Index (en)

A statistical model in survival analysis that asserts that the effect of the study factors (e.g. the intervention of interest) on the hazard rate (the risk of occurrence of an event, such as death, at a point in time) in the study population is multiplicative and does not change over time.

A model in which the combined effect of several independent factors is the sum of the isolated effects of each factor.

Note: For example, if a factor X increases a risk by a in the absence of Y, and if a second factor Y increases the risk by b in the absence of X, the combined effect of the two factors is a + b.

(Related concept: multiplicative model)

The probability of rejecting the null hypothesis when it is true.

Note 1: The alpha level is usually set at a probability of 0.05, but other commonly used levels are 0.1 and 0.01.

Note 2: Related concepts include hypothesis testing and “type 1 error”.

See mean.

A statistical method that explicitly includes a prior probability distribution based on a subjective opinion or objective evidence, such as the results of previous research.

Note: Bayesian analysis uses Bayes' theorem to update the prior probability distribution in light of the results of a study, in order to produce a posterior distribution. It can be used in a single study or in a meta-analysis. Statistical inference (point estimates, confidence intervals, etc.) is based on the posterior distribution. The posterior distribution can also be used as the prior distribution for the next study. This approach is controversial when it depends on opinions, which may vary. However, its use has become commonplace in economic evaluation, as it allows the creation of complex models with different evidence sources and the determination of uncertainty.

In hypothesis testing, the probability of a Type II error, i.e. the probability of concluding incorrectly that a null hypothesis is true.

Note: For example, β could be the probability of concluding that an intervention is not effective when it has a true effect. (1-β) is the statistical power of a test allowing for rejection of a null hypothesis that is truly false (e.g. detecting the effect of an intervention that truly exists).

(Related concepts: hypothesis testing, statistical power)

Data that can have only two values, such as dead or alive, smoker or non-smoker, present or absent, or man or woman.

Note: This is a specific case of a categorical data, where the number of categories is equal to 2.

Syn.: dichotomous data.

Data that can be classified into two or more categories.

Note: When there is an order to the categories, the term used is ordinal data (e.g. stages of cancer or level of education). When there is no order, the term used is nominal data (e.g. blood group, civil status or ethnic origin). There is no mathematical relationship between the values (e.g. a person with Stage IV cancer is not twice as sick as a person with Stage II cancer).

A range of values below and above the point estimate that has a given probability of including the true value of a given parameter, such as a treatment effect.

Note: The confidence interval is the area of uncertainty for the estimating of a parameter. The use of this interval reflects the fact that a study provides one estimate of a parameter, out of the many estimates that would be possible if the study were repeated several times. If an X% CI is constructed for each repetition, X% of the intervals will contain the true value of the parameter. Investigators typically use confidence intervals of 90%, 95% or 99%. Thus, a 95% confidence interval indicates that there is a 95% probability that the confidence interval calculated from a particular study includes the true value of the parameter. If the interval includes a null value (a difference in means of 0, an odds ratio or a relative risk of 1, or a correlation coefficient of 0, for example), the null hypothesis cannot be rejected. A narrow confidence interval around a point estimate indicates a more precise estimate than a wide confidence interval.

A meta-analysis based on Bayesian statistics for combining results of multiple studies that have different research designs, such as randomized controlled trials and observational studies, by adjusting the results of each individual study for its methodological biases before combining the results into a probability distribution for the parameter(s) of interest.

A table presenting a cross-classification of categorical data such that the categories of one characteristic are indicated horizontally (in rows) and the categories of another characteristic are indicated vertically (in columns).

Note: Each cell of the table will indicate the number or proportion of individuals who have both the characteristic on its row and in its column. The simplest contingency table is the fourfold, or 2x2 table, which is used in clinical trials, for example, to compare dichotomous outcomes for two groups.

Numerical data with a potentially infinite number of possible values on a continuum.

Note: Height, weight and blood pressure are examples of continuous data.

A number between -1 and +1 that expresses the strength of the linear association between two numerical variables.

Note: In a sample, the estimate is noted as r. A correlation coefficient of 0 indicates that there is no linear relationship between the two variables. A correlation coefficient of +1 indicates that there is a perfect positive linear relationship, and a correlation coefficient of -1 indicates that there is a perfect negative linear relationship.

