Types of Data in Biostatistics

Introduction

Before selecting a statistical test, calculating a confidence interval, or building a regression model, you need to know what kind of data you have.

This sounds simple, but data classification is one of the most important foundations of biostatistics.

Consider several variables collected in a clinical trial:

All of these variables can appear in the same clinical database, but they do not represent the same type of information.

The distinction matters because statistical procedures make assumptions about the structure of the outcome or predictor being analyzed.

The Major Data Classifications

A useful first classification divides data into two broad groups:

Within these broad groups, several more specific classifications are useful:

Categorical Data

Categorical data classify observations into groups or categories.

For example, suppose a randomized clinical trial has three treatment groups:

• Placebo
• Low-dose treatment
• High-dose treatment

The treatment variable is categorical because each patient belongs to one of several categories.

The labels themselves do not necessarily represent numerical quantities.

Examples of Categorical Variables

Categorical data are often summarized using:

• Counts
• Percentages
• Proportions
• Rates
• Contingency tables

Nominal Data

Nominal data are categorical data in which the categories have no inherent ranking.

For example:

There is no mathematical sense in which Drug B is "greater than" Drug A.

The categories are simply different.

Examples of Nominal Variables

• Blood type: A, B, AB, O
• Country
• Clinical site
• Genotype category
• Treatment group
• Disease subtype

If numerical codes are used, they should generally be treated as labels rather than measurements.

For example:

1 = Placebo
2 = Drug A
3 = Drug B

The mean of these codes has no useful clinical interpretation.

Ordinal Data

Ordinal data are categorical observations with a meaningful order.

For example, disease severity might be classified as:

We know that severe disease represents greater severity than moderate disease, but we do not necessarily know that the difference between mild and moderate is numerically identical to the difference between moderate and severe.

Examples of Ordinal Data

Binary Data

Binary data have exactly two possible categories.

Examples include:

• Response: Yes / No
• Death: Yes / No
• Pregnancy: Yes / No
• Relapse: Yes / No
• Adverse event: Yes / No
• Positive test / Negative test

A binary variable is a special case of categorical data.

It is frequently represented as:

For example:

Y = 1  if the patient responds
Y = 0  if the patient does not respond

Binary outcomes are central to clinical research because many important endpoints are naturally expressed as events or non-events.

Proportions and Binary Outcomes

Suppose 42 of 100 patients respond.

The observed response proportion is:

or 42%.

The underlying statistical model may treat each patient outcome as a Bernoulli random variable:

The total number of responses then follows a binomial distribution:

This is why binomial methods are so common for single-arm response-rate analyses and sample-size calculations.

Numerical Data

Numerical data represent quantities measured or counted using numbers.

Examples include:

• Age
• Weight
• Height
• Blood pressure
• Serum concentration
• Creatinine
• Number of adverse events
• Duration of treatment

Numerical data can then be divided into discrete and continuous data.

Discrete Data

Discrete data take separate, countable values.

For example, the number of hospitalizations might be:

A patient cannot have 2.73 hospitalizations.

Similarly, the number of adverse events is generally a count:

Examples of Discrete Variables

• Number of adverse events
• Number of hospitalizations
• Number of prior treatments
• Number of exacerbations
• Number of lesions
• Number of responders

Discrete variables often arise from counting.

Continuous Data

Continuous data arise from measurements that can, in principle, take any value within a range.

Examples include:

• Weight
• Height
• Temperature
• Blood pressure
• Serum concentration
• Drug clearance
• Area under the concentration-time curve
• QT interval

For example, body weight could theoretically be:

The precision recorded in a database may be limited, but the underlying quantity is conceptually continuous.

Discrete vs. Continuous

Count Data

Count data are a particularly important form of discrete data.

A count variable records how many times an event occurs.

Examples include:

• Number of seizures
• Number of hospital admissions
• Number of adverse events
• Number of asthma exacerbations
• Number of infections

A basic count variable is often modeled using a Poisson distribution:

where \(\lambda\) represents the expected count over the specified observation period when the Poisson assumptions are appropriate.

In practice, count data can exhibit greater variability than a Poisson model allows. This is commonly called overdispersion and can motivate negative-binomial or other models.

Interval Data

An interval scale has meaningful differences between values, but zero does not represent an absolute absence of the quantity.

