March 2015 1

Back to Basics, 2015POPULATION HEALTH (1):

Epidemiology Methods, Critical Appraisal,

Biostatistical Methods

Dr. Nicholas Birkett

School of Epidemiology, Public Health and Preventive Medicine

Other resources available on Individual & Population Health web site

March 2015 2

THE PLAN (1)

• Session 1 (March 17, 1300-1700)– Evaluation of investigations

• Sensitivity, specificity, validity, PPV• Application to diagnostic tests, screening

– Critical Appraisal– Intro to Biostatistics– Brief overview of epidemiological research

methods

March 2015 3

THE PLAN (2)

• Aim to spend about 2.5 to 3 hours on lectures– Review MCQs in remaining time

• A 10 minute break about half-way through• You can interrupt for questions, etc. if

things aren’t clear.– Goal is to help you, not to cover a fixed

curriculum.

4March 2015

INVESTIGATIONS (1)

• 78.2– Determine the reliability and predictive value

of common investigations– Apply concepts to screening and diagnostic

tests.

March 2015 5

Reliability

• = reproducibility. Does it produce the same result

every time?

• Related to chance error

• Averages out in the long run

• In patient care you hope to do a test only once– Therefore, you need a reliable test

March 2015 6

Validity

• Whether a test measures what it purports to measure in long run– is a disease present (or absent)

• Normally use criterion validity– Compare test result to a gold standard

• Link to SIM web on validity

March 2015 7

Reliability Low High

Low

Validity

High

•

••

•

•

•

•

• •

••

•

•••

•• ••••

Reliability and ValidityTarget shooting as a metaphor

•• •

March 2015 8

Test Properties (1)Diseased Not diseased

Test +ve 90 5 95

Test -ve 10 95 105

100 100 200

True positives False positives

False negatives True negatives

March 2015 9

Test Properties (2)

Diseased Not diseased

Test +ve 90 5 95

Test -ve 10 95 105

100 100 200

Sensitivity = 0.90 Specificity = 0.95

March 2015 10

2x2 Table for Testing a Test

Gold standard

Disease Disease

Present Absent

Test Positive a (TP) b (FP)

Test Negative c (FN) d (TN)

SensitivitySpecificity

= a/(a+c) = d/(b+d)

March 2015 11

Test Properties (6)

• Sensitivity =Pr(test positive in a personwith disease)

• Specificity = Pr(test negative in a person without disease)

• Range: 0 to 1– > 0.9: Excellent– 0.8-0.9: Not bad– 0.7-0.8: So-so– < 0.7: Poor

March 2015 12

Test Properties (7)

• Sensitivity and Specificity

– Values depend on cutoff point between normal/abnormal

– Generally, high sensitivity is associated with low specificity and vice-versa.

– Not affected by prevalence, if ‘case-mix’ is constant

• Do you want a test to have high sensitivity or high specificity?

– Depends on cost of ‘false positive’ and ‘false negative’ cases

– PKU – one false negative is a disaster

– Ottawa Ankle Rules: insisted on sensitivity of 1.00

March 2015 13

Test Properties (8)

• Sens/Spec not directly useful to clinician

– Know only the test result

• Patients don’t ask:

– “If I’ve got the disease, how likely is that the test will be positive?”

• They ask:

– “My test is positive. Does that mean I have the disease?”

→ Predictive values.

March 2015 14

Predictive Values

• Based on rows, not columns– PPV interprets positive test

– NPV interprets negative test

• Depend upon prevalence of disease, so must be determined for each clinical setting

• Immediately useful to clinician– The probability that the patient has the disease

March 2015 15

Test Properties (9)Diseased Not diseased

Test +ve 90 5 95

Test -ve 10 95 105

100 100 200

PPV = 0.95

NPV = 0.90

March 2015 16

2x2 Table for Testing a Test

Gold standard

Disease Disease

Present Absent

Test + a (TP) b (FP) PPV = a/(a+b)

Test - c (FN) d (TN) NPV= d/(c+d)

a+c b+d N

March 2015 17

Prevalence of Disease

• Prevalence: the probability that someone has a disease,

condition at a point in time.

