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Appendix B

Glossary of Statistical and Clinical Trials Terms

Acceptance region The set of values of a test statistic for which the null hypothesis is not rejected.

Acceptance sampling A sampling method by which the sample is taken from groups or batches as they pass a specified time point, e.g., age, followed by sampling of individuals within the sampled groups.

Acquired immunodeficiency syndrome (AIDS) The late clinical stage of infection with human immunodeficiency virus (HIV), recognized as a distinct syndrome in 1981. The surveillance definition includes HIV-infected persons who have less than 200 CD4 + T lymphocytes per μL or a CD4 + T lymphocyte percentage of total lymphocytes of less than 14 percent, accompanied by any of 26 clinical conditions (e.g., opportunistic infection, Kaposi's sarcoma, wasting syndrome).

Adaptive cluster sampling A procedure in which an initial set of subjects is selected by a sampling procedure and, whenever the variable of interest of a selected subject satisfies a given criterion, additional subjects whose values are in the neighborhood of those for that subject are added to the sample.

Adaptive sampling A sampling procedure in which the selection process depends on the observed values of some variables of interest.

Additive effect A term used when the effect of administering two treatments together is the sum of their separate effects.



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Page 130 Appendix B Glossary of Statistical and Clinical Trials Terms Acceptance region The set of values of a test statistic for which the null hypothesis is not rejected. Acceptance sampling A sampling method by which the sample is taken from groups or batches as they pass a specified time point, e.g., age, followed by sampling of individuals within the sampled groups. Acquired immunodeficiency syndrome (AIDS) The late clinical stage of infection with human immunodeficiency virus (HIV), recognized as a distinct syndrome in 1981. The surveillance definition includes HIV-infected persons who have less than 200 CD4 + T lymphocytes per μL or a CD4 + T lymphocyte percentage of total lymphocytes of less than 14 percent, accompanied by any of 26 clinical conditions (e.g., opportunistic infection, Kaposi's sarcoma, wasting syndrome). Adaptive cluster sampling A procedure in which an initial set of subjects is selected by a sampling procedure and, whenever the variable of interest of a selected subject satisfies a given criterion, additional subjects whose values are in the neighborhood of those for that subject are added to the sample. Adaptive sampling A sampling procedure in which the selection process depends on the observed values of some variables of interest. Additive effect A term used when the effect of administering two treatments together is the sum of their separate effects.

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Page 131 Additive model A model in which the combined effect of several factors is the sum of the effects that would be produced by each of the factors in the absence of the others. Adjustment A procedure for summarization of a statistical measure in which the effects of differences in composition of the population being compared have been minimized by statistical methods. Examples are adjustment by regression analysis and by standardization. See standardization. Adverse event An undesirable or unwanted consequence experienced by a subject during a clinical trial irrespective of the relationship to the study treatment. Age standardization A procedure for adjusting rates, e.g., death rates, designed to minimize the effects of differences in age composition when comparing rates for different populations. Algorithm Any systematic process that consists of an ordered sequence of steps in which each step depends on the outcome of the previous one. Algorithm, clinical An explicit description of steps to be taken in patient care in specified circumstances. Alpha (α) The probability of a Type I error. The value of a is usually 0.05. See significance level. Alternative hypothesis The hypothesis against which the null hypothesis is tested. Analysis of covariance (ANCOVA) An extension of the analysis of variance that allows consideration of the possible effects of covariates on the response variable, in addition to the effects of the factor or treatment variables. The covariates are assumed to be unaffected by treatments, and in general, their relationship to the response is assumed to be linear. Analysis of variance (ANOVA) A statistical technique that isolates and assesses the contributions of categorical independent variables to variations in the mean value of a continuous dependent variable. The total variance of a set of observations are partitioned according to different factors, e.g., sex, age, treatment groups, and compared by way of F tests. Differences between means can then be assessed. Arc sin transformation A transformation of the form 2 arc sin ~ enlarge ~ , used to stabilize the variance of a binomial random variable. Area sampling A sampling method in which a geographical region is subdivided into smaller areas (counties, villages, city blocks, etc.), some of which are selected at random, and the chosen areas are then subsampled or completely surveyed. See cluster sampling. Area under curve (AUC) A useful way of summarizing the information from

