Biostatistics Flashcards
Adjusted Rate
A summarizing procedure for a statistical measure in which the effects of differences in composition of the populations being compared have been minimized by statistical methods. E.g. Adjustment by regression analysis & by standardization. Performed on rates or relative risks, commonly because of differing age distributions in population that are being compared. Mathematical procedure used to adjust rates for age differences is direct or indirect standardization.
alpha
The probability of a type I error, the error of rejecting a true null hypothesis. i.e. declaring a difference exists when it does not. Wrongly reject the null
Type I error
Alpha. Rejecting the null when it is true.
alternative hypothesis
A supposition, arrived at from observation or reflection, that leads to refutable predictions. ANy conjecture cast in a form that will allow it to be tested and refuted.
analysis of covariance (ANCOVA)
Used for an extention of ANOVA that alllows for possible effects of continuous concomitant variables (covariates) on the response variable, in addition to the effects of the factor or treatment variables. Usually assumed that covariates are unaffected by treatments and that their relationship to the response is linear. If such a relationship exists then inclusion of covariates in this way decreases the error mean square and hence term now appears to also be more generally used for almost any analysis seeking to assess the relationship between a response variable and a number of explanatory variables.
analysis of variance (ANOVA)
The separation of variance attributable to one cause from the variance attributable to others. By partitioning the total variance of a set of observations into parts due to particular factors, for example, sex, treatment group, etc, and comparing variances (mean squares) by way of F-tests, differences between means can be assessed. The simplest analysis of this type involves a one-way design, in which N subjects are allocated, usually at random, to the k different levels of a single factor. The total variation in the observations is then divided into a part due to differences between level means (the between groups sum of squares) and a part due to the differences between subject in the same group (the within groups sum of squares, or the residual sum of squares). *SEE ANOVA TABLE. If the means of the populations represented by the factor levels are the same, then within the limits of random variation, the between groups mean square and within groups mean square, should be the same. Whether
Bayes’ theorem
A procedure for revising and updating the probability of some event in the light of new evidence. Originates in a essay by the REverend Thomas Bayes. *SEE EQUATION
Beta
The probability of a type II error, the error of failing to reject a false null hypothesis i.e. declaring that a difference does not exist when in fact it does. Failing to reject the null when you should reject the null
Type II error
Beta. Failing to reject the null when you should
Bias
In general terms, deviations of results or inferences from the truth, or processes leading to such deviation. More specifically, the extent to which the statistical method used in a study does not estimate the quantity thought to be estimated, or does not test the hypothesis to be tested. In estimated usually measured by the difference between a parameter estimate and its expected value. *SEE EQUATION
Binary variable (binary observation)
Observations which occur in one of two possible states, these often being labeled 0 and I. Such data is frequently encountered in medical investigations; commonly occurring examples include ‘dead/alive’, ‘improved/not improved’ and ‘depressed/not depressed’. Data involving this type of variable often require specialized techniques for their analysis such as logical regression
binomial distribution
The distribution of the number of ‘successes’, X in a series of n-independent Bernoulli trials where the probability of success at each trial is p and the probability of failure is q=1-p. Specifically the distribution is given by *SEE EQUATION
Biostatistics
A branch of science which applies statistical methods to biological problems. Encompasses the design of biological experiments, especially in medicine and health sciences.
bivariate
outcomes belong to two categories, e.g. yes/no, acceptable/defective “bivariate binomial distribution”
Blinded study
A procedure used in clinical trials to avoid the possible bias that might be introduced if the patient and/or doctor knew which treatment the patient is receiving. Clinical trials should use max degree of blindness that is possible, although in some areas it is impossible. e.g. surgery
Double-blind
If neither the patient nor doctor are aware of which treatment has been given.
SIngle-blind
only one of the patient or doctor is unaware
Bonferroni correction
A procedure for guarding against an increase in the probability of a type I error when performing multiple significance tests. TO maintain the probability of a type I error at some selected value each of the m tests to be performed is judged against a significance leve (a/m). FOr a small number of simultaneous tests (up to 5) this method provides a simple and acceptable answer to the problem of multiple testing. It is however highly conservative and not recommended if large numbers of tests are to be applied, when one of the many other multiple comparison procedures available is generally preferable.
case-control study
The observational epidemiologic study of persons with the disease or other outcome variable of interest and a suitable control (comparison, reference) group of persons without the disease.