The classic example is temperature measured in Celsius.

The difference between 20°C and 30°C is the same size as the difference between 30°C and 40°C.

However, 40°C is not meaningfully "twice as hot" as 20°C.

This distinction matters because ratios require a meaningful zero point.

Ratio Data

Ratio data have all the properties of interval data plus a meaningful absolute zero.

Examples include:

• Weight
• Height
• Age
• Drug concentration
• Clearance
• Time duration
• Laboratory concentration

For example, if one concentration is 20 ng/mL and another is 10 ng/mL, the first is twice the second in the ratio-scale sense.

Interval vs. Ratio

Measurement Scales in One Framework

The classical measurement-scale framework consists of four levels:

The hierarchy can be summarized as:

Each step adds information about the mathematical structure of the data.

One Variable Can Have Multiple Descriptions

A common source of confusion is treating data classifications as mutually exclusive labels.

They are not.

For example, age can be described as:

• Numerical
• Continuous in its underlying measurement concept
• Ratio-scaled

Number of hospitalizations can be described as:

• Numerical
• Discrete
• Count data
• Ratio-scaled

Disease severity classified as mild, moderate, or severe can be described as:

• Categorical
• Ordinal
• Discrete in the sense that only defined categories are observed

Clinical Trial Endpoints by Data Type

Clinical trials use many different endpoint structures.

The endpoint type often determines the broad family of statistical methods that should be considered.

Binary Outcomes and Common Methods

Binary outcomes are often analyzed using methods such as:

• Binomial confidence intervals
• One-sample proportion tests
• Two-sample proportion tests
• Fisher's exact test
• Chi-square tests
• Logistic regression
• Exact binomial methods

For example, if the endpoint is response versus non-response, logistic regression models the probability of response.

where \(p\) is the probability of the binary outcome.

Nominal Outcomes and Contingency Tables

Suppose a study records disease subtype:

The categories are nominal because there is no inherent ordering of the subtypes.

Methods for categorical association may include chi-square or exact tests, depending on the study design, sample size, and assumptions.

Ordinal Outcomes and Common Methods

Suppose pain severity is recorded as:

The ordering contains information.

Possible methods include:

• Mann–Whitney or Wilcoxon rank-sum methods for suitable two-group comparisons
• Wilcoxon signed-rank methods for suitable paired comparisons
• Ordinal logistic regression
• Proportional-odds models
• Other ordinal regression models

Continuous Outcomes and Common Methods

Continuous outcomes include measurements such as:

• Weight
• Blood pressure
• Biomarker concentration
• Cholesterol
• QT interval
• Change from baseline

Common methods include:

• t-tests
• ANOVA
• ANCOVA
• Linear regression
• Linear mixed-effects models
• Repeated-measures models

The appropriate method still depends on the design and assumptions. Being continuous does not automatically mean that a t-test is appropriate.

Count Outcomes and Common Methods

Suppose the primary endpoint is the number of migraine attacks during a 12-week treatment period.

The outcome is a count:

Potential methods include:

• Poisson regression
• Negative-binomial regression
• Zero-inflated models in appropriate settings
• Generalized linear mixed models for repeated counts

Exposure time may also matter.

For example, if patients are followed for different lengths of time, an incidence-rate analysis may incorporate an exposure offset.

where \(t_i\) represents the relevant exposure or observation time.

Time-to-Event Data

Time-to-event data record the time until an event occurs.

Examples include:

• Overall survival
• Progression-free survival
• Time to relapse
• Time to hospitalization
• Time to treatment discontinuation

These data have an important feature that distinguishes them from ordinary continuous measurements: censoring.

For example, suppose a patient has not experienced progression when the study ends.

We may know that:

but we do not know the patient's eventual progression time.

Common Time-to-Event Methods

Important methods include:

• Kaplan–Meier estimation
• Log-rank testing
• Cox proportional-hazards regression
• Parametric survival models
• Accelerated failure-time models
• Restricted mean survival time analysis

The survival function is:

It represents the probability of remaining event-free beyond time \(t\).

Longitudinal Data

Longitudinal data consist of observations collected from the same participant over time.

For example, a clinical trial might measure systolic blood pressure at:

• Baseline
• Week 2
• Week 4
• Week 8
• Week 12

The resulting data are not independent observations because measurements from the same patient are generally related.

