The absolute risk reduction (ARR) is the difference in risk between two groups. The number needed to treat (NNT) is 1 divided by the ARR.
Glossary
Plain-language explanations of the statistical terms used on this site. Underlined words in the chooser and on method pages link here.
- Absolute risk reduction and NNT
- Adjusted analysis
An analysis that takes other variables into account, so the effect of the main factor is estimated with those variables held fixed.
- Bland-Altman limits of agreement
The range in which most differences between two methods fall: the mean difference plus or minus 1.96 times the SD of the differences.
- Bonferroni correction
A simple correction for multiple testing: divide the significance level by the number of tests.
- Categorical and binary variable
A categorical variable has categories without a natural order (blood group). A binary variable has two (yes or no).
- Causal diagram (DAG)
A drawing of what you think causes what. It helps to choose which variables to adjust for.
- Censoring
A patient's follow-up ended before the event happened, for example because the study ended or the patient was lost. You know the patient was event-free until then.
Do not drop censored patients and do not treat them as having had the event.
- Clustering
Patients grouped within wards, doctors or hospitals are more alike than unrelated patients. Use a mixed model or GEE.
- Cohen's kappa
Agreement between two raters beyond what chance would give. 0 means chance level, 1 means perfect agreement.
- Collinearity
Two or more predictors that are strongly related to each other, which makes their separate effects hard to estimate.
- Competing event
An event that prevents the event you study from happening, such as death before relapse.
- Confidence interval
A range of values that is compatible with your data. A 95% confidence interval is made so that, over many studies, 95% of such intervals contain the true value.
It shows direction, size and precision of an effect, which a p-value does not.
- Confounder
A factor that is related to both the exposure (or treatment) and the outcome, and so can distort the association between them.
Example: patients who smoke are older and also have more heart disease, so age confounds the link between smoking and heart disease. In a randomized trial, randomization takes care of confounding on average.
- Continuous variable
A measurement on a numeric scale, such as blood pressure or HbA1c.
- Covariate
An extra variable you include in a model, usually to adjust for it, such as age or sex.
A covariate can be a confounder, but it does not have to be.
- Effect size
How large an effect is, in meaningful units: a difference in means, an odds ratio, a hazard ratio. Report it with its confidence interval.
- Events per variable
The number of events (not patients) limits how many predictors a model for a yes/no or time-to-event outcome can hold reliably.
- GEE
Generalized estimating equations: a way to analyse correlated measurements that gives population-average effects.
- Hazard ratio
Compares how fast an event happens in two groups at any moment in time. A hazard ratio of 0.5 means the event rate is half as high.
- Histogram
A bar chart of how often values occur in ranges. It shows the shape of your data: symmetric, skewed, or with outliers.
- Independent observations
Each value comes from a different patient, and no value tells you anything about another.
Repeated measurements on one patient, two eyes of one patient, or patients from the same ward are not independent. Ignoring this makes confidence intervals too narrow and p-values too small.
- Intention-to-treat
Analysing patients in the groups they were randomized to, whatever treatment they actually received. It keeps the benefit of randomization.
- Interaction
The effect of one factor depends on the level of another. For example a treatment that works in men but not in women.
- Intraclass correlation (ICC)
A measure of agreement or reliability between measurements of the same quantity, from 0 to 1.
- Kaplan-Meier curve
A step curve that shows the probability of staying event-free over time, taking censoring into account.
- Log transformation
Taking the logarithm of each value. It often makes right-skewed data roughly normal. Results are back-transformed to ratios of geometric means.
- Mean and standard deviation
The mean is the average. The standard deviation (SD) tells how far values typically are from the mean. Use them for roughly symmetric data.
- Median and IQR
The median is the middle value. The interquartile range (IQR) is the range holding the middle half of the values. Use them for skewed data.
- Missing data
Values that were not recorded. How you handle them can change the result. Report how many are missing and how you dealt with them.
- Mixed model and random effect
A model that includes a random effect (for example per patient) to allow for correlated measurements.
