Nutritional Epidemiology

Lecture 3 of 4Dr. Sarah McMullenRoom 37, North Lab

Epidemiological studies What do we need to measure?

– Exposure of interest

– Outcome of interest

– The relationship between exposure and outcome

• To understand the role of hypothesis testing and confidence intervals in assessing the significance of observed associations

• To be able to recognise and interpret significant diet-disease associations in the types of analyses commonly presented in the literature

Learning objectives

Evaluating Associations If we observe an exposure/disease

association, we must consider

– Is the association valid? Do the study findings reflect the true relationship between the exposure and disease? Or do they reflect chance, bias or

confounding?

– Is the association causal? Is there sufficient evidence to infer that a causal association exists between the exposure and the disease?

Chance To understand why chance could be involved

it is important to consider sampling error

– Rarely can a whole population be studied– Instead, a SAMPLE of the population is studied– The observations of the sample provide an

ESTIMATE of what would be observed in the true population

– Variation will always exist between random samples from the same population – sampling error

– BY CHANCE, an association may be observed due to sampling error alone

Chance

Sample number

Mea

n ch

oles

tero

l co

ncen

tratio

ns

(mm

ol/l)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Plasma cholesterol concentrations were measured in two groups of students sampled from a population of students.

Do the mean values for samples 1 and 2 appear different?

Chance

Sample number

Mea

n ch

oles

tero

l co

ncen

tratio

ns

(mm

ol/l)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

NO! If we look at the mean values for repeated random samples of students from the population, we can see that the mean values of groups 1 and 2 could have occurred by chance due to the large variation between samples.

Chance

In practice, we can not take repeat samples An estimate of sampling error is required to

determine whether the observation is accounted for by chance or not

Sample number

Mea

n ch

oles

tero

l co

ncen

tratio

ns

(mm

ol/l)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

An estimation of sampling error is calculated from– Standard deviation of data from

group– Number of subjects in groupThis estimate is referred to as

the– Standard error of the mean– Confidence intervals

Chance Statistical tools must be used to estimate

sampling error and determine how likely it is that the observation occurred by chance

– Hypothesis testing and P-values

– Estimation and Confidence intervals

Hypothesis testing P-value

– Probability that result would have occurred by chance alone (i.e. if null hypothesis were true)

– Usual threshold for significance ~ P = 0.05 – If the study was repeated 100 times, a significant

difference could occur by chance only 5 times.

– The bigger the sample size, the smaller the difference needs to be to prove statistically significant

– But is it biologically significant??

Comparing meansM

ean

chol

este

rol

conc

entra

tions

(m

mol

/l)

Control HF diet

Figure 1. Mean circulating cholesterol concentrations in adult Wistar rats fed a control (n=12) or high fat (HF, n=12) diet for a period of 6 weeks. P<0.05.

r = +0.23

Correlation

Average consumption of meat (g/person/day)

Incid

ence

of C

olon

ca

ncer

Cas

es p

er 1

00,0

00

in 2

002

Examines strength of association between exposure and outcome

Correlation coefficient (r)Describes strength of the association+1 perfect positive 0 no association -1 perfect negative

r = +0.89

Correlation

Average consumption of meat (g/person/day)

Incid

ence

of C

olon

ca

ncer

Cas

es p

er 1

00,0

00

in 2

002

Examines strength of association between exposure and outcome

Correlation coefficient (r)Describes strength of the association+1 perfect positive 0 no association -1 perfect negative

Correlation

Average consumption of meat (g/person/day)

Incid

ence

of C

olon

ca

ncer

Cas

es p

er 1

00,0

00

in 2

002

Examines strength of association between exposure and outcome

Correlation coefficient (r)Describes strength of the association+1 perfect positive 0 no association -1 perfect negative

r = -0.89

r2 = 79 %79 % of variation in one

variable accounted for by the other

p = 0.02 (p<0.05)

Regression How much does the outcome change for a given change in exposure?