• For diagnostic tests:– Is your best guess about the probability that the patient has

the disease, before you do the test

• Also known as Pretest Probability of Disease

(a+c)/N in 2x2 table

• Is closely related to Pre-test odds of disease:

(a+c)/(b+d) in 2x2 table

March 2015 18

Test Properties (10)Diseased Not diseased

Test +ve a b a+b

Test -ve c d c+d

a+c b+d a+b+c+d =N

Prevalence odds

Prevalence proportion

March 2015 19

Prevalence and Predictive Values

• Predictive values of a test are dependent on the pre-test prevalence of the disease

– Tertiary hospitals see more pathology then FP’s

– Their positive tests are more often true positives.

• Most tests are developed and studied in tertiary care settings.

• How do you determine how useful a test is in a different patient setting?

March 2015 20

Prevalence and Predictive Values

• Process is often called ‘calibrating’a test– Relies on the stability of sensitivity &

specificity across populations.

– Allows us to estimate what the PPV and NPV would be in a new population.

March 2015 21

Methods for Calibrating a Test

Four methods can be used:– Apply definitive test to a consecutive series of

patients from the new population • rarely feasible, especially during the LMCCs

– Nomogram• only useful if you have access to the nomogram

March 2015 22

Methods for Calibrating a Test

Four methods can be used (cnt’d):

– Hypothetical table• Assume the new population has 10,000 people

• Fill in the cells based on the prevalence, sensitivity

and specificity [My recommended way]

– Bayes’s Theorem (Likelihood Ratio)

• You need to be able to do one of the middle 2.

• The easiest is using a hypothetical table.

• We pretend that we could do a new study in your patient population• Assume a practice size

• 10,000 makes the numbers nice

• Figure out how many patients with disease you would expect to see

• Figure what test results you would expect to see• Compute PPV

March 2015 23

Calibration by hypothetical table

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Calibration by hypothetical table

Disease Present

Disease Absent Total PV

Test +ve 4th 7th 8th 10th

Test -ve 5th 6th 9th 11th

Total 2nd 3rd 10,000

March 2015

Fill cells in following order:

“Truth”

Sensitivity

Specificity

Pre-test Prevalence

March 2015 25

Test Properties (11)

Diseased Not diseased

Test +ve 450 25 475

Test -ve 50 475 525

500 500 1,000

Tertiary care: research study. Prev=0.5

PPV = 0.89

Sens = 0.90 Spec = 0.95

March 2015 26

Test Properties (12)

Diseased Not diseased

Test +ve

Test -ve

10,000

Primary care: Prev=0.01

PPV = 0.1538

9,900

90

10

100

495

9,405

585

9,415

Sens = 0.90 Spec = 0.95

March 2015 27

Calibration by Bayes’ Theorem

• You don’t need to learn Bayes’ theorem• Instead, work with the Likelihood Ratio (+ve)

– Equivalent process exists for Likelihood Ratio (–ve), but we shall not calculate it here

• Consider the following table (from a research study)– How do the ‘odds’ of having the disease change

once you get a positive test result?

March 2015 28

Test Properties (13)Diseased Not

diseased

Test +ve

90 5 95

Test -ve

10 95 105

100 100 200 Pre-test odds = 1.00

Post-test odds (+ve) = 18.0

Odds (after +ve test) are 18-times higher than the odds before you had the test. This is the LIKELIHOOD RATIO.

March 2015 29

Calibration by Bayes’s Theorem

• Likelihood ratios are related to sens & spec– LR(+) =

• Sometimes given as the definition of the LR(+)

• LR(+) is fixed across populations.–Bigger is better.

March 2015 30

Calibration by Bayes’s Theorem

• How does this help?• Remember:

– Post-test odds(+) = pretest odds * LR(+)– And, the LR(+) is ‘fixed’ across populations

• To ‘calibrate’ your test for a new population:– Get the LR(+) value from the reference source– Estimate the pre-test odds for your population– Compute the post-test odds– Convert to post-test probability to get PPV

March 2015 31

Converting between odds & probabilities

• if prevalence = 0.20, then

• pre-test odds = = 0.25 (1 to 4)

• if post-test odds = 0.25, then • PPV = = 0.20

March 2015 32

Example of Bayes' Theorem(sens 90%, spec 95%, ‘new’ prevalence 1%)

• Compare to the ‘hypothetical table’ method (PPV=15.38%)

March 2015 33

Calibration with Nomogram

• Graphical approach which avoids arithmetic• Scaled to work directly with probabilities

– no need to convert to odds• Draw line from pretest probability

(=prevalence) through likelihood ratio– extend to estimate posttest probabilities

• Only useful if someone gives you the nomogram!

