Mohammad Aljawadi, PharmD PhD Nora A. Kalagi, MSc

Aug 2015 PHCL 435

Measuring associations between exposures and outcomes

Risk assessment measures

• Introduction• Risk estimates• 95% Confidence interval • Interpretation• Summary

Outline

• Most epidemiological research involves the study of therelationship of one type of event or characteristic to another.

• Example: * Does alcohol intake increase the risk of lung cancer?

Alcohol Lung cancer (exposure) (outcome)

* Does hepatitis B vaccination protect against liver cancer Hepatitis B vaccine Liver cancer (exposure) (outcome)

Introduction

The Exposure • May be associated with either an increased or a decreased

occurrence of disease or other specified health outcome• May relate to the environment, lifestyle, inborn or

inherited characteristics.• The term risk factor is often used to describe an exposure

variable.

The Outcome • A broad term for any defined disease, state of health,

health-related event or death. • In some studies, there may be multiple outcomes.

Introduction

• The exposures and outcomes are specific to study hypotheses andshould always be clearly defined before the study starts.

• In most instances, it is not sufficient to collect information only on theexposure and outcome of interest, because of mixed up effect ofanother exposure on the same outcome, the two exposures beingcorrelated. This phenomenon is known as confounding

Introduction

• Data on the exposures may be obtained through

Personal interviews (either face-to-face or by telephone)

Self-administered questionnaires Diaries of behavior, reference to records Biological measurements and measurements in the

environment Family member

Introduction

7

Association

A statistical relationship between two or more variables

Risk Probability conditional or unconditional of the occurrence of

some event in time

Probability of an individual developing a disease or change inhealth status over a fixed time interval, conditional on theindividual not dying during the same time period

Definitions

Risk measures

Estimates that quantitatively describe the amount of riskassociated with a particular exposure in a sample populationand the development or prevention of disease.

• They can quantify the association between the exposure

to a particular drug and an adverse drug reaction.

Definitions

• Risk estimates are part of our daily lives.

• Measures of risk are communicated to patients via newspapers, television, and the Internet daily, while communicated to practitioners via studies published in medical journals.

• These risk measures become important in the clinicaldecision-making process for both patients and practitioners.

• It is important to have a clear understanding of risk measuresto appropriately interpret and apply the estimates.

Risk Estimates

Risk measures are difficult to use for many reasons,

1) Conflicting results obtained from different studies. *

• For example, early observational studies have reported a positiveassociation between calcium channel blocker use and cancer, whereasmore recent observational studies have reported a negativeassociation.

• When conflicting information pertaining to risk is published, itbecomes difficult for both practitioners and patients to use riskestimates for clinical decision-making.

• A clear understanding of study design and the derivation

of risk estimates allows practitioners to determine themost reliable risk estimates to use in the midst ofconflicting results.

2) Confusion around the actual interpretation ofthe results of a study regarding risk estimates.

• Two readers may interpret, communicate, and use the

results of a study very differently. • Ex. Risk of body weight & death

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• When we rely on others to summarize study results involvingrisk estimates, we are often faced with conflicting results,depending on the writer's skills and perspective.

• The more adept a pharmacist becomes in evaluating andinterpreting risk estimates, the more effective he/she will bein helping patients to sort through the conflicting informationthey receive.

• Epidemiologist are often interested in assessing the presenceof association expressed by differences in disease frequency.

• Measuring frequency can be based on either Absolutedifferences between measures of disease frequency in groupsbeing compared (e.g exposed vs unexposed) or Relativedifferences or risk.

Measurement of exposures and

outcomes

Absolute differences vs. Relative differences or risk.

• Measures based on absolute differences are often preferredwhen public health main goal is often an absolute reduction inthe risk of undesirable outcome

• In contrast, etiologic studies that are searching disease causesand determinants usually rely on relative differences in theoccurrence of discrete outcome.

1) Measures of association based on ratios

Odd Ratio (OR)Relative Risk (RR)Attributable risk (AR)

Measures2) of association based on absolutedifferences:

Risk Estimates

• RR, OR and AR can be estimated from a 2 x 2contingency table in cohort, case control studies andclinical trials.

