epid7120exam1

The study of health and illness in human populations

The study of the distribution and determinants of health-related states or events in specified populations and the application of this study to control health problems

Disease occurrences are determined by factors that can be identified and measured

modification of these factors is an effective way to prevent disease or to increase survival (public health)

To evaluate and describe distribution and trends in health and disease

To compare subgroups

To provide the basis for planning health services and prevention activities

To generate hypotheses

To calculate measures of disease frequency

To elucidate the determinants of disease

To test specific etiologic (or preventative) hypotheses

To suggest potential for health promotion or disease prevention

Population (type and how observed)

Method of data collection

Unit of analysis

Selection of study participants

Type of outcome measure

How is the population observed
- Cross-sectional or longitudinal

How are they selected?

Who do they represent?
- Internal and external validity

Primary vs Secondary

Ways to measure exposure and disease status

Individuals
Groups

Levels of subject selection:
Target Population: population to which results can be applied

Source Population: the population, defined in general terms and enumerated if possible, from which eligible subjects are drawn

Eligible Population: the population of subjects eligible to participate

Study Participants: those people you contribute data to the study

Downward: first target pop -->source pop --> eligible pop --> study participants

Upward: target pop <--source pop <-- eligible pop <-- study participants

population to which results can be applied

the population, defined in general terms and enumerated if possible, from which eligible subjects are drawn

the population of subjects eligible to participate

those people you contribute data to the study

Upward: target pop <--source pop <-- eligible pop <-- study participants

population to which results can be applied

the population, defined in general terms and enumerated if possible, from which eligible subjects are drawn

the population of subjects eligible to participate

those people you contribute data to the study

A longitudinal study is a correlational research study that involves repeated observations of the same items over long periods of time — often many decades. It is a type of observational study.

Unlike cross-sectional studies, longitudinal studies track the same people, and therefore the differences observed in those people are less likely to be the result of cultural differences across generations. Because of this benefit, longitudinal studies make observing changes more accurate and they are applied in various other fields. In medicine, the design is used to uncover predictors of certain diseases. In advertising, the design is used to identify the changes that advertising has produced in the attitudes and behaviors of those within the target audience who have seen the advertising campaign.

three primary measurement scales. These are continuous (quantitative,
scale), ordinal (semi-quantitative, ranked), and categorical (qualitative, nominal). However, to simplify matters, we
may treat ordinal outcomes as either continuous or categorical, based on judgement and depending on whether
distributional assumptions can be met.

quantitative information consists of both quantitative data - the numbers - and categorical data - the labels that tell us what the numbers measure.

Qualitative variable are those that express a qualitative attribute such as hair color, eye color, religion, favorite movie, gender, and so on. The values of a qualitative variable do not imply a numerical ordering. Values of the variable “religion” differ qualitatively; no ordering of religions is implied. Qualitative variables are sometimes referred to as categorical variables. Values on qualitative variables do not imply order, they are simply categories. Quantitative variables are those variables that are measured in terms of numbers. Some examples of quantitative variables are height, weight, and shoe size.

• Prevalence: frequency of existing cases
• Incidence: frequency of new cases
• New cases are called incident cases.
• Existing cases are called prevalent cases.

Cross-sectional studies (also known as Cross-sectional analysis) form a class of research methods that involve observation of all of a population, or a representative subset, at a defined time.

They differ from case-control studies in that they aim to provide data on the entire population under study, whereas case-control studies typically include only individuals with a specific characteristic, with a sample, often a tiny minority, of the rest of the population.

Both are a type of observational study. Unlike case-control studies, they can be used to describe absolute risks and not only relative risks. They may be used to describe some feature of the population, such as prevalence of an illness, or they may support inferences of cause and effect.

Longitudinal studies differ from both in making a series of observations more than once on members of the study population over a period of time.

quantitative

By calculating measures of disease frequency and association

Used to enumerate the occurrence of disease (or whatever your outcome is) in a specified population in a specified period of time.

The frequency of disease can be measured for either incidence or prevalent cases.

The frequency can be expressed as either a count (an absolute measure) or as a relative measure

Reflect the strength of the statistical relationship between exposure status and disease occurrence. (example: relative risk, odds ratio)

Reflect the extra number of cases attributable to or prevented by the exposure in a particular population during a given time. (example: attributable risk)

Compares the disease frequency between 2 or more groups at different exposure levels.

Counts can be of incident or prevalent cases

Important to health planners

Used in monitoring the occurrence of disease outbreaks

This is generally the job of state and county health departments and federal agencies like the CDC.
We can count incident OR prevalent cases.

Often we are obliged to measure the burden of disease indirectly. The number of TB notifications varies with the iincidence of disease but unless we know the proportion of incident cases that are notified it is hard to determine the iincidence from the notification rate. Measuring the prevalence of disease is easier than measuring incidence since we only need to carry out one survey. Then if we know the average duration of disease, that is to say the time between developing disease and being cured or dying, we can make an estimate of incidence from prevalence. And of course the prevalence of infectious disease is important in its own right since it is this that determines transmission. Another way in which we might try to get an estimate of incidence is through the case-fatality rate. If we know the proportion of people who will die after they have developed TB and if have an independent measure of the total number of people who die of TB, through vital registration data, for example, we can combine these to estimate the incidence of TB.

prevalence is dependent on both incidence and duration of the disease after onset - duration is determined by either survival for fatal disease or recovery for nonfatal diseases.

In a pop in a stead-state situation the relationship between prev and disease incidence and duration can be expressed as:
(point prev/1-point prev)= I*D

The difference between I and PP is: its duration and magnitude of its PP.

When PP is relatively low (0.05 or less) than (1-PP) is almost = 1 therefore

PP=I*D

prevalence is dependent on both incidence and duration of the disease after onset - duration is determined by either survival for fatal disease or recovery for nonfatal diseases.

In a pop in a stead-state situation the relationship between prev and disease incidence and duration can be expressed as:
(point prev/1-point prev)= I*D

The difference between I and PP is: its duration and magnitude of its PP.

When PP is relatively low (0.05 or less) than (1-PP) is almost = 1 therefore

PP=I*D

the prevalence ratio is the effect measure of interest when we are interested in the public health burden of disease, although in this situation the absolute prevalence and the prevalence difference are usually of more interest. However, when we are interested in disease etiology, the POR a) estimates the incidence rate ratio with fewer assumptions than are required for the prevalence ratio; b) can be estimated using the same methods as for the odds ratio in case-control studies, namely, the Mantel-Haenszel method and logistic regression; and c) provides practical, analytical, and theoretical consistency between analyses of a prevalence study and those of a prevalence case-control study based on the same study population. For these reasons, the POR will continue to be one of the standard methods for analyzing prevalence studies and prevalence case-control studies.