3434

Example of Nomogram (pretest probability 1%, LR+ 18, LR– 0.105)

Pretest Prob. LR Posttest Prob.

1%

18

.105

15%

0.01%

March 2015

Cautionary Tale #1: Data Sources

March 2015 35

The Government is extremely fond of amassinggreat quantities of statistics. These are raised to the nth degree, the cube roots are extracted, andthe results are arranged into elaborate and impressive displays. What must be kept ever in mind, however, is that in every case, the figures are first put down by a village watchman, and he puts down anything he damn well pleases!

Sir Josiah Stamp,Her Majesty’s Collector of Internal Revenue.

March 2015 36

78.2: CRITICAL APPRAISAL (1)

• “Evaluate scientific literature in order to critically assess the benefits and risks of current and proposed methods of investigation, treatment and prevention of illness”

• Covered in Toronto Notes• Let’s discuss hierarchy of evidence

– as used by Task Force on Preventive Health Services

March 2015 37

Hierarchy of evidence(lowest to highest quality, approximately)

• Systematic reviews• Experimental (Randomized)• Quasi-experimental• Prospective Cohort• Historical Cohort• Case-Control• Cross-sectional• Ecological (for individual-level exposures)• Case report/series• Expert opinion

} similar/identical

Cautionary Tale #2: Analysis

March 2015 38

Consider a precise number: the normal body temperature of 98.6°F. Recent investigations involving millions of measurements have shown that this number is wrong: normal body temperature is actually 98.2°F. The fault lies not with the original measurements - they were averaged and sensibly rounded to the nearest degree: 37°C. When this was converted to Fahrenheit, however, the rounding was forgotten and 98.6 was taken as accurate to the nearest tenth of a degree.

March 2015 39

Biostatistics Core Concepts (1)

• Sample: – A group of people, animals, etc. which is used to represent

a larger ‘target’ population.• Best is a random sample• Most common is a convenience sample.

– Subject to strong risk of bias.

• Sample size: – the number of units in the sample

• Much of statistics concerns how samples relate to the population or to each other.

March 2015 40

Biostatistics Core Concepts (2)

• Mean: – average value. Measures the ‘centre’ of the data. Will be roughly

in the middle.

• Median: – The middle value: 50% above and 50% below. Used when data

is skewed.

• Variance: – A measure of how spread out the data are.

– Defined by subtracting the mean from each observation, squaring,

adding them all up and dividing by the number of observations.

March 2015 41

Biostatistics Core Concepts (3)

• Standard deviation: – square root of the variance.

42March 2015

March 2015 43

Biostatistics Core Concepts (4)

• Standard error (of the mean):

– Standard deviation looks at the variation of the data

in individuals

– We usually study samples.• Select 10 people

• measure BMI

• take the group average

March 2015 44

Biostatistics Core Concepts (5)

• Standard error (of the mean):– Select a sample

• compute the mean

– Repeat many times.• Each time, we get a mean of the sample

– What is the distribution of these means?• Will be ‘normal’, ‘Gaussian’ or ‘Bell curve’

– Mean of the means• same as population mean

– Variance of the means smaller than population variance

– Standard error of the mean

March 2015 45

Biostatistics Core Concepts (6)

• Confidence Interval: – A range of numbers which tells us where the

correct answer lies. • For a 95% confidence interval, we are 95% sure that

the true value lies inside the interval.

– Usually computed as: mean ± 2 SE

March 2015 46

Example of Confidence Interval

• If sample mean is 80, standard deviation is 20, and sample size is 25 then:

– We can be 95% confident that the true mean lies within the range:

80 ± (2*4) = (72, 88).

March 2015 47

Example of Confidence Interval

• If the sample size were 100, then

– 95% confidence interval is:80 ± (2*2) = (76, 84).

– More precise.

March 2015 48

Biostatistics Core Concepts (7)

• Random Variation (chance): – every time we measure anything, errors will

occur.– Any sample will include people with values

different from the mean, just by chance.– These are random factors which affect the

precision (SD) of our data but not the validity.– Statistics and bigger sample sizes can help here.