Note: It cannot be concluded from the correlation that there is a cause-and-effect relationship.

A range of values around the central estimate of a parameter, constructed using Bayesian methods.

Note: The credible interval is the Bayesian equivalent of a confidence interval, but the interpretation of it is slightly different: the probability that a parameter is in an X% credible interval is X/100. For example, a 95% credible interval (0.82-1.36) for an odds ratio for mortality means that there is a 0.95 probability that the odds ratio in the population is between 0.82 and 1.36.

A meta-analysis presenting the gradual accumulation of the results of studies as the studies are added.

Note: In a cumulative meta-analysis graph, each horizontal line represents the integration of the preceding studies, rather than the results of a single study. The studies are integrated one at a time and in a specified order (e.g. according to the date of publication or quality).

The number of independent comparisons that can be made between the members of a sample of patients.

Note: This concept refers to the number of independent contributions to a sampling distribution (such as chi-square distribution). In a contingency table, it is the number of cells that can be filled freely, without changing the totals. In a table with i lines and j columns, ddl = (i – 1)*(j - 1) (for example, in a 2 x 2 table comparing two groups for a dichotomous outcome, such as death, the chi-square distribution associated with it has one degree of freedom).

See binary data.

A set of data is said to be discrete if the values/observations belonging to it are distinct and separate, i.e. they can be counted (1,2,3,....).

Note 1: Examples include the number of patients in a doctor’s surgery; sex (male, female); blood group (O, A, B, AB).

Note 2: Discrete data is the counterfactual to continuous data

In statistics, a mathematical function describing the frequency of each value of a variable.

A dimensionless measure of the degree of presence of a phenomenon in the population of interest.

Note: In the case of continuous variables, it is generally defined as the difference in means between the experimental and control groups, divided by the standard deviation of the control group or both groups. When different scales (pain assessment, for example) are used to measure an outcome, they become comparable.

Note: This measure is used to determine the size of a sample.

In a study, the relationship between the outcome observed when an intervention is applied and the outcome observed in a control group.

Note: This relationship may be expressed as a number needed to treat, odds ratio, risk difference, relative risk, standardised mean difference or weighted mean difference.

(Related concept: treatment effect)

The proportion of the members of a group in whom an event is observed over a specified period of time.

Note: If an event (e.g. a stroke) is observed in 32 subjects out of a group of 100 monitored over one year, the stroke rate is 0.32 a year.

In hypothesis testing, an error that occurs when it is incorrectly concluded that a null hypothesis is true.

Note: For example, a Type II error is made if no difference is detected between the outcomes in an experimental group and those in a control group when in fact such a difference exists. The probability of making this type of error is designated as beta (β).

Syn.: Type II error.

In hypothesis testing, an error that occurs when it is incorrectly concluded that a null hypothesis is false.

Note: For example, a Type I error is made if a difference is detected between the outcomes in an experimental group and those in a control group when in fact such a difference does not exist. The probability of making this type of error is designed as alpha (α).

Syn.: Type I error.

In a meta-analysis, a statistical model that takes only within-study variability into account in assessment of the degree of uncertainty (confidence interval) of the combined effect from the studies.

Note: The fixed-effect model assumes that the units analysed are the units of interest and, consequently, that they make up the population of units. In such a model, variation between the estimates of effect from each study (heterogeneity) does not affect the confidence interval.

(Related concepts: random effects model, Peto method)

Alternative spelling: fixed effect model

A scatter diagram in which each point represents a study, relating the estimate of effect and the sample size (or another indicator of the precision of the study).

Note: In the absence of publication bias, the scatter diagram will form an inverted funnel. A hole in the lower left corner of the funnel indicates the presence of publication bias.

A method of statistical inference for evaluating the plausibility of the null hypothesis in the light of the observed data.

Note: The null hypothesis is assumed to be true at the outset, but, if that assumption proves wrong when the observed data are examined, it is rejected in favour of the alternative hypothesis (negative of the null hypothesis).

A measure of the degree of agreement between two measures of the same categorical variable over and above the agreement that is due to chance alone.

Note: The agreement between two raters or between two measurement times for one rater can be measured.

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Deeks JJ. Systematic reviews of evaluations of diagnostic and screening tests. In: Egger M, Davey Smith G, Altman DG, editors. Systematic reviews in health care: meta-analysis in context. 2nd ed. London: BMJ Books; 2001. p. 248-82.