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Page 132 a series of measurements made on an individual over time or for a doseresponse curve. Calculated by adding the areas under the curve between each pair of consecutive observations, using for example, the trapezium rule. Arithmetic mean The sum of all the values in a set of measurements divided by the number of values in the set. Assigned treatment The treatment designated to be given to a patient in a clinical trial as indicated at the time of enrollment. Association Statistical dependence between two or more events, characteristics, or other variables. Most often applied in the context of binary variables forming a two-by-two contingency table. A positive association between two variables exists when the occurrence of higher values of a variable is associated with the occurrence of higher values of another variable. A negative association exists when the occurrence of higher values of one variable is associated with lower values of the other variable. Assumptions The conditions under which statistical techniques give valid results. Attack rate The cumulative incidence of a disease or condition in a particular group, during a limited period of time, or under special circumstances such as an epidemic. Attributable risk A measure of the association between exposure to a particular factor and the risk of a particular outcome, calculated as: ~ enlarge ~ incidence rate among exposed − incidence rate among unexposed/incidence rate among exposed Attrition The loss of subjects over the period of a longitudinal study. See missing values. Average An average value represents or summarizes the relevant features of a set of values, and in this sense the term includes the median and the mode. Balanced design An experimental design in which the same number of observations is taken for each combination of the experimental factors. Bar chart A graphical representation for displaying discrete data organized in such a way that each observation can fall into one and only one category of the variable. Frequencies are listed along one axis, and categories of the variable are listed along the other axis. The frequencies of each group of observations are represented by the lengths of the corresponding bars. See histogram. Baseline data A set of data collected at the beginning of a study.

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Page 133 Bathtub curve The shape taken by the hazard rate for the event of death in humans. It is relatively high during the first year of life, decreases fairly soon to a minimum, and begins to climb again sometime around ages 45 to 50. Bayesian confidence interval An interval of a posterior distribution such that the density at any point inside the interval is greater than the density at any point outside. For any probability level, there is generally only one such interval, which is often known as the highest posterior density region. Bayesian inference Statistical inference based on Bayes's theorem. The focus of the Bayesian approach is the probability distribution of any unknowns, given available information. The process deals with probabilities of hypotheses and probability distributions of parameters, which are not taken into account in classical statistical inference. Bayes's theorem A theorem in probability theory named after Thomas Bayes (1702–1761), an English clergyman and mathematician. It is a procedure for revising and updating the probability of some event in the light of new evidence. In its simplest form, the theorem is written in terms of conditional probabilities as: ~ enlarge ~ where P(A|B) denotes the conditional probability of event A conditional on event B. The overall probability of an event among a population before knowing the presence or absence of new evidence is called prior probability. The updated probability of the event after receiving new information is called posterior probability. Bell-shaped distribution A probability distribution having the overall shape of a vertical cross-section of a bell. Examples are normal distribution and Student's t distribution. Benefit-cost ratio The ratio of net present value of measurable benefits to costs. Calculation of a benefit-cost ratio is used to determine the economic feasibility or success of a program. Beta (b) The probability of a Type II error. Bias Deviation of results or inferences from the truth or processes leading to such a deviation. Any trend in the collection, analysis, interpretation, publication, or review of data that can lead to conclusions that are systematically different from the truth. Statistical bias occurs when the extent to which the statistical method used in a study does not estimate the

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Page 134 quantity thought to be estimated or does not test the hypothesis to be tested. Bimodal distribution A probability distribution or a frequency distribution with two modes. Binary sequence A sequence whose elements take one of only two possible values, usually denoted 0 or 1. Binary variable A variable having only two possible values, usually labeled 0 or 1. Data involving this type of variable often require specialized statistical techniques such as logistic regression. Binomial distribution The probability distribution of the number of occurrences of a binary event in a sample of n independent observations. The distribution is associated with two mutually exclusive outcomes, e.g., death or survival, success or failure. Bioassay The quantitative evaluation of the potency of a substance by assessing its effects on tissues, cells, live experimental animals, or humans. Bioequivalence The degree to which clinically important outcomes of treatment by a new preparation resemble those of a previously established preparation. Bioequivalence trials Trials carried out to compare two or more formulations of a drug containing the same active ingredient to determine whether the different formulations give rise to comparable levels in blood. Biological efficacy The effect of treatment for all persons who receive the therapeutic agent to which they were assigned. It measures the biological action of a treatment among compliant persons. Biological plausibility The criterion that an observed, presumably or putatively causal association fits previously existing biological or medical knowledge. Biometry The application of statistical methods to the study of numerical data on the basis of observations of biological phenomena. Biostatistics The application of statistical methods to biological and medical problems. Biplots A graphical display of multivariate data designed to show any structure, pattern, or relationship between variables. Bit A unit of information consisting of one binary digit. Bivariate data Data in which the subjects each have measurements on two variables. Bivariate distribution The joint distribution of two random variables, x and y.