March 2015 49

Biostatistics Core Concepts (8)

• Bias: – A systematic factor which causes two groups to

differ. • A study uses a two section measuring scale for

height which was incorrectly assembled (with a 1” gap between the upper and lower section).

• Under-estimates height by 1” (a bias).

– Bigger numbers and statistics don’t help much; you need good design instead.

March 2015 50

BIOSTATISTICSInferential Statistics

• Describing things is fine but limited• Want to compare different groups to see if they

differ– New drug treatments compared to old ones– Exposure to pollutants and risk of cancer

• Inferential statistics makes this possible– Based on samples from a population.– Inferences are valid only if samples are representative

(to avoid bias).

March 2015 51

BIOSTATISTICSInferential Statistics

• Polls, surveys, etc. use inferential statistics to infer what the population think based on talking to a few people.– 1,000 people can represent all of Canada

• RCTs use them to infer treatment effects, etc.• 95% confidence intervals are a very common way

to present these results.

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An experiment (1)

• We need some data to show this• Here is a ‘toonie’• I will toss it to generate some data (heads or

tails)– [Write the sequence on the board]

March 2015

53

An experiment (2)

• At some point, you get suspicious– the number of ‘heads’ in a row exceeds what is

reasonable.

• This is the core of hypothesis testing

March 2015

54

An experiment (3)• Start with a theory

– Null Hypothesis• My coin is ‘fair’

• Generate some data

• Check to see if the data is consistent with the theory.– if the data is ‘unlikely’, then reject the theory or null

hypothesis.

• Statistics just puts a mathematical overlay on top of

this intuitive approach

March 2015

March 2015 55

Hypothesis Testing (1)• Used to compare two or more groups.

– We first assume that the two groups have the same outcome results.• null hypothesis (H0)

– Generate some data– From the data, compute some number (a statistic)

• Under this null hypothesis (H0), this should be ‘0’.

– Compare the value I get to ‘0’.• If it is ‘too large’, we can conclude that our assumption (null

hypothesis) is unlikely to be true

• reject the null hypothesis

March 2015 56

Hypothesis Testing (2)

• We quantify the extent of our discomfort with the null hypothesis through the p-value.

• Reject H0 if the p-value is ‘too small’

• What is ‘too small’?– arbitrary.– tradition sets it at < 0.05

March 2015 57

Hypothesis Testing (3)

• P-value– Assume that the null hypothesis is true.– How likely is it that our statistic would be as

big as we saw (or bigger).

• We can reject or accept the null hypothesis

March 2015 58

Example of significance test

• Is there an association between sex and smoking: – 35 of 100 men smoke but only 20 of 100 women smoke

• Usually present data in a 2x2 table:Smoke Don’t

smoke

Men 35 65 100

Women 20 80 100

55 145 200

• Compare observed #’s to what we would have expected

March 2015 59

Example of significance test• Calculate the chi-square (the statistic)

– = 5.64.– If there is no effect of sex on smoking (the null

hypothesis), a chi-square value as large as 5.64 would occur only 1.8% of the time.• p=0.018

– Gives moderate evidence to reject the null hypothesis

– Would conclude that sex affects smoking prevalence

March 2015 60

Example of significance test

• Instead of computing the p-value, could compare your statistic to the ‘critical value’– The value of the Chi-square which gives

p=0.05 is 3.84– Since 5.64 > 3.84, we conclude that p<0.05

March 2015 61

Hypothesis Testing (3)• Common methods used are:

– T-test– Z-test– Chi-square test– ANOVA

• Approach can be extended through the use of regression models– Linear regression– Logistic regression– Cox models– Can relate many independent variables to one dependent variable.

March 2015 62

Hypothesis Testing (4)• Need to introduce some more terms (sorry)• p-values are key for interpreting hypothesis tests.• Modern approach is to present 95% confidence

intervals of the treatment effect rather than a p-value– Gives estimate of the range of potential treatments

• Hypothesis testing is still useful• Now, we need to get to statistical power.• So, a bit more stuff.