Categorical data
Represent types of data which may be divided into groups. Examples of categorical variable are race, sex, age group, and educational level. While the latter two variables may also be considered in a numerical manner by using exact values for age and highest grade completed, it is often more informative to categorize such variables into a relatively small number of groups.
censored observation
AN observation (Xi) in some variable of interest is said to be censored if it is known only that Xi-=Li (left-censored) or Xi=Ui (right-censored) where Li and Ui are fixed values. SUch observations arise most frequently in studies where the main purpose variable is time until a particular event occurs (for example, time to death) when at the completion of the study, the event of interest has not happened to a number of subjects.
Central Limit Theorem
If a random variable Y has population mean and population variance, then the sample mean, y bar, based on n observations, has an appropriate normal distribution with a mean and variance/n, for sufficiently large n. The theorem occupies an important place in statistical theory. IN short, the Central Limit Theorem states that if the sample size is large enough, the distribution of sample means can be approximated by a normal distribution, even if the original population is not normally distributed.
Chi-Square Distribution
based on a normally distributed population with variance o2, with randomly selected independent samples of size n and computed sample variance s2 for each sample. The sample statistic X2=(n-1)s2/o2. The chi-square distribution is skewed, the values can be zero or positive but not negative, and is different for each number of degrees of freedom. Generally, as the number of degrees of freedom increases, the chi-square distribution approaches a normal distribution.
Chi-Square Statistic
A statistic having, at least approximately, a chi-squared 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. The result of using the ordering in this way is a test that is more powerful than using the chi-squared statistic to test for independence
clinical trial
A research activity that involves the administration of a test regimen to humans to evaluate its efficacy and safety. The term is subject to wide variation in usage, from the first use in humans without any control treatment to a rigorously designed and executed experiment involving test and control treatments and randomization.
Phase I trial
Safety and pharmacologic profiles. The first introduction of a candidate vaccine or a 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. Usually involve fewer than 100 healthy volunteers
Phase II trial
Pilot efficacy studies. Initial trial to examine efficacy usually in 200 to 500 volunteers; with vaccines, the focus is on immunogenicity, and with drugs, on demonstration of safety and efficacy in comparison to other existing regimens. Usually but not always, subjects are randomly allocated to study and control groups.
Phase III trial
Extensive clinical trial. This phase is intended for complete assessment of safety and efficacy. It involves larger numbers, perhaps thousands, of volunteers, usually with random allocation to study and control groups, and may be a multicenter trial
Phase IV trial
With drugs, this phase is conducted after the national drug registration authority (e.g., the FDA) has approved the drug for distribution or marketing. Phase IV trials may include research designed to explore a specific pharmacologic effect, to establish the incident of adverse reactions, or to determine the effects of long-term use. Ethical review is required for phase IV clinical trials, but not for routine post marketing surveillance.
Coefficient of variation
The measure of spread for a set of data defined as 100 x standard deviation/mean
CV=s/x bar(100)=sample
CV=o/miu(100)=population
Originally proposed as a way of comparing the variability in different distributions, but found to be sensitive to errors in the mean. The ratio of the standard deviation to the mean. This is meaningful only if the variable is measured on a ratio scale
cohort study
(concurrent, follow-up, incidence, longitudinal, prospective) The analytic method of epidemiologic study in which subsets of a defined population can be identified who are, have been, or in the future may be exposed or not exposed, or exposed in different degrees, to a factor or factors hypothesized to influence the probability of occurrence of a given disease or other outcome
complementary event
Mutually exclusive events A and B for which Pr(A)+Pr(B)=1 where Pr denotes probability
conditional probability
The probability that an event occurs given the outcome of some other event. usually written, Pr (A|B) For example, the probability of a person being colour blind given that the person is male is about 0.1, and the corresponding probability given that the person is female is approximately .0001. It is not, of course, necessary that Pr(A|B)=Pr(A|B); the probability of having spots given that a patient has measles, for example, is very high, the probability of measles given that a patient has spots is, however much less. If Pr(A|B)=Pr(A|B) then the events A and B are said to be independent.
confidence interval
A range of values, calculated from the sample observations, that is believed, with a particular probability, to contain the true value of a population parameter. E.g. A 95% confidence interval implies that were the estimation process repeated again and again, then 95% of the calculated intervals would be expected to contain the true parameter value.
