Some districts reach every child. Others leave thousands behind.

The mystery of the 100 facilities

You supervise 100 health facilities. A handful keep missing children, quarter after quarter, no matter what you try. The question that keeps you up at night is simple: why does coverage stay low in these places?

Most of us answer that question by rounding up the usual suspect. "It's the training." Or "it's the fridge." We pick one lever, pull it, and wait for coverage to climb. Then it doesn't, and we're baffled, because on paper that facility had the training. The trouble is that low coverage rarely has one cause sitting alone in a room. It usually shows up when a few things go wrong at the same time, and a facility can survive one weak spot but not a particular combination of them.

Here are two facilities that sat through the exact same training. One does fine. One keeps falling short. Watch what's actually different.

Both facilities had trained staff, so "more training" was never going to rescue Facility B. The training was fine. It just isn't worth much when the vaccines spoiled before they reached an arm. Diagnosing that correctly, instead of ordering another training, is exactly the kind of problem Coincidence Analysis was built to solve.

A method for combinations, not lone culprits

Coincidence Analysis (CNA) is a configurational comparative method. In plain terms, it looks for configurations, which are just bundles of conditions that travel together with an outcome, instead of putting each factor on trial one at a time. It was developed by Michael Baumgartner, and it is custom-built for the messy, multi-outcome structures that real programs are made of. It is happiest when causes work in teams.

CNA earns its keep precisely when programs behave the way immunization programs actually behave:

• Several things have to go wrong together before coverage really sinks.
• Different combinations can drag coverage down in different settings.
• Causal chains exist. Weak supervision leads to sloppy planning, which leads to missed children.
• Implementation varies from facility to facility and district to district, so one-size answers rarely fit.

Conjunctivity, equifinality, and causal chains

Everything CNA does rests on three ideas. Learn these three words and you have the heart of the method. Bonus: they make you sound very impressive in meetings.

1 · Conjunctivity, the "AND" idea

A condition might only matter when it is joined to others. A broken cold chain on its own may be survivable, but a broken cold chain and no outreach and no supervision, all in the same place, is how coverage quietly collapses. The conditions gang up.

2 · Equifinality, the "many roads" idea

Different combinations can lead to the same sad outcome. One facility ends up with low coverage because of a broken cold chain plus no supervision. Another, with a perfectly good fridge, still ends up low because of no community mobilisation plus no outreach funding. Same destination, different roads. That is called equifinality, and CNA is one of the few methods polite enough to report every road instead of insisting there's only one.

3 · Causal chains, the "knock-on" idea

One factor can act through another. Weak supervision doesn't reach out and lower coverage by itself. It leads to weaker session planning, and weaker planning is what loses the children. It works down a chain, like a rumour:

"Can't I just run a regression?"

It is a fair question, and one every analyst should ask. Logistic regression is an excellent, well-tested tool, and if your question is "which single factor moves the outcome most, holding the others constant," you should reach for it, not CNA. The two methods are not rivals so much as instruments tuned to different questions.

The catch is that regression, by design, estimates the average independent contribution of each factor. It answers "how much does supervision matter on its own?" But immunization coverage rarely fails because of one factor acting on its own. It fails when a broken cold chain meets missing supervision in the same place, at the same time. That is a question about combinations, and it is a different question than the one regression is built to answer.

This is also why CNA does not report coefficients, p-values, or "the effect of supervision." Those numbers answer the ranking question. CNA answers the recipe question, and it speaks in a different language: combinations, pathways, and the conditions an outcome depends on. Keeping the two questions straight now will save you a great deal of confusion later.

Asking a question CNA can actually answer

CNA does not answer "by how much does X move coverage." It answers a sharper, more useful question: "which conditions, alone or in combination, make the difference to the outcome." In the words of the method's own literature, CNA hunts for difference-making conditions, the necessary and/or sufficient combinations that an outcome actually depends on. Good CNA questions are always shaped that way, and the best ones point straight at a problem you can fix.

Here are five questions immunization teams genuinely ask, written the way CNA likes them:

The first four ask which difference-making conditions sit behind an outcome. The fifth is special: it asks about a pathway, a chain where one condition feeds the next. CNA is one of the few methods that can model these multi-step, multi-outcome structures, which is exactly why it suits messy program systems.

The phrase "difference-making conditions" runs throughout the applied CNA literature. See, for example, studies framed explicitly around difference-making roles and pathways in the references at the end of this course.

Every row is a "case"

In CNA, the thing you compare is called a case, and every case becomes one row in your data table. In immunization work, a case can sit at almost any level of the system:

• A health facility, which is the most common choice for supervision studies.
• An LGA, district, or state.
• An outreach site, or even a whole country.

Three decisions before you touch the data

A CNA study is mostly won or lost at the planning table, long before R enters the picture. Three decisions matter most.

