Categorical Data

Categorical Data in Trials, Meta-Analysis and Decision Models

Many of the outcomes that drive health technology assessment are recorded as categories, not as measured amounts. Death, hospital admission, relapse, response to treatment and the levels of the EQ-5D questionnaire each place a patient in one of a fixed set of groups, and the analysis then works with counts and proportions. The form of the data fixes which effect measures a trial or meta-analysis can report, and those measures become the event probabilities, transition probabilities and treatment effects that a decision model runs on. Measured quantities such as blood pressure or costs are continuous data, the subject of a separate article on continuous data.

Nominal, ordinal and binary categories

The Cochrane Handbook asks review authors to identify the data type of each outcome early, because the available effect measures depend on it. Of its five common types, two are categorical in form. Dichotomous or binary data arise when each outcome is one of only two possible categorical responses, and ordinal data when each outcome is one of several ordered categories, or is generated by scoring and summing categorical responses.

Categories without any order are nominal. Ali and Bhaskar describe nominal variables as data merely classified into categories that cannot be arranged in any order, and call the two-category case dichotomous or binary. Some texts reserve "categorical" for unordered variables, while the Cochrane Handbook describes ordinal outcomes as ordered categories; the broader sense is used here.

Two neighbouring types are easily confused with binary data. Events that can happen more than once, such as repeated admissions, are count data, and the Handbook calls treating them as dichotomous a common error. Time-to-event data can be analysed as dichotomous only when every patient's status is known at a fixed time point; otherwise survival analysis with a hazard ratio is the appropriate summary.

Effect measures for a binary outcome

A two-group trial with a binary outcome reduces to a two-by-two table of events and non-events. From that table the Cochrane Handbook derives the risk ratio, the odds ratio and the risk difference, with the number needed to treat obtained from the risk difference.

$$RR = \frac{S_E / N_E}{S_C / N_C}, \qquad OR = \frac{S_E / F_E}{S_C / F_C}, \qquad RD = \frac{S_E}{N_E} - \frac{S_C}{N_C}$$

where $S_E$ and $S_C$ are the numbers with the event in the experimental and comparator groups, $F_E$ and $F_C$ the numbers without it, and $N_E$ and $N_C$ the group totals. Risk is the probability of the event, and odds are the probability that it occurs divided by the probability that it does not. The null value is 1 for the two ratios and 0 for the risk difference.

The Handbook records the properties that matter most in practice.

• Odds and risks diverge when events are common. A risk of 0.5 is an odds of 1 and a risk of 0.95 an odds of 19, so reading an odds ratio as a risk ratio overstates the effect, especially when risks exceed about 20%.
• The risk ratio has a ceiling. It cannot exceed 1 divided by the comparator group risk, so with a comparator risk of 0.66 it cannot exceed 1.5.
• Zero cells affect the ratios. Neither ratio can be computed when the comparator group has no events, and it is customary to add 0.5 to each cell, while the risk difference can be computed for any study.
• The choice of event matters for the risk ratio. Switching events and non-events turns an odds ratio into its reciprocal and reverses the sign of a risk difference, but can change a risk ratio's estimate and significance.

The risk difference is also called the absolute risk reduction, and one minus the risk ratio, as a percentage, is the relative risk reduction. Ratio measures are typically analysed on a logarithmic scale in meta-analysis, and logistic regression models the log odds of a binary outcome when covariates must be adjusted for.

Ordinal scales and the EQ-5D descriptive system

Ordinal outcomes sit between binary and continuous data. The Cochrane Handbook describes a proportional odds model, which assumes one odds ratio holds for every way of splitting the ordered categories into success and failure. Longer ordinal scales are often analysed as continuous, and shorter ones are collapsed into two groups, which the Handbook considers especially appropriate when an established, defensible cut-point exists. It warns that a cut-point chosen to maximise the difference between trial arms can induce bias.

The EQ-5D-5L descriptive system is a familiar ordinal measure in health economics. It has five dimensions, mobility, self-care, usual activities, pain or discomfort and anxiety or depression, each with five levels from no problems to extreme problems, and one level from each dimension defines one of 3,125 health states. The EuroQol user guide states that the level numbers are labels with no arithmetic properties, so state 21111 cannot be assumed better than 13111 and the digits should not be added into a score. A value set converts the profile into a health state utility value, and the choice of value set is itself a methods question. NICE's interim methods statement (PMG51, August 2026) makes the EQ-5D-5L descriptive system and the new UK 5L value set its preferred approach for adults in reference-case analyses, replacing the PMG36 advice (section 4.3.16) to map 5L responses onto the 3L value set, which still applies to topics started before the statement.

The user guide notes that levels are sometimes dichotomised into "no problems" (level 1) and "any problems" (levels 2 to 5). Ordinal measurement as a property of scales is covered under ordinal scaling, and category rating is a valuation method that places states in ordered categories.

Categories as health states and model inputs

A state-transition model is built on categorical data. The ISPOR-SMDM task force report on state-transition modelling says such models rest on mutually exclusive and collectively exhaustive health states, so a modelled individual is in only one state in any cycle. The state occupied in each cycle of a Markov model is therefore a categorical variable, and counts of patients moving between states are the data behind transition probabilities. The NICE manual (PMG36, section 4.7.3) gives how states of health are categorised as an example of structural uncertainty.

Binary trial outcomes enter models as event probabilities. In probabilistic sensitivity analysis the NICE manual (section 4.7.10) asks for distributions that represent the available evidence, not ones chosen arbitrarily, and the ISPOR-SMDM task force on parameter estimation calls beta distributions a natural match for binomial data. Where a chance node has more than two branches, Briggs, Ades and Price argue for the Dirichlet distribution, the multivariate equivalent of the beta, which keeps branch probabilities summing to 1 and, in a Bayesian framework, overcomes zero counts for some transitions.