Effect measures in prevalence studies

Environmental Health Perspectives, July, 2004 by Neil Pearce

When studying the etiology of a disease, it is better to analyse incidence rather than prevalence, since prevalence mixes in the duration of a condition, rather than providing a pure measure of risk.

Etiologic research focuses on the factors that influence the change in status

1. Cumulative Incidence (risk, incidence proportion)
Probability of a disease free individual developing disease over a specified time period, conditional on not dying from another cause

Probability of dying (any cause) over a specified time period, then an unconditional probability

Range 0 to 1, no dimensions

2. Incidence Density (Rate)

Instantaneous occurrence of new cases of disease at a point in time, per unit time, relative to the size of the population at risk

Range 0 to infinity, has dimensions

For either formula:
Number of new events in a defined population over a specified period of time/Population at risk for the event over the specified period of time

1. Directly using the Simple Cumulative Method
2. Estimated by using the Life Table approach (Actuarial)
3. Estimated by the Kaplan Meier Method (survival)
4. Approximated by the Incidence Density Method
5. Cox Regression (Proportional Hazards Model) -

Data Requirement:
No losses to follow-up (for any reason including study termination or loss from competing outcomes)

Generally, period of risk is short - But this is not mandatory

Assumes a closed population - All individuals included in the calculation are followed up for the entire period of study

CI(t0, t) = I/N’0

I = # events (t0, t) ;
N’0 = # disease free at t0;
t0 = start of follow up;
t = end of follow up

- A systematic record of a group’s mortality or morbidity experience,

- over the study period which is broken up into specific time intervals.

- Probabilities of survival and of cumulative incidence (CI) are calculated for each interval
- Overall cumulative survival is calculated for the study period
- Lets you calculate CI over intervals

To examine the distribution of time between 2 events

When there are losses to follow-up ( so the simple method will not work)

When there is an extended period of risk

When exact times of disease occurrence and withdrawal are unknown

When the rate of disease varies over the follow-up period

When you are interested in knowing interval-based risk

mqx = mdx / lx - (0.5) mcx

mqx = interval based probability of the event

mdx = number of events occurring in that interval

lx = population at risk at the beginning of the interval called the effective number at risk

mcx = number of losses (censored observations) occurring in that interval

x= time at the beginning of the interval

m= time at the end of the interval, length of time

mpx = 1- mqx
(1 – probability of an event)

mpx = (mpx) (mpx) (mpx)

For example,
3q0 = (1p0) (2p1) (3p2)

mqx = 1 – (mpx) (mpx)(mpx)

For example,
3q0 = 1 – (1p0) (2p1) (3p2)

Create a synthetic fixed cohort from the open cohort

Subject No in the y-axis
Follow-up Months in the X-axis

2q1 = 1/4 – (0.5)(1) = 0.286

x=1
lx=4
mdx=1
mcx=1

Does not require complete follow-up, i.e. it handles censoring.

Does not require the exact times at which events and withdrawals occurred.

Follow-up period of interest must be split into successive intervals (these don’t have to be equal).

The rate of disease (after loss) of withdrawals is the same as the rate for those who remain under observation

Independence between withdrawal and survival

Disease and withdrawals occur midway through the interval, on average

Participants survive at risk for entire study period, i.e. risk is conditional on survival

No secular trend in risk

Handles loss to follow-up

Independence between withdrawal and survival

Lack of secular trends

No need to categorize follow-up time into intervals, intervals are based on the exact time when the event occures

Risk is estimated for the follow-up time corresponding to each case occurrence

Primary distinction: no assumption about uniformity of withdrawals

qi = di /ni

di = number of events occurring at time i

ni = number of individuals under observation at time i

pi = 1 – qi

Si = (pi) (pi) (pi)

1 - Si

It is common to plot the cumulative survival (Si) or risk for the entire follow-up period – called a “survival curve”
Reflects the distribution of time to occurrence of all outcome events observed during the follow-up

Si in the y-axis
Time in the x-axis

The complements of the Kaplan-Meier estimated cumulative survival probabilities show
the CUMULATIVE RISK of recurrence throughout the study period.

Relies on the mathematical relationship between rate and risk in a time period where the RATE IS CONSTANT OVER THE TIME PERIOD.

It approximates cumulative incidence (risk) using incidence rates.

The simplest situation (introduced in Epid 603), when the risk is low, say <.1, and the rate is constant over the time period, the relationship is simple:

CI (approx =) Incidence RATE x specified tme period

In summary:
The population is decreasing each year as people die,

But the formula does not take this reduction into account,

therefore,

We have overestimated the death rate.

For a constant rate, the relationship is exponential, not linear.

Although the formula provides a risk that is the same throughout the follow-up period, there is actually an exponential reduction in the size of the cohort

If the 1-year risk is 10%, the 5-year risk is not 50%, (it’s something less)

when the time is short enough that the rate is still constant over the time period:

CI(t0, t) = 1 – e - [incidence rate * delta]

ID = the rate over the time period

delta = the elapsed time (age) between the t0 and time t

the age/time stratified density method

CI(t0, t) = 1 – e [-(sum of IDj (Delta j)]

Delta j = the duration of the jth interval
IDj = Ij/PTj =the estimated ID for the jth interval

Each age-specific ID is constant over the entire age interval for which that rate is estimated

Each age-specific ID is constant over calendar time (no secular trends) during relevant time frame

A measure of risk – the probability of an event in a specified time period/interval

Used in predicting risk, a measure of disease frequency

Method of calculation depends on :

Length of the underlying time period of “risk’

Features of the cohort

Simple Cumulative

fixed cohort = whent the exposure group in a cohort study represent groups that are defined at the start of f/u, with no movement of individusas between exposure groups are called fixed cohorts. if no losses occur from a fixed cohort it satisfies the close pop defination. --> in thi s situatoin the unconditioal risks and average survival time s can be measured directly.

Life Table :
Classical or Kaplan-Meier

Incidence Density

Dynamic cohort - the terms open or dynamic population describe a population in which the person-time experience can accrue from a changing roster of individuals.

closed cohorts add no new people over time and loses members only to death, open pop may gain members over time, or lose membesrs who are still alive throug emigration.

A risk (cumulative incidence) is a probability with no unit (although the element of time is implicit). It’s range is 0- 1.

A rate is a ratio where the denominator is usually person-time at risk and has a unit. The range is 0 - infinity.