A simplified structure might look like:

This is both continuous and longitudinal data.

Repeated-Measures Data

Repeated-measures data are a special case of correlated observations in which the same experimental unit is measured more than once.

Repeated measurements may be:

• Continuous
• Binary
• Ordinal
• Count-valued

For example, repeated pain assessments might be ordinal, while repeated biomarker measurements might be continuous.

The data type of the measurement still matters even though the measurements are repeated.

Cross-Sectional vs. Longitudinal Data

Independent vs. Paired Data

Another important distinction concerns whether observations are independent.

Two treatment groups may consist of different patients:

These are typically independent groups.

In contrast, if each patient has a measurement before and after treatment, the observations are paired:

The difference is calculated within patient.

This distinction affects whether an analysis should use paired or independent methods.

Data Type vs. Distribution

Data type and probability distribution are related but not identical concepts.

For example, a continuous variable could be approximately:

• Normal
• Log-normal
• Gamma
• Weibull
• Approximately symmetric without a simple named distribution

A count variable might follow:

• Poisson
• Negative binomial
• Another count distribution

A binary variable can be modeled using a Bernoulli distribution at the individual-observation level.

Transformation Does Not Necessarily Change the Scientific Data Type

Suppose drug concentration is measured on a ratio scale.

An investigator might analyze:

instead of \(C\).

The analysis variable is now the logarithm of concentration, but the underlying scientific measurement remains drug concentration.

Similarly, a continuous biomarker might be transformed using a logarithm, square root, or another transformation to improve model fit.

Why Log Transformation Is Common in Pharmacokinetics

Pharmacokinetic concentrations are often positive and right-skewed.

A logarithmic transformation can produce a more symmetric analysis scale:

This is one reason pharmacokinetic analyses frequently report geometric means and geometric mean ratios.

For example:

The transformation changes the analysis scale; it does not mean the original concentration variable was categorical or discrete.

Data Type and Summary Statistics

The appropriate descriptive summary depends on the structure of the data.

These are common conventions, not rigid rules.

The underlying distribution and scientific question should guide the summary.

Mean vs. Median

For a continuous variable, the arithmetic mean is:

The median is the middle observation after ordering the data.

The mean can be strongly affected by extreme observations, while the median is more resistant to outliers.

For example, consider hospital length of stay:

The distribution is right-skewed because one patient stayed much longer than the others.

A median and interquartile range may provide a more useful descriptive summary than the mean and standard deviation in such a setting.

Data Type and Graphical Displays

The type of data also influences the most informative visualization.

A Common Mistake: Treating IDs as Measurements

Patient identification numbers are numerical strings, but they are not numerical measurements.

For example:

Patient 1001
Patient 1002
Patient 1003

The fact that 1003 is numerically larger than 1001 has no scientific meaning.

Patient ID is therefore essentially a nominal identifier.

A Common Mistake: Treating Treatment Codes as Continuous

Suppose:

0 = Placebo
1 = Low dose
2 = High dose

If these values represent treatment categories, the coding itself does not make the variable continuous.

However, dose may also be represented by an actual numerical quantity such as:

Now the variable represents a quantitative dose.

The distinction is between a category label and a measured or assigned quantity.

A Common Mistake: Treating Ordinal Data as Continuous

Suppose a questionnaire records:

1 = Strongly disagree
2 = Disagree
3 = Neutral
4 = Agree
5 = Strongly agree

The categories have a meaningful order.

But the coding does not establish that the psychological distance between "Strongly disagree" and "Disagree" is exactly equal to the distance between "Agree" and "Strongly agree."

There are circumstances in which researchers analyze multi-item scales using methods designed for approximately continuous scores, particularly when the scale has many categories and appropriate measurement properties.

But this is a modeling decision, not something established merely by the presence of numbers 1 through 5.

Data Type and Regression Models

Regression models are often selected according to the outcome variable.

This table is a starting point, not a substitute for checking the study design, estimand, distribution, independence structure, and model assumptions.

The Outcome Usually Drives the Model Family

Suppose the predictor is age.

Age can appear in many different models.

For example:

• Age predicting response → logistic regression
• Age predicting a biomarker → linear regression
• Age predicting number of hospitalizations → count regression
• Age predicting survival → survival regression

The predictor being continuous does not determine the model by itself.

