be seen as a probability can be calculated DIRECTLY in *cohort* studies EX: the risk of lung cancer in smoking vs. the risk of lung cancer in non-smokers

calculating attributable risk AR in total population (PAR)

aka population attributable risk PAR *PAR* = (incidence in total pop) - (incidence in unexposed) *PAR %* = [(incidence in total pop.) - (incidence in unexposed)] / incidence in total pop. must know the incidence in the entire population!!! ^ can be calculated with values: - incidence among exposed - incidence among non-exposed - proportion of total pop that is exposed *incidence in total pop* = (incidence in exposed X % exposed in population) + (incidence in non-exposed X % unexposed in population)

measures of association

assess the relationship between factors (exposures) that influence the likelihood of developing an outcome (disease) reflect the magnitude of a statistical relationship between 2 variables (e.g. exposure and disease) - often multiple variables

RR = 1.4 95% CI = 0.7 - 2.6 p-value = .10 What does the CI indicate about the null hypothesis? a) Reject the null since the CI contains 1 b) Do not reject the null since the CI contains 1

b) Do not reject the null since the CI contains 1

RR = 1.4 95% CI = 0.7 - 2.6 p-value = .10 What does the RR indicate? a) Positive association between pesticides and breast cancer hence, a protective association b) Positive association between pesticides and breast cancer hence, there may be a causal association c) 60% risk of breast cancer among those exposed to pesticides compared to those not exposed

b) Positive association between pesticides and breast cancer hence, there may be a causal association

Identifying how much risk is accountable by a single specific factor is ____________ and it is calculated by _____________ . a)Relative Risk; (Risk in exposed) - (risk in unexposed) b)Attributable Risk; (Risk in exposed) - (risk in unexposed) c)Relative Risk; (Risk in unexposed) - (risk in exposed) d)Attributable Risk; (Risk in unexposed) - (risk in exposed)

b)Attributable Risk; (Risk in exposed) - (risk in unexposed)

A prospective cohort study was conducted to estimate the effects of certain herbicides and insecticides in causing Chronic Lymphocytic Leukemia (CLL) and a relative risk of 1.7 was calculated. This means: a)Exposed are less at risk than unexposed b)Risk in exposed is greater than risk in unexposed c)The exposed have the same risk as unexposed therefore there is no association d)We can only measure odds ratios in this study

b)Risk in exposed is greater than risk in unexposed

In a cohort study of obesity and myocardial infarction, the odds ratio was calculated to be 4.5 while the relative risk was 2.5. What is the explanation for the difference in OR and RR? a. MI is rare condition b. MI is not rare condition c. Obesity is rare exposure c. Obesity is not rare exposure

b. MI is not rare condition

A matched case-control study was designed to evaluate the role of genes in RA. To calculate the OR, we use: a. concordant pairs b. discordant pairs c. both concordant and discordant pairs d. ad/bc

b. discordant pairs

RR = 1.4 95% CI = 0.7 - 2.6 p-value = .10 What does the 95% CI indicate? a) The result is statistically significant b) Pesticides can either be protective or harmful as regards to breast cancer incidence depending on mode of contact c) The result is not statistically significant

c) The result is not statistically significant

Power is: a)Usually set at 0.2 or 0.1 b)Usually set at a 'p' of less than or equal to .05 or .01 c)1-Beta d)None of the above

c)1-Beta

The characteristic being observed or measured to establish their influence on the outcome (Examples: causal variable, predictor variable, exposure variable, treatment variable, explanatory variable) a)Dependent variable b)Extraneous variable c)Independent variable d)Outcome variable

c)Independent variable

A study is conducted on the relationship between smoking and lung cancer. If a researcher wants to know the ratio of risk of disease in exposed to risk of disease in unexposed, he will be calculating the: a)Odds Ratio b)Attributable Risk c)Relative Risk d)PAR

c)Relative Risk

The researchers conducted a study to observe the relationship between smoking and Emphysema and set the alpha to 0.05. A Relative Risk of 1.3 was obtained with a p-value of 0.15. What can we say about the results: a)The results are true b)Results are unlikely due to chance c)Results are likely due to chance and We do not reject H0 d)The results are likely due to chance and We reject the H0

c)Results are likely due to chance and We do not reject H0

Two case-control studies were conducted. The odds ratios for study A was 2.3 (CI = 1.5 - 3.1) and the odds ratio for study B was 5.1 (CI = 2.2 - 8.0). What can we conclude from these two studies (sample sizes are the same)? a)Study A has higher variability compared to the study B. b)Study A has lower precision compared to the study B c)Study A has lower variability and higher precision compared to study B d)Neither study is statistically significant

c)Study A has lower variability and higher precision compared to study B

When is odds ratio a good estimate of relative risk? a)When the exposure is greater in cases compared to control. b)When the exposure is greater in controls compared to cases. c)When the disease or condition being studied is rare. d)When the disease or condition being studied is frequent.

c)When the disease or condition being studied is rare.