Draw your assumptions before the data argues back

A conceptual framework is just a picture of what you think causes what. Drawing it forces you to be honest about your assumptions, and it gives you something to hold your CNA results up against later. Here are two chains an immunization team might sketch for low coverage:

Three kinds of data CNA accepts

CNA reads simple tables. The only real craft is "calibrating" each condition, which is a fancy word for turning messy reality into clean, comparable values. There are three flavours, and the cna package happily handles all of them.

Crisp-set, the easiest, plain yes or no

Every condition is either present (1) or absent (0). "Was the cold chain broken?" becomes 1 or 0. This is where beginners should start, and it is what we use throughout this course, because life is hard enough already.

Multi-value, for more than two levels

When a condition has natural steps, say supervision quality runs 0 = poor, 1 = moderate, 2 = good, you can use multi-value coding. CNA reads it fine, as long as the levels are clearly defined and you don't make them up on the spot.

Fuzzy-set, for degrees of membership

Sometimes "present" is a matter of degree. A value of 0.85 means "strongly, but not perfectly, in the set of low-coverage facilities." Fuzzy values run between 0 and 1. It's powerful, but save it for the day crisp-set feels boringly easy.

The dataset we'll carry through the course

Picture your supervision teams visiting six facilities and recording, for each one, whether four things were missing or broken, plus whether coverage was low. Everything is crisp-set: 1 means yes, 0 means no. Because we're in problem-solving mode, our conditions are framed as gaps, and the outcome is LowCov, where 1 means coverage fell below target.

Clean before you compute

CNA is unforgiving of dirty data, because it reads every row as a real case and takes each one seriously. Before you analyse anything, walk this checklist:

• Missing values. CNA needs complete rows, so decide how to handle gaps before you start, not after.
• Duplicates. The same facility entered twice quietly bends the patterns without telling you.
• Coding errors. A stray 2 in a yes-or-no column will be read literally and believed without question.
• Logical contradictions. "Cold chain broken = 1" alongside "Refrigerator functional = Yes" cannot both be true, so go investigate.

Don't panic at the algebra

Most people meet their first CNA result and feel their stomach drop. The screen shows something like this, and it looks like algebra homework you thought you had escaped:

A*B + C*D ↔ Y

Take a breath. There is nothing to fear here, because a CNA formula is just a sentence wearing a lab coat. Once you know the three words it is built from, you can read any result in the course, and any result your own data ever produces.

The whole vocabulary, in three words

Every CNA formula is made of three little symbols. That is the entire language. Learn these and you are fluent.

So that scary formula A*B + C*D ↔ Y simply says: "When you have A and B together, or C and D together, you tend to find Y." That's it. A sentence about two recipes for the same result.

A note for the precise: the double arrow ↔ is technically an equivalence. It says the left side is both sufficient for the outcome (where you see the combination, you see Y) and, taken as a whole, necessary for it (where you see Y, you find one of these combinations). "Goes with" is a faithful shorthand for that, and you will meet the full story in the model-evaluation modules.

Read it like a sentence

Here is the trick that makes everything click. Swap the letters for the real conditions, read left to right, and say the symbols out loud as their plain words. Watch a real immunization formula turn into an ordinary observation:

Train * Cold * Super ↔ Coverage

One more, with two pathways

When a formula has a + in it, that is equifinality showing up in the algebra: two different roads to the same place. Read each side as its own little sentence, joined by "or":

NoCold*NoSuper + NoComm*NoOutreach ↔ LowCov

Out loud: "Low coverage goes with a broken cold chain and missing supervision, or with no community mobilisation and no outreach." Two recipes for the same disappointing result. A district could land in low coverage by either route, which is exactly why you need to know which route a given place is on before you spend a naira fixing it.

Two free programs, fifteen minutes

R is the calculator that runs CNA. RStudio is the comfortable room you run it in. You install both once, they cost nothing, and nobody will quiz you on how they work under the hood.

Talk to R like a calculator

Type this into the Console and press Enter. R answers right away, no small talk.

2 + 2

That [1] simply means "this is the first, and in this case only, answer." Now let's store a number in a variable using the arrow <-, which is R's slightly dramatic way of saying "put this into."

# put the number 42 into a box named "coverage"
coverage <- 42

# now look inside the box
coverage

Adding CNA's tools to R

R doesn't know how to do Coincidence Analysis straight out of the box. You teach it by installing the cna package, a free add-on published on CRAN, the official R software library. You install it once, then load it at the start of every session.