Data Type and Hypothesis Tests

The same clinical question can require different tests depending on the outcome.

Suppose two treatment groups are being compared.

Thus, "compare Drug A and Drug B" is not enough information to choose a statistical test.

You also need to know what is being measured and how the observations were collected.

A Worked Example: Classifying a Clinical Trial Dataset

Consider the following simplified clinical trial database.

Notice that the numerical value 58 in the Age column and the numerical value 3 in the Adverse Event Count column have very different statistical meanings.

Age is a measurement of a continuous quantity.

Adverse event count is a discrete event count.

Step 1: Identify What the Variable Represents

Before thinking about statistical software, ask:

Step 2: Identify the Study Structure

Data type alone is not enough.

Suppose the outcome is continuous.

A single measurement per patient might be analyzed differently from five measurements per patient.

Likewise, a binary outcome from independent groups differs from a binary outcome repeatedly measured on the same patient.

Data Type and Missing Data

Missingness can also interact with the type of data.

For a continuous outcome, missing data may occur for a laboratory measurement.

For a binary endpoint, the issue may be an unknown responder status.

For longitudinal data, some patients may have measurements at baseline and Week 4 but not Week 8.

The missing-data strategy should therefore be considered together with the endpoint definition and analysis model.

Data Type and Outliers

Outliers have different meanings depending on the variable.

A very large value for a continuous laboratory measurement may be an actual biological observation, a measurement error, or a data-entry error.

A count of 30 adverse events may be unusual but still entirely legitimate.

A categorical value outside the permitted categories may instead indicate a coding or data-management problem.

Data Type and Normality

A common misconception is: "continuous data should be normally distributed."

That is not generally true.

Continuous variables can have many different distributions.

Normality is an assumption of some statistical procedures or models, not a definition of continuous data.

For example, a continuous variable may be strongly right-skewed and still be perfectly valid continuous data.

Data Type and Parametric Methods

Parametric methods typically make assumptions about the distribution or conditional distribution of the data.

For example, a linear model may be appropriate for a continuous outcome when its assumptions are reasonably satisfied.

If the outcome is binary, however, ordinary linear regression may not be the natural primary model for the probability because predicted values can fall outside the interval \([0,1]\).

Logistic regression instead models the log odds:

Why Data Classification Matters for Sample Size

Sample-size calculations depend strongly on the endpoint type.

For example, sample size for a single proportion is fundamentally different from sample size for a continuous mean.

Similarly, sample size for a survival endpoint must account for event information and potentially censoring.

Data Type in Regulatory Clinical Trials

Clinical trials commonly contain multiple endpoint types within the same study.

For example, a Phase III trial may collect:

• A primary time-to-event endpoint
• Binary responder status
• Continuous laboratory measurements
• Ordinal adverse-event severity
• Count data for hospitalizations
• Repeated patient-reported outcomes

There is therefore rarely one statistical method that applies to every variable in the database.

The statistical analysis plan should define how each prespecified endpoint and important analysis variable will be handled.

A Practical Data Classification Decision Tree

Worked Example: Choosing the Analysis Family

Suppose a randomized clinical trial measures five outcomes.

The correct approach begins by identifying the endpoint structure before selecting a test.

Data Type Does Not Automatically Determine One Statistical Test

It is tempting to memorize rules such as:

Continuous → t-test
Categorical → chi-square
Ordinal → Wilcoxon
Time-to-event → log-rank

These shortcuts can be useful for learning, but they are incomplete.

The final method depends on additional factors:

• Study design
• Number of groups
• Independence
• Repeated measurements
• Distribution
• Sample size
• Censoring
• Missing data
• Covariates
• Target estimand
• Model assumptions

Common Data Types in Biostatistics

The Difference Between Data Type and Study Design

Data type describes the variable.

Study design describes how the observations were generated.

For example, a binary response can arise in:

• A single-arm Phase II trial
• A two-arm randomized trial
• A crossover study
• A longitudinal study
• A diagnostic accuracy study

The outcome is binary in all five cases, but the appropriate statistical analysis may differ.

The Difference Between Data Type and Estimand

The same outcome type can support different estimands.

