Starting RiskRIZWANUL KARIM

RiskRisk generally refers to the probability of some untoward event.Risk is the probability that people who are exposed to certain risk factors will subsequently develop a particular disease more often than similar people who are not exposed

Important JargonExposure (E) an explanatory factor; any potential health determinant; the independent variableDisease (D) the response; any health-related outcome; the dependent variable Measure of association (syn. measure of effect) a statistic that quantifies the relationship between an exposure and a diseaseMeasure of potential impact a statistic that quantifies the potential impact of removing a hazardous exposure

"For the things of this world cannot be made known without a knowledge of mathematics."- Roger Bacon

Measures of association are mathematical comparisonsMathematic comparisons can be done in absolute terms or relative terms Let us start with this ridiculously simple example:I have $2 You have $1

Absolute ComparisonIn absolute terms, I have $2 $1 = $1 more than youNote: the absolute comparison was made with subtractionIt is as simple as that

Relative ComparisonRecall that I have $2 and you have $1. In relative terms, I have $2 $1 = 2, or twice as much as youNote: relative comparison was made by division

Applied to RisksSuppose, I am exposed to a risk factor and have a 2% risk of disease. You are not exposed and you have a 1% risk of the disease.Of course we are assuming we are the same in every way except for this risk factor.In absolute terms, I have 2% 1% = 1% greater risk of the diseaseThis is the risk difference

Applied to RisksIn relative terms I have 2% 1% = 2, or twice the riskThis is the relative risk associated with the exposure*

Terminology*For simplicity sake, the terms risk and rate will be applied to all incidence and prevalence measures.

Difference Measures Comparing disease occurrence among the exposed with the disease occurrence among the unexposed comparison group by subtracting one from the other.

Risk DifferenceRisk Difference (RD) absolute effect associated with exposurewhere R1 risk in the exposed group R0 risk in the non-exposed groupInterpretation: Excess risk in absolute terms

Risk/Rate Difference (also called Attributable Risk/Rate) RD/AR = Rate or risk in exposed (Rexp) Rate or risk in unexposed (Runexp)

For CI: CIexp - CIunexp = a / (a+b) - c / (c+d)

For IR: IRexp - IRunexp = a / PTexp - c / PTunexp

RD/AR = 0 when there is no association

Hypertension

Non Fatal Heart AttackExample

YesNoTotalYes11713,30513,422No125106,416106,541Total242119,721119,963

RD = CIexp - CIunexp = 117 / 13,422 - 125 / 106,541 = .00872 - .00117 = .00755 or 755 / 100,000 Interpretation: The excess occurrence of non-fatal heart attack among these hypertensive women was 755 per 100,000. Or, if hypertension causes non-fatal heart attacks then 755 cases of non-fatal heart attack per 100,000 women could be eliminated if the hypertension were treated. Solution

Risk/Rate Difference (continued)/ Attributable risk Purpose: Gives information onthe absolute effect of exposure on disease occurrence. the excess disease risk in the exposed group compared to the unexposed group. the public health impact of an exposure, that is, how much disease would be prevented if the exposure were removed. This assumes that the exposure causes the disease.

Rate/Risk Ratio (also called Relative Risk)

Comparing Disease occurrence among exposed with Disease occurrence among comparison group (usually unexposed)

Rate/Risk Ratio (also called Relative Risk) RR= Rate or risk in exposed group (Rexp) / Rate or risk in unexposed group (Runexp)For CI: CIexp / CIunexp = a / (a+b) / c / (c+d)For IR: IRexp / IRunexp = a / PTexp / c / PTunexp

Rate/Risk Ratio (also called Relative Risk) Purpose: Gives information on the relative effect of the exposure on the disease. Tells you how many times higher or lower the disease risk is among the exposed as compared to the unexposed. Is commonly used in etiologic research

Example: Cohort study of hypertension and cardiovascular morbidity and mortality(Nurses Health Study) Hyper-tensionNon Fatal Heart Attack

YesNoTotalYes11713,30513,422No125106,416106,541Total242119,721119,963

Example: Cohort study of hypertension and cardiovascular morbidity and mortality (Nurses Health Study) RR = CIexp / CIunexp = 117/13,422 = .00872 = 7.5 125/106,541 .00117 Interpretation: Women with hypertension have 7.5 times the risk of having a non-fatal heart attack compared to women without hypertension.

Comparison of RR and RD/AR Annual Mortality Rate Per 100,000Conclusion: Cigarette smoking is a much stronger risk factor for lung cancer but (assuming smoking is causally related to both diseases) the elimination of cigarettes would prevent far more deaths from coronary heart disease.