March 2015 63

Hypothesis Testing (5)• Hypothesis tests can get things right or wrong• Two types of errors can occur:

– Type 1 error (alpha)– Type 2 error (beta)

• P-value– Essentially the alpha value

• Power– Related to type 2 error (Beta)

March 2015 64

Hypothesis testing (6)

No effect Effect

No effect No error Type 2 error (β)

Effect Type 1 error (α)

No error

Actual Situation

Results of Stats Analysis

March 2015 65

Hypothesis Testing (7)• Statistical Power:

– ‘Easy’ to show that a drug increases survival by 10 times– ‘Hard’ to show that a drug increases survival by 1.2 times– More likely to ‘miss’ the small effect than the large effect– Statistical Power is:

• The chance you will find a difference between groups when there really is a difference of a given amount.

• Basically, this is 1-β

– Power depends on how big a difference you consider to be important

March 2015 66

How to improve your power?

• Increase sample size• Improve precision of the measurement tools

used (reduces standard deviation)• Use better statistical methods• Use better designs• Reduce bias

67

TIME FOR A BREAK!

March 2015

Cautionary Tale #3: Anecdotes

March 2015 68

Laboratory and anecdotal clinical evidence suggest that some common non-antineoplastic drugs may affect the course of cancer. The authors present two cases that appear to be consistent with such a possibility: that of a 63-year-old woman in whom a high-grade angiosarcoma of the forehead improved after discontinuation of lithium therapy and then progressed rapidly when treatment with carbamezepine was started, and that of a 74-year-old woman with metastatic adenocarcinoma of the colon which regressed when self-treatment with a non-prescription decongestant preparation containing antihistamine was discontinued. The authors suggest ...... ‘that consideration be given to discontinuing all nonessential medications for patients with cancer.’

March 2015 69

Epidemiology overview

• Key study designs to examine– Case-control

– Cohort

– Randomized Controlled Trial (RCT)

• Confounding

• Relative Risks/odds ratios– All ratio measures have the same interpretation

• 1.0 = no effect

• < 1.0 protective effect

• > 1.0 increased risk

– Values over 2.0 are of strong interest

March 2015 70

The Epidemiological Triad

Host Agent

Environment

March 2015 71

Terminology

• Prevalence: – The probability that a person has the outcome of

interest today. Relates to existing cases of disease. Useful for measuring burden of illness.

• Incidence: – The probability (chance) that someone without the

outcome will develop it over a fixed period of time. Relates to new cases of disease. Useful for studying causes of illness.

March 2015 72

Prevalence• On July 1, 2015, 140 graduates from the U.

of Ottawa medical school start working as R1’s.

• Of this group, 100 had insomnia on June 30.

• Therefore, the prevalence of insomnia is:

March 2015 73

Incidence Proportion (risk)

• On July 1, 2015, 140 graduates from the U. of Ottawa medical school start working as R1’s.

• Over the next year, 30 develop a stomach ulcer.• Therefore, the incidence proportion (risk) of an

ulcer in the first year post-graduation is:

March 2015 74

Incidence Rate (1)

• Incidence rate is the ‘speed’ with which people get ill.

• Everyone dies (eventually). It is better to die later

death rate is lower.• Compute with person-time denominator:

PT = # people * duration of follow-up

March 2015 75

Incidence rate (2)• 140 U. of Ottawa medical students were

followed during their residency– 50 did 2 years of residency– 90 did 4 years of residency– Person-time = 50 * 2 + 90 * 4 = 460 PY’s

• During follow-up, 30 developed ‘stress’.• Incidence rate of stress is:

March 2015 76

Prevalence & incidence

• As long as conditions are ‘stable’ and disease is fairly rare, we have this relationship:

That is,

Prevalence ≈ Incidence rate * average disease duration

March 2015 77

Cohort study (1)

• Select non-diseased subjects based on their exposure status• Main method used:

• Select a group of people with the exposure of interest

• Select a group of people without the exposure

• Can also simply select a group of people without the disease and study a range of exposures.

• Follow the group to determine what happens to them.

March 2015 78

Cohort study (2)

• Compare the incidence of the disease in exposed and unexposed people• If exposure increases risk, incidence will be

higher in exposed subjects than unexposed subjects

• Compute a relative risk.

• Framingham Study is standard example.