Incidence Density (ID) = I / PT (in a specified population during a specified period of time period

I = # of incident cases occurring during the time period

PT =amount of person time experienced by the population at risk during follow-up

Measures the force (velocity) of disease occurrence change

Instantaneous occurrence of new cases of disease at a point in time, per unit time, relative to the size of the population at risk.

The text makes a distinction between incidence density (denominator is based on individual data) and incidence rate (denominator based on aggregate data). In reality, these terms are used interchangeably.

Since we cannot measure the instantaneous rate, we estimate an average rate for a given period.

One unit of person-time is equivalent to any other unit.

ID obscures any fluctuation in rates over time, ASSUMES A STEADY STATE of disease occurrence so it represents an AVERAGE RATE.

IF RATES FLUCTUATE OVER TIME, ID MAY VARY for the same person-time followed, based on the actual – calendar - time of follow-up

Depends on how much the investigator knows about individual follow-up times

1. If duration of follow-up (from entry until withdrawal) is known for each individual, ID can be calculated directly
2. If the duration of individual follow up is not known ID can not be calculated directly but it can be estimated.

PT = sum of (delta) ti

(delta) ti = duration of follow-up for individual i

(1)PT = N’((delta) t)

N’ = estimated size of population at risk (often census data or vital satistics data)
(delta)t = duration of observed follow-up

Must assume that the population is stable (constant size and age distribution)
Used to calculate rates from vital statistics data

(2) PT (average population) = (initial population +final population) / 2

Used to determine the average population of a defined cohort

Independence between censoring and survival

Lack of secular trends

ID individual data ~ ID aggregate data when withdrawals and events occur uniformly (more likely to occur with large sample and short intervals)

Risk of event ~ constant over time during the interval risk: when this is not true, the follow-up can be divided in smaller intervals and ID calculated from each interval.

TP=PAR

Incidence Density using TP in calculating person time
= true rate

TP approx = PAR

Incidence Density using TP in calculating person time approximates the true rate

TP>PAR

Incidence Density using TP in calculating person time is less than the true rate

Incidence Density using TP in calculating person time

TP>PAR

Incidence Density using TP in calculating person time is less than the true rate

Another measure of disease frequency

The ratio of the probability of the event / probability of no event

Can be calculated for incidence or prevalence
Odds ~ a proportion when the proportion (either CI or prevalence) is <0.1

q / (1 – q)
Where q = probability of the event

Prev / ( 1 – prevalence)

.20 / (1-.20) = 0.25

Another way to express the odds is 1:4 odds of being a smoker

Although there’s nothing wrong about expressing disease occurrence in terms of the odds, it is not often done in epidemiology

(Recall: odds ~ proportion when the proportion - either the CI or prevalence - is <0.1)

When risk = 0.80 --> odds = 4

When risk = 0.50 --> odds = 1.0

When risk = .20 --> odds = .25

When risk = .10 --> odds = .11

When risk = 0.01 --> odds = 0.0101

No element of time is in CI, but have to have element of time in ID.

Used to determine whether an association exists between an outcome and a study factor

Reflects the strength of the STATISTICAL RELATIONSHIP between the study factor and the disease

Involves a DIRECT COMPARISON OF FREQUENCY MEASURES for different values or categories of the study factor

Involves a comparison group which is ARBITARARY AND SET BY THE INVSETIGATOR (usually considered the unexposed or least exposed)

calculate the RATIO of the attack rate between exposed and unexposed [ attack rate E / attack rate UE]

SUBTRACT the risk in the Exposed from the risk in the unexposed
[ attack rate E - attack rate UE]

Cumulative Incidence Ratio ( CIR, Risk Ratio)

Incidence Density Ratio (IDR, Rate Ratio)

Odds Ratio (OR)

Attributable risk in the exposed (AR E, % AR E )

Population attributable risk (PAR, % PAR)

Mean differences (continuous outcomes)

Usually, Relative differences via relative risk/rate or relative odds

absolute difference - mean differences (continous outcomes)

absolute difference - via attributable risk in exposed

absolute difference - Population attribuatable risk

absolute difference - efficacy

Ratio Measures (Relative Risk)

Cumulative Incidence Ratio (Risk Ratio)

Incidence Density Ratio (Rate Ratio)

Odds Ratio

The distribution of CIR, (0, +∞), is not symmetric and not normal.

A log transformation is usually applied to CIR.

If Ln(CIR) has an approximately normal distribution, the mathematical characteristics of this distribution can be used to construct a confidence interval.

CIR = CIe/CIne =

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

A comparison of risk estimates
Generally calculated from cohort studies based on internal comparison of the cumulative incidence (risk) of the exposed and unexposed groups

The number or proportion of a group (cohort) of people who experience the onset of a health-related event during a specified time interval; this interval is generally the same for all members of the group, but, as in lifetime incidence, it may vary from person to person without reference to age.

the ratio of the cumultive incidence rate in the exposed to the unexposed.

Over the one year of the study, CI of developing malaria among those who took their anti-malria pills was 6.0, compared to those who didn't take their anti-malaria pills.

Ratio comparison of 2 average rates

Typically calculated from a cohort study drawn from a single defined population, either fixed or dynamic

An internal comparison of incidence densities (rates) of the exposed and unexposed groups

IDR = IDe/IDne = (Ae/Te)/(Ane/Tne)

Pop-time (t0, t)

Ae= Disease and Exposed
Ane= Diseased and unexpoed
Te=Pop-time in exposed
Tne= Pop-time in unexposed

Mothers who consume alcohol during pregnancy are 5 times as likely to have a child with Fetal Alcohol Syndrome as those who do not consume alcohol during pregnancy.

CI (0-3) = 1 – e (-ID x 3)

For exposed: CI (0-3) = 1 – e (-.01 x 3) = .0296

Unexposed: CI (0-3) = 1 – e (-.002 x 3) = .006

Risk Ratio = .0296 / .006 = 4.93

Calculated primarily from case-control studies, but also used for cohort studies (because it’s easy to calculate with logistic regression)

Same interpretation as CIR or IDR, with 1.0 being the null value

Can calculate either the exposure odds ratio or the disease odds ratio – these are mathematically equivalent.**

Some synonyms: probability relative odds, risk relative odds

OR is a valid measure of association, but is often used to approximate the CIR/IDR in case-control studies
We’ll cover this in greater detail in our lecture on case-control studies

odds of disease among the exposed / odds of disease among the non-exposed

OR disease = OR exposure

odds of exposure among diseased / odds of exposure among the non-diseased

odds of exposure in diseased/odds of exposure in non-diseased
= (a:c)/(b:d) = ad/bc

(a:b)/(c:d) = ad/bc

ORdis = (150/76)/(78/69) =1.75
The odds of develping a stomach ulcer among those who consume asprin is 1.75 times greater than those who don't consume asprin.

