32 Communicating a Finished Analysis

The single biggest problem in communication is the illusion that it has taken place.

William H. Whyte, Is Anybody Listening? (1950)

Why this chapter exists

The book has taught the reader to produce a defensible analysis and has stopped there. Chapter 4 covers the register in which a statistician should speak to a clinician, and Chapter 22 covers the figure, but neither addresses the artifact the reader will actually be judged on. A working biostatistician delivers findings in three forms, and writes some of them weekly: the talk, the memo, and the response to reviewers. A book that devotes a chapter to SAS on grounds of employability cannot reasonably be silent about the three documents that constitute the job.

32.1 Prerequisites

Answer the following questions to see if you can bypass this chapter. You can find the answers at the end of the chapter in Section 32.15.

Why is the order in which you conducted an analysis almost never the right order in which to present it?
Your primary analysis found no effect. What, precisely, is the difference between reporting that as ‘no evidence of an effect’ and as ‘evidence of no effect’, and which one are you usually entitled to?
A reviewer asks you to re-run the primary analysis with a different exclusion criterion. What in your compendium determines whether that costs you an hour or a week?

32.2 Learning objectives

By the end of this chapter you should be able to:

Structure a set of findings as an argument rather than as a chronology, using the and/but/therefore skeleton.
Give a twenty-minute talk to a clinical audience that leads with the conclusion and defends it afterward.
Write a one-page memo to a principal investigator that a busy reader can act on in four minutes.
Write a point-by-point response to reviewers that concedes what should be conceded and defends what should be defended, on technical grounds.
Report a null result without either apologizing for it or overclaiming it.
Give and receive structured peer review on an analysis.

32.3 Orientation

An analysis is a chronology: you obtained the data, cleaned it, described it, modeled it, checked the model, and arrived at an estimate. That chronology is the right order for doing the work, for the compendium, and for the methods section. It is the wrong order for almost every act of communication, because it withholds the thing the audience came for until the end, and asks them to hold six irrelevant facts in memory on the promise that the payoff is coming.

Presenting an analysis is not narration. It is argument: here is the claim, here is the evidence, here is what would have changed my mind. The three genres in this chapter are three audiences for that argument, differing in how much of the evidence they want and how much of the argument they will tolerate being told. The talk gets the least evidence and the most argument; the response to reviewers gets the most evidence and the least latitude.

32.4 The statistician’s contribution

Everything in this chapter is judgment; there is no tool.

Lead with the answer. The clinical collaborator has one question, and it is the one they asked you three months ago. Answer it in the first sentence, then defend the answer. Statisticians resist this, because the defense is where the work was and the answer feels unearned without it. The audience does not share that feeling. They experience a withheld conclusion as evasion, and their attention is spent before you reach it.

Calibrate the claim to the evidence, in both directions. Overclaiming is the familiar sin, and the more common one. The opposite failure is real and is a particular affliction of the careful: a hedge so complete that the reader cannot tell what you found, and therefore substitutes their own prior. If the confidence interval excludes any clinically meaningful effect, say so plainly. If it does not, say that plainly too. The verbs matter, and the discipline of Chapter 4, that ‘we found X’ and ‘the data are consistent with X’ and ‘we cannot rule out X’ are three different claims, is the whole of the skill.

Decide what the audience should do differently. Every communication has an implicit request: fund this, publish this, stop this, change the protocol, collect more data, believe nothing yet. If you cannot state the request, you are not yet ready to write. A memo that ends without one is a memo the PI files and forgets.

Do not let the reviewer set the statistics. A reviewer who asks for a subgroup analysis is asking for something that, performed as asked, is exploratory and uncalibrated (Chapter 24). You should do it, report it, and label it. What you must not do is quietly promote it into the confirmatory frame because a reviewer requested it. The request does not launder the inference, and the response letter is where you say so, politely and once.

These judgments are what distinguish a statistician who is consulted again from one who is merely correct.