Confounding variable
(confounding factor, lurking variable, a confound, confounder) an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable. The methodologies of scientific studies need to control for these factors to avoid a type 1 error: a false positive conclusion that the dependent variables are in a causal relationship with the independent variable. Confounding is a major threat to the validity of inferences made about cause and effect i.e. internal validity as the observed effects should be attributed to the confounder rather than the independent variable. A confounding variable is associated with both the probable cause and the outcome. *SEE PARAGRAPH
Contingency table
The table arising when observations on a number of categorical variable are cross-classified. Entries in each cell are the number of individuals with the corresponding combination of variable values. Most common are two-dimensional tables involving two categorical variables. *SEE EXAMPLE. The analysis of such two-dimensional tables generally involves testing for the independence of the two variables using chi-squared statistics
Continuous data
result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions or jumps, e.g. blood pressure
Controlled tiral
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
Correlation Coefficient r (Pearson’s R)
An index that quantifies the linear relationship between a pair of variables. In a bivariate normal distribution, for example, the parameter, p. An estimator of P obtained from n sample values of the two variable of interest is Pearson’s product moment correlation coefficient, r, given by *SEE EQUATION. The coefficient takes values between -1 and 1, with the sign indicating the direction fo the relationship and the numerical magnitude its strength. Values of -1 and 1 indicate that the sample values fall on a straight line. A value of zero indicates the lack of any linear relationship between the two variables.
Covariate
Often used simply as an alternative name for explanatory variables, but perhaps more specifically to refer to variables that are not of primary interest in an investigation, but are measured because it is believed that they are likely to affect the response variable and consequently need to be included in analyses and model building
Cox regression model (proportional hazards model)
A statistical model use din survival analysis developed by D.R. Cox in 1972 asserting that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time
critical value
The value with which a statistic calculated from sample data is compared in order to decide whether a null hypothesis should be rejected. The value is related to the particular significance level chosen.
Crossover rate
The proportion of patients in a clinical trial transferring from the treatment decided by an initial random allocation to an alternative one
Cross-sectional study
A study that examines the relationship between diseases or other health-related characteristics and other variables of interest as they exist in defined population at one particular time
Cumulative frequency distribution
The tabulation of a sample of observations in terms of numbers falling below particular values. The empirical equivalent of the cumulative probability distribution. *SEE TABLE
degrees of freedom
the number of independent units of information in a sample relevant to the estimation of a parameter or calculation of a statistic. FOr example, in a two-by-two contingency table with a given set of marginal totals, only on e of the four cell frequencies is free and the table has therefore a single degree of freedom. IN many cases the term corresponds to the number of parameters in a model.
Dependent variable (response of outcome variable)
The variable of primary importance in investigations since the major objective is usually to study the effects of treatment and/or other explanatory variables on this variable and to provide suitable models for the relationship between it and the explanatory variables.
Descriptive statistics
general term for methods of summarizing and tabulating data that make their main features more transparent. E.g. calculating means and variances and plotting histograms
dichotomous observation
A nominal measure with two outcomes (male or female, survival yes or no). also called binary
dichotomous scale
one that arranges items into either of two mutually exclusive categories, e.g. yes/no, alive/dead.
discrete data
result when the number of possible values is either a finite number or a countable number
discrete variable
a countable and finite variable, e.g. grade
distribution (population)
any finite or infinite collection of units, which are often people but may be for example institutions, events, etc.
double-blinded trial
a procedure used in clinical trials to avoid the possible bias that might be introduced if the patient and/or doctor knew which treatment the patient is receiving. Neither patient nor doctor are aware of which treatment has been given the trial is termed double-blind
dummy coding
provides one way of using categorical predictor variables in various kinds of estimation models (effect coding) such as linear regression. Dummy coding uses only ones and zeros to convey all of the necessary information on group membership
dummy variable (indicator variable)
a variable taking only on e of two possible values, one (usually 1) indicating the presence of a condition, and the other (usually 0) indicating the absence of the condition, used mainly in regression analysis
effect or effect size
a measure of the strength of the relationship between two variables. In scientific experiments, it is often usefult o know not only whether an experiment has a statistically significant effect, but also the size of any observed effects. In practical situations, effect sized are helpful for making decisions. Effect size measures are the common currency of meta-analysis studies that summarize the findings from a specific area of research
effective sample size
the sample size after dropouts, deaths and other specified exclusions from the original sample
expected frequencies
usually encountered in the analysis of contingency tables. Such frequencies are estimates of the values to be expected under the hypothesis of interest. IN a two-dimensional table, for example, the values under independence are calculated from the product of the appropriate row and column totals divided by the total number of observations
experiment (in probability)
involves performing a number of trials to measure the chance of the occurrence of an event or outcome
experiment
a study in which the investigator intentionally alters one or more factors under controlled conditions in order to study the effects of doing so
experimental study
a study in which conditions are under the direct control of the investigator. In epidemiology, a study in which a population is selected for a planned trial of a regimen whose effects are measured by comparing the outcome of the regimen in the experimental group with the outcome of another regimen in a control group
explanatory variable
the variables appearing on the right-hand side of the equations defined, for example, multiple regression or logistic regression, and which seek to predict or explain the response variable. ALso commonly known as the independent variables
factor
an event, characteristic, or other definable entity that brings about a change in a health condition or other defined outcome
factor analysis
a set of statistical methods for analyzing the correlations among several variables in order to estimate the number of fundamental dimensions that underlie the observed data and to describe and measure those dimensions. Used frequently in the development of scoring systems for rating scales and questionnaires.