ORexp= (150/78) / (76/69) = 1.75
The odds of consuming asprin and developing a stomach ulcer is 1.75 times greater than those who dont have a stomach ulcer.

Disease Incidence Risk:
q+ = a/a+b
q- = c/c+d

Probablity Odds of Disease
q+ / (1- q+) = a/b

q- / (1-q-) = c/d

Because for many it’s easier to interpret

Because it is impossible to calculate the RR with certain designs (case-control)

It’s easy to adjust an OR for confounding and can be derived from modeling (logistic regression)

OR (event) is the exact reciprocal of the OR (nonevent)

OR is a good approximation of the CIR/IDR when disease is rare in the population

In a case-control study, if controls are selected to represent the total population (rather than just non-cases), then OR ~ CIR/IDR without regard for disease prevalence in the population. (Miettienen, 1976)

Under certain sampling schemes, OR ~ CIR/IDR more directly, without regard for disease prevalence

Odds ratio (event) is the exact reciprocal of the OR (nonevent)

Example:
Assume E = Female, D = Dead
Alive F=308
Alive M = 142
Dead F = 154
Dead M = 709

OR = 0.1

The reciprocal would be OR (alive) = 1/0.1 = 10.0

(308/154) / (142/709) = 10.0

Odds Ratio is biased away from the null ( in both directions)

Recall,

OR= (q+ / 1-q+)/(q- / 1-q-)

RR = q+ /q-

So, 1- q- / 1- q+ defines the built in bias between RR & OR

When disease is rare, this bias is negligible

Example (data from text tables 3-3 and 3-4):

OR = RR x ‘built in bias’

If, RR = 6.0 and CI UE = .0030 and CI E = .0180
OR = 6.0 x [(1-.0030) / (1-.0180)] = 6.09

If, RR= 6.09 and CI UE = .0705 and CI E = .2529
OR = 6.0 x [(1- .0705) / (1-.2529)] = 7.46

If, RR= 3.59 and CI UE = .0705 and CI E = .2529
OR = 3.59 x [(1- .0705) / (1-.2529)] = 4.46

Alive F=308
Alive M = 142
Dead F = 154
Dead M = 709

Importance of structuring data in a 2x2 table

Assume: E = Female, D = Dead
RR = (154/462) / (709/851) = 0.4

Assume E = Male, D = Dead
RR = (709/851) / (154/462) = 2.5

Assume E = Female, D = Alive
RR = (308/462) / (142/851) = 3.99

OR = RR??
Assume E = Male, D = Dead - OR = 10.0

Assume E = Dead, D = Male - OR = 10.0
Recall, OR exp = OR dis
Assume E = Female, D = Dead - OR = 0.1

All ratio measures have the same reference point, a null value of 1.0 (no association)

Comparisons across studies of different designs can be made, because
OR ~ CIR/IDR
IDR ~ CIR

The strength of the association between a study factor and outcome is one element (an important one) used to assess causality

May be deceptive in addressing the impact of the risk factor in assessing an individual’s risk due to an exposure

Example: Risk of lung cancer and CHD for smokers and non-smokers

A)
Lung Cancer &Smoker 0.06
Lung Cancer & NonSmoke 0.01
CHD & Smoke 0.4
CHD % Nonsmoke 0.2

B)
Lung Cancer & CIRsmoke 6.0
Lung Cancer & Excess Risk smoking 0.05
CHD & CIR smoking 6.0
CHD & Excess Risk smoking .2

Note: CIR for Lung Cancer considerably higher than that for CHD, but smoking has a greater absolute impact on CHD as demonstrated by the excess risk measure.

These are measure of association between an exposure and outcome based on the absolute difference between two risk/rate estimates.

Difference measures are calculated by subtracting the frequency estimates of the reference group from the comparable estimate of the exposure group.

Attributable Risk (risk difference, excess fraction, etiologic fraction)
Attributable Risk in Exposed ( called Incidence Density Difference if using rates)

Percent Attributable Risk in the Exposed

Levin’s Population Attributable Risk

Difference between risk estimates of different exposure levels and a reference level

The excess, above background, associated with the exposure under study

Theoretically, the absolute excess incidence that would be prevented by eliminating the exposure.

ARexp has the same unit as the incidence measure (dimensionless if CI; time-1 if ID).

ARe =CIe - CIne

or

IDD = IDe - IDne
ARexp has the same unit as the incidence measure (dimensionless if CI; time-1 if ID).

Excess risk of taking anti-malarial pills attributed to the development of malaria among Peace Corps volunteers in Kenya, 1997

ARexp = (60/1000) – (10/1000) = 0.05

5% excess risk of developing malaria among those who take anti-malarial medication versus those who do not take anti-malarial medication.

The percent of the total risk in the exposed group attributable to the exposure, IF CAUSALITY HAS BEEN ESTABLISHED.

Formulas:
%ARexp = (CIe - CIne /CIe) * 100
%ARexp = ((CIR* – 1.0)/CIR*) * 100
*Can use IDR or OR

%ARexp = ((IDe - IDne)/IDe) *100

%ARexp is equivalent to percent efficacy when assessing an intervention such as a vaccine.
The group receiving the intervention is considered “nonexposed”, which has a lower incidence of the disease that is targeted by the vaccine.

83.3% of the total risk in the group taking anti-malarial medication is attributable to taking the medication, conditional on the establishment of causality.

The excess risk in the total population attributable to the exposure if a causal relationship is assumed.

Population attributable risk is a function of 2 parameters, prevalence of exposure in the population & the magnitude of the increase in incidence associated with the exposure.

It is population specific, therefore, frequency of exposure is taken into account

Cannot project the results from one population to another if the frequency of exposure differs between the populations

Pop AR% = ((CIpop - CIne)/CIpop) x 100

PopAR% = ((pe(CIR*-1)/ (pe(CIR* – 1) + 1) *100

pe: prevalence of exposure in the population

* Can use IDR or OR

When pe is high

Therefore, Pop AR% ~ ARexp when pe is high

When pe is low

%PAR = ((.197 – 0.162)/ .197) = 17.8%

17.8% of the total risk of CHD in the population is attributable to being a current smoker.