- Monotone relationship
A relationship that keeps going one way: as one variable rises, the other either always rises or always falls. It can level off or curve, but it never turns around.
- Multiple testing
Every extra test you run raises the chance of at least one false positive. Test one prespecified main question, and correct when you test many.
Corrections include Bonferroni, Holm and Tukey, depending on the situation.
- Normal distribution
The symmetric, bell-shaped distribution that many tests assume. Most values are near the mean and few are far away.
Normal data is not a requirement for every test, and with larger samples the tests that assume it are fairly robust to mild skew.
- Null hypothesis
The starting assumption of a test, usually 'no difference' or 'no association'. A test asks whether your data are surprising if the null hypothesis were true.
- Odds ratio
Compares the odds of an outcome between two groups. An odds ratio of 2 means the odds are twice as high. With a common outcome it overstates the risk ratio.
Odds are the number of events divided by the number of non-events.
- Ordinal variable
A variable with ordered categories where the gaps are not necessarily equal, such as a pain score or tumour grade.
- Outcome
What you measure in every patient to answer your question, for example blood pressure, death or length of stay.
Also called the dependent variable or response.
- Outlier
A value that is far away from the rest. Check whether it is an error or a real, extreme patient before deciding what to do.
- Overdispersion
Counts that vary more than a Poisson model expects. It makes confidence intervals too narrow. Negative binomial regression allows for it.
- P-value
The probability of seeing a result at least as extreme as yours if there were really no effect. It is not the probability that the hypothesis is true, and it says nothing about the size of the effect.
Report the exact p-value together with the effect size and its confidence interval.
- Paired data
Every value in one group has a partner in the other: the same patient before and after, two eyes of one patient, or a matched case and control.
Use a paired test. It works on the differences within each pair.
- Parametric and non-parametric tests
Parametric tests (such as the t-test) compare means and assume a distribution. Non-parametric tests (such as Mann-Whitney) use ranks and assume less.
Non-parametric tests are not 'assumption-free'. They also need independent observations, and they answer a slightly different question.
- Power
The chance that a study finds an effect of a given size if it is really there. 80% is a common target.
Power depends on the sample size, the size of the effect, the variation in the data and the significance level.
- PPV and NPV
The positive predictive value is the proportion of positive tests that are right. The negative predictive value is the same for negative tests. Both depend on how common the condition is.
- Proportional hazards
The assumption of a Cox model that the hazard ratio is the same at every time point.
- Q-Q plot
A plot of your data against the values you would expect if they were normal. Points close to the straight line mean roughly normal data.
- Rank
The position of a value when all values are put in order, from smallest to largest. Rank-based tests use ranks instead of the values themselves.
- Rate ratio
Compares the number of events per unit of person-time between two groups, for example admissions per year.
- Reference category
The category that all other categories are compared with in a model, for example standard care.
- Regression
A model that describes how an outcome changes with one or more factors, holding the others fixed.
- Residuals
The differences between the observed values and the values the model predicts. Plots of residuals show whether the model assumptions hold.
- Risk ratio (relative risk)
The risk of an outcome in one group divided by the risk in another. A risk ratio of 2 means the risk is twice as high.
- ROC curve and AUC
A plot of sensitivity against 1 - specificity for every cut-off of a test. The area under the curve (AUC) summarises how well the test separates patients.
- Sample size
The number of patients you need to answer your question with enough power. Work it out before you collect data.
- Sensitivity and specificity
Sensitivity is the proportion of patients with the condition that the test finds. Specificity is the proportion of patients without it that the test correctly clears.
- Significance level (alpha)
The cut-off for the p-value below which you call a result statistically significant. Usually 0.05, chosen before you look at the data.
- Skewed distribution
A distribution that is not symmetric: it has a long tail on one side, such as length of stay or costs.
A log transformation often makes right-skewed data more symmetric.
- Stepwise selection
Letting software add or remove predictors by p-value. It overfits and biases results. Choose predictors on clinical grounds.
- Type I and type II error
A type I error is a false positive: finding an effect that is not there. A type II error is a false negative: missing an effect that is there.
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