Reference details:

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Porta M (ed). A Dictionary of Epidemiology. Sixth edition. A Handbook for the International Epidemiological Association. Oxford: Oxford University Press, 2014

Reference details:

A measure of the strength of a diagnostic test to distinguish between persons who do or do not have a target condition.

Note 1: A positive likelihood ratio compares the probability of a positive test result in persons with the disease with the probability of a positive test result in persons without the disease. A negative likelihood ratio compares the probability of a negative test result in persons without the disease with the probability of a negative test result in persons with the disease.
Note 2: Positive likelihood ratios greater than 10 or negative likelihood ratios less than 0.1 are sometimes judged to provide convincing diagnostic evidence.
Note 3: A positive likelihood ratio is calculated as: sensitivity ÷ (1 minus specificity). A negative likelihood ratio is calculated as: (1 minus sensitivity) ÷ specificity.
Note 4: In statistics, an alternative meaning of the likelihood ratio exists. It is the ratio of the values of the likelihood function at two different parameter values or under two different data models. See also likelihood ratio test.

A natural logarithm used in logistic models and graphical representations of odds ratios.

A statistical regression model that estimates the probability of a value of a dichotomous variable on the basis of multiple predictor variables.

A subjective evaluation of the size of the estimated effect in a clinical setting.

A chi-square test for taking categorical confounding variables into account when doing a weighted sum of the associations in each of the categories, called strata.

Note: In meta-analyses, the strata are the various studies included.

A measure of central tendency calculated by dividing the sum of all the observed values by the number of observations.

Note: The word mean used alone generally refers to the arithmetic mean.

Syn.: arithmetic mean

A measure of central tendency corresponding to the value below which 50% of the observations are found.

Note: The median is the midpoint of observations ranked in ascending order. It can provide a better estimate of the mean when extreme values cause asymmetry in the distribution of the observations.

In a meta-analysis, a regression model for studying the relationship between the different study characteristics and the estimation of the effect observed in these studies.

Note: The study characteristics are, for example, the method of distribution into the groups, the type of blinding, the initial risk and the intervention administration schedule.

The proportion of deaths in a given population within a specified period (usually one year).

Note: The rate is often expressed as a number per 100,000, to facilitate interpretation (e.g. 18.3 deaths per year per 100,000 persons).

See regression analysis.

Several statistical tests done on the same observations.

Note: In a study, the sample size and the alpha level are set according to the principle that a single null hypothesis will be tested at the end of the study, once all the data have been gathered. If more than one statistical test is undertaken, e.g. pairwise comparisons of several interventions, or tests on different variables, at different timepoints or on different sub-groups, there will be an increase in the planned overall Type I error (alpha) probability. Some statistical methods are proposed to take multiple testing into account, but they are controversial.

A model in which the combined effect of two or more factors is the product of the isolated effects of each factor.

Note: For example, if a factor X multiplies a risk by a in the absence of Y, and if a second factor Y multiplies the risk by b in the absence of X, the combined effect of the two factors will be a x b.

(Related concept: additive model)

In hypothesis testing, a proposal that there is no association between two variables or no difference between two values.

Note: For example, the null hypothesis could indicate that an intervention has no effect, i.e. that there is no true difference between the results obtained in the experimental group and the control group.

Data classified into two or more categories where there is a natural order to the categories, such as non-smokers, ex-smokers, light smokers and heavy smokers.

Syn.: ordered categorical data

In hypothesis testing, the probability that a parameter to be tested has a value as extreme or more extreme than the value that would be observed if the null hypothesis were true.

Note: If the p value associated with the statistical test is equal to or greater than the alpha level that was determined (0.01 or 0.05, for example), this means that the association or difference observed may be due to chance and that the null hypothesis cannot be rejected. However, if the p value is less than the alpha level that was determined, the association or difference is statistically significant and the null hypothesis is rejected.

Alternate spelling: p-value

In a meta-analysis, a method used to combine odds ratios.

Note: The calculations are straightforward and easy to interpret, but the result may sometimes differ substantially from that obtained using other methods. The Peto method is based on a fixed-effect model.

A numerical value obtained in a sample and considered the best estimate of the population from which the sample is taken.

Note: For example, x and s are point estimates of µ and σ, which represent the mean and the standard deviation. A confidence interval is typically constructed around the point estimate.