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Page 135 Blinding A procedure used in clinical trials to avoid the possible bias that might be introduced if the patient or doctor, or both, knew which treatment the patient would be receiving. A trial is double blind if both patient and doctor are not aware of treatment given; if either the doctor or the patient is not aware of treatment given, the trial is single blind. Also called masking. Block A term used in experimental design to refer to a homogeneous grouping of experimental units designed to enable the experimenter to isolate and, if necessary, eliminate variability due to extraneous causes. Block randomization A random allocation procedure used to keep the numbers of subjects in the different groups of a clinical trial closely balanced at all times. Blot, Western, Northern, Southern Varieties of tests using electrophoresis, nucleic acid base pairing, or protein-antibody interaction to detect and identify DNA or RNA in samples. The Southern blot is used to identify a specific segment of DNA in a sample. The Northern blot detects and identifies samples of RNA. The Western blot is widely used in a test for detection of human immunodeficiency virus infection. Bootstrap A data-based simulation method for statistical inference that can be used to study the variability of estimated characteristics of the probability distribution of a set of observations and provide confidence intervals for parameters in situations in which these are difficult or impossible to derive in the usual way. Bonferroni correction A procedure for guarding against an increase in the Type I error when performing multiple significance tests. To maintain the Type I error at some selected value, a, each of the m tests to be performed is judged against a significance level, a/m. This method is acceptable for a small number of simultaneous tests to be performed (up to five). Causality The relating of causes to the effects that they produce. A cause is termed “necessary” when it must always precede an effect. This effect need not be the sole result of the one cause. A cause is termed “sufficient” when it inevitably initiates or produces an effect. Any given cause may be necessary, sufficient, neither necessary nor sufficient, or both necessary and sufficient. Censored observation Observation with an unknown value due to the occurrence of an event (e.g., death, loss to follow-up, or termination of study) before the occurrence of the event of interest in the study.

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Page 136 Central limit theorem The tendency for the sampling distribution of means to be a normal (Gaussian) distribution, even if the data do not have a Gaussian distribution, for sufficiently large numbers of subjects. Central range The range within which the central 90 percent of values of a set of observations lie. Central tendency A property of the distribution of a variable usually measured by statistics such as the mean, median, and mode. Chimerism In genetics, the presence in an individual of cells of different origin, such as of blood cells derived from a dizygotic cotwin. Chi-square distribution The probability distribution of the sum of squares of a number of independent standard normal variables. Chi-square test Any statistical test based on comparison of a test statistic to a chi-square distribution. The most common chi-square tests (e.g., the Mantel-Haenszel and Pearson chi-square tests) are used to detect whether two or more population distributions differ from one another. These tests usually involve counts of data and may involve comparison of samples from the distribution under study or comparison of a sample to a theoretically expected distribution. Chi-square test for trend A test applied to a two-dimensional contingency table in which one variable has two categories and the other has k ordered categories to assess whether there is a difference in the trend of the proportions in the two groups. Clinical decision analysis A procedure designed to provide insight into the structure of a clinical problem and to identify the main determinants of diagnostic and therapeutic choice. This procedure is useful to small numbers of clinical cases, even to a single patient (see n-of-1 study). The procedure has four stages: 1. Definition of the clinical problem and structuring it as a decision tree. This includes description of the patient, of the possible diagnostic and therapeutic actions, and of the possible outcomes after treatment. 2. Estimation of probabilities for diagnostic and therapeutic outcomes. 3. Performance of the requisite computations for determination of the preferred course of action. 4. Presentation of the results of the analysis in a clinically useful way. Clinical epidemiology Epidemiological study conducted in a clinical setting, usually by clinicians, with patients as the subjects of study. It uses the

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Page 137 information from classic epidemiology to aid decision making about identified cases of disease. Clinical trial A prospective study that involves human subjects, designed to determine the effectiveness of a treatment, a surgical procedure, or a therapeutic regimen administered to patients with a specific disease. Clinical trials have four phases: Phase I Safety and pharmacologic profiles. This involves the initial introduction of a candidate vaccine or drug into a human population to determine its safety and mode of action. In drug trials, this phase may include studies of dose and route of administration. Phase I trials usually involve less than 100 healthy volunteers. Phase II Pilot efficacy studies. This initial trial aims to examine efficacy in about 200 to 500 volunteers. The focus of vaccine trials is immunogenicity, whereas with drugs the focus is on the demonstration of safety and efficacy in comparison with those of other existing regimens. Often, subjects are randomly allocated to study and control groups. Phase III Extensive clinical trial. This phase aims to complete assessment of safety and efficacy. It involves large numbers, possibly thousands, of volunteers from one center or many centers (a multicenter trial), usually with random allocation to study and control groups. Phase IV This phase is conducted after the national drug registration authority (the Food and Drug Administration in the United States) has approved the drug for distribution or marketing. The trial is designed to determine a specific pharmacological effect or the effects of long-term use or to establish the incidence of adverse reactions. Ethical review is required in phase IV trials. Clinical versus statistical significance The distinction between results in terms of their possible clinical importance rather than simply in terms of their statistical significance. For example, very small differences that have little or no clinical importance may turn out to be statistically significant. The implications of any finding in a medical investigation must be judged on both clinical and statistical grounds. Clinimetrics The study of indices and rating scales used to describe or measure symptoms, physical signs, and other clinical phenomena in clinical medicine. Closed sequential design See sequential analysis. Cluster analysis A set of statistical methods for constructing a sensible and