# download and install the cna package (needs internet, do this once)
install.packages("cna")

# switch the tools on for this session
library(cna)

Type the supervision table into R

Let's recreate the Module 9 table as a data.frame, which is just R's name for a spreadsheet. Each c(...) is one column, listing the six facilities' values from top to bottom. Type carefully; R is a stickler for commas.

library(cna)

# build the supportive-supervision dataset (6 facilities)
# conditions are GAPS; outcome LowCov = 1 means coverage fell below target
immunization <- data.frame(
  NoTrain = c(0, 0, 1, 0, 1, 0),
  NoCold  = c(1, 0, 1, 0, 0, 1),
  NoSuper = c(0, 1, 0, 0, 0, 1),
  NoComm  = c(0, 0, 1, 1, 0, 1),
  LowCov  = c(1, 1, 1, 0, 0, 1)
)

# look at it
immunization

Six rows, five columns. R now holds your supervision data exactly as you designed it, missing children and all.

One function does the heavy lifting

The whole method is wrapped in a single function: cna(). You hand it your data and tell it which column is the outcome. It quietly searches for the minimally sufficient and necessary combinations, then assembles them into solution formulas while you sip your tea.

# ask: which combinations of gaps go together with LowCov = 1 ?
model <- cna(immunization, outcome = "LowCov")

Running this stores the result in model but prints nothing yet, which feels anticlimactic. Don't worry. Viewing it is the very next module.

Your first solution formula

Type the model's name to print it. CNA reports its solution as a formula. For our supervision data, the pattern that perfectly separates the low-coverage facilities from the healthy ones is this:

model

Look back at Module 9. Every low-coverage facility had a broken cold chain or no supervision, and the two healthy facilities had neither. Notice what's missing from the formula: NoTrain and NoComm never made the cut, because they showed up on both the good and the bad side. CNA quietly ignored the red herrings and kept only what actually makes the difference, and it confirmed the pattern holds for every single case, with consistency and coverage both at 1.000. We unpack those two numbers in Part 8.

The five symbols CNA speaks in

Every CNA formula is built from a tiny vocabulary. Learn these five and you can read any solution the package ever hands you.

So a formula like NoCold*NoComm + NoSuper would read: "(broken cold chain AND no mobilisation) OR (no supervision)." That single line captures both conjunctivity, the *, and equifinality, the +, at the same time. Two ideas, one tidy line.

A conjunctural road to low DTP3

Suppose you study low DTP3 coverage with four gap conditions: untrained staff, recent stockout, broken cold chain, and no supervision. A common CNA result is a single bundle, where low coverage needs several gaps to gang up at once.

library(cna)

# columns: NoTrain, Stockout, NoCold, NoSuper, LowDTP3 (all 0/1)
m_dtp3 <- cna(dtp3_data, outcome = "LowDTP3")
m_dtp3

Interpretation: DTP3 collapses where a stockout, a broken cold chain, and absent supervision all land in the same place. No single gap is the villain. This is conjunctivity, the gangs-up idea, showing its face in a real coverage indicator. It also tells you that fixing only one of the three may not be enough on its own.

Two roads to too many zero-dose children

Now an equifinality example. Conditions, all framed as gaps: no outreach, no community volunteers, no settlement mapping, no outreach funding. Outcome: HighZeroDose, meaning too many children never got a single dose. CNA can report two separate roads joined by OR.

m_zd <- cna(zerodose_data, outcome = "HighZeroDose")
m_zd

Interpretation: a district can end up with too many zero-dose children either because outreach was never funded, or because it lacked active volunteers and had no settlement map to work from. The + is the gift here. It tells you there are two different problems wearing the same uniform, so the fix in one district may not be the fix in the next.

Which gaps go with poor-quality sessions?

This is the study supervision teams care about most, because it's about them. Research question: which combinations of weak supervisory practices go together with poor-quality immunization sessions? Conditions, as gaps: no checklist used, no action plan developed, no feedback given, no follow-up visit. Outcome: PoorQuality.

library(cna)

# NoChecklist, NoActionPlan, NoFeedback, NoFollowUp, PoorQuality (0/1)
m_sup <- cna(supervision_data,
             outcome = "PoorQuality")

m_sup

Interpretation: sessions turn out poor either when the supervisor skips both the checklist and the on-the-spot feedback, or whenever there's simply no follow-up visit at all. A visit that ticks a checklist but never comes back is still a visit that loses quality. CNA tells you which combination of missing practices to fix, not just which single box to scold someone about.

Consistency: does the pattern keep its promise?

CNA gives every solution two scores. The first is consistency, and it answers a simple question: when this combination of gaps is present, does low coverage actually show up too?

In code, you set the bar with the con argument:

# accept patterns that hold at least 90% of the time
cna(immunization, outcome = "LowCov", con = 0.9)

Coverage: how much of the outcome does the pattern explain?

The second score is coverage, an evaluation measure that you should not confuse with vaccination coverage. It answers: of all the facilities that had the outcome, what share does this pattern account for?