For a binary endpoint, investigators might target:

• Risk difference
• Risk ratio
• Odds ratio
• Response probability

For a continuous endpoint, they might target:

• Mean difference
• Median difference
• Geometric mean ratio
• Change from baseline

For time-to-event outcomes, they might target:

• Hazard ratio
• Survival probability at a specified time
• Median survival
• Restricted mean survival time

Data Type and Baseline Covariates

Not every variable in a clinical trial is an endpoint.

Baseline covariates can have many different data types.

Regression models can incorporate these different predictor types using appropriate coding or functional forms.

Dummy Variables for Nominal Predictors

Suppose treatment has three categories:

Placebo
Drug A
Drug B

A regression model cannot generally insert the text labels directly into a numerical linear predictor.

Instead, indicator variables can be created.

For example, using placebo as the reference:

The model can then estimate treatment effects relative to placebo.

Ordinal Predictors Need Careful Coding

An ordinal predictor can sometimes be represented using:

• Indicator variables for each category
• A numeric score when a linear trend is scientifically justified
• Other ordered-effect parameterizations

These approaches make different assumptions.

For example, coding:

Mild     = 1
Moderate = 2
Severe   = 3

That assumption should be justified rather than made automatically.

Data Type and Missing Values

Missing data are not themselves a data type, but the consequences of missingness depend on the variable.

Examples include:

Importantly, a censored time-to-event observation is not necessarily the same thing as an ordinary missing observation.

For a censored patient, we often know that the event has not occurred through a particular time.

Censoring Is Information

Suppose a patient is followed for 18 months without progression.

We may not know the eventual progression time, but we do know:

That information contributes to survival analysis.

Simply deleting the patient would discard information and generally produce biased results.

Data Type and Distributional Assumptions

Different data types lead to different natural probability models.

These are modeling frameworks rather than rules that every dataset must obey.

Why Data Classification Is the First Step

Imagine being asked: "Which statistical test should I use?"

That question is incomplete.

A better sequence is:

Quick Reference: Data Types

Common Mistakes

1. Assuming numbers automatically mean numerical data. Patient IDs and treatment codes can contain numbers while remaining nominal variables.
2. Ignoring ordering in categorical data. Mild, moderate, and severe are not equivalent to three unrelated categories.
3. Assuming ordinal scores are automatically continuous. The numerical coding does not guarantee equal distances between categories.
4. Calling every numerical variable continuous. Event counts are discrete.
5. Treating time-to-event data as ordinary continuous data. Censoring requires survival-analysis methods.
6. Ignoring repeated measurements. Observations from the same patient are generally correlated.
7. Confusing data type with distribution. Continuous does not mean normal.
8. Choosing a test from the outcome type alone. Study design, independence, estimand, and other factors also matter.
9. Assuming one statistical method applies to the whole dataset. A clinical trial can contain binary, continuous, ordinal, count, and time-to-event endpoints simultaneously.

Practical Workflow for Biostatisticians

Worked Example Summary

Consider these common clinical variables:

The Most Important Concept

The most important lesson is that data classification is more than putting variables into "categorical" and "continuous" boxes.

A good biostatistical analysis considers several dimensions simultaneously.

• Is the variable categorical or numerical?
• If categorical, is it nominal or ordinal?
• If numerical, is it discrete or continuous?
• Is it a count?
• Is there a meaningful zero?
• Are observations independent?
• Are measurements repeated?
• Does the endpoint involve censoring?
• What quantity is the analysis intended to estimate?

Once these questions are answered, the appropriate statistical methods become much easier to identify.

References

Agresti, A. (2018). An Introduction to Categorical Data Analysis, 3rd ed. Wiley.
Agresti, A. (2010). Analysis of Ordinal Categorical Data, 2nd ed. Wiley.
Altman, D.G. (1991). Practical Statistics for Medical Research. Chapman & Hall.
Fisher, L.D. & van Belle, G. (1993). Biostatistics: A Methodology for the Health Sciences. Wiley.
Hosmer, D.W., Lemeshow, S. & Sturdivant, R.X. (2013). Applied Logistic Regression, 3rd ed. Wiley.
McCullagh, P. & Nelder, J.A. (1989). Generalized Linear Models, 2nd ed. Chapman & Hall.
Pinheiro, J.C. & Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS. Springer.
Therneau, T.M. & Grambsch, P.M. (2000). Modeling Survival Data: Extending the Cox Model. Springer.