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Page 138 informative classification of an initially unclassified set of data using the variable values observed on each individual or item. Cluster sampling A sampling method in which each unit (cluster) selected is a group of persons (all persons in a city block, a family, a school, or a hospital) rather than an individual. Code of conduct A formal statement of desirable conduct that research workers or practitioners are expected to honor. Examples are the Hippocratic Oath, the Nuremberg Code, and the Helsinki Declaration. Coefficient of concordance A measure of the agreement among several rankings or categories. Coefficient of determination The square of the correlation coefficient between two variables. It gives the proportion of the variation in one variable that is accounted for by the other. Coefficient of variation A measure of spread for a set of data, defined as 100 x standard deviation / mean. Originally proposed as a way of comparing the variability in different distributions but found to be sensitive to errors in the mean. Collinearity Very high correlation between variables. See multicollinearity. Comorbidity A disease(s) that coexist(s) in a study participant in addition to the index condition that is the subject of study. Conditional probability The probability that event A occurs given the outcome of some other event, event B; usually written P(A|B). Conditional probabilities obey all the axioms of probability theory. See Bayes's theorem. Confidence interval The computed interval with a given probability, e.g., 95 percent, that the true value of a variable such as a mean, proportion, or rate is contained within the interval. Confidence limits The upper and lower boundaries of the confidence interval. Confidence profile method A method of meta-analysis that uses a set of quantitative techniques that include parameters, functions, and prior distributions (in a Bayesian application). Its goal is to use evidence to derive maximum likelihood estimates and covariances (in a non-Bayesian application) or joint probability distributions (in a Bayesian application) for parameters of interest. Distributions and estimates can be used to make decisions about interventions or calculations of other parameters or to plan research to gather additional information about any parameter. Confounding A process observed in some factorial designs in which a measure of the effect of an exposure on risk is distorted because of the

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Page 139 association of the exposure with some other factor(s) that influences the outcome under study. Confounding variable A variable that can cause or prevent the outcome of interest, is not an intermediate variable, and is associated with the factor under investigation. Contingency table A tabular cross-classification of data such that subcategories of one characteristic are indicated horizontally (in rows) and subcategories of another characteristic are indicated vertically (in columns). The simplest contingency table is the fourfold or two-by-two table analyzed by using the chi-square statistic. Three- and higher-dimensional tables are analyzed by using log-linear models. Continual reassessment method An approach that applies Bayesian inference to determine the maximum tolerated dose in a phase I trial. The method begins by assuming a logistic regression model for the dosetoxicity relationship and a prior distribution for the parameters. After each patient's toxicity result becomes available, the posterior distribution of the parameters is recomputed and used to estimate the probability of toxicity at each of a series of dose levels. Control group Subjects with whom comparison is made in a case-control study, randomized controlled trial, or some other variety of epidemiological study. Controlled trial A phase III clinical trial in which an experimental treatment is compared with a control treatment, the latter being either the current standard treatment or a placebo. Control statistics Statistics calculated from sample values X1, X2, . . ., Xn that elicit information about some characteristic of a process that is being monitored. Correlation The degree to which variables change together. Correlation coefficient An index that quantifies the linear relationship between a pair of variables. The coefficient takes values between −1 and 1, with the sign indicating the direction of the relationship and the numerical magnitude indicating its strength. A value of zero indicates the lack of any linear relationship between two variables. Correlation matrix A square, symmetric matrix with rows and columns corresponding to variables in which the off-diagonal elements are correlations between pairs of variables and the elements on the main diagonal are unity. Cost-benefit analysis An economic analysis in which the costs of medical care and the benefits of reduced loss of net earnings due to the preven-