Reflect the excess number of cases attributable to the exposure

Reflect the expected effect of changing the distribution of one or more risk factors in a particular population

Useful from a public health perspective – when attributable risk is high, the risk factor is of importance to the health of the community

The impact of smoking in terms of absolute excess rate is about the same for both Lung Cancer and CHD
From a public health perspective on prevention, although the IDR for lung cancer > IDR for CHD, the absolute excess is the same

Relative differences are used most often when evaluating the DETERMINANTS of disease because they represent the magnitude of the association. This information is critical in the determination of causality.

ONCE CAUSALITY IS ASSUMED, absolute differences are more important measures from the perspective of public health administration and policy.

What type of study? Cohort – longitudinal study
Discriptive group – single group cohort
Calculated incidence
Possible limited generalizability
No case definition – DMI or DMII
Under estimate of DMI bc parents prob not in the military if had h/o DMI

Chort: A group of individuals that share a common characteristic

Example:
Birth cohort: individuals born in the same period (often year)

Exposure cohort: individuals sharing a common exposure (often an occupational exposure such as asbestos, etc.)

The observation of a cohort(s) over time to measure a stated outcome.

Descriptive (measures of frequency)
To describe the incidence of an outcome over time or to describe the natural history of disease
Analytic (measures of association)

To analyze the relation between occurrence of outcomes and risk factors (or predictive factors)

: forward, incident cases

Recruited in healthy, but at risk for the disease of concern.
Then broken into exposure status – follow them forward and measure disease status.

sufficient EVIDENCE has accumulated from other studies to indicate a prospective cohort study is warranted

a NEW AGENT is introduced and requires monitoring for its possible association with adverse health outcomes (levaquin, vioxx)

TEMPORAL association is unclear from a case-control study

impressive results are obtained from a c-c study (either positive or negative) and issues of VALIDITY (selection or information bias) are evident or are a concern

Although it has been concluded that the evidence for a causal association between dampness and respiratory morbidity is strong, this evidence is based mainly on cross-sectional studies and

prevalence case-control studies;

few prospective studies have been conducted

Selecting a cohort (sampling frame, sampling and recruitment, external vs internal validity)

Exposure assessment

Follow-up

Considered gold standard in observational studies
Less prone to bias bc information bias – not relying on recall
Randomized control trials overall gold standard – due to the randomization.

Any well-defined population (geographic, occupational, membership in HMOs)

Typically evaluate multiple hypotheses

Primary Justification : external validity

Tend to be very large, geographical, occupational, member of hmo, choosing peeps from the pop to answer a specific question
Numbers needed pends on the prevalence, rare/common,

Advantages
Estimation of distribution and prevalence of relevant exposure variables

Calculation of risk factor trends over time
Strong internal validity

Strong external validity (primary justification)

Disadvantages
Expensive, logistically complicated

Often associated with large loss to follow-up

If exposure is rare, inefficient

Total population
Probability samples of the population


The extent to which a cohort sample is representative of the total reference population depends on the completeness of the population frame available to sample from as well as participation rates.
please refer to Delnevo et al article as an example.

Similar to the concept of the source population

Depends on eligibility criteria for inclusion

Initial response of the sample

Stability of the cohort on follow-up.

Requires variability of exposure and outcome levels

Susceptibility of the population to the risk factor

May ensure the cohort has exposure of interest

Less likely to be lost to follow-up because of lower mobility (military, occupational cohort)

May have relevant information on exposure & potential confounders in the medical and employment records

Reduced ability to generalize results to the general population

Access to data may be limited

Generally, smaller sample sized needed

EXTERNAL COMPARISON GROUPS: chosen from a different source population
often general population controls from area are used

must be susceptible to the same selective factors as the E group

less costly if data already available

sometimes called SMR studies

Target Population: population to which results ccan be applied

Source Population: the population, defined in general terms and enumerated if possible, from which eligible subjects are drawn

Eligible Population: the population of subjects eligible to participate

Study Participants: those people you contribute data to the study

Downward

upward

Definition of exposure: intensity, duration

Induction period

Latency

Changing exposures

Allocation of person-time in the above examples

Categorizing exposure

Duration of time that it takes from exposre to onset of disease

Time during which exposure occurs ≠ time at risk

Example: radiation exposure and leukemia, ~3.5 years.

Exposure is classified as high, medium and low based on the amount of time working in a job where you are exposed to radiation ≠ PT at risk.

What do you do with the person-time that accrues prior to the induction time?

Only include time at risk of the outcome in the denominator of the rate.

Duration of time from disease initiation to disease detection.

Very relevant when considering covariates such as detection bias, etc

Changing exposures:
Calculation of rates (as opposed to risks) allows flexibility in the analysis of cohort data.

An individual can contribute follow-up to several different exposure-specific rates, depending on details of the study hypothesis

The definition of the exposure group corresponds to the definition of PT eligible for each level of exposure.

How to handle changing exposures depends also on cross over effects. If the effect of being exposed is cumulative, you can not change exposure groups when exposure ceases.

Categorizing exposures:
Often there is no guidance on appropriate categories of exposure.

Or the line between exposed and unexposed is not defined

No problem if your data are continuous

If you want to calculate rates directly, you must observe populations within categories of exposure.

Common error: apportioning to PT time, the unexposed time of a person who eventually becomes exposed.

Occupational study where exposure is categorized according to duration of employment in a particular job. Highest exposure category is at least 20 years of employment. If a worker has been employed 30 years, it is a mistake to assign that employee to the 20+ years of employment because they only reached that exposure in the last 10 years. That’s the time frame relevant to 20+ years of exposure.

Is Mold Exposure a Risk Factor for Asthma?:

It is not clear whether molds are merely markers of dampness or are causally related to the symptoms associated with dampness.

Assessment of exposure to molds is often done by questionnaire.

It is unknown to what extent questionnaire reports of mold growth correlate with exposure to relevant mold components .

Is Mold Exposure a Risk Factor for Asthma?:
If mold exposure is quantified –

Perhaps the most important problem, one that has rarely been acknowledged in the studies published to date, is that air sampling for mold for than 15 minutes is often impossible, and air concentrations usually vary a great deal over time.

The few studies that have included repeated exposure measurements of mold have shown considerable temporal variation in concentrations, even over very short periods of time.

Variability in isolated genera was even more substantial.

Systematic, standardized data collection procedures on all or a sample of cohort members regardless of exposure status to avoid surveillance bias.

Data collection relies on primary and secondary collection procedures
- linking of established dbf; professional, government, etc

Controlling loss to follow-up is key.
- baseline recruitment strategy; key identifiers for searching, adequate info to analyze differences in participation rates.
Downside - longer questionnaire, interview may inhibit recruitment
- mail, telephone survey, - both, monetary incentives, etc.

