Introduction and Overview

You are the duty epidemiologist at a regional health authority on a Tuesday afternoon. Three minutes ago, your phone buzzed: a paediatrician at a community clinic just called to say she has seen four children from the same school presenting with bloody diarrhoea over two days. She is requesting stool cultures and wants to know whether you have seen anything similar elsewhere. By the time you put the phone down, you will need to know, quickly, whether four cases is unusual for this organism in this catchment, whether a notifiable disease report has already been filed, who else needs to be looped in, and what data sources you can pull within the next hour. That sequence of questions is what this lesson is about. The infrastructure that lets you answer them is called public-health surveillance, and the structured response that follows is called outbreak investigation.

2.1 What Public-Health Surveillance Is, and What It Is For

The classic working definition, attributed to Langmuir (1963) and refined by Thacker & Berkelman (1988), is the ongoing, systematic collection, analysis, interpretation, and dissemination of health-related data for the planning, implementation, and evaluation of public-health practice. Each of those verbs is doing real work. Ongoing distinguishes surveillance from a one-time study. Systematic rules out anecdote. Analysis and interpretation rule out a passive data warehouse. Dissemination for action rules out research that is never returned to the people who can act on it. A famous shorthand attributed to Langmuir (EIS founder) is that surveillance only counts if it “closes the loop”: information must come back out as decisions, alerts, or programs, otherwise the system is just bookkeeping.

2.2 The Surveillance Action Loop

It helps to picture surveillance as a closed loop with four moving parts: data sources (clinical reports, lab results, vital records, administrative data), data systems (the registries, dashboards, and notifiable-disease platforms that ingest and store data), analysis and interpretation (the epidemiologists who turn case counts into rates, anomalies, and narratives), and action (the case finding, control measures, public communications, and policy decisions that flow from the analysis). Each handoff between these stages is also a place where the system can leak: a clinician who never reports a case, a province that does not share data with the federal level, an analyst who does not see a signal in time, or a recommendation that never reaches a decision-maker.

For the rest of this section we focus on the data-system layer because it determines what kinds of signals you can detect at all. The four conventional system types differ on a single axis: who is doing the work of finding cases.

2.3 The Four Surveillance System Types

Most public-health surveillance systems can be sorted into one of four types; the syndromic category is the newest, codified by the CDC framework of Buehler and colleagues (2004). They are not mutually exclusive, since a single disease can be tracked by several at once, but they have different strengths, costs, and biases.

A fifth category, laboratory-based surveillance, is sometimes broken out separately because it sits beside (rather than under) the clinician's desk: provincial public-health labs aggregate isolates from clinical labs, perform serotyping or whole-genome sequencing, and feed the results into both passive and active systems. PulseNet Canada is the best-known example, the network that enabled the 2008 Maple Leaf listeriosis outbreak to be linked across provinces by genome (Gilmour et al., 2010).

2.4 The Notifiable Disease Reporting Flow in Canada

For passive surveillance to function, every link in the chain has to do its part. The Canadian flow looks like this:

1. Clinician or laboratory identifies a case of a notifiable disease (e.g., a positive shiga-toxin-producing E. coli culture or a clinical diagnosis of measles). Each province publishes its own list of conditions reportable under public-health legislation.
2. Local Medical Officer of Health (MOH) or regional health authority receives the report (typically within 24 hours for urgent conditions, longer windows for routine ones). The MOH may immediately initiate case investigation, contact tracing, or public-health control measures.
3. Provincial / territorial public-health authority (e.g., BCCDC, Public Health Ontario, the Quebec INSPQ) aggregates reports from the regional level, performs initial analysis, and shares anonymized aggregate data with the federal level.
4. Public Health Agency of Canada (PHAC) publishes nationally aggregated counts in CNDSS and feeds disease-specific products like FluWatch and the CCDSS. PHAC also reports onward under the WHO International Health Regulations (2005) for events of international concern; the post-SARS rationale for that regime is laid out by Heymann & Rodier (2004).

