**Medical statistics** deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years but the term has not come into general use in North America, where the wider term 'biostatistics' is more commonly used.^{ [1] } However, "biostatistics" more commonly connotes all applications of statistics to biology.^{ [1] } Medical statistics is a subdiscipline of statistics. "It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, but also takes into account the intrinsic variation inherent in most biological processes." ^{ [2] }

**Pharmaceutical statistics** is the application of statistics to matters concerning the pharmaceutical industry. This can be from issues of design of experiments, to analysis of drug trials, to issues of commercialization of a medicine.

There are many professional bodies concerned with this field including:

- European Federation of Statisticians in the Pharmaceutical Industry (EFSPI)
- Statisticians In The Pharmaceutical Industry (PSI)

There are also journals including:

- For describing situations

- Incidence (epidemiology) vs. Prevalence vs. Cumulative incidence
- Many medical tests (such as pregnancy tests) have two possible results: positive or negative. However, tests will sometimes yield incorrect results in the form of false positives or false negatives. False positives and false negatives can be described by the statistical concepts of type I and type II errors, respectively, where the null hypothesis is that the patient will test negative. The precision of a medical test is usually calculated in the form of positive predictive values (PPVs) and negative predicted values (NPVs). PPVs and NPVs of medical tests depend on intrinsic properties of the test as well as the prevalence of the condition being tested for. For example, if any pregnancy test was administered to a population of individuals who were biologically incapable of becoming pregnant, then the test's PPV will be 0% and its NPV will be 100% simply because true positives and false negatives cannot exist in this population.
- Transmission rate vs. force of infection
- Mortality rate vs. standardized mortality ratio vs. age-standardized mortality rate
- Pandemic vs. epidemic vs. endemic vs. syndemic
- Serial interval vs. incubation period
- Cancer cluster
- Sexual network
- Years of potential life lost
- Maternal mortality rate
- Perinatal mortality rate
- Low birth weight ratio

- For assessing the effectiveness of an intervention

- Survival analysis
- Proportional hazards models
- Active control trials: clinical trials in which a kind of new treatment is compared with some other active agent rather than a placebo.
- ADLS(Activities of daily living scale): a scale designed to measure physical ability/disability that is used in investigations of a variety of chronic disabling conditions, such as arthritis. This scale is based on scoring responses to questions about self-care, grooming, etc.
^{ [3] } - Actuarial statistics: the statistics used by actuaries to calculate liabilities, evaluate risks and plan the financial course of insurance, pensions, etc.
^{ [4] }

- Herd immunity
- False positives and false negatives
- Rare disease
- Hilda Mary Woods – the first author (with William Russell) of the first British textbook of medical statistics, published in 1931

**Biostatistics** are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experiments and the interpretation of the results.

An **actuary** is a business professional who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms.

In finance, the **net present value** (**NPV**) or **net present worth** (**NPW**) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

**Epidemiology** is the study and analysis of the distribution, patterns and determinants of health and disease conditions in defined populations.

**Prevalence** in epidemiology is the proportion of a particular population found to be affected by a medical condition at a specific time. It is derived by comparing the number of people found to have the condition with the total number of people studied, and is usually expressed as a fraction, a percentage, or the number of cases per 10,000 or 100,000 people.

**Actuarial science** is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance, and other industries and professions. More generally, actuaries apply rigorous mathematics to model matters of uncertainty.

**Binary classification** is the task of classifying the elements of a given set into two groups on the basis of a classification rule. Contexts requiring a decision as to whether or not an item has some qualitative property, some specified characteristic, or some typical binary classification include:

**Pulmonary embolism** (**PE**) is a blockage of an artery in the lungs by a substance that has moved from elsewhere in the body through the bloodstream (embolism). Symptoms of a PE may include shortness of breath, chest pain particularly upon breathing in, and coughing up blood. Symptoms of a blood clot in the leg may also be present, such as a red, warm, swollen, and painful leg. Signs of a PE include low blood oxygen levels, rapid breathing, rapid heart rate, and sometimes a mild fever. Severe cases can lead to passing out, abnormally low blood pressure, and sudden death.

**Survival analysis** is a branch of statistics for analyzing the expected duration of time until one or more events happen, such as death in biological organisms and failure in mechanical systems. This topic is called **reliability theory** or **reliability analysis** in engineering, **duration analysis** or **duration modelling** in economics, and **event history analysis** in sociology. Survival analysis attempts to answer questions such as: what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival?

In evidence-based medicine, likelihood ratios are used for assessing the value of performing a diagnostic test. They use the sensitivity and specificity of the test to determine whether a test result usefully changes the probability that a condition exists. The first description of the use of likelihood ratios for decision rules was made at a symposium on information theory in 1954. In medicine, likelihood ratios were introduced between 1975 and 1980.