32.5 The narrative arc

The most portable structure for a scientific argument has three parts, and it is easier to remember as a skeleton of conjunctions than as a diagram.

And. The stable state of the world, which the audience already accepts. ‘Patients hospitalized with heart failure have a thirty-day readmission rate of about twenty-five per cent, and post-discharge home-health visits are widely believed to reduce it.’

But. The disruption. The reason the work exists. ‘But the belief rests on observational studies in which the patients who received visits were systematically healthier than those who did not.’

Therefore. The response, and the finding. ‘Therefore we randomized 1,500 patients, and we find that home-health visits reduce thirty-day readmission by 4.2 percentage points, with a confidence interval from 1.1 to 7.3.’

Three sentences, and the audience now knows what you did, why, and what you found. Everything else in the talk or the memo is support for the third sentence. Table 32.1 contrasts the structure with the chronology it replaces.

Table 32.1: The chronology is the order in which the work was done, and the order the methods section follows. The argument is the order in which it should be presented. The estimate is the last thing computed and the first thing said; the chronology becomes the defense rather than the narrative.

Chronology (the order you worked)	Argument (the order you present)
obtain data	And: the accepted background
clean	But: why the work exists
describe	Therefore: the estimate, stated first
model	the defense: design, model, diagnostics
diagnose	what would change my mind
estimate

The final element of the argument is the one statisticians most often omit and the one that most raises a skeptical audience’s trust: state what would have changed your mind. ‘If the sensitivity analysis under a plausible MNAR mechanism had moved the estimate below one percentage point, I would not be presenting this.’ A speaker who volunteers the conditions under which they would have been wrong is a speaker worth believing.

32.6 The talk

Twenty minutes, a clinical audience, most of whom will not remember a number.

The first two minutes carry the talk. Deliver the arc above. If the audience leaves after two minutes they should have the finding. Everything after is for those who want to know whether to believe it.

One idea per slide, and the idea is the title. A slide titled ‘Results’ says nothing. A slide titled ‘Home-health visits reduced readmission by 4.2 points’ says the thing, and the figure beneath it is the evidence for the title. If a listener reads only the titles, they should get the argument.

Show the estimate with its uncertainty, once, and large. The coefficient plot of Chapter 22, with the interval, is the single most important object in the talk. Do not bury it in a regression table, and do not show a regression table at all unless someone asks.

Anticipate the three questions. For any clinical analysis they are, reliably: how did you handle the patients who dropped out, could this be confounding, and does it hold in the subgroup I care about. Have a backup slide for each. A backup slide answered in ten seconds does more for your credibility than the entire prepared talk.

Do not show code. Ever, in this genre. The compendium is where the code lives, and the audience is not there to audit it. A single line naming the repository and the DOI, at the end, discharges the obligation.

32.7 The memo

One page, to a principal investigator, usually in response to ‘what did you find?’ or ‘is this worth pursuing?’.

The memo has a fixed shape, and its virtue is that the reader can stop at any point and still have something usable.

The finding, in one sentence, with the number and its interval. No preamble.
The request. What you want the reader to do. Approve the manuscript, drop the arm, collect more data, stop.
The three things they should know. The design in one line, the estimate in one line, the principal threat to it in one line.
The caveats, ranked. Not an exhaustive list. The two or three that could actually change the conclusion, in descending order of how much they could change it.
What you propose to do next, with a time cost.

The discipline is subtractive. Anything that does not survive the question ‘would the PI act differently if they knew this?’ comes out. Most methods detail comes out. The model specification comes out. Diagnostics come out. They live in the compendium, and the memo says where.

32.7.1 Worked example: a memo

To: Dr. X, Cardiology From: A. Statistician Re: HF-HOME primary analysis, 2026-06-15

Finding. Home-health visits within seven days of discharge reduced thirty-day all-cause readmission by 4.2 percentage points (95% CI 1.1 to 7.3; from 24.8% to 20.6%). The pre-specified primary analysis supports the trial’s hypothesis.