# require patterns that are both reliable AND broadly explanatory
cna(immunization, outcome = "LowCov",
    con = 0.9, cov = 0.9)

Choosing well, and looking under the hood

When CNA hands you several candidate models, weigh them on four criteria, three statistical and one stubbornly human:

• Simplicity. Fewer conditions are easier to explain and easier to act on.
• Consistency. How reliably the pattern holds.
• Coverage. How much of the outcome it accounts for.
• Program plausibility. Does it actually make public-health sense?

To inspect any formula's scores directly, use condTbl(), which builds a tidy summary table of consistency and coverage for whatever conditions you pass it. To probe a formula facility by facility, use condition().

library(cna)

# score a specific formula against the data
condTbl("NoCold + NoSuper <-> LowCov", immunization)

# see exactly which facilities each road covers
condition("NoCold + NoSuper", immunization)

Would the finding survive a small nudge?

A result you plan to act on should not fall apart the moment the data or the thresholds wobble a little. Robustness asks exactly that. The CNA ecosystem has a dedicated companion package for it called frscore, which scores how "fit-robust" your models are across a whole range of consistency and coverage thresholds, so you don't have to do it by hand and lose an afternoon.

# install once
install.packages("frscore")

library(frscore)

# re-analyse across many thresholds and score robustness in one call
fr <- frscored_cna(immunization,
                   fit.range = c(1, 0.7),
                   granularity = 0.1)
fr

Turn the dials and watch what happens

Even without a special package, you can run a quick sensitivity check by hand. Run CNA at a couple of different thresholds and see whether the story stays the same or suddenly changes its tune.

# strict
cna(immunization, outcome = "LowCov", con = 0.9, cov = 0.9)

# relaxed
cna(immunization, outcome = "LowCov", con = 0.85, cov = 0.85)

If the same pattern survives both runs, your confidence quietly goes up. If a tiny change rewrites the whole solution, treat the finding as fragile and say so plainly in your report. Honesty here saves embarrassment later.

Translate the symbols back into the field

A formula is the start of the work, not the end. Nobody ever approved a budget because a slide said NoCold + NoSuper. Decision-makers need plain language, so compare these two ways of saying the exact same thing:

Same finding, two very different audiences. The first is a code fragment only you understand. The second is something a state immunization officer can read once, repeat in a meeting, and act on by Friday. Always carry the result that last mile into program language.

Say what CNA actually found, and not one inch more

The most common interpretation error is over-claiming causation from a single configurational study. CNA identifies dependency structures consistent with a causal reading. It does not, on its own, prove that one thing causes another. Keep your language honest:

A reusable skeleton for the results section

Every CNA write-up moves through the same nine beats. Copy this order and you'll never leave out something a reviewer asks for.

Three boxes a decision-maker reads in two minutes

A policy brief strips the analysis down to what a busy director actually needs: the problem, the finding, and the recommendation. No methods section, no R output, no suspense. Here is our supervision study written up as a brief.

One finding, one instruction

The executive summary is the whole brief boiled down to one sentence of finding and one sentence of action. If a director reads nothing else, they read this.

Run a full study, start to finish

You supervise 50 facilities, and a stubborn share of them keep posting low coverage. Outcome: LowCov. Conditions: untrained staff, no supervision, broken cold chain, no outreach, no community mobilisation. Here is the entire workflow as one connected script, every step you have learned, in order.

library(cna)
library(frscore)

# 1 . IMPORT: read your facility data from a CSV file
data <- read.csv("facility_data.csv")

# 2 . INSPECT: sanity-check structure and values before analysing
str(data)       # column types and a peek at values
summary(data)   # min/max catches stray codes (e.g. a 2 in a 0/1 column)

# 3 . ANALYSE: run CNA for the LowCov outcome
fit <- cna(data, outcome = "LowCov", con = 0.9, cov = 0.9)

# 4 . REVIEW: print solutions, ordered by fit
fit

# 5 . INTERPRET: score and inspect a chosen pathway case-by-case
condTbl(csf(fit)$condition, data)

# 6 . ROBUSTNESS: does the finding survive threshold changes?
fr <- frscored_cna(data, fit.range = c(1, 0.8), granularity = 0.1)
fr

# 7 . RECOMMEND: translate the surviving pathway into program language
# 8 . BRIEF: write Problem / Finding / Recommendation (Modules 29 and 30)

What you can now do

By finishing this curriculum you should be able to:

• Explain CNA, along with conjunctivity, equifinality, and causal chains, in plain language.
• Formulate CNA-shaped research questions for immunization programs.
• Design a study: define outcomes, choose conditions, draw a framework.
• Prepare and clean crisp-set supervision datasets.
• Install and use R, RStudio, and the cna package.
• Run cna() models and read solution formulas.
• Interpret consistency and coverage, and compare candidate models.
• Run robustness checks with frscore and sensitivity analyses.
• Translate configurational findings into policy briefs and executive summaries.
• Use CNA to push immunization program performance forward.