Two features of this flow deserve emphasis. First, public-health legislation is provincial in Canada, so the list of notifiable conditions and reporting timelines differ across provinces. A condition might be urgent-reportable in one province and routine in another. Second, the federal level receives aggregated, de-identified data only; PHAC cannot pull individual records. This federal-provincial division is one reason that the COVID-19 pandemic exposed gaps in real-time data sharing, because the legal architecture was not designed for the latency that a respiratory pandemic demands.

Introduction and Overview

An earlier section sketched four types of surveillance system. This section turns to the actual products a Canadian epidemiologist works with. They sit in three layers: federal, provincial/territorial, and the long-running data infrastructure that underpins both. Knowing which product to reach for, and what its limitations are, is most of the practical skill of the job.

2.5 The Federal Layer

PHAC operates several headline products. They are aggregated and curated, the agency cannot dispense individual-level data, and they each have a different cadence, scope, and intended audience.

2.6 The Provincial Layer (with BC examples)

The federal products are valuable for the country-level view, but most case-level work happens provincially. In British Columbia, the BC Centre for Disease Control (BCCDC) is the analytic and operational arm of provincial public health, and most of its products are publicly available.

2.7 The Long-Running Data Infrastructure

Most surveillance products do not generate their own data; they read from infrastructure that exists for other reasons.

• Vital statistics (births, deaths, marriages, divorces) are the oldest population health data in Canada, with continuous coverage since the late 19th century in some provinces. They are the denominator for life expectancy and the numerator for mortality surveillance.
• Cancer registries: the Canadian Cancer Registry aggregates provincial cancer registries and is one of the few systems with active follow-up and complete case ascertainment. The BC Cancer Registry is the provincial source.
• Health-administrative data: the Discharge Abstract Database (DAD, hospital admissions), the National Ambulatory Care Reporting System (NACRS, ED visits), and provincial Medical Services Plan billing claims (MSP in BC). CCDSS and many academic studies are built on top of these.
• Population health surveys: the Canadian Community Health Survey (CCHS) is the workhorse cross-sectional survey for self-reported health behaviours and outcomes; the Canadian Health Measures Survey (CHMS) layers in physical measurement.
• Wastewater-based surveillance: a rapidly maturing infrastructure since 2020. PHAC and many provinces now sample wastewater for pathogens (SARS-CoV-2, influenza, mpox) as a non-clinical signal that is independent of who seeks testing.

2.8 Data Quality: Five Dimensions to Question Every Source

Every surveillance product makes tradeoffs across these five dimensions. When you read a public-health report, the report's author has implicitly resolved each one:

1. Timeliness: how long from event to data product? Wastewater can be days. CNDSS can be months.
2. Completeness: what fraction of true events are captured? STIs are notoriously incomplete; cancer registries are nearly complete.
3. Representativeness: do the captured cases reflect the affected population? Sentinel networks usually do not.
4. Sensitivity: will the system detect a true outbreak when it occurs? Syndromic surveillance is highly sensitive, passive surveillance often is not.
5. Predictive value positive: when the system flags an event, is it real? Inversely related to sensitivity, especially for syndromic systems.

Introduction and Overview

Surveillance is meant to detect signals; outbreak investigation is what you do when a signal turns into a problem. This section gives you the operational vocabulary: what counts as an outbreak, the standard 10-step framework that organizes the response, and the specifically Canadian protocol used for foodborne investigations.

2.9 What Counts as an Outbreak?

The textbook definition is the occurrence of more cases of a disease than expected in a given population, place, or time. Each italicized phrase is doing work. “More than expected” presupposes a baseline: the local 5-year average for influenza in the same week, or the seasonal threshold from a regression model. “Population, place, time” says outbreaks are local: 30 cases of Campylobacter across Canada in a week is not unusual; 30 cases at one wedding is.

The decision to call something an outbreak is partly statistical and partly operational. Statistically, you can compare current counts to a baseline distribution and apply a threshold (e.g., the upper 95% confidence limit of the 5-year mean). Operationally, an outbreak declaration mobilizes resources, triggers a coordinated response, and may require public communication, and authorities are reasonably cautious about both over- and under-calling.

