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Study Design and Analysis in Epidemiology: ��Where does modelling fit?

MMED 2025

Carl

Earlier contributors: Cari van Schalkwyk & Steve Bellan

Slide Set Citation: DOI:10.6084/m9.figshare.5038784

The ICI3D Figshare Collection

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Goals

Define Epidemiology
Discuss metrics of epidemiology

Measures of disease
Measures of effect

Describe basic study designs used in epidemiology
Discuss error, bias and confounding
Compare and contrast statistical models and dynamic models

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Defining Epidemiology

“The study of the distribution and determinants of health-related states and events in populations, and the application of this study to control health problems.”

John M Last �Dictionary of Epidemiology

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Risk Factors & Intervention Epidemiology�

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Risk Factor: A characteristic that is correlated with a measure of disease.�

Often used synonymously with covariate.�
Protective factors: Risk factors that are negatively associated with disease

Varieties of Infectious Disease Epidemiology

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Varieties of Infectious Disease Epidemiology

Risk Factors & Intervention �
Outbreak �

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Clinical �
Surveillance

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How does mathematical modeling fit?

Subfield: � Linking pattern with process across scales

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�

Methodologies used in other epi subfields

Importance of knowledge breadth

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Goals

Define Epidemiology
Discuss metrics of epidemiology

Measures of disease
Measures of effect

Describe basic study designs used in epidemiology
Discuss error, bias and confounding
Compare and contrast statistical models and dynamic models

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Measures of Disease

Prevalence:

Proportion of the population with infection or disease at a given time point

Incidence:

The number of new cases that occur within a given population and period of time
Sometimes stated as a raw number of cases per time window, such as 1000 cases of influenza in a month
For comparison of incidence between populations (or within a population that is changing in size), incidence should be standardized (e.g., on a per capita basis or per 100,000 population per time period)

Survival �(time to event, e.g., death)

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Measures of Covariates (risk factors)

Binary: smoker, circumcised��
Nominal/Categorical: geographic region��
Continuous: birth weight, T-cell count��
Ordinal: education, socioeconomic status (SES)�

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Measures of Effect

How do you measure the effect of a risk factor on a disease?

Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Measures of Effect

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Compare measure of disease across levels/values of risk factors �
Relative Risk - magnitude of association between risk factor & disease

Ratio of rates or proportions

Prevalence Ratio
Incidence rate Ratio
Odds Ratio

Attributable risk – public health impact of risk factor on disease

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Goals

Define Epidemiology
Discuss metrics of epidemiology

Measures of disease
Measures of effect

Describe basic study designs used in epidemiology
Discuss error, bias and confounding
Compare and contrast statistical models and dynamic models

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Epidemiological Studies

Descriptive Epidemiology

Baseline data on distribution of disease
Surveillance�

Analytic Epidemiology – Measure Effect

Ecological Studies
Cross-sectional Studies
Retrospective Case-Control Studies
Prospective Cohort Studies
Randomized Controlled Trials

Mathematical epidemiology

Mechanistically understand how the effects of risk factors lead to the distribution of disease

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Observational

Experimental

Most studies are both

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Ecological Studies

Measurements made at population rather than individual level.�
Weaker inference, but easier to gather data.

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a.k.a

Correlational studies

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Bousquet et al (2021) Cabbage and fermented vegetables: From death rate heterogeneity in countries to candidates for mitigation strategies of severe COVID-19. Allergy DOI: 10.1111/all.14549

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Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Ecological study:�HIV prevalence (UNAIDS) vs�circumcision prevalence (DHS)

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Williams et al. The Potential Impact of Male Circumcision on HIV in Sub-Saharan Africa. Plos Medicine 2006

Circumcision prevalence

HIV prevalence

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Cross-Sectional Studies

Snapshot of diseases & risk factors.�
Cannot establish temporal relationship.�
Relatively cheap & easy.�
Population must be large to study rare disease.�
Not great for diseases of short duration. Why?

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a.k.a

Surveys

Prevalence studies

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Relative Risk: Prevalence Ratio

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	Disease	No Disease	Total (Margins)
Exposed	a	b	a+b
Not exposed	c	d	c+d
Total (Margins)	a+c	b+d	a+b+c+d

Prevalence Ratio (PR):�prevalence in exposed population divided by prevalence in unexposed population.

PR < 1 exposure correlates with reduced risk of disease

PR > 1 exposure correlates with increased risk of disease

Contingency table or 2x2 table:

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Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Cross-sectional study:�HIV prevalence (DHS) vs�circumcision prevalence (DHS)��SA 2016 DHS:

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Njeuhmeli et al. Voluntary Medical Male Circumcision: Modeling the Impact and Cost of Expanding Male Circumcision for HIV Prevention in Eastern and Southern Africa. Plos Medicine 2011

	HIV+	HIV-	Total
Circumcised	143	1121	1264
Not Circumcised	172	760	932
Total	315	1881	2196

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Case-Control Studies

Compare diseased individuals to chosen controls.

