March 2012 1

Back to Basics, 2012POPULATION HEALTH (1):

Epidemiology Methods, Critical Appraisal,

Biostatistical Methods

N. Birkett, MDEpidemiology & Community Medicine

Other resources available on Individual & Population Health web site

March 2012 2

THE PLAN (1)

• Session 1 (March 23, 9:00-12:00)– Diagnostic tests

• Sensitivity, specificity, validity, PPV– Critical Appraisal– Intro to Biostatistics– Brief overview of epidemiological research

methods

March 2012 3

THE PLAN (2)

• Aim to spend about 2-2.5 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 2012

INVESTIGATIONS (1)

• 78.2– Determine the reliability and predictive value

of common investigations– Applicable to both screening and diagnostic

tests.

March 2012 5

Reliability

• = reproducibility. Does it produce the same result every time?

• Related to chance error

• Averages out in the long run, but in patient care you hope to do a test only once; therefore, you need a reliable test

March 2012 6

Validity

• Whether it measures what it purports to measure in long run, viz., presence or absence of disease

• Normally use criterion validity, comparing test results to a gold standard

• Link to SIM web on validity

March 2012 7

Reliability and Validity: the metaphor of target shooting. Here, reliability is represented by consistency, and validity by aim

Reliability Low High

Low

Validity

High

•

•••

•

•

•• •

••

•

••••••

•• ••••

March 2012 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 2012 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 2012 10

2x2 Table for Testing a Test

Gold standardDisease Disease Present Absent

Test Positive a (TP) b (FP)Test Negative c (FN) d (TN)

SensitivitySpecificity

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

March 2012 11

Test Properties (6)• Sensitivity =Pr(test positive in a person

with 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 2012 12

Test Properties (7)• Values depend on cutoff point• Generally, high sensitivity is associated with low

specificity and vice-versa.• Not affected by prevalence, if severity 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 2012 13

Test Properties (8)• Sens/Spec not directly useful to clinician,

who knows only the test result• Patients don’t ask: “If I’ve got the disease,

how likely is a positive test?”• They ask: “My test is positive. Does that

mean I have the disease?”• → Predictive values.

March 2012 14

Predictive Values• Based on rows, not columns

– PPV = a/(a+b); interprets positive test– NPV = d/(c+d); interprets negative test

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

• Immediately useful to clinician: they provide the probability that the patient has the disease

March 2012 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 2012 16

2x2 Table for Testing a Test

Gold standardDisease 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 2012 17

Prevalence of Disease• 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)

March 2012 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 2012 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 tests are more often true positives.

• How to ‘calibrate’ a test for use in a different setting?

• Relies on the stability of sensitivity & specificity across populations.

March 2012 20

Methods for Calibrating a TestFour methods can be used:

– Apply definitive test to a consecutive series of patients (rarely feasible)

– Hypothetical table– Bayes’s Theorem– Nomogram

• You need to be able to do one of the last 3. • By far the easiest is using a hypothetical table.

March 2012 21

Calibration by hypothetical table

Fill cells in following order:“Truth”

Disease Disease Total PV

Present AbsentTest Pos 4th 7th 8th

10th Test Neg 5th 6th 9th

11th Total 2nd 3rd 1st (10,000)

March 2012 22

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 2012 23

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 2012 24

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

March 2012 25

Test Properties (13)Diseased Not

diseasedTest +ve

90 5 95

Test -ve

10 95 105

100 100 200 Pre-test odds = 1.00

Post-test odds (+ve) = 18.0

Post-test odds (+ve) = LR(+) * Pre-test odds = 18.0 * 1.0 = 18.0, but of course you do not know the LR(+)

March 2012 26

Calibration by Bayes’s Theorem

• You can convert sens and spec to likelihood ratios

LR(+) = sens/(1-spec)• LR(+) is fixed across populations just like

sensitivity & specificity.• Bigger is better.• Posttest odds(+) = pretest odds * LR(+)

– Convert to posttest probability if desired…

March 2012 27

Converting odds to probabilities

• Pre-test odds = prevalence/(1-prevalence)– if prevalence = 0.20, then

• pre-test odds = .20/0.80 = 0.25• Post-test probability =

post-test odds/(1+post-test odds)– if post-test odds = 0.25, then

• prob = .25/1.25 = 0.20

March 2012 28

Calibration by Bayes’s Theorem

• How does this help?• Remember:

– Post-test odds(+) = pretest odds * LR(+)• To ‘calibrate’ your test for a new population:

– Use 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 2012 29

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

• LR(+) = .90/.05 = 18 (>>1, pretty good)• Pretest odds = .01/.99 = 0.0101• Positive Posttest odds = .0101*18 = .1818• PPV = .1818/1.1818 = 0.1538 = 15.38%

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

March 2012 30

Calibration with Nomogram

• Graphical approach avoids some arithmetic• Expresses prevalence and predictive values

as probabilities (no need to convert to odds)• Draw lines from pretest probability

(=prevalence) through likelihood ratios; extend to estimate posttest probabilities

• Only useful if someone gives you the nomogram!