2.10 The CDC 10-Step Outbreak Investigation Framework

The reference framework most North American epidemiologists learn is the CDC's 10-step process, articulated in the modern era by Reingold (1998) and elaborated in the CDC Field Epidemiology Manual. The steps look orderly on paper but in practice you often work several at once and revisit earlier ones as new information arrives.

2.11 The Canadian FIORP and Its Multi-Jurisdictional Structure

For foodborne outbreaks specifically, Canada operates under the Foodborne Illness Outbreak Response Protocol (FIORP), summarised by Vik & Hexemer (2014), which formalizes the roles of the federal partners and provincial/territorial public-health authorities. Three federal partners share the load:

• PHAC: epidemiology and surveillance lead, including PulseNet Canada (the lab network that does whole-genome sequencing of bacterial isolates).
• Canadian Food Inspection Agency (CFIA): food-safety investigations, traceback, and product recalls.
• Health Canada: risk assessment of contaminated products and health-impact guidance.

FIORP defines escalation triggers (when a multi-jurisdictional outbreak exists), establishes an Outbreak Investigation Coordinating Committee (OICC) for inter-provincial events, and lays out communication protocols. The 2008 Maple Leaf listeriosis outbreak (the deli-meat-associated Listeria monocytogenes outbreak that killed 22 Canadians) is the case that drove the modern revisions to FIORP and to the supporting infrastructure of PulseNet.

2.12 Real-Time vs Retrospective: A Standing Tension

An outbreak investigation is run under two competing pressures. Speed, since every day of delay can mean more illness, pushes you toward early hypotheses and precautionary control measures. Accuracy, since falsely accusing a food product or a venue has real costs, pulls in the other direction. Experienced investigators learn to act on confident-enough evidence, communicate uncertainty honestly, and revise control measures as data evolve. The skill is partly statistical and partly ethical: who bears the cost of being wrong in either direction is rarely symmetric.

Introduction and Overview

The two preceding sections gave you the institutional and methodological vocabulary. This section makes them concrete: a real Canadian outbreak walked through against the 10-step framework, and a hands-on R activity in which you investigate a simulated outbreak yourself. You will leave this section having previewed the methods that the rest of this course formalizes: the attack rate (the proportion of an at-risk group who fall ill), the 2×2 table, and the risk and rate ratios, all computed on data you have generated and interrogated yourself.

2.13 Case Study: The 2017–18 Romaine Lettuce E. coli O157:H7 Outbreak

Between November 2017 and February 2018, PHAC and US CDC investigated a multi-jurisdictional outbreak of E. coli O157:H7 infections that ultimately involved 42 confirmed cases across 5 Canadian provinces (and 25 cases across 15 US states). All five affected Canadian provinces were in eastern Canada (Ontario, Quebec, New Brunswick, Nova Scotia, and Newfoundland and Labrador); western provinces were not involved. One death was reported among the 42 Canadian cases, a case fatality rate of about 2% (roughly 2 in every 100 diagnosed cases died). The outbreak is a useful teaching case because it shows the full FIORP machinery in motion and makes the role of whole-genome sequencing visible.

Three teaching points are worth pulling out of this case. First, the outbreak would not have been detected at all without genomic surveillance; the case counts in any one province in any one week looked like background noise. Second, the case-case study design is a pragmatic alternative to a traditional case-control study when controls are hard to recruit during a fast-moving foodborne investigation; you trade some validity for considerable speed. Third, control measures (the public advisory) were issued before the source was definitively confirmed; precaution is a defensible public-health stance when downside asymmetry favours acting early.

2.14 Why Surveillance Comes Early, and What You Will Build On It

Surveillance comes early in this course on purpose: every later lesson depends on having data to design against, sample from, measure with, and reason about. The outbreak workflow you will run below previews methods you have not yet formally met: sampling (a later lesson), questionnaire design for hypothesis-generating interviews (a later lesson), measures of disease frequency such as attack rates and incidence (a later lesson), measures of association including risk ratios and odds ratios (a later lesson), and the validity and confounding vocabulary that arrives in later lessons. Modern surveillance is also being reshaped by big-data and machine-learning approaches reviewed by Mooney & Pejaver (2018). Treat the 2×2 tables and risk ratios you compute in the R activity as a working preview; the formal derivations and validity diagnostics come in the lessons that follow. The point of doing it now is to ground the rest of the course in a concrete operational setting that needs all of it.