(Related concept: confidence interval)

The probability of a hypothesis test correctly detecting a real effect.

Note 1: Power is also the probability of avoiding a Type II error and therefore corresponds to (1 - β).

Note 2: A power analysis may be performed to determine whether a sample size will have sufficient power to reject a false null hypothesis, and so find the effect described by the alternative hypothesis.

Note 3: Related terms include hypothesis testing, beta (β), and statistical power.

1) A quality of a point estimate obtained from a set of observations having a small variance.

Note: A narrow confidence interval around a point estimate indicates a more precise estimate of effect than a wide confidence interval. Note that a precise estimate is not necessarily accurate.

2) A measure of the likelihood of random errors in the results of a study, meta-analysis or measurement.

Note: In a meta-analysis, the weight given to the results of each study in the overall estimate of the effect of an intervention is often based on the precision of each study, which is estimated using the inverse of the variance of the estimate of effect or the sample size.

3) In a literature search, the number of relevant citations, divided by the total number of citations retrieved, i.e. the proportion of studies meeting the inclusion criteria for a clinical trials register or a literature review.

(Related concept: accuracy)

A mathematical function describing the probabilities associated with each value.

Note: For example, normal, chi square, binomial or Poisson distribution.

In a meta-analysis, a statistical model in which both the within-study variance and the between-studies variances are included in the assessment of the degree of uncertainty (confidence interval) of the combined effect of the studies.

Note: If there is significant heterogeneity among the results of the studies included in a meta-analysis, a random effects model will give wider confidence intervals than a fixed-effect model.

(Related concepts: fixed-effect model)

A deviation due to chance between a point estimate and the value of the estimated parameter.

Note: Random error leads to about the same number of results greater than the true value sought and results lower than this value. It is independent of the effects of systematic biases. In general, the larger the mean sample size is, the smaller the random error is.

A method of randomization that ensures that, at any point in a trial, an equal number of subjects have been allocated to each comparison group.

Note: Permuted blocks are often used in combination with stratified randomization.

See ROC curve.

A method consisting of selecting a mathematical model (linear or logistic regression, for example) that explains the data to describe or predict the effect of one or more independent variables X on a dependent variable Y.

Note: The terms are used as follows: linear regression when the variable Y is continuous, logistic regression when Y is a dichotomous variable, simple regression when there is a single variable X, and multiple regression when there are several variables X.

In the evaluation of a diagnostic or screening test, a graphical depiction of the relationship between the true positive ratio (sensitivity) and the false positive ratio (1 - specificity) for various positivity cut-off points of the test.

Note: The area under the ROC curve is an expression of a test’s performance independent of the patient population and can be used to compare several tests.

See random error.

The difference between two means, divided by an estimate of the within-group standard deviation.

Note: When a continuous variable (such as pain) is measured in a variety of ways across studies (using different scales), it may prove impossible to compare or combine the study results in a meta-analysis. If the effects are expressed as a standardised value, the results can be combined, since they are no longer expressed as units of measurement. Standardised mean differences are sometimes referred to as a “d index.”*

*Concept introduced by J. Cohen (1988).

Alternative spelling: standardized mean difference (SMD)

See power.

In hypothesis testing, a conclusion drawn when the null hypothesis is rejected, i.e. when the p-value is below the pre-determined alpha level.

(Related concept: p-value)

See hypothesis testing.

In a systematic review of studies on diagnostic or screening tests, a graphical depiction of the relationship between the true positive ratio (sensitivity) and the false positive ratio (1 - specificity) in all of the individual studies on a given test.

Note: A regression line can be fitted through these points.

See alpha.

See beta.

A factor that can have different values.

Note: The values measured in a study are data.

A measure of the variation shown by a set of observations, defined by the sum of the squares of deviations from the mean, divided by the number of degrees of freedom in the set of observations.

An extension of least squares regression used when there is heterogeneity in the variances or dependence between the observations.

Note: This method is often used in meta-regression, and the weights then correspond to the precision of each study’s estimate of effect.

In a meta-analysis, when study results measured using the same scale are being combined, the difference between two means, weighted by the precision of the study.

Note: The precision of the study’s estimate of effect may, for example, correspond to the inverse of the variance.

(Related concept: standardised mean difference)