Worked example with one trial outcome carried into a model

All numbers in this example are illustrative. A trial randomises 200 patients to a new service and 200 to usual care and records hospital admission within 12 months, with 40 admissions under the new service and 60 under usual care.

1. Compute risks and odds. The risks are 40/200 = 0.20 and 60/200 = 0.30. The odds are 40/160 = 0.25 and 60/140 = 0.4286.

2. Compute the three effect measures.

$$RR = \frac{0.20}{0.30} = 0.667, \qquad OR = \frac{0.25}{0.4286} = 0.583, \qquad RD = 0.20 - 0.30 = -0.10$$

where the two ratios are unitless and the risk difference is a difference in probability. The number needed to treat is 1 divided by 0.10, or 10 patients per admission avoided, and the relative risk reduction is 33.3%. Read as a risk ratio, the odds ratio would suggest a 41.7% reduction.

3. Apply each measure to the model population. Suppose the model population has a usual-care admission probability of 0.50. A constant risk ratio gives 0.50 × 0.667 = 0.333. A constant odds ratio turns odds of 1 into odds of 0.583, a probability of 0.583/1.583 = 0.368. A constant risk difference gives 0.50 minus 0.10, which is 0.40.

4. Interpret. Per 1,000 patients the model avoids about 167, 132 or 100 admissions depending on which measure is held constant, and at an illustrative GBP 3,000 per admission the savings are about GBP 500,000, GBP 395,000 or GBP 300,000. The trial result is identical in all three cases, so the spread comes from an assumption about which measure transfers to a new baseline risk, and it deserves a scenario analysis.

Dichotomising continuous and ordinal measures

Turning a measured quantity into two categories is common in clinical research and costly in information. Altman and Royston state that dichotomising at the median reduces statistical power by as much as discarding a third of the data, and that choosing an "optimal" cut-point by minimum P value risks a spuriously significant result.

A responder analysis applies the same step to a trial endpoint, classing each patient as a responder or non-responder by a threshold. Snapinn and Jiang contrast it with what they call probably the most common check of comparing the observed effect against a minimal clinically important difference. Under their model with normally distributed outcomes, comparing responder rates needed about 60% more patients than comparing means at the most favourable threshold, and 4,053 against 526 per group at a threshold far from the group means. They recommend basing significance on the most powerful analysis, usually of the continuous variable, and judging clinical relevance from both the mean difference and response rates. A model with responder and non-responder states needs a binary input, and that input inherits the cut-point.

Categorical data compared with nearby ideas

Continuous data, which the Handbook defines as a measurement of a numerical quantity, are summarised by a mean difference or a standardised mean difference instead. Misclassification is the error of assigning an observation to the wrong category, and the kappa statistic measures agreement between raters assigning categories beyond chance. Ali and Bhaskar list the chi-square, Fisher's exact and McNemar's tests for categorical variables, and the chi-square distribution underlies the first.

Limitations and common misreadings

Most errors with categorical data come from treating categories as if they carried more, or less, information than they do. The six below recur in reviews and models.

1. Reading an odds ratio as a risk ratio. The two diverge when events are common, and the misreading exaggerates the effect.
2. Doing arithmetic on category codes. EQ-5D level numbers are labels, and only a value set turns a profile into a utility.
3. Choosing a cut-point after seeing the data. A data-driven threshold inflates the apparent difference between arms.
4. Dichotomising when the measured value is available. Power falls and information about the size of change is lost.
5. Treating repeated events as one binary outcome. Patients with several events are counted once and the timing is lost.
6. Assuming a relative effect transfers unchanged. The measure held constant across populations changes a model's result, as the worked example shows.

Sources

• Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, et al (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.5. Cochrane; 2024. Sections 6.1, 6.4.1, 6.5.1, 6.6.1, 6.7.2.1 and 6.8.1. https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-06
• Ali Z, Bhaskar SB. Basic statistical tools in research and data analysis. Indian Journal of Anaesthesia. 2016;60(9):662-669. https://doi.org/10.4103/0019-5049.190623
• EuroQol Research Foundation. EQ-5D-5L User Guide version 4.1. Updated September 2026. https://euroqol.org/information-and-support/documentation/user-guides/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 2022, last updated 13 October 2026. Sections 4.3.16, 4.7.3 and 4.7.10. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• National Institute for Health and Care Excellence. Interim methods statement: implementing the EQ-5D-5L value set (PMG51). Published 27 August 2026. Sections 1.6 to 1.8 and 1.18. https://www.nice.org.uk/process/pmg51/chapter/statement-on-using-the-eq-5d-5l-value-set and https://www.nice.org.uk/process/pmg51/chapter/process-considerations
• Siebert U, Alagoz O, Bayoumi AM, Jahn B, Owens DK, Cohen DJ, Kuntz KM. State-transition modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3. Value in Health. 2012;15(6):812-820. https://doi.org/10.1016/j.jval.2012.06.014
• Briggs AH, Weinstein MC, Fenwick EAL, Karnon J, Sculpher MJ, Paltiel AD. Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6. Value in Health. 2012;15(6):835-842. https://doi.org/10.1016/j.jval.2012.04.014
• Briggs AH, Ades AE, Price MJ. Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework. Medical Decision Making. 2003;23(4):341-350. https://doi.org/10.1177/0272989X03255922
• Altman DG, Royston P. The cost of dichotomising continuous variables. BMJ. 2006;332:1080. https://doi.org/10.1136/bmj.332.7549.1080
• Snapinn SM, Jiang Q. Responder analyses and the assessment of a clinically relevant treatment effect. Trials. 2007;8:31. https://doi.org/10.1186/1745-6215-8-31