Quality of study depends entirely on how controls are chosen.

Good for rare diseases.

Relatively cheap & quick.

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Case Control Studies: Odds Ratios

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	Disease	No Disease	Total (Margins)
Exposed	a	b	a+b
Not exposed	c	d	c+d
Total (Margins)	a+c	b+d	a+b+c+d

Odds ratio is the ratio of odds in the diseased population divided by the odds in the �non-diseased population.

OR < 1 means exposure correlates with reduced risk of disease

OR > 1 means exposure correlates with increased risk of disease

Controls: Number chosen by researcher.

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Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Case-control study:�

Sassan-Morokro et al, High rates of sexual contact with female sex workers, sexually transmitted diseases, and condom neglect among HIV-infected and uninfected men with tuberculosis in Abidjan, Cote d'Ivoire, JAIDS, 1996

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	HIV+	HIV-	Total
Circumcised	15	19	34
Not Circumcised	475	220	695
Total	490	239	729

	HIV+	HIV-	Total
Circumcised	48	121	169
Not Circumcised	101	272	373
Total	149	393	542

Quigley et al. Sexual behaviour patterns and other risk factors for HIV infection in rural Tanzania: a case–control study, AIDS, 1997

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Cohort Studies

Follow a selected population through time

Establishes temporal relationships
Can measure incidence�

Takes lots of resources, money, & time!�
Poor design for rare diseases.

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a.k.a

Prospective studies

Longitudinal studies

Follow-up studies

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Relative Risk: Cumulative Incidence Ratio

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	Disease	No Disease	Total (Margins)
Exposed	a	b	a+b
Not exposed	c	d	c+d
Total (Margins)	a+c	b+d	a+b+c+d

Cumulative Incidence Ratio (CIR):�cumulative incidence in exposed population divided by cumulative incidence in unexposed population.

CIR < 1 exposure correlates with reduced risk of disease

CIR > 1 exposure correlates with increased risk of disease

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Cohort Data and Person-Time

X marks occurrence of disease X

O Marks death

Cumulative Incidence

Total number of person-time

Immunity

Time joining the study

Death

5 / 12 = 0.42

X marks occurrence of disease X

O Marks death

Dealing with person-time

CI = 5/12
Is the incidence rate = 5/ (12 * 5.5 years) = ?
But person 3 died between years 1 & 2, and others died before the study was over. So this is not the best way to count incidence.
We want to know the rate of incidence per year a person was alive, or person years.
32 person-years = 4.5 + 5.5 + 1. + 2.5 + 4.5 + 1.5 + .5 + 2.5 + 2.5 + 2.5 + 2.5 + 1.5 if disease would be measured at any time.
26 person-years = 4 + 5 + 1 + 2 + 4 + 1 + 2 + 2 + 2 + 2 + 1 if disease is only measured at year intervals
If disease conferred lifetime immunity then you cannot count person-time after an individual has become immune to measure incidence because they are no longer at risk

Consider example of cohort study of 10 people over 10 years with weekly checkups. One person has influenza at the first checkup. They all get hit by a truck leaving the clnic. Is 1/10 people * 10 years the best estimate of incidence?

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Cohort Data and Person-Time

X marks occurrence of disease X

O Marks death

Incidence rate

Number of disease occurrence

= 5

Total number of person-time (X confers immunity)

= 26 years

Incidence rate=5/26=0.19 per person year

X marks occurrence of disease X

O Marks death

Dealing with person-time

CI = 5/12
Is the incidence rate = 5/ (12 * 5.5 years) = ?
But person 3 died between years 1 & 2, and others died before the study was over. So this is not the best way to count incidence.
We want to know the rate of incidence per year a person was alive, or person years.
32 person-years = 4.5 + 5.5 + 1. + 2.5 + 4.5 + 1.5 + .5 + 2.5 + 2.5 + 2.5 + 2.5 + 1.5 if disease would be measured at any time.
26 person-years = 4 + 5 + 1 + 2 + 4 + 1 + 2 + 2 + 2 + 2 + 1 if disease is only measured at year intervals
If disease conferred lifetime immunity then you cannot count person-time after an individual has become immune to measure incidence because they are no longer at risk

Consider example of cohort study of 10 people over 10 years with weekly checkups. One person has influenza at the first checkup. They all get hit by a truck leaving the clnic. Is 1/10 people * 10 years the best estimate of incidence?

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Relative Risk: Incidence Rate Ratios

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	Disease	No Disease	Total (Margins)
Exposed	a	-	PY_e
Not exposed	c	-	PY₀
Total (Margins)	a+c	-	PY_e+ PY₀

Incidence Rate Ratio is the ratio of the incidence rate of the exposed population to that of the unexposed population.