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Page 140 tion of premature death or disability are considered. The general rule for the allocation of funds in a cost-benefit analysis is that the ratio of marginal benefit (the benefit of preventing an additional case) to marginal cost (the cost of preventing an additional case) should be equal to or greater than 1. Cox's proportional hazards model A method that allows the hazard function to be modeled on a set of explanatory variables without making restrictive assumptions about the dependence of the hazard function on time. Estimates of the parameters in the model, i.e., β1, β2, . . ., βp, are usually obtained by maximum likelihood estimation and depend only on the order in which events occur, not on the exact time of their occurrences. Critical region The values of a test statistic that lead to rejection of a null hypothesis. The size of the critical region is the probability of obtaining an outcome belonging to this region when the null hypothesis is true, i.e., the probability of a Type I error. See also acceptance region. Critical value The value with which a statistic calculated from sample data is compared to determine whether a null hypothesis should be rejected. The value is related to the particular significance level chosen. Cross-validation The division of data into two subsets of approximately equal size, one of which is used to estimate the parameters in some model of interest and the other of which is used to assess whether the model with these parameter values fits adequately. Cumulative frequency distribution A listing of the sample values of a variable together with the proportion of the observations less than or equal to each value. Decision analysis An approach that involves identification of all available choices and the potential outcomes of each in a series of decisions that must be made about aspects of patient care: diagnostic procedures, therapeutic regimens, and prognostic expectations. The range of choices can be plotted on a decision tree, where at each branch or decision node the probabilities of each outcome are displayed. Decision function A concept used in decision analysis that tells the experimenter how to conduct the statistical aspects of an experiment and what action to take for each possible outcome. See also loss function. Decision tree A graphical representation of the alternatives available at each stage in the process of decision making, where decision options are represented as branches and subsequent possible outcomes are represented as further branches. The decisions and the eventualities are presented in

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Page 166 Sampling zeros Zero frequencies that occur in the cells of contingency tables because of inadequate sample size. Saturated model A model that contains all main effects and all possible interactions between factors. Such a model contains the same number of parameters as observations and results in a perfect fit for a data set. Scatter diagram, scattergram, scatterplot A graphic method of displaying the distribution of two variables in relation to each other. Selection bias The bias that may be introduced into clinical trials and other types of medical investigations whenever a treatment is chosen by the individual involved or is subject to constraints that go unobserved by the researcher. Semi-interquartile range Half the difference between the upper and lower quartiles. Sensitivity An index of the performance of a diagnostic test, calculated as the percentage of individuals with a disease who are correctly classified as having the disease, i.e., the conditional probability of having a positive test result given that the disease is present. Sensitization Administration of antigen to induce a primary immune response. Sequential analysis A method of analysis in which a statistical test of significance is conducted repeatedly over time as the data are collected. After each observation, the cumulative data are analyzed and one of the following three decisions is taken: stop the data collection, reject the null hypothesis, and claim statistical significance; stop the data collection, do not reject the null hypothesis, and state that the results are not statistically significant; continue the data collection since the accumulated data are inadequate to draw a conclusion. Three types of sequential analysis are: open-ended sequential analysis, used in studies that continue indefinitely until sufficient evidence to reject or fail to reject the null hypothesis has accumulated; closed-ended sequential analysis, in which the maximum size of the sample has been set and as data are accumulated and analyzed there is an option to terminate the study before data from the planned sample size have accumulated; and group sequential analysis, in which interim analysis is undertaken at planned numbers of intervals, with each interval having accumulated data for a specified number of samples.

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Page 167 Sequential sums of squares A term in regression analysis that refers to the contribution of variables as they are added to the model in a particular sequence. It is the difference in the residual sum of squares before and after adding a variable. Sickle cell anemia A hereditary, genetically determined hemolytic anemia, one of the hemoglobinopathies, occurring almost exclusively in African Americans, characterized by arthralgia, acute attacks of abdominal pain, ulcerations of the lower extremities, and sickle-shaped erythrocytes in the blood. Significance level The level of probability at which it is agreed that the null hypothesis will be rejected, conventionally set at 0.05. Significance test A statistical procedure that, when applied to a set of observations, results in a p value relative to some hypothesis. Examples include Student's t test, z test, and Wilcoxon's signed rank test. Sign test A test that can be used when combining results of several studies, e.g., in meta-analysis. The test considers the direction of results of individual studies, whether the associations demonstrated are positive or negative. Similarity coefficient Coefficients that range from zero to unity and that are used to measure the similarity of the variable values of two observations from a set of multivariate data. Most commonly used on binary variables. Simpson's paradox A form of confounding in which the presence of a confounding variable changes the direction of an association. It may occur in meta-analysis because the sum of the data or results from a number of different studies may be affected by confounding variables that have been excluded by design features from some studies but not others. Singly censored data Censored observations that occur in clinical trials in which all the patients enter the study at the same time point and in which the study is terminated after a fixed time period. Skewness The lack of symmetry in a probability distribution. Spatial data A collection of measurements or observations on one or more variables taken at specified locations and for which the spatial organization of the data is of primary interest. Specificity An index of the performance of a diagnostic test, calculated as the percentage of individuals without the disease who are classified as not having the disease, i.e., the conditional probability of a negative test result given that the disease is absent. Square root transformation A transformation of the form , ~ enlarge ~ often used to make random variables suspected to have a Poisson distribution