Request. Approval to proceed to manuscript, targeting submission in six weeks.

What you should know.

Design: 1,500 patients, 1:1 randomized, stratified by site and baseline ejection fraction. The analysis is the one pre-specified in SAP v1.0, tagged before unblinding.

Estimate: the interval excludes zero but includes effects as small as 1.1 points. The trial was powered to detect 4.5, so we are estimating an effect at roughly the size we planned for, with the imprecision that implies.

Principal threat: 6.3% of patients had no outcome ascertainable from the state health-information exchange. These are handled by multiple imputation, and the pre-specified MNAR sensitivity analysis moves the estimate to 3.6 points (CI 0.4 to 6.8). The conclusion is directionally robust but the lower bound is close to zero.

Caveats, ranked.

The missing outcomes above. If patients lost to the exchange were readmitted at a substantially higher rate than those retained, the effect could fall below clinical relevance. I do not think this is likely, because loss to the exchange is driven by out-of-state address rather than by illness, but it is the assumption the result rests on and the manuscript must say so.

Open-label design. Readmission is a hard endpoint and unlikely to be influenced by knowledge of arm, but the decision to admit is a clinician’s judgment and is not fully hard.

Single health system. External validity is unaddressed.

Next. Draft methods and results in two weeks. I propose adding the tipping-point analysis for the missing outcomes (roughly one day) because a reviewer will ask for it and it is cheaper to have it than to be asked.

Notice what the memo does not contain: the model formula, the covariate list, the diagnostics, the Table 1, the software versions. It contains a pointer to the compendium, where all of that lives, and it contains every fact on which the PI’s decision turns. It is also honest in a specific way that matters: it volunteers that the lower bound is close to zero and that the sensitivity analysis erodes the estimate. A PI who learns that from a reviewer instead of from you will not trust the next memo.

32.8 Null results

The analysis found nothing. This happens constantly, and the handling of it separates careful statisticians from the rest.

The first distinction is the one in this chapter’s quiz. Absence of evidence is not evidence of absence. A wide confidence interval that includes zero means you could not distinguish the effect from nothing; it does not mean the effect is nothing. The claim you are entitled to is ‘we found no evidence that X’, not ‘we found that X does not work’. The second claim requires an interval narrow enough to exclude any effect you would have cared about, and you should say so explicitly when you have it:

The confidence interval (from -0.4 to 0.6 percentage points) excludes the 2-point difference the trial was designed to detect and, indeed, excludes any difference we would regard as clinically meaningful. This is not an inconclusive result; it is a reasonably precise null.

That is a strong scientific statement and a publishable one. Contrast it with the same data described as ‘the difference was not statistically significant (p = 0.72)’, which tells the reader nothing about whether the study was informative.

The second distinction is between a null result and a failed study. A trial that enrolled half its target and produced an interval spanning every effect from harmful to miraculous has not produced a null result; it has produced no result, and the honest report says so. Presenting an underpowered null as evidence of no effect is one of the more consequential forms of misreporting in the clinical literature, and the statistician is the only person on the team positioned to stop it.

Check your understanding: what may you claim?

Question. Your trial estimates a treatment effect of 0.3 percentage points with a 95% confidence interval from -3.9 to 4.5. The minimum clinically important difference agreed at the outset was 2 points. The PI would like to write ‘the intervention was not effective’. What do you say?

Answer.

You say that the sentence is not supported. The interval includes effects as large as 4.5 points, more than twice the minimum clinically important difference, so the data are entirely consistent with a clinically important benefit. They are also consistent with a clinically important harm. The study did not distinguish these possibilities, and the correct report is that it was uninformative about effects in the range that matters: ‘we found no evidence of an effect, but the study cannot exclude a clinically important benefit or harm’.