Average consumption of meat (g/person/day)

Incid

ence

of C

olon

ca

ncer

Cas

es p

er 1

00,0

00

in 2

002

Plots a regression line through the data

Linear regressionAssesses the effect of one predictor variable

Multiple regression Includes more than one predictor variabler =

+0.96p = 0.02 (p<0.05)

Relative Risk (RR)Or Rate RatioRatio of the incidence in the exposed group divided by the incidence in the unexposed group

Incidence in exposed group = 9/11= 0.818

Incidence in unexposed group =3/14= 0.214

RR =3.82

Relative Risk (RR) – Example 1

With Outcome

Without Outcome

Exposedn=11

Unexposedn=14

9 2

311

Relative Risk (RR)Or Rate RatioRatio of the incidence in the exposed group divided by the incidence in the unexposed group

Incidence in exposed group =3/11=0.273

Incidence in unexposed group =8/14=0.571

RR =0.478

Relative Risk (RR) – Example 2

With Outcome

Without Outcome

Exposedn=11

Unexposedn=14

3 8

86

Relative risk / Odds ratio Unexposed/control group RR/OR =

1 If the exposure increases risk RR/OR > 1 If the exposure is protective RR/OR < 1 But is the risk of outcome significantly

increased or decreased?

1 2 3 4-4 -3 -2

CONTROL

INTE

RVENTION

Confidence intervals– Tell us the range within which the actual

population value is likely to lie Based on estimates of sampling error

Commonly used in cohort and case-control studies– Risk in unexposed or control group set at 1– Risk in exposed or case group calculated

(relative risk or odds ratio)– Confidence interval for exposed or case group

calculated

Confidence intervals

95% confidence interval– 95 % confident that the true population mean

lies within the given range– If the range of the confidence interval for the

exposed/case group includes 1, there is no significant difference between the groups (sampling error)

Confidence intervals

1 2 3 4-4 -3 -2

CONTROL

INTE

RVENTION

Relative RiskWeight

(pounds)Cases Total no.

of women

RR

<128 206 5763 1

129-140 236 5701 1.17

141-155 308 6107 1.45

156-174 283 5274 1.56

>174 335 5754 1.83

Risk of breast cancer increases with increasing body weight(as shown by increasing risk relative to those <128 pounds)

But at which rates is the RR significantly higher?

Cohort StudyRelative risk of post-menopausal breast cancer in woman grouped by body weight at 18 years of age.Adjusted for BMI and WHRSellers, 2002

Relative RiskWeight

(pounds)Cases Total no.

of womenRR 95 %

confidence interval

Significantly increased?

P-value for trend

<128 206 5763 1 n/a n/a

129-140 236 5701 1.17 0.97 - 1.42

141-155 308 6107 1.45 1.21 - 1.75

156-174 283 5274 1.56 1.28 - 1.90

>174 335 5754 1.83 1.49 - 2.24 P<0.001

RR significantly increased in groups weighing >174 pounds

The association between weight and RR is also assessed by correlation analysis (P-value for trend) ~ assess dose response relationship

Odds RatioMET

h/weekOR 95 %

confidence interval

Significantly decreased?

P-value for trend

0-25 1 n/a

25-<50 1.17 0.53 - 2.55

50-<80 0.49 0.22 - 1.07

>80 0.29 0.12 - 0.72 P<0.001

Confidence intervals are similarly calculated for odds ratios

Must calculate the 95 % confidence interval– 95 % certain that the population mean lies within the range

given– If the range includes 1 ~ OR is not significantly increased

In this case risk is reduced (<1) by increased exercise

Case-control studyEffect of physical activity level on risk of breast cancer.Adjusted ORGilliland, 2002

Odds RatioOR

(95 % CI)

1 20.5

It is important to consider– The effect size– The range of the

confidence interval– The significance of

the effect

– What do each of these tell us about the data?

• To understand the role of hypothesis testing and confidence intervals in assessing the significance of observed associations

• To be able to recognise and interpret significant diet-disease associations in the types of analyses commonly presented in the literature

Learning objectives

Study size and power Too few experimental units

– Poor estimate of true population mean– High standard error of mean/wide confidence

interval– Difficult to show statistical significance

Power– Probability of being able to demonstrate a

statistically significant finding, should one exist

A successful study must be adequately powered