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Page 168 more suitable for techniques such as analysis of variance by making their variances independent of their means. Standard deviation (SD) The most commonly used measure of the spread of a set of observations. Equal to the square root of the variance. Standard error (SE) The standard deviation of the sampling distribution of a statistic. For example, the standard error of the sample mean of n observations is σ / , ~ enlarge ~ where σ2 is the variance of the original observations. Standardization A set of techniques used to remove as much as possible the effects of differences in age or other confounding variables when comparing two or more populations. The common method uses weighted averaging of rates specific for age, sex, or some potential confounding variable(s) according to some specified distribution of these variables. Standard normal distribution A normal distribution with zero mean and unit variance. Standard normal variable A random variable having a standard normal distribution. Standard scores Variable values transformed to zero mean and unit variance. Statistic A numerical characteristic of a sample, e.g., sample mean and sample variance. Statistical significance An estimate of the probability of the observed or greater degree of association between independent and dependent variables under the null hypothesis. The level of statistical significance is usually stated by the p value. Statistical test A procedure that is intended to decide whether a hypothesis about the distribution of one or more populations or variables should be rejected or accepted. Stem-and-leaf plot A method of displaying data resembling a histogram in which each observation is split into two parts, with multiples of 10 along the “stem” and the integers forming the “leaves.” The stems are arranged in a column, and the leaves are attached to the relevant stem. Stochastic process A process that incorporates some element of randomness, in a series of random variables, xt, where t assumes values in a certain range T. In most cases xt is an observation at time t and T is a time range. Stopping rules Procedures that allow interim or sequential analyses in clinical trials at predefined times and that specify the conditions or criteria under which the trial shall be terminated while preserving the Type I error at some prespecified level.

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Page 169 Stratified logrank test A method for comparing the survival experiences of two groups of subjects given different treatments when the groups are stratified by age or some other prognostic variable. Stratified randomization A randomization procedure in clinical trials in which strata are identified and subjects are randomly allocated to treatments within each stratum without sacrificing the advantages of random allocation. Structural zeros Zero frequencies occurring in the cells of contingency tables that arise because it is theoretically impossible for an observation to fall in the cell. Student's t distribution The probability distribution of the ratio of a standard normal variable to the square root of a variable with a chi-square distribution. The shape of the distribution varies with n, and as n gets larger the shape of the t distribution approaches that of the standard normal distribution. Student's t tests Significance tests for assessing hypotheses about population means. One version, known as single-sample t test, is used in situations in which it is required to test whether the mean for a population takes a particular value. Another version, known as independent-samples t test, is applied when independent samples are available from each population and is designed to test the equality of the means for the two populations. Subgroup analysis The analysis of particular subgroups of patients in a clinical trial to assess possible treatment-subgroup interactions. Analysis of many subgroups for treatment effects can increase overall Type I error rates. Subjective end points End points in clinical trials that can be measured only by subjective clinical rating scales. Surrogate end point In clinical trials it refers to an outcome measure that an investigator considers to be highly correlated with an endpoint of interest but that can be measured at lower expense or at an earlier time. In some cases, ethical issues may suggest the use of a surrogate endpoint. Survival function The probability that the survival time of an individual is longer than some particular value. A plot of this probability against time is called a survival curve and is a useful component in the analysis of such data. Symmetrical distribution A probability distribution or frequency distribution that is symmetrical about some central value. Systematic allocation Procedures for allocating treatments to patients in a

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Page 170 clinical trial that attempts to emulate random allocation by using some systematic scheme, such as giving treatment A to those people with birth dates on even dates and treatment B to those with birth dates on odd days. Systematic error A term often used in a clinical laboratory to describe the difference in results caused by a bias of an assay. Target population The collection of individuals, items, measurements, etc., about which it is required to make inferences. At times it is used to indicate the population from which a sample is drawn, and at times it is used to denote any reference population about which inferences are required. t distribution The distribution of a quotient of independent random variables, the numerator of which is a standardized normal variate and the denominator of which is the positive square root of the quotient of a chi-square-distributed variate and its number of degrees of freedom. Test statistic A statistic used to assess a particular hypothesis in relation to some population. The essential requirement of such a statistic is a known distribution when the null hypothesis is true. Tied observations A term usually applied to ordinal variables to indicate observations that take the same value on a variable. Time-dependent covariates Covariates whose values change over time. Examples are age and weight. Time-independent covariates Covariates whose values remain constant over time. An example is a pretreatment measurement of some characteristic. Tmax A measure traditionally used to compare treatments in bioequivalence trials. It is the time at which a patient's highest recorded values occur. Total sum of squares The sum of the squared deviations of all the observations from their mean. Trapezium rule A simple rule for approximating the integral of a function, f(x), between two limits. Treatment allocation ratio The ratio of the number of subjects allocated to the two treatments in a clinical trail. Equal allocation is most common in practice, but it may be advisable to allocate patients randomly in other ratios when a new treatment is compared with an old one, or when one treatment is much more difficult or expensive to administer. Treatment cross contamination An instance in which a patient assigned to receive a particular treatment in a clinical trial is exposed to one of the other treatments during the course of the trial.