Risk Estimates

• The confidence intervals determine the reliability of therisk estimate obtained in the sample.

• confidence intervals are defined as the range within whichthe true effect lies with a certain degree of assurance.

Point Estimate ± Confidence Coefficient *Standard Error

• A large CI indicates a low level of precision of the RR or OR,whereas a small CI indicates a higher precision of the RR orOR.

What about confidenceintervals?

• In practice, the 95% CI is often used as a proxy for thepresence of statistical significance if it does not overlap thenull value (e.g. OR=1).

• 95% confidence interval means that, if a study were

conducted 100 times, the true measure of association (e.g.,relative risk) would fall within the intervals 95 times.

• In other words, the investigator may have 95% assurance,or confidence, that the true measure of association (e.g.,relative risk) lies within the confidence interval.

• Is the likelihood of developing the disease in the exposedgroup relative to the unexposed group; i.e. A measure of association between the exposure and

the outcome.

• Risk of an event = probability that the event occurs

• Relative Risk= probability that event occurs in the exposed probability that event occurs in the unexposed Or

Relative risk (RR)

Relative risk (RR)

• Constructing a Confidence Interval for the Relative Risk issimilar to constructing a CI for the Odds Ratio

• A Relative Risk = 1.0 indicates ‘no association’ between theexposure and the disease.

• If the 95% confidence interval for the RR does not contain1.0 we can conclude that there is a statistically significant*

association between the exposure and the disease. * at the 0.05 significance level

• If the 95% confidence interval for the RR contains 1.0, the

association is not significant at the 0.05 level.

Confidence Interval for Relative Risk

• The null hypothesis in a comparison of two groups states that the

proportion of subjects with the outcome of interest is equal in the exposedand the unexposed groups.

• Ho: RR= 1

• Interpretation of RR

Relative risk

Null hypothesis

Protective effect

Q….What is The relative risk for developing asthma forcollege X students living in the city compared with collegeX students living in the country. Using the 2x2contingency table.

Example

Answer….

Students in college X who live in the city have 1.86 times the risk ofdeveloping asthma than students in college X who live in the country.

• Consider the results of three different studies. Therelative risk and the corresponding 95% confidence

interval for each study were as follows:

Example

• the odds ratio is used to estimate the relative risk in a case-controlstudy.

• Represents the odds that an outcome will occur given a particularexposure, compared to the odds of the outcome occurring in the

absence of that exposure..

• Odds of an event = probability that the event occurs

probability that the event does not occur

• Odds Ratio= odds of event for occurrence in exposed odds of event occurrence in non exposed

Odd Ratio (OR)

Odds vs. Risk:

Among 5 persons one is sick:

Risk=1/5=0.2 20%

Odds=1/4=0.25 25%

• Odds ratios are used to compare the relative odds of theoccurrence of the outcome of interest (e.g. disease ordisorder), given exposure to the variable of interest (e.g.health characteristic, aspect of medical history).

• The odds ratio can also be used to determine whether aparticular exposure is a risk factor for a particular outcome,and to compare the magnitude of various risk factors for thatoutcome.

OR, when is it used?

• An Odds Ratio = 1 indicates ‘no association’ between theexposure and the disease.

• If the 95% confidence interval for the OR does not contain 1.0we can conclude that there is a statistically significant*association between the exposure and the disease. * at the0.05 significance level

• If the 95% confidence interval for the OR contains 1.0, theassociation is not significant at the 0.05 level.

Interpretation of 95% ConfidenceInterval of OR

• The null hypothesis when using the odds ratio states,

Ho: OR = 1.

Odd Ratio

Q…. What is The Odd ratio for developing asthma for collegeX students living in the city compared with college X studentsliving in the country. Using the 2x2 contingency table.

Example

Answer….

Relative risk can be used to measure the associationbetween exposure and outcome in cohort studies andclinical trials, but not in case-control study.

• Why?

Relative risk and case control design:

• In case-control studies, subjects are chosen based ondisease status and then compared for rates of exposure.