IRR < 1 means exposure correlates with reduced risk of disease

IRR > 1 means exposure correlates with increased risk of disease

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Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Cohort study:�

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Cameron et al. Female to male transmission of human immunodeficiency virus type 1: risk factors for seroconversion in men. The Lancet 1989

	HIV+	HIV-	Total Pwks
Circumcised	6	-	2966
Not circumcised	18	-	1016
Total (Margins)	24	-	3982

Nairobi, Kenya 1987
293 clients of female sex workers (73% circumcised)
Mean follow-up of 14 weeks

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Randomised Controlled Trials

Experimental or Intervention Studies�
Establishes temporal relationships�
Addresses confounding (more to come)

Causal evidence

Another in depth lecture on this follows!

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Example

How could you measure whether circumcision influences the risk of HIV infection?�

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Randomised Controlled Trial:�

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Auvert et al. Randomized, Controlled Intervention Trial

of Male Circumcision for Reduction of HIV

Infection Risk: The ANRS 1265 Trial. Plos Medicine 2005

	HIV+	HIV-	Total PYs
Circumcised	20	-	2,354
Not circumcised	49	-	2,339
Total (Margins)	69	-	4693

Johannesburg, SA 2003
3274 men aged 18-24
Half circumcised at 0 months, other half offered at end

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Goals

Define Epidemiology
Discuss metrics of epidemiology

Measures of disease
Measures of effect

Describe basic study designs used in epidemiology
Discuss error, bias and confounding
Compare and contrast statistical models and dynamic models

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Random Error

How many people must be in a study for the measure of effect to believable?�

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Statistical Approach:�Assign probabilities to our findings being a product of random error rather than a real phenomenon.

Estimate =

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Bias

Difference between observed value and true value due to all causes other than random error.��

Bias does not go away with greater sample size!

Bias must be dealt with during study design!�

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Selection Bias

Error due to systematic differences between those who take part in the study and those who do not.

John Last, Dictionary of Epidemiology�

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Information Bias

A flaw in measuring exposure or outcome data that results in different quality (accuracy) of information between comparison groups.

John Last, Dictionary of Epidemiology�

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Survivor Bias

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Non-response Bias

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Confounding

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Literacy

HIV Status

	HIV+	HIV-
Literate	660	340
Illiterate	180	820

What if some of the study population were much younger than others?

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Confounding

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Pooled	HIV+	HIV-
Literate	660	340
Illiterate	180	820

6-15 years old	HIV+	HIV-
Literate	30	270
Illiterate	90	810

16-24 years old	HIV+	HIV-
Literate	630	70
Illiterate	90	10

6-15 year olds: Literacy = 300/1200 = 25%�

16-24 year olds: Literacy = 700/800 = 87.5%

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Confounding

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Literacy

HIV Status

	HIV+	HIV-
Literate	660	340
Illiterate	180	820

Age

CONFOUNDING

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How do you deal with confounding?

Study Design

Randomize participants to treatment groups (RCTs)
Restrict participants to one group of the confounders

Study Analysis

Multivariable modeling statistically adjusts for effect of one risk factor, given the presence of a confounder
Stratification conducts a separate analysis for each level of the confounder

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Goals

Define Epidemiology
Discuss metrics of epidemiology

Measures of disease
Measures of effect

Describe basic study designs used in epidemiology
Discuss error, bias and confounding
Compare and contrast statistical models and dynamic models

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By developing dynamic models in a probabilistic framework, we can account for dependence, random error, and bias while linking patterns at multiple scales.

Statistical Models

Dynamical Models

Assume independence of individuals

Explicitly focus on inter-dependence of individuals (X transmitted disease to Y)

Account for random error and bias in data to assess relationships and find correlations that may imply causality

Explicitly model (hypothetically ‘declare’) specific mechanisms, to explore their interactions

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Questions in Epidemiology

Is male circumcision effective against HIV acquisition?

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Statistical Models

Dynamic Models

By how much would population level HIV incidence decrease if we circumcise 50% of all men?

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Summary

Epidemiology seeks to measure and understand the causes of disease
Epidemiologists conduct observational and experimental studies to obtain data

Incidence and prevalence
RR’s, OR’s, attributable risk

Epidemiological studies are subject to bias, confounding, and variability
Traditionally, focus on discovering correlations that may lead to identification of causal factors
Dynamic models, informed via epidemiologic studies, can answer questions traditional studies can’t

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Title: Study Design and Analysis in Epidemiology: Where does modelling fit?

https://figshare.com/collections/International_Clinics_on_Infectious_Disease_Dynamics_and_Data/3788224

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Clinic on the Meaningful Modeling of Epidemiological Data

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