Hypothesis Testing

Field Epidemiology

Hypothesis

• Hypothesis testing is conducted in etiologic study designs such as the case-control or cohort as well as the experimental study designs.

• An hypothesis is a a statement of association between exposure (predictor) and an outcome (disease or health event).

• Hypotheses are one-tailed or two tailed.The null hypothesis states that there is no association.

Examples

• Smoking is not associated with lung cancer (Null hypothesis)

• Smoking is associated with a higher incidence of lung cancer (One-tailed hypothesis)

• Smoking is associated with a lower incidence of lung cancer (or it is protective) (One-tailed hypothesis)

• Smoking has some association with lung cancer (uncertain of how it influences lung cancer) (Two-tailed hypothesis)

Rules of Thumb

• Usually there is one main hypothesis and a couple of secondary hypotheses

• The more specific you are in your statement of hypothesis, the easier it will be to answer your question

• Usually stated in the paper as “The purpose of the study is to….”

Epidemiologic Decision Making

Disease No DiseaseExposure a b a+bNo Exposure c d c+d

a+c b+d N

Relative Risk

R.R.= a/(a+b)

------------

c/(c+d)

RR = the likelihood of developing the disease in the exposed group compared to the unexposed group

Relative Risk for a disease exposure

CVD No CVD Obesity 75 25 100 No Obesity 25 75 100 100 100 200

RR = 75/100 = 3.00 25/100

C.I. (2.10 - 4.29)

Relative Risk for preventive intervention

Disease No Disease Counseling 25 75 100 No Counseling 50 50 100 75 125 200

RR = 25/100 = .50 50/100

C.I. (.39-.79)

Relative Risk Calculation

RR = =

Ct No CT TotalUsed Condoms 30 70 100Did not useCondoms

60 40 100

90 110 200

Attributable Risk

• AR = Ie - Io

the difference between incidence rates in the exposed and nonexposed groups

Odds Ratio

• a/c

b/d• or the odds of

exposure in disease

compared to odds of exposure in

non diseased

• a*d

b*c• mathematically

equivalent to the

simpler formula

Odds Ratio

O.R. = 60 * 70 = 3.50 40 * 30

Ct No CT TotalDouching 60 30 90No douching 40 70 110

100 100 200

T-test - Continuous data

Number Mean CD4

Standard Deviation

p-value

Men 4350 326 288 < .001 Women 925 431 330

Formula t-test = mean A - mean B - diff Null variance for the entire study pop

Which group is more immuno-suppressed?

C.I. For Mean CD4

Number Mean S.D. S.E. 95% C.I. Men 4350 326.2 288.4 4.37 317.6 - 334.8 Women 925 430.7 330.1 10.86 409.4 - 451.9

T-test

• If the sample sized are different - first must pool the variances

• pooled var = (4015-1)71.0 + (955-1)84.9 =74

(4015+955-2)

t-test = 34.8-29.9 - 0 =4.9 =16

________________

41(1/4015+1/955) .23

Normally Distributed Data

Std. Dev = 8.83 Mean = 34.0N = 5877.00

AGE_YRS

Age at Entry

Freq

uenc

y

1600

1400

1200

1000

800

600

400

2000

Non-normally distributed data

Std. Dev = 298.80 Mean = 344.5N = 5275.00

TH_L_CNT

CD4/mm3

Freq

uenc

y

1200

1000

800

600

400

200

0

2 Test of statistical association

• Used to determine statistical association for categorical data

2 = (O - E) 2

E

2 Test - Categorical data

< 200 200 p-value Men 37.6 62.4 < .001

Women 20.4 79.6

2 Test of statistical association

• Used to determine statistical association for categorical data

2 = (O - E) 2

E

2 Calculation

ER use No ER use TotalGiven Hotline Number 200 300 500

No Hotline Number 200 300 500400 600 1000

ER use No ER use TotalGiven Hotline Number 100 400 500

No Hotline Number 300 200 500400 600 1000

(100-200)2 + (400-300)2 + (300-200)2 + (200-300)2 200 300 200 300

2 = 166.7, 1 D.F. (look up in table)

Multivariable techniques

Continuous Outcome Categorical Outcome

Linear regression Logistic Regression

Generalized estimating equations (GEE)

Cox Regression

ANOVA GEE

Polychotomous