31April 2011 31

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

Pretest Prob. LR Posttest Prob.

1%

18

.105

15%

0.01%

March 2012

March 2012 32

Are sens & spec really constant?

• Generally, assumed to be constant. BUT…..• Sensitivity and specificity usually vary with

severity of disease, and may vary with age and sex • Therefore, you can use sensitivity and specificity

only if they were determined on patients similar to your own

• Risk of spectrum bias (populations may come from different points along the spectrum of disease)

Cautionary Tale #1: Data Sources

March 2012 33

The Government is extremely fond of amassinggreat quantities of statistics. These are raised to the nth degree, the cube roots are extracted, and

the 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 2012 34

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”

• UTMCCQE does not present hierarchy of evidence (e.g., as used by Task Force on Preventive Health Services)

March 2012 35

Hierarchy of evidence(lowest to highest quality, approximately)

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

}similar/identical

Cautionary Tale #2: Analysis

March 2012 36

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 2012 37

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 2012 38

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.

• Standard deviation: – square root of the variance.

March 2012 39

BIOSTATISTICS Core concepts (3)• Standard error:

– , where n is sample size. – Is the standard deviation of the sample mean, so

measures the variability of that mean.• Confidence Interval:

– A range of numbers which tells us where we believe the correct answer lies. • For a 95% confidence interval, we are 95% sure that

the true value lies in the interval, somewhere.– Usually computed as: mean ± 2 SE

March 2012 40

Example of Confidence Interval• If sample mean is 80, standard deviation is 20, and

sample size is 25 then:– SE = 20/5 = 4.

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

80 ± (2*4) = (72, 88).

• If the sample size were 100, then – SE = 20/10 = 2.0, and

• 95% confidence interval is 80 ± (2*2) = (76, 84). • More precise.

March 2012 41

Core concepts (4)

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

occur. – In addition, by selecting only a few people to

study (a sample), we will get 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 2012 42

Core concepts (5)

• 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).

• Over-estimates height by 1” (a bias).– Bigger numbers and statistics don’t help much;

you need good design instead.

March 2012 43

BIOSTATISTICSInferential Statistics

• Draws inferences about populations, based on samples from those populations. – Inferences are valid only if samples are representative

(to avoid bias).• Polls, surveys, etc. use inferential statistics to infer

what the population thinks based on talking to a few people.

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

to present these results.

March 2012 44

Population from which sample is drawn Sample

Target population

Inferences drawn

(Confidence intervalused to indicate

accuracy of extrapolating

results to broaderpopulation from which

sample was drawn)

Your practicepatients

March 2012 45

┼ ┼

Increasing random error

Increasing systematic error (bias)

Population parameter

Results from different samples

Effects of bias and random error on study results

┼ ┼

┼

Bias

Random error

March 2012 46

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)

– Compute some number (a statistic) which, under this null hypothesis (H0), should be ‘0’.

– If we find a large value for the statistic, then we can conclude that our assumption (null hypothesis) is unlikely to be true (reject the null hypothesis).

March 2012 47

Hypothesis Testing (2)• Formal methods use this approach by determining

the probability that the value you observe could occur – The p-value.

• Reject H0 if that value exceeds the critical value expected from chance alone.

March 2012 48

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

• Toronto notes are wrong in saying this relates 2 variables. It can relate many independent variables to one dependent variable.

– Logistic regression– Cox models

March 2012 49

Hypothesis Testing (4)• Once you select a method for hypothesis testing,

interpretation involves:– Type 1 error (alpha)– Type 2 error (beta)– P-value

• Essentially the alpha value

– Power• Related to type 2 error (Beta)

March 2012 50

Hypothesis testing (5)

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 2012 51

Hypothesis Testing (6)• P-value:

– The probability of making a type 1 error• You observe a value for your statistic

– Z=1.96

• If the null hypothesis were to be true, you can figure out the probability of observing a value of your statistic which is as big or bigger than this

– 0.05

• This is the p-value

– If the null hypothesis is true, how likely would I be to observe a value of my statistic that is a big as I did (or bigger).• This is not quite the same as saying the chance that the group

difference is ‘real’

March 2012 52

Example of significance test• Is there an association between sex and smoking:

– 35 of 100 men smoke but only 20 of 100 women smoke

• 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

– Can also compare your statistic to the ‘critical value’• The value of the Chi-square which gives p=0.05• 3.84• Since 5.64 > 3.84, we conclude that p<0.05

March 2012 53

Hypothesis Testing (7)• Power:

– 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 2012 54

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

Cautionary Tale #3: Anecdotes

March 2012 55

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 2012 56

Epidemiology overview• Key study designs to examine (SIM web link)

– 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 2012 57

The Epidemiological Triad

Host Agent

Environment

March 2012 58

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 2012 59

Prevalence

• On July 1, 2007, 140 graduates from the U. of O. medical school start working as interns.