Lung CancerCoronary Heart DiseaseCigarette Smoker140669Non Smoker10413RR14.01.6RD130/100,000/YR256/100,000/YR

OddsOdds, is the ratio of two probabilities, p the probability of an event) to that of (1-p) 1- the probability of the event. Odds and probability contain the same information, but they express it differently:Odds = probability of an event /(1- the probability of the event)Probability = Odds / (1+ Odds)

Odds ratio in a case control study

Calculation of Proportions Exposed in a Case-Control studyFirst selectCases ( with disease)Controls(without disease)Then MeasureThe ExposureWere exposedabWere not exposedcdtotalsa + cb + dProportion exposed

Odds ratio in a Case-control study

Cases(with disease)Control(without disease)History of ExposureabNo historyOf Exposurecd

People with the diseasePeople without the diseaseCasesControlsStart With :andThen determine Exposure History:and

The Odds Ratio (Relative Odds)In acase-controlstudy, however, we do not know the incidence in the exposed population or the incidence in the non-exposed population because we start with diseased people (cases) and non-diseased people (controls).

Hence, in a case-control study wecannotcalculate the relative risk directly.

The odds of an event can be defined as the ratio of the number of ways the event can occur to the number of ways the event cannot occur.

Odds ratio in a Case-control study

Cases(with disease)Control(without disease)History of ExposureabNo historyOf Exposurecd

Theoddsof a case having been exposed area:cor

Theoddsof a control having been exposed areb:dor

in acase-control study, is defined asthe ratio of the odds that the cases were exposed to the odds that the controls were exposed. This is calculated as follows:

Calculating Odds ratio

Example of calculating an Odds Ratio from a case control StudyFirst selectCHD CasesControlsThen MeasurePast ExposureSmokersNon-SmokersTotals200 (a + c)400 (b + d)Proportions of Smoking Cigarette56%44%Odds ratio

112 (a)176 (b)88 (c)224 (d)

Population Risk/Rate Difference (PRD) /population attributable riskPurpose: Measures excess disease occurrence among the total population that is associated with the exposure. Helps to evaluate which exposures are most relevant to the health of a target population.

Population Risk/Rate Difference (PRD) /Population attributable risk Two formulas for PRD:PRD/PAR = (RD/AR) (Pexp) where Pexp = proportion of population that is exposed, and RD/AR is the risk or rate difference PRD/PAR = Rtotal - Runexp where Rtotal = risk/rate in total population and Runexp = risk/rate among unexposed

Population Risk/Rate Differenceexample HypertensionNon-fatal Heart Attack

YesNoTotalYes11713,30513,422No125106,416106,541Total242119,721119,963

PRD/PAR = [(117/13,422) - (125/106,541)] x (13,422/119,693) = (.00755) x (.112) = .00085or PRD/PAR = 242/119,963 - 125/106,541 = .00202 - .00117 = .00085 or 85/100,000Interpretation: Hypertension results in an excess incidence of 8.5/10,000 non-fatal heart attacks in the total study population. Or, if hypertension were eliminated, 8.5/10,000 cases of non-fatal heart attacks could be eliminated among the total study population. (Assumes that hypertension causes heart attacks.)Solution

Population Risk/Rate Difference A relatively weak risk factor (in terms of relative risk) that is quite prevalent could account for more of disease incidence in a population than a stronger risk factor that is rarely present.

Thank you

Chapter 8: Association & Impact*Epi Kept Simple*We compare the weight of a man of 100 kg to the weight of a woman of 50 kg. -Absolute comparisons are derived by subtraction and using (original units of measure kg)-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}Chapter 8: Association & Impact*Epi Kept Simple*We compare the weight of a man of 100 kg to the weight of a woman of 50 kg. -Absolute comparisons are derived by subtraction and using (original units of measure kg)-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}Chapter 8: Association & Impact*Epi Kept Simple*We compare the weight of a man of 100 kg to the weight of a woman of 50 kg. -Absolute comparisons are derived by subtraction and using (original units of measure kg)-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}Chapter 8: Association & Impact*Epi Kept Simple*We compare the weight of a man of 100 kg to the weight of a woman of 50 kg. -Absolute comparisons are derived by subtraction and using (original units of measure kg)-{Relative comparisons are derived by division (the division cancels out units, making a unit-free comparison}Chapter 8: Association & Impact*Epi Kept Simple*Lets apply arithmetic to risks. These are the formulas. {The formulas are simple: RD is a subtraction and RR is a division. The key is to understand how we interpret the RR and the RD. They both quantify the relation between E and D, but they tell you something different about the association. Going through lots of examples in the book will help understand subtleties.}Chapter 8: Association & Impact*Epi Kept Simple*Lets apply arithmetic to risks. These are the formulas. {The formulas are simple: RD is a subtraction and RR is a division. The key is to understand how we interpret the RR and the RD. They both quantify the relation between E and D, but they tell you something different about the association. Going through lots of examples in the book will help understand subtleties.}