Đo lường kết hợp-Đào Thị Minh An

03/10/15 Đào thị minh an, MD PhD- Khoa y tế công cộng - Đại học y Hà Nội Case-control studies ◆ Selection of cases – Case definition is very important – All cases have an equal probabili

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§o l êng kÕt hîp

Dao Thi Minh An, MD PhD

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03/10/15 Đào thị minh an, MD

PhD- Khoa y tế công cộng - Đại học y Hà Nội

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PhD- Khoa y tế cụng cộng - Đại học y Hà Nội

(Nghiên cứu Thuần tập)

Nguy co tuong doi (RR)= CIe/CI0 = a/(a + b) : c/(c + d)

Trong đó: CIe: Số mới mắc tích luỹ ở nhóm có phơi nhiễm

CI0: Số mới mắc tích luỹ ở nhóm không phơi nhiễm

(Nghiên cứu Bệnh-Chứng)

Tỷ suất chênh (Odd Ratio) OR= ad/bc

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◆ RR = CIe/CI0 = a/(a + b) : c/(c

+ d) (Nghiªn cøu ThuÇn tËp)

◆ CIe: Sè míi m¾c tÝch luü ë

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◆ Nguy c¬ quy thuéc (Attributable Risk)

◆ AR = Ie - Io = CIe - CIo

◆ AR = CIe - CIo = a/(a+b) - c/(c+d)

◆ Nguy c¬ quy thuéc phÇn tr¨m (AR%)

◆ AR% = AR/Ie x 100 = (Ie - Io)/Ie x 100

◆ AR% = AR/Ie x 100

◆ Nguy c¬ quy thuéc quÇn thÓ (PAR)

◆ PAR =IT -Io

◆ hay PAR=(AR)(Pe)

◆ IT: Tû lÖ bÖnh cña quÇn thÓ

◆ IO: Tû lÖ m¾c bÖnh ë nhãm kh«ng ph¬i nhiÔm

◆ Pe: Tû lÖ nh÷ng c¸ thÓ cã ph¬i nhiÔm trong quÇn thÓ

◆ Nguy c¬ quy thuéc quÇn thÓ phÇn tr¨m (PAR%)

◆ PAR% = PAR :IT x100

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Prevalence

◆ Prevalence (a proportion):

– the proportion of the population at a given time that

have the factor of interest

– Prevalence of an exposure

» what proportion of this class have BMI > 25

» what proportion of this class have hypertension

◆ Point Prevalence - existing cases at a point in time

◆ Period Prevalence - existing cases plus those

developing over a specified period of time

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in Number

cases prevailing

of Number

P =

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Prevalence

Choice of denominator may be difficult

◆ in 1997 there were 1854 cases of syphilis in Harris County

◆ what should be used for the denominator?

◆ 55 cases of a new disease reported in three states

◆ what should be used for the denominator?

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Incidence

◆ Incidence density: the probability (risk) of an individual

developing the disease (outcome) during a specific period of time, using total person-time as the denominator One

subject followed one year contributes one person-year (PY)

time -

person Total

period given time

a during disease

of cases Number

=

density

I

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ofstart the

atrisk

at Population

periodstudy

aoverdisease

ofcasesnew

Number

=

I

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Incidence, Prevalence

What was prevalence of disease in 1992?

What is risk of developing disease within 2 years?

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Measure of Disease Association

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Case Reports and Medical Advancement

These all started with case reports - what study design next?

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What next?

– create case definition

– active case finding

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The case-control study

◆ Retrospective study design

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Retrospective vs prospective study designs

d c

b a

Present(Cases)

Absent(Controls)

Disease

Retrospective(Case-control)

Present(Exposed)

Absent(Not Exposed)

Risk Factor

Prospective

(Cohort)

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Case control studies

d c

b a

Disease Status

YesNo

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Case-control studies

◆ Selection of cases

– Case definition is very important

– All cases have an equal probability for

selection: reduce selection bias

◆ Selection of controls

– Identical in every respect except disease of

interest

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Case control studies

◆ More easily replicated

◆ Can test hypotheses

Weaknesses

◆ Uncertainty is disease time relationship

exposure-◆ Representativeness of cases or controls

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Case-control and the Odds Ratio

c+da+b

a+c

dc

Nb+d

YN

Disease Exposure

Odds of exposure if case = [a / (a+c)] / [c / (a+c)] = a/c

Odds of exposure if control = [b / (b+d)] / [d /(b+d)] = b/d

Odds exposure given disease = (a/c)/(b/d) = (a*d)/(c*b)

How much risk

is too much risk?

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Case-control and the Odds Ratio

YN

Cases Controls Exposed 70 30 100 RR = 70/100 ÷ 30/100 = 2.3 Not Exposed 30 70 100 OR = 70/30 ÷ 30/70 = 5.4

100 100 200

Cases Controls Exposed 70 300 370 RR = 70/100 ÷ 300/1000 = 4.6 Not Exposed 30 700 730 OR = 70/30 ÷ 30/70 = 5.4

100 1000 1100

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TSS - 3 case-control studies

Cases Controls Tampon users 50 43 reported p=0.02

Non-users 0 7

Cases Controls Tampon users 30 71 reported p=0.014

Non-users 1 22

Cases Controls Tampon users 12 32 p = 0.20

(12/0) / (32/8) =

6.5

NOTE: A correction factor of 0.5 was added to each cell when 1 cell contained 0

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Study Methods

◆ CDC - 1: 52 TSS cases with age-matched

acquaintance controls

◆ Wisconsin Study: 31 cases, 93 controls from

gynecologic clinics, matched only for menstruation

◆ Utah: 12 TSS cases, 40 neighborhood-matched

controls

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Matched Pair analysis

How many cases used tampons continually?