factorial designs
designs which allow two or more questions to be addressed in an investigation. The simplest factorial design is one in which each of two treatments or interventions are either present or absent, so that subjects are divided into four groups; those receiving neither treatment, those having only the first treatment, those having only the second treatment and those receiving both treatments. Such designs enable possible interactions between factors to be investigated. A very important special case of a factorial design is that where each of k factors of interest has only two levels; these are usually know as 2k factorial designs.
false-negative
the proportion of cases in which a diagnostic test indicates disease is absent in patients who have the disease
false-positive
the proportion of cases in which a diagnostic test indicates disease is present in disease-free patients
F distribution (variance ratio distribution)
the distribution of the ratio of two independent quantities each of which is distributed like a variance in normally distributed samples. So named in honor of R.A. Fisher
FIsher’s exact test
An alternative procedure to use of the chi-squared statistic for assessing the independence of two variables forming a tow-by-two contingency table particularly when the expected frequencies are small. The method consists of evaluating the sum of the probabilities associated with the observed table and all possible two-by-two tables that have the same row and column totals as the observed data but exhibit more extreme departure from independence. Hypergeometric distribution
Fisher’s z-transformation
A transformation of Pearson’s product moment correlation coefficient, r given by *SEE EQUATION
frequency (occurrence)
the frequency or occurrence of a disease and other attribute or event in a population without distinguishing between incidence and prevalence
frequency distribution
lists data values (individually or by groups of intervals), along with their corresponding frequencies (or counts)
frequency table
a way of summarizing data; used as a record of how often each value or set of values of a variable occurs. Used to summarize categorical, nominal, and ordinal data. It may also be used to summarize continuous data once the data is divided into categoriw
F-test
a test for the equality of the variances of two populations having normal distributions, based on the ratio of the variances of a sample of observations taken from each. Most often encountered in the analysis of variance, where testing whether particular variances are the same also test for the equality of a set of means.
Gaussian distribution
normal distribution
gold standard trials
a term usually retained for those clinical trials in which there is a random allocation to treatments, a control group and double-blinding
goodness of fit
degree of agreement between an empirically observed distribution and a mathematical or theoretical distribution
goodness-of-fit test
a statistical test of the hypothesis that data have been randomly samples or generated from a population that follows a particular theoretical distribution or model. the most common such tests are chi-square tests
hazard
inherent capability of an agent or situation to have an adverse effect. A factor or exposure that may effect adversely effect health
hazard rate (force of morbidity, instantaneous incidence rate)
a theoretical measure of the risk of an occurrence of an event, e.g. death or new disease, at a point in time, t, defined mathematically as the limit, as delta t approaches zero, or the probability that an individual well at time t will experience the event by t +delta t, divided by delta t
histogram
A graphical representation of a set of observations in which class frequencies are represented by the areas of rectangles centred on the class interval. If the latter are all equal, the heights of the rectangles are also proportional to the observed frequencies.
historical controls
a group of patients treated in the past with a standard therapy, used as the control group for evaluating a new treatment on current patients. ALthough used fairly frequently in medical investigations, the approach is not to be recommended since possible biases, due to other factors that may have changed over the time, can never be satisfactorily eliminated
homogeneity
a term that is used to indicate the equality of some quantity of interest (most often a variance), in a number of different groups, populations, etc.
homoscedasticity
the contancy of the variance of a measure over levels of the factors under study
hypothesis testing
procedure of assessing whether sample data is consistent or otherwise with statements made about the population
incidence
a measure of the rate at which people without a disease develop the disease during a specific period of time. Incidence=# of new cases of a disease over a period of time/population at risk of disease in the time period. It measures the appearance of disease. # of new events, #new cases of disease in a specified population within a specified period of time. Incidence is not incidence rate
Independence
two events are said to be independent if the occurrence of one is in no way predictable from the occurrence of the other. Two variables are said to be independent if the distribution of values of one is the same for all the values of the other
independent variable (explanatory variable)
variables appearing ont he right-hand side of the equations defining multiple regression or logistic regression, and which seek to predict or explain the response variable
inference (statistical
the process of drawing conclusions about a population on the basis of measurements or observations made on a sample of individuals for the population
Interaction
a term applied when two or more explanatory variables do not act independently on a response variable. *SEE GRAPHIC
intercept
the parameter in an equation derived from a regression analysis corresponding to the expected value of the response variable when all the explanatory variables are zero.