absolute association

can indicate the magnitude of the risk in a group of people with a certain exposure BUT *does not indicate if exposure is associated with increased risk* EX: attributable risk, risk difference used in public health planning, intervention, policy

calculating odds ratio EXAMPLE

case-control study of acute myocardial infarction in people with hypertension *OR* = (ad) / (bc) OR = (220 X 9955) / (9780 X 45) OR = 4.98 people with a MI had *5 times the odds* of reporting severe hypertension compared to those without a MI

calculating relative risk EXAMPLE

cohort study of 1-yr incident of myocardial infarction RR = (a/a+b) / (c/c+d) RR = (180/10,000) / (30/10,000) RR = 6 those with severe hypertension have *6 times the risk* of developing a myocardial infarction than those with normal BP

Epidemiologists tend to use___________ to reinforce the accuracy of their point estimate (RR, OR). a)Attributable Risk b)Measures of association c)P-value d)Confidence intervals

d)Confidence intervals

Researchers conducted a case control to see the effect of high cholesterol on Alzheimers. Out of the 61 Alzheimers cases, 37 had high cholesterol and 24 did not. In the control group, 68 had high cholesterol and 121 did not. What is the odds ratio? a. (37/37+68)/(24/24+121) b. 37/24 c. 37/69 d. (37*121)/(68*24) e. (68*24)/(37*121)

d. (37*121)/(68*24) OR = ad/bc

researchers conducted a case-control study in Alzheimers patients to see the effect of high cholesterol on Alzheimers. Out of 61 cases, 37 had high cholesterol and 24 did not. Out of the control group, 68 had high cholesterol and 121 did not. Calculate the attributable risk. a. (37/37+68) / (24/24+121) b. 37/24 c. (37*121)/(68*24) d. (37/37+68) - (24/24+121) e. (37/37+24) - (68/68+121)

d. (37/37+68) - (24/24+121)

objective of epidemiological studies

determine if there is excessive or reduced risk must compare the *incidence* of those who were exposed to those who were not exposed - case control - cohort - RCT studies all attempt to determine if there is an association between an exposure and an outcome strength of association is calculated

relative association

determines how strong an association exists between exposure and disease EX: relative risk, odds ratio used to assess causal associations

independent variables

factors that are manipulated in an experiment - establish their influence on an outcome (DV) aka - *risk factor* - causal variable (predictor) - exposure variable - treatment variable - explanatory variable

odds ratio MATCHED case-control

for matched pairs, the outcome options are: 1. pairs in which both case and control were exposed (concordant) 2. pairs in which neither the case nor control was exposed (concordant) 3. pairs in which case was exposed, control was not (discordant) 4. pairs in which control was exposed, case was not (discordant) *OR calculation only use DISCORDANT pairs* OR (matched) = b/c

calculating attributable risk EXAMPLE AR in total population (PAR)

given the prevalence = 11% incidence (total) = (incidence in exposed X prevalence) + (incidence unexposed X non-prevalence) incidence (total) = [(189 X .11) + (46 X .89)] = 62 per 1000 PAR = incidence total population - incidence non-exposed PAR = 62 -42 = 16 per 1000

determining excessive risk

must compare the incidence of those who were exposed to those who were NOT exposed measures of association provide info on: - the magnitude of the relationship (strong or weak) between outcome and exposure epidemiological goal: estimate the risk of disease in one group vs. risk of disease in another group ^^^ "relative risk"

when can OR be used to estimate RR?

odds ratio is a good estimate of relative risk, only when: 1) all the cases from an exposed population are represented 2) all the controls from an exposed population are represented 3) *the disease being studied is RARE* *** using OR in common diseases gives a risk 1.4 greater than the actual RR - poor approximation

example calculations: PAR for total population PAR as a proportion

prevalence is 25% 1) *PAR for total pop.* first find incidence in total pop (TI) TI = (31/1000)(.25) + (18.1/1000)(.75) = 7.8 + 13.6 TI = 21.4/1000 PAR = (21.4/1000) - (18.1/1000) = 3.3 per 1000 *interpretation* = in the entire population, for every 10,000 people, 33 cases of lung cancer are attributable to smoking 2) *PAR as proportion* = (21.4-18.1)/21.4 = 15.4% *interpretation* = 15.4% of the incidence of lung cancer in this population can be attributed to smoking

confidence interval

range within which the true magnitude of effects lies, with a state probability (usually 95%) gives more info than p-value - provides a range of hyptheses use point estimates - the smaller the range, the more precise the estimate

CI & precision

the wider the confidence interval, the lower the precision the narrower the interval, the higher the precision CI is not statistically significant if it includes 1.0 (null)

odds ratio

used to approximate the relative risk in *case-control* studies, when the occurrence of diseases are KNOWN odds of an event = the number of ways an event can occur to the numbers of ways an event cannot occur *odds ratio* = P / (1-P) where P = probability of occurrence

calculating odds ratio

used to assess the relative risk in case-control studies *odd ratio = P / (1-P)* can also be used for coroner studies using a 2X2 table: ODDS = (ad) / (bc)

dependent variables

variables that are affected by changes in other variables - what the study hopes to explain - accounts for the effects of independent variables aka - *outcome variable* - response variable - disease variable

extraneous variables

variables that interfere in a relationship between study variables - variables that influence the outcome, but that are not variables of interest aka - *confounding variables* - stratifiers - "noise" variables

relationship between p-value and confidence intervals

when *p < .05*, the CI is greater than 1 when *p = .05*, the CI includes 1 (ex: 1.0 - 1.07) when *p > .05*, the CI crosses 1 (ex: .97 - 1.4) if the confidence interval includes 1, it is not significant