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