# PART A -- read the line list and describe the outbreak
ll <- read.csv("phaa_outbreak.csv", stringsAsFactors = FALSE,
               na.strings = c("", "NA"))
mean(ll$ill, na.rm = TRUE)                  # overall attack rate

# Epidemic curve: histogram of symptom-onset days
hist(ll$onset_day, breaks = seq(0.5, 12.5, 1),
     col = "tomato", main = "Days since the potluck",
     xlab = "Day of symptom onset")

# PART B -- 2x2 table for one suspect food (chicken)
tab <- table(Chicken = ll$chicken, Ill = ll$ill)
addmargins(tab)

a <- tab["1","1"];  b <- tab["1","0"]
c <- tab["0","1"];  d <- tab["0","0"]

rr <- (a/(a+b)) / (c/(c+d))                  # relative risk
se <- sqrt(1/a - 1/(a+b) + 1/c - 1/(c+d))
lo <- exp(log(rr) - 1.96*se);  hi <- exp(log(rr) + 1.96*se)
round(c(RR = rr, lo = lo, hi = hi), 2)

chisq.test(tab)                              # or fisher.test(tab) when small

# PART C -- surveillance time series with a 7-day moving average
curve <- read.csv("phaa_outbreak_curve.csv")
curve$ma7 <- stats::filter(curve$new_cases, rep(1/7, 7), sides = 2)
plot(curve$day, curve$new_cases, type = "h", col = "#0B7B6B",
     xlab = "Day", ylab = "New cases", main = "Surveillance time series")
lines(curve$day, curve$ma7, col = "#CC0033", lwd = 2)

# PART D -- attack rates across all suspect foods, ranked
foods <- c("chicken", "potato_salad", "raw_milk_cheese", "green_salad", "punch")
sapply(foods, function(f) {
  ex <- ll[[f]] == 1
  ar_e <- mean(ll$ill[ex], na.rm = TRUE)
  ar_u <- mean(ll$ill[!ex], na.rm = TRUE)
  round(c(ar_exposed = ar_e, ar_unexposed = ar_u, rr = ar_e/ar_u), 2)
})

Introduction and Overview

An earlier lesson closed with the counterfactual framework: causal inference requires us to compare groups under different exposure conditions. This lesson asks the immediate next question: which people should be in those groups? Sampling sits at the foundation of every study you'll design in this course because the choice of who ends up in the study determines almost everything else: the validity of the results, the generalisability of conclusions, and the bias inventory you spent an earlier course learning to recognise. The four content sections move from broad principles to concrete formulas: this section sets up the population hierarchy, sampling frame, and the probability theory that makes inference from a sample possible; a later section covers types of error and non-probability sampling; a later section details the major probability sampling designs; a later section closes with how to analyse data from complex surveys and how to determine sample size in advance.

Census vs. Sample

When we conduct research, we need data from either all individuals in a population or a subset of them. The process of obtaining this data is called measurement.

In a census, every individual in the population is evaluated. In a sample, data are collected from only a subset. Sampling is generally more convenient and less costly than conducting a full census. Interestingly, even a census can be viewed as a kind of sample: it captures the population at one point in time, making it a "sample" of the population over time.

Descriptive vs. Analytic Studies

Samples support two fundamental types of studies:

Choosing between a census and a sample is the first decision; choosing between a descriptive and an analytic purpose is the second. Both decisions sit on top of an even more fundamental concept: the relationship among the different populations a single study touches.

Hierarchy of Populations

Understanding the different populations involved in a study is essential for evaluating validity. There are three key populations to consider, each nested inside the next. The diagram and accordion below define them in turn; the labels that appear next to the arrows (external validity, sampling frame, internal validity) are the technical vocabulary you will use to talk about how a sample inherits or loses information from the broader population it was meant to represent.