The sentence the PI wants would be defensible only if the interval lay wholly inside the region of clinical indifference, for example from -1.2 to 1.4, which excludes the 2-point difference on both sides. Then, and only then, ‘the intervention was not effective at any clinically meaningful magnitude’ is a claim the data support. The distinction is between a precise null and an inconclusive one, and conflating them is how the literature acquires its ‘negative’ trials that were merely small.

32.9 The response to reviewers

The manuscript comes back with three reviewers and eleven comments, of which five are statistical and land on you. The response letter is its own genre and follows strict conventions.

Quote every comment, respond to every comment, in order. Number them. Reproduce the reviewer’s text verbatim, in a distinguishable typeface, and place your response beneath it. An editor reading the letter must be able to verify, without cross-referencing, that nothing was ignored. Silence on a comment reads as evasion even when it was an oversight.

Say what changed and where. ‘We have added the requested sensitivity analysis (Methods, p. 8; Supplementary Table S6; Figure 3 revised).’ A response that agrees with a point but does not say where the manuscript now reflects it forces the editor to hunt, and irritating the editor is a strictly dominated strategy.

Concede quickly what should be conceded. If the reviewer is right, say so in one sentence, make the change, and move on. Defensive paragraphs attached to a concession make the concession look grudging and invite scrutiny of the rest.

Disagree on technical grounds, once, and without heat. When the reviewer is wrong, the response states the technical reason, offers the analysis that demonstrates it, and stops. It does not restate the point three ways, and it does not imply that the reviewer has failed to read the paper, even when they plainly have not.

Do not let a request change the inferential status of an analysis. This is the statistical judgment at the center of the genre. When a reviewer asks for a subgroup analysis, they are asking for an analysis that was not pre-specified. Perform it, report it, and label it exploratory. The temptation, and it is a real one because the reviewer holds the decision, is to fold it into the results as though it had been planned. It was not, and doing so is precisely the practice Chapter 24 exists to prevent.

32.9.1 Worked example: three responses

Comment 1.3. ‘The authors should report a sensitivity analysis to the missing outcome data, which at 6.3% is not negligible.’

We agree, and we thank the reviewer. A delta-adjustment sensitivity analysis under a plausible MNAR mechanism was pre-specified in SAP v1.0 but, on review, was reported only in the supplement. We have moved it into the main text (Results, p. 12) and added a tipping-point analysis (Supplementary Figure S4). The conclusion is unchanged: the effect estimate falls from 4.2 to 3.6 points, and the interval continues to exclude zero until the imputed outcomes are shifted by more than 1.4 standard deviations, a magnitude we regard as implausible given that loss to follow-up was driven by out-of-state address rather than by clinical status.

Comment 2.1. ‘The effect appears larger in patients with reduced ejection fraction. The authors should present this subgroup as a primary finding, as it is likely the mechanism.’

We have added the subgroup analysis (Supplementary Table S7), which does show a larger point estimate in the reduced- ejection-fraction stratum (5.8 vs 3.1 points), with an interaction test that is not significant (p = 0.31). We respectfully decline to present it as a primary finding, for two reasons. First, it was not pre-specified: the analysis plan (deposited at ClinicalTrials.gov before unblinding, and cited in the Methods) names a single primary analysis in the full randomized population, and promoting a subgroup selected after the data were seen would render its nominal error rate uninterpretable. Second, the trial was not powered for interaction, and an apparent difference of this magnitude between strata is well within what sampling variation produces under a common true effect. We now report the subgroup as exploratory and hypothesis-generating (Results, p. 14; Discussion, p. 19), and we note it as a candidate for prospective testing.

Comment 3.2. ‘A logistic regression is inappropriate here; the authors should have used a Cox model.’

The outcome is binary readmission within a fixed 30-day window, ascertained for all patients, and every patient was followed for the full window or had their outcome ascertained through linkage. There is therefore no censoring to accommodate, and the estimand of interest is a risk difference over a fixed horizon rather than a hazard ratio. A Cox model would answer a different question and would require an assumption (proportional hazards) that the design does not need. We have added a sentence to the Methods (p. 7) making the estimand explicit, which we hope clarifies the choice.