Concurrent
Retrospective
Mixed Design

Advantages:

Study many different outcomes with exposure of interest

Temporal relation not in doubt, therefore, preferred for causal inference

Less prone to selection bias as D status does not influence selection of subjects with respect to exposure

Repeated exposure data can be collected

Provides information on changing risks over time

Modification of risks by increasing age

Disadvantages:

Costly, resource intensive (manpower, time and money)

Loss to follow-up of study subjects

Inefficient for studying diseases with long latency

Inefficient for studying rare diseases
- example : If ID = 5 per 100,000 per year and sample size calculations say you need 100 cases, given an initial cohort of 40,000 subjects follow-up would have to continue for 50 years

“Study effects”

Changing exposure

Withdrawals/loss to follow-up

Basic design allows only 1 risk factor to be studied

An alternative to the cohort study for assessing exposure-disease relationships

Subjects chosen based on disease status and assessed for previous exposure

Exposure data may be measured at the time of the study or gathered from existing data

Analysis by the odds ratio (as an estimate of the relative risk)

Particularly susceptible to certain types of bias which dictates design characteristics

But optimized speed and efficiency.

selection of cases and controls
collection of accurate

exposure data

control of extraneous factors

Used to answer the same research question as in cohort studies:
Is the rate/risk of disease among the exposed different than that among the non-exposed? If yes, in what direction and by how much?

Used as AN EFFICIENCY VERSION of a cohort study

Used to estimate the IDR/CIR with the OR

Only need a percentage of the controls, but the percenage needs to be the same in the E and nE (Sampling Fraction)

Cases must be representative of all cases in the source population – the same ones who would be considered cases if a cohort study was done.

Controls selected so that their exposure distribution reflects the exposure distribution among the person time in the source population,
i.e. the same “source cohort (population)” as the cases.

Both cases and controls must be selected independent of exposure status

The Source Population is:

The source of subjects for a particular study
Defined by the participant selection methods of your study.

Clearly define the source population

Establish strict diagnostic criteria for case definition, independent of exposure (cases really cases)

Either incident or prevalent cases, but incident are ideal

Can be selected cross-sectionally (at a point in time) or longitudinally – longitudinally is a better choice

Can use all cases within the population or a sample of the population

Without a well defined source population, it is difficult or impossible to select unbiased controls.

Is critical and can be difficult

Controls must come from the same source population that gives rise to the cases

Controls must have the same exposure distribution as in the source of the cases

Chosen independent of exposure status, i.e. the same sampling rate for exposed and unexposed controls

If sample size is large enough, problems due to sampling error are avoided

Goal is to choose cases and controls so that their proportion with the risk factor (E) in the study does not vary much more than sampling error from the source population.

When selecting the controls we want to minimize – selection bias and maximize the potential for the OR ~~ the RR

If a disease is rare, all sampling strategies will give the same result (OR ~ IDR/CIR)

If disease is common, different sampling strategies will give different results

Types of Sampling strategies:
Traditional (cumulative) sampling -Case-based case-control study (traditional):

Density Sampling - Case-control study within a cohort (hybrid, ambidirectional):

Case-based case-control study (traditional):
cases and controls are selected at a given point in time from a hypothetical cohort (i.e. at the end of follow-up).

Case cohort study:

Nested case-control study:

Nested case-control study: controls selected at time when each case occurs (incidence density sampling).

Case cohort study: controls are selected from the baseline cohort.

Typically, cases identified as diagnosed during study period from a stated source population

Controls (non-cases) identified from the same source population from among the non-cases at the end of the study period (cumulative sampling).

Exposure to the risk factor of interest is measured/gathered

OR is calculated as an estimate of the IDR/CIR

Selecting controls from those disease-free at the end of the observation period during which cases are identified.

Primarily used only when the disease is rare, otherwise OR doesn’t estimate the IDR/CIR

Selecting controls with this method, they do not represent the source population from which cases come, represent only non-cases (although they do still come from the same source population).

Selection bias may occur when cases and non-cases are not selected from the same source population, or populations with similar relevant characteristics.

Selection bias may occur if loss to follow that happens before the study groups are selected affect their comparability.

only cases with long survival are included.

A cross-sectional ascertainment identifies primarily prevalent cases, that is, those with the longest survival. Cases and controls who die before they can be included in the study may have a different exposure experience compared with the rest of the source population.

It is preferable to ascertain cases concurrently, i.e. to identify and obtain exposure information from cases as soon as possible after diagnosis. Same rules apply to controls.

Controls may be selected from the baseline cohort, i.e. “case-cohort” design.

Controls may be selected from individuals at risk at time each case occurs, i.e. “nested case-control” design.

Likelihood of selection bias diminished with either approach compared to case-based study design.

C-C study conducted within the framework of existing, defined cohort, which becomes the SOURCE POPULATION

Cases are selected from the cohort (all or a sample) as they develop

Controls are selected by random sample of the total cohort at BASELINE

Controls have potential to become a case

OR ~ CIR, no rarity assumption needed

Selection bias is reduced due to control selection within the source population

Within framework of existing, defined cohort, the source population

Controls are a random sample of the cohort (non-cases) at the time the case occurs

Called INCIDENCE DENSITY SAMPLING OR RISK SET SAMPLING

Matching on duration of follow-up

Controls have the potential to become a case

OR ~ IDR, no rarity assumption needed

When a case occurs, a control (non-case) is selected (controls selected longitudinally)

“Matches” control to case based on time

Controls have the potential to later become a case

Ensures that controls represent the source population from which cases come

Rare disease assumption not needed, OR ~ IDR/CIR for both common and rare diseases using this strategy

Example:
Levels of Maternal Serum AFP in Pregnant Women and Subsequent Breast Cancer Risk (AJE 1998;148:719-727)
Univ. of Ca. Berkeley Child Health & Development Studies (CHDS)
1959-1994
Cohort of 12,552 pregnant women
Follow-up conducted by using license records from the department of motor vehicles, and review of death certificates
Nested design
Cases women in the CHDS cohort who developed breast cancer, identified through the California Cancer Registry
Controls were members of the cohort who had not been diagnosed at that point in time with breast cancer
Exposure assessment: Frozen sera accrued between 1959-1966
Data analysis: logistic regression

The estimated exposure odds ratio is a statistically unbiased estimate of the relative risk since cases are included in the sampling frame for the selection of controls.

Efficient when need additional information (particularly detailed exposure information) that are not available for the entire cohort.