• So the investigator cannot estimate the incidence ofdisease. Subjects either have the disease or do not have

the disease at the onset of a case-control study.

• Because the relative risk is merely a ratio of twoincidences, the relative risk is not useful in the contextof a case-control study. Instead, the odds ratio is usedto estimate the relative risk in a case-control study.

Relative risk

• Another measure of risk used in studies.

• The attributable risk provides information on the absoluteeffect of the exposure, describes the excess risk of diseasein those exposed compared with those who wereunexposed.

Attributable Risk or (risk difference)

• Attributable risk allows the investigator to determine howmorbidity and mortality are affected by removing theexposure.

• The null hypothesis for using the attributable risk states, Ho:AR = 0. Means there is no association between exposure andoutcome.

• The attributable risk provides information on the type ofeffect that can be achieved by decreasing or eliminating theexposure.

Attributable Risk

Q….The attributable risk for college X students?

The excess occurrence of asthma attributable to living in the cityis 6593 cases per 100,000.

In other words, if living in the city causes asthma, then 6593 cases ofasthma per 100,000 subjects could be eliminated if living in the city wereeliminated.

Example

• The attributable risk percent provides an estimate ofthe proportion of the disease among the exposed thatis attributable to the exposure.

Attributable Risk Percent

AR % = (RR-1)/RR * 100

Q….The attributable risk percent for college X students

If living in the city causes asthma, then approximately 46% of asthma

among subjects living in the city can be attributed to living in the city andcould, therefore, be eliminated if the subjects did not live in the city.

Example

• The number needed to treat (NNT) is an estimate usedprimarily in pharmacoeconomical studies.

• This estimate represents the number of patients one wouldneed to treat to prevent one clinical event.

• Like the attributable risk, the number needed to treat isused by administrators to allocate health resources.

Number need to treat

Q…. If AR= 0.06595, NNT?

Example

• Absolute Risk

When comparing 2 risks the absolute difference between them isreferred to as the absolute risk reduction (ARR) or the risk difference(RD)

• Relative Risk • the proportion of the original risk that is still present when patients

receive the experimental treatment • The ratio of risk in the treated group to the risk in the control group

(RR) is known as the relative risk

• RRRIs an estimate of the proportion of baseline risk that is removed by thetherapy.

Measuring risk association in RCT

studies

• EER is the experimental event risk= outcome/ Treatment• CER is the control event risk= Outcome/Control

• Relative risk (RR) compares the risk of outcome in the

intervention group (EER) with the risk of outcome in thecontrol group (CER)

• Absolute risk reduction (ARR) calculated by subtracting theEER from the CER.

• Number needed to treat (NNT) is the reciprocal of the ARR

• Relative risk reduction (RRR) can be calculated by eitherdividing the ARR by the CER or subtracting the RR from 1.

Example

Control event rate (CER): 20/100 = 20%.

Experimental event rate (EER): 15/100 = 15%.

Absolute risk reduction or risk difference: CER – EER, 20% – 15% = 5%.

Relative risk: EER/CER = (15/100)/(20/100) × 100% = 75%.

Relative risk reduction: 1 – (EER/CER) × 100% = 1 – 75% = 25%.

• In conclusion, measures of risk allow the quantification ofdegree of risk associated with any number of exposures.

• Risk estimates are point estimates, the estimates obtained inthe particular study population. Therefore, may or may notrepresent the true, or actual, risk that exists in the generalpopulation.

• When evaluating risk estimates, it is important to consider thebaseline risk of developing the disease and the confoundingvariables.

Summary

• Both Odds Ratio and Relative Risk are measures ofassociation (or relationship) between two nominalvariables.

• The Odds Ratio is typically estimated from datacollected in a Case-Control study.

• The Relative Risk can be estimated from datacollected in a Cohort study.

• If there is no association between the two variables,the OR or RR = 1

• An OR or RR > 1.0 or < 1.0 indicates a possiblestatistical relationship (or association) between thetwo variables.

• Hypothesis tests for the OR and RR are not used todetermine statistical significance of the association

• Instead, Confidence intervals of OR or RR areconstructed and used to determine whether or notthe association is statistically significant.