Three comments, three different postures: agree and fix, agree to perform but decline to reframe, and disagree on technical grounds. None of the three is defensive, and all three tell the editor exactly where in the manuscript to look.

Observe also what made the first response cheap to write. The sensitivity analysis existed, because the SAP pre-specified it; the tipping-point analysis took a day, because the compendium rebuilds with one command; and the claim that the plan predates unblinding is verifiable, because the SAP was tagged in Git (Chapter 24) and deposited at the registry. The infrastructure chapters of this book pay their return here, at the moment when a reviewer asks a question six months after you last thought about the analysis.

32.10 Peer review as a practice

The skills above are trained by performing review, not by receiving it. A reviewer who has had to articulate why an analysis is unconvincing writes more convincing analyses.

When reviewing a colleague’s analysis, the questions worth asking, roughly in the order that catches the most:

What is the claim, and can I find it stated in one sentence?
Does the reported estimate come with an interval, and is the interval interpreted rather than merely printed?
Is the primary analysis the one that was pre-specified, and can I verify that from the artifact rather than the prose?
What is the denominator, and does it match the flow diagram?
Which single assumption, if wrong, would most change the conclusion, and does the paper name it?
Would I be able to re-run this?

That list is short by design, and it is the list of a generalist reader. For the statistical content specifically, the most compact published instrument is Harrell’s author checklist (Harrell, 2024), which enumerates the errors a biomedical manuscript makes often enough to be worth checking mechanically: exact p-values rather than ‘NS’ or ‘p < 0.05’, intervals reported alongside tests, continuous variables not categorized, no stepwise selection, missingness documented rather than silently dropped, deviations from the analysis plan stated as deviations, and figures that show the data rather than a bar whose height is a mean. Run it against your own draft before you send it out, which is cheaper than having a reviewer run it for you, and against a colleague’s draft when you are the reviewer. The overlap with Chapter 24 is not accidental: most of the checklist’s items are failures of pre-specification arriving late enough to be expensive.

When receiving review, the discipline is to separate the comment from its tone. A reviewer who is rude and right has still handed you a free defect report. The response letter is not the place to relitigate the tone, and the mildest possible version of the disagreement is invariably the most effective.

32.11 Collaborating with an LLM on communication

Language models write fluent prose and are correspondingly dangerous here, because fluency in this genre is often the vehicle for an overclaim.

Prompt 1: drafting the memo. Paste the estimate, the interval, the design, and the sensitivity results, and ask for a one-page memo in the structure of this chapter.

What to watch for. Calibration. The model will reach for ‘significant’, ‘demonstrates’, and ‘confirms’ where the evidence supports ‘is consistent with’. It will also tend to soften or omit the caveat that hurts. Read the draft asking one question: does any sentence claim more than the interval permits?

Verification. Take each sentence containing a claim and check it against the confidence interval. Then hand the memo to a colleague and ask them what you found and what you want them to do. If they cannot say, the memo has failed regardless of how well it reads.

Prompt 2: drafting the response to reviewers. Paste the reviewer’s comment and your position, and ask for a response.

What to watch for. Two failure modes, in opposite directions. The model is agreeable by disposition and will concede points it should defend, including, characteristically, agreeing to promote an exploratory subgroup analysis because the reviewer asked. It also occasionally produces a defensive paragraph where one sentence would do. You supply the posture; the model supplies the prose.

Verification. For every conceded point, ask whether you actually agree. For every defended point, check that the defense is technical rather than rhetorical.

Prompt 3: adversarial review of your own draft. Paste the results section and ask the model to review it as a hostile statistical reviewer, listing every claim not supported by the reported evidence.