How many cases did not use tampons continually?

What about controls?

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How Big is Big?

– Is an OR of 16 big?

– Is an OR of 16 statistically significant?

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BRIEF INTERLUDE - STATISTICS

about inference and statistical association

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How Big is Big?

– Is an OR of 16 big?

– Is an OR of 16 statistically significant?

Outcome Expected

of Variance

Outcome Expected

Outcome

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◆ The whole purpose for doing research is to learn

something new.

– The result of a research project is the goal

» this is the important information that the researchers want the informed public to remember

– As we read the literature - we should ask ourselves:

» What is the major result?

» What does this result mean?

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Statistical Issues in Epidemiology

◆ We have to remember that epidemiologic studies draw inferences about the experiences of an entire population based on an evaluation of only a sample.

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◆ When studying a sample of the population the observed associations can be due to:

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◆ What do we mean by chance and how does this relate to determining a

“true association”

◆ Where do we start?

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◆ Association does not mean cause and effect

◆ Assessing causality involves judgement based on

the totality of evidence

◆ Making judgements about causality involves a chain

of logic that addresses two major areas:

1 Whether the observed association is valid

2 Whether the totality of evidence supports a

judgement of causality

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◆ The evaluation of the role of chance is done

in 2 steps

1 Estimate the magnitude of the association

– We do this with OR, RR, correlations, AR

2 Hypothesis testing:

– Calculate a test statistic, obtain a p value or

confidence interval

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◆ p-value: the probability of obtaining a sample showing

an association of the observed size or larger by chance alone under the hypothesis that no association exists

◆ Confidence interval: a range of values that one can say,

with a specific degree of confidence, contains the true population value.

◆ Sample statistic: a number which describes some aspect

of a sample which represents a population.

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◆ This can be done by calculating a test statistic of the general format:

◆ The selection of the particular test used depends on the specific hypothesis being tested and characteristics of the collected data.

Outcome Expected

of Variance

Outcome Expected

Outcome

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◆ If we were to toss a coin 30 times while

trying to determine if it was a fair coin, and

we got 24 heads, how would we determine if

24 was different that the expected number?

Observed - Expected (under the null) Estimated variability in the sample

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Observed - Expected (under the null) Estimated variability in the sample

24/30 - 15/30

? Variability

Variability = [p(1-p)/n]1/2 = (24/30*6/30)/301/2 = 0.07 [ (24/30) - (15/30) ] /0.07 = 4.3

p = <0.001

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◆ The p value indicates the possibility that findings at least as extreme as those observed were unlikely to have occurred by chance alone.

◆ In 1000 experiments with 30 tosses with a fair coin -

we would expect only 1 to result in 24 heads or more

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◆ A statistically significant finding does not mean that the results DID NOT occur by chance - only that it is unlikely that they occurred by chance

◆ A non-significant finding does not mean that the

results DID occur by chance.

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◆ More often in epidemiology we are examining

discrete data - the 2 x 2 table presents discrete data Here we are testing whether the distribution of counts

in the 4 cells is different than expected under the null hypothesis

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◆ But how do we determine the expected value for the cells of a 2 x 2 table?

O = Observed Count in a category

E = Expected Count in a category

å = Sum of all categories

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◆ All tests of statistical significance lead to a

– probability statement

– usually expressed as a p value

◆ The p-value obtained is based on the principle that, given the distribution of interest, it is possible to

calculate the exact probability or likelihood of

obtaining a result at least as extreme as that

observed by chance alone assuming there is truly no association.

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◆ A probability of 0.05 is the usual (arbitrary) cut-off

level for statistical significance

◆ If p <0.05, we conclude that chance is an unlikely

explanation for the finding The null hypothesis is rejected, and the statistical association is said to be significant.

◆ If p >0.05, we conclude that chance cannot be

excluded as an explanation for the finding; we fail to reject the null hypothesis.

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◆ No p value

– however small - completely excludes chance

◆ No p value

– however large - completely mandates chance

◆ p values only evaluate the role of chance

– they say nothing about other alternative explanations or about causality

◆ p values reflect the strength of the association and the study sample size

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◆ A small difference may achieve statistical

significance if the sample size is large

◆ A large difference may not achieve statistical

significance if the sample size is too small

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◆ We address these problems by calculating

confidence intervals (CI)

– CI indicates the range within which the true magnitude

of effect lies with a certain degree of assurance The degree of assurance is defined by the p value you

assign.

◆ The CI gives all the information of a p value PLUS the expected range of effect sizes.

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◆ If the null value is included in a 95% confidence

interval, then the corresponding p value is, by

definition, greater than 0.05.

◆ If the null value is not included, the association is considered to be statistically significant.

◆ WHAT IS THE NULL VALUE for Odds Ratios and

Relative Risks (Rate Ratios)?

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be estimated using the chi-square test

statistic Miettinen, Am J Epidemiol 103:226-235, 1976

2

/ 96 1

1

%

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Taylor Series: to estimate the lnOR variance Woolf, Ann

±

e OR

CI

1 1 1 1 96

1

*

% 95

Note: e is a function on you calculator You need a key marked

ex and you enter the OR times e raised to the power of the results between the brackets [ ]

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Taylor Series: to estimate the lnRR variance Katz, Biometrics, 34:469, 1973

Note: e is a function on you calculator You need a key marked

ex and you enter the OR times e raised to the power of the results between the brackets [ ]

a a

b

e RR

CI

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◆ Inference involves making a generalization about a larger group of individuals on the basis of a subset or sample

◆ The p value indicates the probability or likelihood of obtaining a result at least as extreme as that

observed in a study by chance alone, assuming that there is truly no association between the study

variables.

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