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Page 171 Treatment received analysis Analyzing the results of a clinical trial by the treatment received by a patient rather than by the treatment allocated at randomization as in intent-to-treat analysis. Treatment trial Synonym for clinical trial. Trend Movement in one direction of the values of a variable over a period of time. Triple blind A study in which the subjects, observers, and analysts are blinded as to which subjects received what interventions. Truncated data Data for which sample values larger (truncated on the right) or smaller (truncated on the left) than a fixed value are either not recorded or not observed. t test Test that uses a statistic that, under the null hypothesis, has the t distribution to test whether two means differ significantly or to test linear regression or correlation coefficients. Tumorigenic dose 50 (TD50) The daily dose of a compound required to halve the probability of remaining tumorless at the end of a standardized lifetime. Two-armed bandit allocation An allocation procedure for forming treatment groups in a clinical trial in which the probability of assigning a patient to a particular treatment is a function of the observed differences in outcomes for patients already enrolled in the trial. Two-by-two contingency table A contingency table with two rows and two columns formed from cross classification of two binary variables. Two-phase sampling A sampling scheme involving two distinct phases: first, information about particular variables of interest is collected for all members of the sample, and second, information about other variables is collected for a subsample of the individuals in the original sample. Two-stage sampling A procedure most often used in the assessment of quality assurance before, during, and after the manufacture of, e.g., a drug product. This would involve randomly sampling a number of packages of some drug and then sampling a number of tablets from each of these packages. Two-stage stopping rule A procedure sometimes used in clinical trials in which results are first examined after only a fraction of the planned number of subjects in each group have completed the trial. The relevant test statistic is calculated and the trial is stopped if the difference between the treatments is significant at stage 1 level. Otherwise, additional subjects in each treatment group are recruited, the test statistic is

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Page 172 calculated again, and the groups are compared at stage 2 level α2, where α and α2 are chosen to give an overall significance level of α. Two-tailed test A statistical significance test based on the assumption that the data are distributed in both directions from some central value(s). Type I error The error that results when the null hypothesis is falsely rejected. Type II error The error that results when the null hypothesis is falsely accepted. Unanimity rule A requirement that all of a number of diagnostic tests yield positive results before declaring that a patient has a particular complaint. Unbiased estimator An estimator that for all sample sizes has an expected value equal to the parameter being estimated. If an estimator tends to be unbiased as the sample size increases, it is referred to as “asymptotically unbiased.” Uniform distribution The probability distribution of a random variable having constant probability over an interval. The most commonly encountered uniform distribution is one in which the parameters α and β take the values 0 and 1, respectively. Unimodal distribution A probability distribution or frequency distribution having only a single mode. Unit normal variable Synonym for standard normal variable. Univariate data Data involving a single measurement for each subject or patient. Unweighted means analysis An approach to the analysis of two-way and higher-order factorial designs when there are an unequal number of observations in each cell. The analysis is based on cell means, using the harmonic mean of all cell frequencies as the sample size for all cells. U-shaped distribution A probability distribution or frequency distribution shaped more or less like a letter U, although not necessarily symmetrical. The distribution has its greatest frequencies at the two extremes of the range of the variable. Utility In economics, utility means preference for or desirability of a particular outcome. Utility analysis A method in clinical decision analysis in which the outcome refers to being or becoming healthy rather than sick or disabled. Vague prior A term used for the prior distribution in Bayesian inference in the situation in which there is complete ignorance about the value of a parameter.

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Page 173 Validity The extent to which a measuring instrument is measuring what was intended. Validity checks A part of data editing in which one checks that only allowable values or codes are given for the answers to questions asked of subjects. Validity, measurement An expression of the degree to which a measurement measures what it intends to measure. Validity, study The degree to which the inference drawn from a study, especially generalizations extending beyond the study sample, are warranted after taking into account the study methods, the representativeness of the study sample, and the nature of the population from which it is drawn. Variable Any attribute, phenomenon, or event that can have different values from time to time. Variable, antecedent A variable that causally precedes the association of the outcome under study. Variable, confounding See confounding. Variable, control Independent variable other than the “hypothetical causal variable” that has a potential effect on the dependent variable and that is subject to control by analysis. Variable, uncontrolled A (potentially) confounding variable that has not been brought under control by design or analysis. Variance A measure of the variation shown by a set of observations, defined by the sum of squares of the deviation from the mean divided by the number of degrees of freedom in the set of observations. In a population, the second moment about the mean. Variance components Variances of random-effect terms in linear models. For example, in a simple mixed model for longitudinal data, both subject effects and error terms are random, and estimation of their variances is of some importance. In the case of a balanced design, estimation of these variances is usually achieved directly from the appropriate analysis of variance table by equating mean squares to their expected values. When the data are unbalanced, a variety of estimation methods might be used, although maximum likelihood estimation and restricted maximum likelihood estimation are most often used. Variance-covariance matrix A symmetric matrix in which the off-diagonal elements are the covariances (sample or population) of pairs of variables and the elements on the main diagonal are the variances (sample or population) of the variables. Variance inflation factor An indicator of the effect that the other explana-