Validity: Internal and External

Internal validity refers to whether the study results are valid for members of the source population. It indicates whether the study obtained the "correct" answer for that population. Much of epidemiology is dedicated to methods that ensure internal validity.

External validity involves a subjective assessment of whether results can be generalized to the broader target population. It is generally easier to generalize results from analytic studies (which evaluate associations) than from descriptive studies (which estimate prevalence).

The Sampling Frame

The sampling frame is the list of all sampling units in the source population. Sampling units are the basic elements that will be sampled (e.g., households, individuals). A complete list of all sampling units is required for drawing a simple random sample, though some other methods do not require such a complete listing.

The vocabulary of populations and sampling frames is necessary but not sufficient. The deeper question is why we can learn about a whole population from a small sample at all. The answer comes from probability theory.

Probability Theory: Why Sampling Works

Every quantity we estimate from a sample, whether a prevalence, a mean, or a risk ratio, is the value of a random variable. If we drew a different sample tomorrow, the value would be slightly different. Probability theory is the formal language we use to describe how those values vary, and it is what lets us turn a single sample into a defensible statement about a population.

Three concepts do most of the work in introductory biostatistics:

A second idea worth naming is independence. Two observations are independent when knowing the value of one tells you nothing about the value of the other. Independence is the assumption that lets a small random sample stand in for a much larger population, and it is the assumption most often violated in real public-health data (clustered households, repeated measures on the same person, contagion in infectious disease).

Types of Probability Distributions

A probability distribution describes the values a random variable can take and how likely each value is. Distributions split first into discrete (countable outcomes such as 0, 1, 2 cases) and continuous (any value on a range, such as height or blood pressure, time). The handful below are the ones you will encounter again and again in public health.

Discrete distributions

Continuous distributions

Each distribution above describes the underlying behaviour of a single random variable. But when we draw a sample from a population, the quantity we typically care about is a summary of that sample: a mean, proportion, or rate. To make inferences from such summaries, we need one more layer of theory.

Sampling Distributions and the Central Limit Theorem

So far we have talked about distributions of individuals in a population. Now consider the distribution of a statistic, for example the mean of a random sample of n people. Because each sample of size n would give a slightly different mean, the mean itself has a distribution. We call it the sampling distribution of the mean.

Two facts about that sampling distribution drive almost all of frequentist inference:

The CLT is the hidden engine behind the bell curve that shows up everywhere in statistics. It is the reason a 95% confidence interval can be written as estimate ± 1.96 · SE: the 1.96 comes from the Normal distribution that the CLT promises us applies to the estimate, even when we have no idea what shape the underlying population has. The theorem traces from de Moivre (1733) through Laplace's 1812 binomial approximation to Lyapunov's 1901 general proof (Central limit theorem, Wikipedia).

Introduction and Overview

An earlier section set up the population hierarchy and the probability theory behind sampling. This section turns to two practical consequences. First: when we draw conclusions from a sample, we make systematic types of mistake (Type I and Type II errors), and these mistakes are quantifiable. Second: there are sampling strategies that abandon probability theory altogether (convenience samples, judgement samples, snowball samples) with predictable consequences for inference. Both halves of this section give you the vocabulary to evaluate when those approaches are acceptable and when they are not.

Types of Error

In any study based on a sample, the variability of the outcome, measurement error, and sample-to-sample variability all affect results. When making inferences based on sample data, they are subject to error. Within hypothesis testing in analytical studies, there are two key types of error:

The error framework above assumes a probability sample. The next subsection covers what happens when investigators forgo formal random selection altogether, and what that costs them.