interquartile range
a measure of spread giving by the difference between the first and third quartile of a sample
inter-rater reliability (observer variation, inter-rater agreement, concordance)
the degree of agreement among raters. It gives a score of how much homogeneity or consensus there is in the rating given by judges. It is useful in refinind the tools given to human judges, for example by determining if a particular scale is appropriate for measure a particular variable. If various raters do not agree, either the scale is defective or the raters eed to be re-trained. There are a number of statistics which can be used to idetemine inter-rater reliability. Idfferent statistics are appropriate for different types of measurement. Som eoptions are: joint-probability
intervention study
conditions are undre the direct control of the investigator. IN epidemiology, a study in which a population is selected for a planned trial of a regimen whose effects are measured by comparing the outcomes of the region in the experimental group with the outcome of another regiment in a control group.
Kaplan-Meier estimate (product limit method)
a nonparametric method of compiling life or survival tables. This combines calculated probabilities of survival and estimates to allow for censored observations, which are assumed to occur randomly. The intervals are defined as ending each time an event (death, withdrawal) occurs and are therefore unequal
Kappa
a measure of the degree of nonrandom agreement between observers or measurements of the same categorical variable *SEE EQUATION
kurtosis
the extent to which a unimodal distribution is peaked
least squares
a principle of estimation, attributable to Gauss, in which the estimates of a set of parameters in a statistical model are those quantities that minimize the sum of squared differences between the observed values of the dependent variable and the values predicted by the model
level of significance
the level of probability at which it is agreed that the null hypothesis will be rejected. Conventionally set at 0.05.
life table analysis
a procedure often applied in prospective studies to examine the distribution of mortality and/or morbidity in one or more diseases in a cohort study of patients over a fixed period of time. For each specific increment in the follow-up period, the number entering the period, the number leaving during the period, and the number either dying from the disease or developing the disease, are all calculated. It is assumed that an individual not completed the follow-up period is exposed for half this period, thus enabling the data for those ‘leaving’ and those ‘staying’ to be combined into an appropriate denominator for the estimation of the percentage dying from or developing the disease. The advantage of this approach is that all patients, not only those hwo have been involved for an extended period, can be included in the estimation process.
likelihood function
a function constructed from a statistical model and a set of observed data that gives the probability of the observed data for various values of the unknown model parameters. The parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
likelihood ratio
the ratio of the likelihood of observing data under actual conditions, to observing these data under the other, e.g., ‘ideal’ conditions; or comparison of various model conditions to assess which model provides the best fit. LIkelihood ratios are used to appraise screening and diagnostic tests in clinical epidemiology
likelihood ratio test
a statistical test based on the ratio of the maximum value under another statistical model; the models differ in that one includes and the other excludes one or more parameters.
linear regression (of Y on X)
a form of regression analysis in which observational data are modeled by a function which is a linear combination of the model parameters and depends on one or more independent variables. In simple linear regression the model function represents a straight line. THe results of data fitting are subject to statistical analysis. THe data consist of m values taken from observations of the dependent variable (response variable) y. The independent variables are also called regressors, exogenous variables, input variables and predictor variables. In simple linear regression the data model is written *SEE EQUATION
logistic regression
a form of regression analysis used when the response variable is a binary variable. The method is based on the logistic transformation or logit of a proportions, namely *SEE EQUATION.
logistic model
a statistical model of an individual’s risk (probability of disease y) as a function of a risk factor x: *SEE EQUATION
logit (log-odds)
the logarithm of the ratio of frequencies of two different categorical outcomes such as healthy vs sick
logit model
a linear model for the logit (natural log of the odds) of disease as a function of a quantitative factor X: *SEE EQUATION. This model is mathematically equivalent to the logistic model.
log-linear model
a statistical model that uses an analysis of variance type of approach for the modeling of frequency counts in contingency tables
logrank test
a test for comparing two or more sets of survival times, to assess the null hypothesis that ther is no difference in the survival experience of the individuals in the different groups.
longitudinal study (cohort study)
Subjects are measured repeatedly through time.