What to watch for. This is the most valuable of the three prompts, because the model is better at finding overclaims in text than at avoiding them in its own. Expect a mix of real findings and pedantry; the real findings are worth the sort.

Verification. Each flagged claim is a hypothesis about a weakness. Check it against the analysis. The ones that survive are the comments a real reviewer will make, and you now have six weeks rather than six days to address them.

32.12 Principle in use

Three habits decide whether the analysis reaches the reader intact:

Lead with the answer, then defend it. The chronology of the analysis is the order you worked, not the order anyone should hear.
Match the claim to the interval, in both directions. No evidence of an effect is not evidence of no effect, and a precise null is a real finding that deserves to be stated as one.
Never let a request change an analysis’s inferential status. A reviewer may ask for the subgroup. They cannot make it confirmatory.

32.13 Exercises

Take the last analysis you completed and write its and/but/ therefore in three sentences. If the ‘but’ is difficult to write, ask yourself why the analysis was performed.
Write the one-page memo for that analysis, following the five-part structure in this chapter. Give it to a colleague who does not know the project and ask them, without prompting, what you found and what you want them to do. Revise until they can answer both.
Take a published paper reporting a null result. Determine from the reported interval whether it is a precise null or an inconclusive one, and then check what the abstract claims. Write a paragraph on the gap, if any.
Find a set of published reviewer comments and author responses (many journals now publish them). Identify one response that concedes what it should have defended, or defends what it should have conceded, and rewrite it.
Review a colleague’s analysis against the six questions in the peer-review section. Deliver the review in writing. Then ask them which comment was most useful, and why; it is rarely the one you expected.

32.14 Further reading

(Slade et al., 2023), on the communication skills that interdisciplinary team science demands of statisticians.
(Wilke, 2019), whose closing chapters on telling a story with figures are the visual counterpart to the narrative arc taught here.
(Altman & Bland, 1995), the two-page paper this chapter’s null-results section restates at greater length.
(International Committee of Medical Journal Editors, 2024), for the conventions governing what a manuscript and its correspondence must contain.
(Harrell, 2024), the author checklist used in the peer-review section above.
(Schulz et al., 2010) and (Elm et al., 2007), the reporting standards that determine what your results section is obliged to state.
Chapter 24 and Chapter 7, the infrastructure that makes a response to reviewers cheap rather than ruinous.

32.15 Prerequisites answers

Because the chronology withholds the conclusion until the end and asks the audience to retain the preliminaries on the promise of a payoff they cannot yet evaluate. An audience wants the claim first and the evidence second, so that they know what the evidence is evidence for. The chronology remains the right order for the methods section and for the compendium, where the reader’s purpose is verification rather than comprehension. For a talk or a memo, structure the material as an argument: the accepted state of the world, the disruption that motivated the work, the finding, the defense, and the conditions under which you would have concluded otherwise.
‘No evidence of an effect’ says that the study could not distinguish the effect from zero, which is a statement about the study’s resolution. ‘Evidence of no effect’ says that the effect is absent, or at least too small to matter, which is a statement about the world. You are entitled to the second only when the confidence interval excludes every effect you would have regarded as clinically meaningful; a precise null is a real and publishable finding. When the interval is wide and includes important effects in either direction, the study is uninformative in the range that matters, and saying so is the honest report. Presenting an underpowered null as evidence of no effect is a consequential and common misreport, and the statistician is usually the only person positioned to prevent it.
Three things, all of which this book has argued for on other grounds. A pre-specified analysis plan tagged in Git before data lock (Chapter 24), so that you can demonstrate which analysis was primary and when it was fixed. A compendium that rebuilds with one command (Chapter 10, Chapter 13), so that changing the exclusion criterion is an edit and a re-render rather than an archaeological expedition. And a pinned environment (Chapter 11, Chapter 12), so that the re-run six months later produces the published numbers rather than subtly different ones you then have to explain. Without them, the reviewer’s request is a week of reconstruction and a discrepancy you cannot account for.