# Medical statistics

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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

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:

There are also journals including:

## Basic concepts

For describing situations
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]

## Related Research Articles

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 positivediagnosis, and in statistical classification as a false positiveerror. A false positive is distinct from overdiagnosis, and is also different from overtesting.

## References

1. Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN   0-19-850994-4
2. Kirkwood, Betty R. (2003). . Blackwell Science, Inc., 350 Main Street, Malden, Massachusetts 02148–5020, USA: Blackwell. ISBN   978-0-86542-871-3.CS1 maint: location (link)
3. 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.
4. Benjamin, Bernard (1993). The analysis of mortality and other actuarial statistics. England, Institute of Actuaries: Oxford. ISBN   0521077494.