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Page 174 tory variables have on the variance of a regression coefficient of a particular variable, given by the reciprocal of the square of the multiple correlation coefficient of the variable with the remaining variables. Variance ratio distribution Synonym for F distribution. Variance ratio test Synonym for F test. Variance-stabilizing transformations Transformation designed so that the variance of the transformed variable is independent of parameters. Vector A matrix having only one row or column. Venn diagram A graphical representation of the extent to which two or more quantities or concepts are mutually inclusive and mutually exclusive. Virtually safe dose The exposure level to some toxic agent corresponding to an acceptably small risk of suffering an ill effect. From a regulatory perspective, this typically means an increased risk of no more than 10 6 or 10 4 above the background. Volunteer bias A possible source of bias in clinical trials involving volunteers, but not involving random allocation, because of the known propensity of volunteers to respond better to treatment than other patients. Wald's test A test for the hypothesis that a vector of parameters, θ' = [θ1, θ2, . . . , θm], is the null vector. The test statistic is, W = θ̂'V−1θ̂ where θ̂' contains the estimated parameter values and V is the asymptotic variance-covariance matrix of θ̂. Under the hypothesis, W has an asymptotic chi-square distribution with degrees of freedom equal to the number of parameters. Weibull model Dose-response model of the form P(d) = 1 − exp(− bdm), where P(d) is the probability of response due to a continuous dose rate d; and b and m are constants. The model is useful for extrapolating from high- to low-dose exposures, e.g., from animals to human. Weighted average A value determined by assigning weights to individual measurements. Each value is assigned a nonnegative coefficient (weight); the sum of the products of each value by its weight divided by the sum of the weights is the weighted average. Weighted kappa A version of the kappa coefficient that allows disagreements between raters to be differentially weighted to allow differences in how serious such disagreements are judged to be. Weighted least squares A method of estimation in which estimates arise from minimizing a weighted sum of squares of the differences between

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Page 175 the response variable and its predicted value in terms of the model of interest. Often used when the variance of the response variable is thought to change over the range of values of the explanatory variable(s), in which case the weights are generally taken as the reciprocals of the variance. Weight variation tests Tests designed to ensure that manufacturers control the variation in the weights of the tablet forms of the drugs that they produce. Wilcoxon's rank sum test Another name for the Mann-Whitney test. Wilcoxon's signed rank test A distribution-free method for testing the difference between two populations by using matched samples. The test is based on the absolute differences of the pairs of observations in the two samples ranked according to size, with each rank being given the sign of the original difference. Wilk's multivariate outlier test A test for detecting outliers in multivariate data that assumes that the data arise from a multivariate normal distribution. William's test A test used to answer questions about the toxicities of substances and at what dose level any toxicity occurs. The test assumes that the mean response of the variate is a monotonic function of dose. Yates' correction An adjustment proposed by Yates in the chi-square calculation for a two-by-two contingency table that subtracts 0.5 from the positive discrepancies (observed – expected) and adding 0.5 to the negative discrepancies before these values are squared in the calculation of the usual chi-square statistic. This brings the distribution based on the discontinuous frequencies closer to the continuous chi-square distribution from which the published tables for testing chi-square values are derived. Zelen's single-consent design A modified double-blind randomized controlled trial design for the formation of treatment groups in a clinical trial. The essential feature is randomization before informed consent procedures, which is claimed to be needed only for the group allocated to receive the experimental regimen. z test A test for assessing hypotheses about population means when their variances are known. If the null hypothesis is true, z has a standard normal distribution.

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Page 176 SOURCES Dorland's Illustrated Medical Dictionary, 28th edition. 1994. Philadelphia: W. B. Saunders. Eddy, D. M., V. Hasselblad, and R. Shacther. 1992. Meta-Analysis by the Confidence Profile Method. San Diego: Academic Press. Everitt, B. S. 1995. The Cambridge Dictionary of Statistics in the Medical Sciences. Cambridge, United Kingdom: Cambridge University Press. Hirsch, R. P., and R. Riegelman. 1996. Statistical Operations. Analysis of Health Research Data. Cambridge, MA: Blackwell Science. Last, J. M., ed. 1995. A Dictionary of Epidemiology. Oxford: Oxford University Press.