Non-Probability Sampling

Samples drawn without an explicit method for determining each individual's probability of selection are known as non-probability samples. Whenever there is no formal process for random selection, the sample should be considered non-probability. Sample selection that is unrelated to the outcome of interest leaves inference intact, but selection that depends on unmeasured determinants of the outcome produces selection bias, a form of specification error formalised by Heckman (1979) and reviewed for hidden populations by Sudman & Kalton (1986). There are three main types:

Click each card to learn more:

Introduction and Overview

An earlier section closed by walking through what non-probability sampling looks like and why it forfeits inferential validity. This section returns to probability sampling and details the major variants you'll encounter in real surveys. The six tabs below are not interchangeable; each design buys a different combination of cost, complexity, and statistical efficiency. Read the comparison table at the end of the section as a decision aid you can return to whenever you're choosing a design.

What Is a Probability Sample?

A probability sample is one in which every element in the population has a known, non-zero probability of being included. This implies that a formal process of random selection has been applied to the sampling frame. The key advantage is that probability samples allow for valid statistical inferences about the source population.

Types of Probability Sampling

Comparison of Sampling Methods

Introduction and Overview

An earlier section walked through the major probability designs. Real surveys (the CCHS being the canonical Canadian example) typically combine several of these: stratification at the top level, clustering within strata, multistage selection within clusters. That combination is precisely what makes the analysis non-trivial: a complex sample design demands a complex analysis. The first half of this section covers how to do that analysis correctly. The second half closes the loop by walking through how to determine sample size before the data are collected.

Analysing Complex Survey Data

When data come from a complex sampling design (involving stratification, weighting, or clustering), the analysis must account for these features. Ignoring them can lead to incorrect point estimates and underestimated standard errors.

The Design Effect (deff)

The design effect (deff) summarizes the overall impact of the sampling plan on precision. It is the ratio of the variance from the complex sampling design to the variance that would have been obtained from a simple random sample of the same size. The concept and the term were coined by Leslie Kish in his classic textbook Survey Sampling (Kish, 1965) and remain the standard summary statistic for complex-design efficiency.

Finite Population Correction (FPC)

When the proportion of the population sampled is relatively large (>10%), precision improves beyond what would be expected from an "infinite" population. The finite population correction adjusts the estimated variance downward:

Analysing data correctly is necessary but not sufficient. Just as important is making sure you collected enough data to begin with; an underpowered study cannot be rescued by clever analysis. The remainder of this section covers sample-size calculation.

Sample-Size Determination

Choosing the right sample size involves both statistical and non-statistical considerations. Non-statistical factors include available resources (time, money, personnel) and the nature of the sampling frame. Statistical considerations include:

Key Sample-Size Formulae

# PART A -- three probability sampling designs from a 1,000-row frame
set.seed(341)
N <- 1000
frame <- data.frame(id = 1:N,
                    province  = sample(c("BC", "AB", "ON", "QC"), N, replace = TRUE),
                    household = sample(1:300, N, replace = TRUE))

srs   <- frame[sample(N, 100), ]                        # simple random
strat <- do.call(rbind, by(frame, frame$province,
                          function(d) d[sample(nrow(d), 25), ])) # stratified
sel_hh <- sample(unique(frame$household), 30)
clust  <- frame[frame$household %in% sel_hh, ]               # cluster

c(SRS = nrow(srs), Stratified = nrow(strat), Cluster = nrow(clust))

# PART B -- design-corrected prevalence with the survey package
library(survey)
dat <- data.frame(province = sample(c("BC","AB","ON","QC"), 2000, replace = TRUE),
                  smoker   = rbinom(2000, 1, 0.18),
                  weight   = runif(2000, 800, 2200))
des <- svydesign(ids = ~1, strata = ~province, weights = ~weight, data = dat)

mean(dat$smoker)                                # naive (unweighted)
svymean(~smoker, design = des)                  # design-corrected
confint(svymean(~smoker, design = des))         # 95% CI

# PART C -- sample-size calculations + design-effect adjustment
power.prop.test(p1 = 0.15, p2 = 0.10,
                power = 0.80, sig.level = 0.05)        # two proportions
power.t.test(delta = 5, sd = 14,
             power = 0.80, sig.level = 0.05)           # two means (SBP)

n_srs <- 685; rho <- 0.45; m <- 6
ceiling(n_srs * (1 + rho*(m - 1)))                # cluster-adjusted n