March 2015 79

Exposed group

Unexposedgroup

No disease

Disease

No disease

Disease

time

Study begins Outcomes

March 2015 80

Cohort study (3)

YES NO

YES a b a+b

NO c d c+d

a+c b+d N

Disease

Exp

RISK RATIO

Risk in exposed: =

Risk in Non-exposed =

If exposure increases risk, you would expect

to be larger than . How much

larger can be assessed by the ratio of one

to the other:

March 2015 81

Cohort study (4)

YES NO

Yes 42 80 122

No 43 302 345

85 382 467

Death

Exposure

Risk in exposed: = 42/122 = 0.344Risk in Non-exposed = 43/345 = 0.125

March 2015 82

Cohort study (6)

• Historical cohort study• Recruit subjects sometime in the past• Follow-up to the present

• Usually use administrative records

• Can continue to follow into the future

March 2015 83

Cohort study (7)

• Example: cancer in Gulf War Vets• Study is conducted in 2013• Identify soldiers deployed to Persian Gulf

in 1991• Identify soldiers not deployed to Persian

Gulf in 1991• Compare development of cancer in group

1 to that in group 2 from 1991 to 2010

March 2015 84

Case-control study (1)• Select subjects based on their final outcome.

– Select a group of people with the outcome/disease (cases)

– Select a group of people without the outcome (controls)

– Ask them about past exposures– Compare the frequency of exposure in the two groups

• If exposure increases risk, the odds of exposure in the case should be higher than the odds in the controls

– Compute an Odds Ratio– Under many conditions, OR ≈ RR

March 2015 85

Disease(cases)

No disease(controls)

Exposed

Unexposed

Exposed

Unexposed

The study begins by selecting

subjects based on

Reviewrecords

Reviewrecords

March 2015 86

Case-control study (2)

YES NO

YES a b a+b

NO c d c+d

a+c b+d N

Disease?

Exp?

ODDS RATIO

Odds of exposure in cases =

Odds of exposure in controls =

If exposure increases risk, you would to find more

exposed cases than exposed controls. That is, the

odds of exposure for cases would be higher

This can be assessed by the ratio of one to the

other:

March 2015 87

Yes No

Yes 42 18

No 43 67

85 85

Exposure

Odds of exp in cases: = 42/43 = 0.977Odds of exp in controls: = 18/67 = 0.269

Case-control study (3)Death

March 2015 88

Randomized Controlled Trials

• Basically a cohort study where the researcher decides which exposure (treatment) the subject get.– Recruit a group of people meeting pre-specified

eligibility criteria.– Randomly assign some subjects (usually 50% of them)

to get the control treatment and the rest to get the experimental treatment.

– Follow-up the subjects to determine the risk of the outcome in both groups.

– Compute a relative risk or otherwise compare the groups.

March 2015 89

Randomized Controlled Trials (2)

• Some key design features–Allocation concealment–Blinding (masking)

• Patient• Treatment team• Outcome assessor• Statistician

–Monitoring committee

March 2015 90

Randomized Controlled Trials (3)

• Two key problems–Contamination

• Control group gets the new treatment

–Co-intervention• Some people get treatments other than

those under study

March 2015 91

Randomized Controlled Trials: Analysis

• Outcome is often an adverse event– RR is expected to be <1

• Not a serious issue but does complicate interpretation of

‘standard’ measures

• Often use special variants of these measures.

• Absolute risk reduction

March 2015 92

Randomized Controlled Trials: Analysis

• Relative risk reduction

Number needed to treat (1)

Consider a clinical trial of a new drug. How many people do we need to treat to prevent one death?

– Incidence rate for the control group is 2 cases per 5 person years.

– Incidence rate for the experimental group is 1 case per 5 person years.

5/6/2014

Number needed to treat (2)

• Treat five people for one year:– Control therapy: 2 deaths– Exp therapy: 1 death– PREVENTED = 1 death

NNT = 5.

• What is the risk difference:– 2/5 – 1/5 = 1/5

5/6/2014

• Number needed to treat, (to prevent one adverse event)

March 2015 95

Randomized Controlled Trials: Analysis

• Relative risk reduction

Number needed to treat (3)

For diseases with rare outcomes, you will need to treat many people to prevent one outcome, even if the reduction in risk is high:

Relative risk reduction = 0.1

IR (Old Rx) = 10/1,000

IR (New Rx) = 1/1,000

RD = 9/1,000

NNT = 1000/9

= 1115/6/2014

March 2015 97

RCT – Example of Analysis

Asthma No Total Incid

attack attack

Treatment 15 35 50 .30

Control 25 25 50 .50

Relative Risk = 0.30/0.50 = 0.60

Absolute Risk Reduction = 0.50 - 0.30 = 0.20

Relative Risk Reduction = 0.20/0.50 = 40%

Number Needed to Treat = 1/0.20 = 5

March 2015 98

Confounding

• Does alcohol drinking cause oral cancer?– Do a case-control study

– OR=3.4 (95% CI: 2.1-4.8).