OR dis = OR exp
There is a built-in bias away from the null
OR can approximate the RR in specific situations

Used to answer the same research question as in cohort studies:
- Is the rate/risk of disease among the exposed different than that among the non-exposed? If yes, in what direction and by how much?

USED AS AN EFFICENT VERSION OF A COHORT STUDY

USED TO ESTIMATE IDR/CIR WITH THE OR

Only used when you want to estimate RR

Rare = disease < 0.10

Most diseases are rare

If controls are selected to represent the source population

CIR

IDR

Selection Bias –
Information Bias –

can occur when cases and controls are not selected from the same source population
When selective survival occurs

can occur when there is bias in the measurement of exposure resulting in misclassification since exposure is ascertained after disease has occurred.

Less expensive and time consuming than cohort design

Good for studying the etiology of rare diseases

Good for studying diseases with long latency periods

Possible to study many different exposures with respect to outcome of interest

Causal inference less clear (temporal ambiguity)

Often cannot estimate the frequency of disease in a population

Insufficient for studying rare exposures

Particularly susceptible to both selection and information biases

Involves the comparison of GROUP-LEVEL variables rather than comparison of INDIVIDUAL-level data.

A study that includes ecologic level (as opposed to individual level data.)

They can be any design (cohort, case-control)
- Often a geographically defined variable is used (eg: a country, a census tract, etc)

We know the marginal frequencies of exposure and disease

We do not know the joint distribution of exposure and disease

Data collection: levels of measurement

Levels of analysis: common level for which data on all variables are reduced and analyzed

Interpretation: target levels of inference

Aggregate: means or proportions

Environmental: physical characteristics of place/individual analogue; e.g. hours of sunlight

Global: attributes of groups or places/no individual analogue; e.g. healthcare system, law, population density

Individual level

Group level

Multilevel level

Biologic: inference stated in terms of individual risks

Ecologic: inference stated in terms of group rates

Contextual: use of both individual level with group level data to separate the effects of the 2 on each other.

Subject grouping:

_ By place: multiple-group design
Meat Consumption and Colon Cancer: A Multi-National study

_By time: time-trend design

_By place and time: mixed design
Example: Is hard drinking water a protective risk factor for CVD mortality?
-- The absolute change in CVD mortality rate between 1948-1964 in 83 towns.

Low cost and convenience

Measurement limitations of individual-level studies

Design limitations of individual-level studies; i..e. limited variability in exposure

Interest in ecologic effects

ecosocial analyses of disease distribution, population health, and health inequities.

Krieger, N. Public Health. 2008;98:221–230. doi:10.2105/AJPH.2007.111278)

Not able to calculate rate or risks directly due to lack of information

Regress group-specific disease rates on group specific exposure rates
__ Linear, logistic, multi-level analysis (contextual analysis, hierarchical regression), etc.

Ecologic bias

Temporal ambiguity - uncertainty about exposure preceding disease

Collinearity - covariates more highly correlated at group level

Confounder control - Adjusting for confounders may increase bias

The inability of the ecologic inference to accurately estimate the biologic effect at the individual level.

Classic example:
Ecologic study assessing the relation between religion and suicide rates in Prussian communities in the late 19th century (Durkheim 1951).

He found that there was a correlation between being Protestant and suicide rates

Conclusion: Being Protestant is a risk factor for suicide

Ecologic Fallacy: It is possible that most of the suicides w/in the communities were committed by Catholics, who were a minority and more socially isolated.

Within-group misclassification
- Nondifferential misclassification leads to bias away from null vs. toward null in individual level analysis

Lack of adequate data
- Data may be crude, - incomplete or unreliable
Incomparable data across groups/countries

Migration across groups
- Can cause ecologic bias

Generating individual-level etiologic hypotheses

Appropriate when broad social or cultural factors are of interest

Alternative to collecting sensitive or expensive data from individuals

Testing impact of group wide interventions

“ Comprehensive theoretical model of causality – one that considers all factors influencing the occurrence of disease- often requires taking into account the role of upstream and ecological factors (including environmental, sociopolitical and cultural) in the causal chain”.

Would it be practical to conduct alternative ways of studying the same question (eg, cohort study, randomized control trial) or was the ecological study the only alternative?

Are the subjects in the ecological study representative of the group, place, or population of interest?

Were the exposure and outcome variables measured and defined in the same or a similar way across the different populations or groups that are being studied?

Have data been collected on important confounding variables that might also explain the exposure–outcome relationship and have they been statistically adjusted for? If data are not available on key factors, is it reasonable to assume that their prevalence is similar in the different groups or populations being compared?

Is the identified ecological relationship between the exposure and outcomes biologically plausible and consistent which what is already known about a given topic at an individual-subject level?

What is the strength of the quantitative and statistical associations between the exposure and the outcome? The stronger the associations, the greater the likelihood of a true causal relationship.

Have the investigators interpreted their data with appropriate caveats? Did they acknowledge the possibility of an ecological fallacy? Were alternative explanations for the association between exposure and outcomes considered by the investigators?

Have the study data been collected at multiple levels (eg, individual, physician, hospital, community, or country)? If yes, was multilevel modeling considered or used for analyzing the data?

Sampling is almost always used when conducting surveys and when conducting epidemiologic studies

National Center for Health Statistics (NCHS) is the principal health statistics agency in the US (http://www.cdc.gov/nchs/about.htm).

Examples of NCHS surveys:
The National Health and Nutrition Examination Survey
The National Health Interview Survey

Health agencies conduct surveys to
assess health status of populations;
guide the allocation of resources; and
evaluate health policies.

Sampling is often discussed in the context of survey research.

But sampling is an important element of all epidemiologic study designs:
Selecting the sample for a cross-sectional study
Selecting subjects in a cohort study
Selecting cases and controls in a case-control study
Assigning subjects to study groups in a clinical t

Target population: the population to which you want to apply the findings of your study (e.g. the total U.S. population, or all children in the U.S.)


Source (Survey) population: the population that is practical to include (e.g. the civilian non-institutionalized US population).


The differences between the target and survey populations need to be identified, justified, and documented.

The consequences of the differences should also be assessed. in terms of
-Internal validity (selection bias)
-External validity

Instrument that includes all units of the survey population – e.g. Lists, maps

Inclusion and exclusion criteria must be stated: who is eligible to be in the sample population.

Incomplete or inaccurate lists can be a problem – called Coverage Error.

Probability sampling
Each member of the survey population has a chance to be selected.
A random method of selection is used.
The probability of selection is known.

