Labels, Targets, and the Limits of Ground Truth

Different label sources create different strengths and failure modes. A direct observed outcome records the quantity the task genuinely concerns, and usually arrives late. A human annotation captures nuance and needs guidance and calibration. A weak or programmatic label scales cheaply and carries the biases of whatever rule or source wrote it. The proxy is the one that looks free, and it is the row with the case law.

A commercial risk-prediction algorithm used to manage the health of populations had to score “health need”. The label it was actually taught was future health-care cost. Obermeyer and colleagues dissected it in Science in 2019. At the 97th percentile of risk score — the point at which patients are auto-identified for the care programme — Black patients had 26.3% more chronic illnesses than White patients: 4.8 against 3.8 distinct conditions, P < 0.001. Predicting active chronic conditions instead of cost would have raised the Black share of those auto-identified from 17.7% to 46.5%. Nothing in the machinery had to change for that. Only the column it was taught to predict. The abstract ends with the general lesson: “We suggest that the choice of convenient, seemingly effective proxies for ground truth can be an important source of algorithmic bias in many contexts.” Regulators moved the same day. On 25 October 2019 the New York State Department of Financial Services and Department of Health wrote jointly to UnitedHealth Group about the same product, Optum's Impact Pro.

Medicine had already run the proxy question as a randomised trial. The Cardiac Arrhythmia Suppression Trial chose encainide and flecainide because they suppressed ventricular premature beats after myocardial infarction, a strong predictor of sudden death. Of 2,309 patients recruited, 1,727 — 75% — had their arrhythmia suppressed and were randomised. Over an average of 10 months the drugs did to the proxy exactly what they had been selected to do. The outcome it stood for moved the other way: “Encainide and flecainide accounted for the excess of deaths from arrhythmia and nonfatal cardiac arrests (33 of 730 patients taking encainide or flecainide [4.5 percent]; 9 of 725 taking placebo [1.2 percent]; relative risk, 3.6; 95 percent confidence interval, 1.7 to 8.5).” Total mortality was 56 of 730 against 22 of 725, 7.7% against 3.0%, relative risk 2.5. Those two arms were discontinued in April 1989.

A proxy that tracks the goal in historical data can still move against it once something starts optimising the proxy. Evidence of proxy validity is not a formality on a checklist. It is the difference between the two studies above and a system nobody audited.

Clear language helps teams notice when their model is learning a measurement process rather than the intended concept. The phenomenon of interest is the underlying state people care about. The target definition is the operational rule that says what will be predicted and over what horizon — the 90 days, the 100 EUR, the choice of cost rather than chronic conditions. The recorded label is the value that actually lands in the table, after observation, annotation, or programmatic generation. Confusing the three is how a documented policy decision gets discussed as if it were a fact of nature.

Two qualified annotators can disagree. The instructions may be vague, the example may lack context, or the concept may have a genuine boundary case. Majority vote produces one label but can erase uncertainty that matters later.

How much gets erased has been measured, with annotators nobody would call careless. Breast biopsy slides went to 115 pathologists in active practice across eight US states, who returned 6,900 individual interpretations. Three experienced experts had already agreed a consensus reference diagnosis for each slide. Agreement with it was 75.3% overall.

That single figure hides the shape of the problem. Concordance ran at 96% for invasive carcinoma and 87% for benign without atypia. For atypia it was 48% (95% CI, 44%–52%), with 17% of interpretations overinterpreted and 35% underinterpreted. Disagreement also rose with denser breast tissue, lower pathologist caseload and smaller practice setting. Elmore and colleagues put the conclusion this way: “In this study of pathologists, in which diagnostic interpretation was based on a single breast biopsy slide, overall agreement between the individual pathologists' interpretations and the expert consensus–derived reference diagnoses was 75.3%, with the highest level of concordance for invasive carcinoma and lower levels of concordance for DCIS and atypia.”

A project reporting one agreement number would have reported 75.3%. It would never have seen the category where specialists reading the same slide agreed less than half the time. Measure agreement by category and slice, inspect examples with disagreement, and decide whether the task needs clearer guidance, multiple labels, an “uncertain” option, or a different target. Perfect agreement is not always realistic or desirable.

A content-moderation project becomes more reliable when the guide records decisions. Those decisions would otherwise live only in reviewers' heads.

At Google the guide was made executable. On three production classification tasks the engineers did not hand-label at all. They wrote labelling functions that reused knowledge already sitting in the organisation: heuristics, taxonomies, existing models. A generative model reconciled the disagreements among them into probabilistic training labels. The system was Snorkel DryBell, published in 2019. The classifiers it produced were “of comparable quality to ones trained with tens of thousands of hand-labeled examples”. Converting non-servable organisational resources into servable models bought “an average 52% performance improvement”.

In that arrangement the labelling policy is version-controlled code. It can be diffed, reviewed, and rerun against last month's data.

A customer observed for five days cannot yet receive a reliable label for “churn within 60 days.” A loan still being repaid has an unresolved long-term outcome. Treating unresolved cases as negatives corrupts the target.

Clinical-trial regulation writes this distinction into binding text, and gives the target definition a name of its own. The name is the estimand. ICH E9(R1), the addendum on estimands adopted in November 2019, defines it as “a precise description of the treatment effect reflecting the clinical question posed by the trial objective”. That is an object separate from any recorded measurement. It is assembled from named attributes, not inherited from whatever the database happened to store.

The guideline then separates two things that look alike in a data table. An outcome can change meaning because something happened: a subject switching treatment is an intercurrent event. Or the outcome can simply not have happened yet. A subject for whom no outcome event can be observed because the trial has ended is the second case: “The latter is administrative censoring which needs to be addressed as a missing data problem in the statistical analysis.”

Possible responses include waiting, choosing an earlier outcome, excluding immature examples, or using methods designed for censored time-to-event data. The right choice depends on the decision. It also depends on the cost of delayed feedback.

Label quality improves through an explicit operating loop, not a one-time instruction document. Define the construct in writing, including the edge cases left unresolved. Pilot a shared sample, so several reviewers label the same varied examples. Then analyse the disagreement, separating instruction problems, missing context, random mistakes, and genuine ambiguity — the 48% atypia figure is what the last category looks like when it is measured rather than averaged away. Revise definitions, examples and escalation rules, then test again. Then monitor production, auditing slices, reviewers, policy versions, and model-selected examples over time.