• BUT, the effect of alcohol is ‘mixed up’ with the

effect of smoking.– Smoking causes mouth cancer

– Heavy drinkers tend to be heavy smokers.

– Smoking is not part of causal pathway for alcohol.

March 2015 99

The Confounding Triangle

Alcohol Oral cancer

Smoking

Causal

Association

March 2015 100

Confounding• The effect of this third factor ‘confounds’

the relationship we are interested in.– Produces a biased results.– Can make result more or less strong than it

really is

• A confounder is an extraneous factor which is associated with both exposure and outcome, and is not an intermediate step in causal pathway

March 2015 101

Confounding• Proper statistical analysis must adjust

for the confounder.• We do a statistical adjustment (logistic

regression is most common): –OR=1.3 (95% CI: 0.92-1.83)

March 2015 102

The Confounding Triangle

Exposure Outcome

Confounder

Causal

Association

March 2015 103

Standardization (1)

• The (made-up) mortality from prostate cancer was:– 1950: 50/100,000

– 2000: 100/100,000

• Were men dying at twice the rate in 2000?

• Population is older in 2000 than 1950.

• Distorts the comparison.

• Standardization adjusts for age differences

• Always should be used when presenting incidence and

mortality trends in a population

March 2015 104

Standardization (2)

• The essential idea– If only the two populations had the same age, we’d

be OK– Let’s fake things out.– Define a standard population– For each of your two populations, figure out how

many deaths would have occurred if only the population were the same as the standard one.

– Now, compare the two rates

March 2015 105

Standardization (3)

• Direct:– yields age-standardized rate (ASMR)

• Indirect:– yields standardized mortality ratio (SMR)

• You don’t need to know how to do this

March 2015 106

Measures of Population Health (1)

• Mortality rates– crude

• Overall all-cause mortality rate

– specific• mortality rate for a specific group (men), disease (lung cancer), etc.

– standardized• Mortality rate adjustment to take account of the aging population

March 2015 107

Mortality data

• Life expectancy: – average age at death if current mortality rates

continue. Derived from a life table.

• Potential Years of Life Lost (PYLL): – subtract age at death from some “acceptable” age of

death.– Sum up over a group

• estimates ‘potential’ years of life lost due to early death• Places more emphasis on causes that kill at younger ages.

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0 100 200 300 400 500

HIV/AIDS

Respiratory disese

Suicide and violence

Unintentional injury

Circulatory disease

Cancer

Mortality rate (per 100,000) PYLL (000)

Impact of different causes of death in Canada 2001: Mortality rates and PYLL

Source: Statistics Canada

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Measures of population health (2)

• Mortality is a ‘crude’ measure of population health

• Need to consider–morbidity–quality of life–disability– and so on.

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Measures of population health (3)

• Many other measures have been developed• Quality Adjusted Life Years (QALYs)

– Years lived are weighted according to quality of life, disability, etc.

• Two ‘classes’ of these types of measures:– Health expectancies point up from zero– Health gaps point down from ideal

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Attributable Risks (1)

• Would like to know the amount of a disease which might be

prevented if we eliminate a risk

• Tricky area since there are several measures with similar names.– Attributable risk

– Attributable fraction

– Population Attributable Risk

– and so on

• Gives an upper limit on amount of disease which we

can prevent.

• Meaningful only if association is causal.

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Attributable Risks (2)

• Two main targets for these measures• The amount of disease due to exposure in the

exposed subjects. The same as the risk difference.

• The proportion of risk attributed to the exposure in the general population – depends on

• Risk due to exposure• How common the exposure is.

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Attributable risks (3)

ExpUnexp

Risk Difference or Attributable Risk

Iexp

Iunexp

RD = AR = Iexp - Iunexp

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Attributable risks (4)

ExpUnexp

PopulationAttributable Risk

Iexp

Iunexp

Ipop

Population

115

THE END

March 2015

116March 2015