• Of this group, 100 had insomnia the night before.

• Therefore, the prevalence of insomnia is:

100/140 = 0.72 = 72%

March 2012 60

Incidence Proportion (risk)• On July 1, 2007, 140 graduates from the U.

of O. medical school start working as interns.

• Over the next year, 30 develop a stomach ulcer.

• Therefore, the incidence proportion (risk) of an ulcer in the first year post-graduation is:

30/140 = 0.21 = 214/1,000 over 1 yr

March 2012 61

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 2012 62

Incidence rate (2)• 140 U. of O. 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 2012 63

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 2012 64

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.• Compare the incidence of the disease in exposed and unexposed people

• If exposure increases risk, there should be more cases in exposed subjects than unexposed subjects

• Compute a relative risk.

• Framingham Study is standard example.

March 2012 65

Exposed group

Unexposedgroup

No disease

Disease

No disease

Disease

time

Study begins Outcomes

March 2012 66

Cohort study (2)

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 2012 67

Cohort study (3)

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 2012 68

Cohort study (4)

• 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

• Example: cancer in Gulf War Vets• Identify soldiers deployed to Gulf in 1991• Identify soldiers not deployed to Gulf in 1991• Compare development of cancer from 1991 to 2010

March 2012 69

Case-control study (1)• Select subject 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, there should be more exposed cases than exposed controls

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

March 2012 70

Disease(cases)

No disease(controls)

Exposed

Unexposed

Exposed

Unexposed

The study begins by selecting

subjects based on

Reviewrecords

Reviewrecords

March 2012 71

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 2012 72

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 2012 73

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 2012 74

Randomized Controlled Trials (2)• Some key design features

– Allocation concealment– Blinding (masking)

• Patient• Treatment team• Outcome assessor• Statistician

– Monitoring committee• Two key problems

– Contamination• Control group gets the new treatment

– Co-intervention• Some people get treatments other than those under study

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

March 2012 75

Randomized Controlled Trials: Analysis

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

• Absolute risk reduction

• Relative risk reduction

March 2012 76

RCT – Example of Analysis

Asthma No Total Incid attack attack

Treatment 15 35 50 .30Control 25 25 50 .50

Relative Risk = 0.30/0.50 = 0.60Absolute Risk Reduction = 0.50-0.30 = 0.20Relative Risk Reduction = 0.20/0.50 = 40%Number Needed to Treat = 1/0.20 = 5

March 2012 77

Confounding• Interest in the effect of an exposure on an outcome

– Does alcohol drinking cause oral cancer?

• BUT, the effect of alcohol is ‘mixed up’ with the effect of smoking.• The effect of this third factor ‘confounds’ the relationship we are

interested in.– Produces a biased results.– Can make result more or less strong

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

• Proper statistical analysis must adjust for the confounder.

March 2012 78

The Confounding Triangle

Exposure Outcome

Confounder

Causal

Association

March 2012 79

Confounding (example)• Does heavy alcohol drinking cause mouth cancer?

– Do a case-control study– OR=3.4 (95% CI: 2.1-4.8).

• BUT– Smoking causes mouth cancer– Heavy drinkers tend to be heavy smokers.– Smoking is not part of causal pathway for alcohol.

• Therefore, we have confounding.• We do a statistical adjustment (logistic regression is most

common): – OR=1.3 (95% CI: 0.92-1.83)

March 2012 80

Standardization• An method of adjusting for confounding (usually used for

differences in age between two populations)• Refers observed events to a standard population, producing

hypothetical values• Direct:

– yields age-standardized rate (ASMR)

• Indirect:– yields standardized mortality ratio (SMR)

• You don’t need to know how to do this• Nearly always used when presenting population rates and trends.

March 2012 81

Mortality dataThree ways to summarize them

• Mortality rates (crude, specific, standardized)• PYLL:

– subtracts age at death from some “acceptable” age of death.

– Places more Emphasis on causes that kill at younger ages.

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

Derived from life table.

March 2012 82

Summary measuresof population health

• Combine mortality and morbidity statistics, in order to provide a more comprehensive population health indicator– QALY

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

• Two types:– Health expectancies point up from zero– Health gaps point down from ideal

March 2012 83

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

March 2012 84

Attributable Risks (1) (SIM web link)

• Generally, tries to give an estimate of the amount of a disease which might be prevented– Gives an upper limit on amount of preventable disease.– Meaningful only if association is causal.

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

– The amount of disease due to exposure in the exposed subjects. The same as the risk difference. • Can also express as attributable fraction.

• Often, we want at the proportion of risk attributed to the exposure in the general population – depends on how common the exposure is).

March 2012 85

Attributable risks (2)

ExpUnexp

Risk Difference or Attributable Risk

Iexp

Iunexp

RD = AR = Iexp - Iunexp

March 2012 86

Attributable risks (2)

ExpUnexp

PopulationAttributable Risk

Iexp

Iunexp

Ipop

Population