The **positive and negative predictive values** are the proportions of positive and negative results in statistics and diagnostic tests that are true positive and true negative results, respectively. The positive predictive value is sometimes called the positive predictive agreement, and the negative predictive value is sometimes called the negative predictive agreement. The PPV and NPV describe the performance of a diagnostic test or other statistical measure. A high result can be interpreted as indicating the accuracy of such a statistic. The PPV and NPV are not intrinsic to the test ; they depend also on the prevalence. The PPV can be derived using Bayes' theorem.

Given a population whose members each belong to one of a number of different sets or classes, a **classification rule** or **classifier** is a procedure by which the elements of the population set are each predicted to belong to one of the classes. A perfect classification is one for which every element in the population is assigned to the class it really belongs to. An imperfect classification is one in which some errors appear, and then statistical analysis must be applied to analyse the classification.

The following outline is provided as an overview of and topical guide to actuarial science:

**Sensitivity** and **specificity** are statistical measures of the performance of a binary classification test, also known in statistics as a classification function, that are widely used in medicine:

In statistical hypothesis testing, a **type I error** is the rejection of a true null hypothesis, while a **type II error** is the non-rejection of a false null hypothesis. Much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility for non-deterministic algorithms. By selecting a low threshold (cut-off) value and modifying the alpha (p) level, the quality of the hypothesis test can be increased. The knowledge of Type I errors and Type II errors is widely used in medical science, biometrics and computer science.

In statistics, when performing multiple comparisons, a **false positive ratio** is the probability of falsely rejecting the null hypothesis for a particular test. The false positive rate is calculated as the ratio between the number of negative events wrongly categorized as positive and the total number of actual negative events.

**Pre-test probability** and **post-test probability** are the probabilities of the presence of a condition before and after a diagnostic test, respectively. *Post-test probability*, in turn, can be *positive* or *negative*, depending on whether the test falls out as a positive test or a negative test, respectively. In some cases, it is used for the probability of developing the condition of interest in the future.

In medical testing with binary classification, the **diagnostic odds ratio** is a measure of the effectiveness of a diagnostic test. It is defined as the ratio of the odds of the test being positive if the subject has a disease relative to the odds of the test being positive if the subject does not have the disease.

The **evaluation of binary classifiers** compares two methods of assigning a binary attribute, one of which is usually a standard method and the other is being investigated. There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent on the prevalence, and metrics that depend on the prevalence – both types are useful, but they have very different properties.

In medical testing, and more generally in binary classification, a **false positive** is an error in data reporting in which a test result improperly indicates presence of a condition, such as a disease, when in reality it is not present, while a **false negative** is an error in which a test result improperly indicates no presence of a condition, when in reality it is present. These are the two kinds of errors in a binary test They are also known in medicine as a **false positive****diagnosis**, and in statistical classification as a **false positive****error**. A false positive is distinct from overdiagnosis, and is also different from overtesting.

- 1 2 Dodge, Y. (2003)
*The Oxford Dictionary of Statistical Terms*, OUP. ISBN 0-19-850994-4 - ↑ Kirkwood, Betty R. (2003).
*essential medical statistics*. Blackwell Science, Inc., 350 Main Street, Malden, Massachusetts 02148–5020, USA: Blackwell. ISBN 978-0-86542-871-3.CS1 maint: location (link) - ↑ S, KATZ; FORD A B; MOSKOWITZ R W; JACKSON B A; JAFFE M W (1963). "Studies of Illness in the Aged".
*Journal of the American Medical Association*.**185**(12): 914–9. doi:10.1001/jama.1963.03060120024016. PMID 14044222. - ↑ Benjamin, Bernard (1993).
*The analysis of mortality and other actuarial statistics*. England, Institute of Actuaries: Oxford. ISBN 0521077494.

- Altman, D.G. (1991),
*Practical Statistics for Medical Research*, CRC Press, ISBN 978-0-412-27630-9 - Armitage, P.; Berry, G.; Matthews, J.N.S. (2002),
*Statistical Methods in Medical Research*, Blackwell, ISBN 978-0-632-05257-8 - Bland, J. Martin (2000),
*An Introduction to Medical Statistics*(3rd ed.), Oxford: OUP, ISBN 978-0-19-263269-2 - Kirkwood, B.R.; Sterne, J.A.C. (2003),
*Essential Medical Statistics*(2nd ed.), Blackwell, ISBN 978-0-86542-871-3 - Petrie, Aviva; Sabin, Caroline (2005),
*Medical Statistics at a Glance*(2nd ed.), WileyBlackwell, ISBN 978-1-4051-2780-6 - Onwude, Joseph (2008),
*Learn Medical Statistics*(2nd ed.), DesignsOnline.co.uk

- Health-EU Portal EU health statistics

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