Auditing Units and Derived Dataset Variables

Why Audit Units and Derived Variables?

A dataset can contain plausible-looking numbers that are wrong because a unit was misunderstood, a time conversion was applied inconsistently, or a formula was implemented incorrectly. Such errors can change the scale or meaning of an analysis variable without making the dataset obviously invalid. An independent review therefore checks not only whether values are present, but whether each value can be reconstructed from its inputs using the documented units, formula, and conventions.

This audit concerns unit consistency and derived dataset variables such as dose-normalized measurements, elapsed time, and body-size measures. It does not establish that a variable belongs in a particular analysis or that a model uses it correctly. The core review question is narrower: given the stated inputs and derivation, does the dataset value have the right numerical value and unit?

Establish the Unit Contract Before Recalculation

For each audited variable, identify the source fields, their units, the intended formula, and the output unit. Also record conventions that affect interpretation: whether dose means administered or prescribed dose, whether time is measured from the actual or scheduled event, and which height and weight measurements are paired. Unit labels should be explicit. “Time” alone is not sufficient if the stored values might represent minutes, hours, or calendar timestamps.

A basic dimensional check asks whether the units on the right-hand side of a formula combine to the unit claimed on the left. Conversion factors should be written with units so that cancellation is visible. For example, converting minutes to hours uses a factor equal to one:

The minutes cancel, leaving hours. This does not by itself prove that the recorded number is correct: the source unit and conversion factor must also be verified. It does expose many errors, such as multiplying by 60 when converting minutes to hours.

Recalculation is meaningful only when the inputs and conventions are adequately specified. If a field’s unit is undocumented, or if an event’s date, time zone, or reference event is ambiguous, an auditor should report that limitation rather than silently assume a convention. Preserve the original fields and create an independently calculated comparison value; overwriting source data removes useful evidence about how a discrepancy arose.

Worked Recalculations

A Reproducible Audit Procedure

A useful audit separates checking the definition from checking the implementation. First confirm the formula, input fields, units, and conventions in the available documentation. Then independently calculate a comparison value from the source fields. Compare that value with the dataset output using a tolerance appropriate to the variable’s rounding precision. Exact equality is appropriate only when the derivation and storage are expected to produce exactly the same representation.

For a formula with a constant, check that the constant’s unit convention is documented. For example, the Mosteller BSA expression is conventionally used with height in centimetres and weight in kilograms. A numeric check using different units is not a valid independent verification unless the formula has also been transformed correctly.

Diagnostics, Alternatives, and Limitations

A strong review combines spot checks with systematic checks. Manual calculations are transparent and useful for validating a formula on selected records, especially edge cases. Automated assertions can then check every row for conditions such as missing inputs, nonpositive denominators, impossible date ordering under the stated convention, or disagreement beyond a defined rounding tolerance. These approaches complement each other: a script can apply the wrong formula consistently, while a few manual checks may miss a rare error affecting only a subset of records.

Useful diagnostic patterns include a constant factor-of-60 discrepancy in time values, a factor-of-1,000 discrepancy associated with grams versus milligrams, negative elapsed times caused by incorrect date handling, and abrupt changes in a derived variable when source-unit conventions change. Summaries and plots can help locate such patterns, but unusual values are flags for investigation, not proof of an error. A high concentration or large BSA might be valid; the audit tests derivation and unit consistency, not clinical plausibility alone.

The audit also has limits. Recomputing a value cannot establish that its source measurement is accurate, that the documented formula is scientifically appropriate, or that the variable is appropriate for a particular analysis. A mismatch may arise from rounding, an undocumented transformation, a wrong source record, or an implementation error. Each possibility should be distinguished using the available records and documentation. If the derivation cannot be reconstructed, record the variable as not independently verified rather than presenting an assumed reconstruction as fact.

Common Pitfalls

• Treating unit labels as decoration. The wrong reasoning is that a number stays the same when its label changes. In fact, 0.180 g and 180 mg are equal quantities but different numeric values; convert before applying a formula.
• Subtracting clock times without dates. A later clock time can occur on the next calendar day. Use complete timestamps or an explicit day-boundary rule.
• Checking arithmetic but not the definition. Correctly dividing concentration by dose does not verify that the documented dose is the intended denominator. Confirm what the variable is defined to use.
• Comparing rounded values as if exact. A small difference may be due to storage precision. Set and document a tolerance based on the known rounding process; do not use a tolerance so wide that it hides a substantive unit error.
• Silently repairing inputs. Changing raw values or choosing a different height or weight can make a result appear to match while obscuring the original discrepancy. Keep source values intact and record any proposed correction separately.