Non-probability sampling (e.g. convenience sampling, snowball sampling)
Limited ability to extrapolate from your sample to a larger population.

Simple random sampling

Systematic sampling

Sampling with stratification

Cluster and multistage sampling

SRS: any of the possible subsets of n distinct elements from the population of N is equally likely to be chosen.

Therefore, every element in the population has the same probability of being selected.

However, not all sampling schemes in which every element has the same probability of being selected is SRS.

SRS without replacement offers a better precision than SRS with replacement.

If the size of the population is large relative to the sample, the difference is minimal.

In large-scale surveys, SRS is not used very often due to inconvenience.

If SRS was used, sample mean is an unbiased estimator of the population mean.

Variance of the sample mean = (1 - n/N)*(sample variance / n)

For large populations, sample size (n) rather than the sampling fraction (n/N) affects the precision of survey results more.

Systematic sampling involves taking every Kth element after a random start.

Each element in the population has the same chance of being selected, but the probabilities of different sets of elements being included in the sample are not all equal.

If we were to select 3 individuals out of 10 and take every third person after a random start (1, 2, 3, or 4),
what is the probability that both #1 and #2 are selected?
What is the probability that both #1 and #4 are selected?

For systematic sampling to take place, it is necessary to assume that the list has an approximately random order.

If there is a pattern with respect to the variables of interest and the sampling interval coincides with the pattern, systematic sampling will not result in a good sample.

First, classify the population into subpopulations (strata), based on existing information (e.g. grades in a school), and then select separate samples from each of the strata using SRS or other methods.

If the strata sample sizes are proportional to the strata population sizes (i.e. a uniform sampling fraction is used), it is known as PROPORTIONATE STRATIFICATION; otherwise, it is considered DISPROPORTIONATE STRATIFICATION

Variable of interest: # of hours/day of TV viewing in high school students.

We could take a 10% sample using SRS, or classify all students based on grades (9th – 12th) and then take a SRS sample from each grade (stratum).

Compared with SRS of the same size, a proportionate stratification sample with SRS in each of the strata will have a similar or smaller variance.

The gain in precision is large if the within-strata variation is small and/or the between-strata variation is large.

Sometimes used to allocate a sufficient sample size to specific strata so that separate estimates of adequate precision will be available for those strata.

The stratum that is given a higher sampling fraction usually has
a relatively small size (e.g. minority groups in national surveys); or
a relatively high variance in terms of the variable of interest.

Disproportionate stratification can result in a higher variance of the sample mean than a SRS of the same size.

The target population : all homes in New Orleans (except for specific excluded neighborhoods)

Exclusion: FEMA trailers and unoccupied housing

Total study sample size = 100

Issues: sampling frame, and the sampling strategy.

Stratify by neighborhood (defined by planning district), weighted by occupancy rates
Calculated as follows: proportion overnight occupancy p/n’hood (Rapid Population Estimate data) X the number of pre-K housing units (2000 Census) p/n’hood.
That number was used to determine the proportion of total housing p/n’hood currently occupied in New Orleans.
The sample size p/n’hood was weighted: total occupied Housing Units in planning district / total occupied housing units in New Orleans

For example, 56% of French Quarter (FQ) was occupied (RPE). That translates to ~ 3,267 (.56 x 5881 total occupied units 2000 Census). Total occupied units in New Orleans = 64,481 (RPE). So, FQ has 5% of total occupied HU. So, 5% of the sample came from the French Quarter.

Logic: The repopulation of N.O. would eventually be a function of both pre-Katrina occupancy patterns and the amount of devastation

Groups of elements can be considered clusters (e.g. different classes in a school, different communities in a city). Often only a sample of the clusters are included in a study or survey.

Two-stage cluster sampling: Only a sample of all the elements in selected clusters are included.

Multistage cluster sampling: A hierarchy of clusters is used – this is sometimes loosely described as cluster sampling.

In sampling with stratification, all strata would be included in the final sample. We would like to have strata that are internally homogeneous and externally heterogeneous.

In cluster sampling, only a sample of the clusters will be included in the final sample. We would like each cluster to be as heterogeneous as possible.

Major assumption of cluster sampling is that the cluster represents the whole.

Compared with an SRS of the same size, cluster sampling often (although not all the time) leads to a loss in precision.

The justification for cluster sampling is the reduced cost (time and money).

1. BEFORE SUBMITTING A RESEARCH PROPOSAL, to estimate the approximate sample size needed to test relevant hypotheses

2. When a study is underway, to evaluate whether the planned sample size is still satisfying, given any new information

3. After a study is completed, power and sample size calculations can be conducted to help interpret your results (ie a statistically insignificant finding may be due to limited power)

Sample Size:
Calculated to choose the adequate number of subjects needed to detect a certain magnitude of effect with minimal statistical error
Numerous formulas exist for calculating sample size

Power:
Probability of identifying an effect when one truly exists (ie rejecting the null hypothesis when it is actually false, reducing type II error)

1-alpha

Reject Ho when Ho is true

alpha

Accept Ho when Ho is false

Beta

1. Type I error (alpha):
The standard is 0.05.

2. Power (1-Beta):
The ability to detect a difference if one truly exists. The standard is 80%.

3. Proportion with factor (prevalance or incidence)
Proportion of baseline population exposed to the factor of interest (C-C study) with dichotomous outcomes.
Proportion of baseline population that has the disease of interest (cohort or intervention studies) with dichotomous outcomes.

4. Magnitude of effect you want to detect:
The difference in outcome rates between the two groups, the RR or OR.

Previous studies

Pilot studies

If none is available, investigator uses best judgment to provide a range of values or the most conservative estimates.

n=((p1q1 + p2q2)*(Za +Zb)squared) / (p1 - p2)*(p1-p2)

where,
n = # subjects in each group
p1 = frequency of outcome in group 1
p2 = frequency of outcome in group 2
q1 = 1 - p1
q2 = 1 - p2

Zb = ((p1-p2) * (sqrt (n)) / (sqrt (p1q1 + p2q2)) -Za

we’ll need 3,098 subjects in each group.

For a total of 6,196 participants

Given the proportion of controls exposed (p2) and the odds ratio predicted (OR), the proportion of cases exposed (p1) is given by:

p1 = (p2*OR)/(1+p2(OR-1)

First, calculate the frequency of exposure in the cases using the frequency in controls and the odds ratio:

Second, use these to calculate n:

So, we’ll need approximately 280 cases and 280 controls.

decreases

Decreasing β error (increasing power)

Decreasing clinical significance (e.g., treatment difference you are trying to detect)

Increasing variability in the observed data