|
Cochran–Mantel–Haenszel Statistics
In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data. It allows an investigator to test the association between a binary predictor or treatment and a binary outcome such as case or control status while taking into account the stratification. Unlike the McNemar test, which can only handle pairs, the CMH test handles arbitrary strata sizes. It is named after William G. Cochran, Nathan Mantel and William Haenszel. Extensions of this test to a categorical response and/or to several groups are commonly called Cochran–Mantel–Haenszel statistics. It is often used in observational studies in which random assignment of subjects to different treatments cannot be controlled but confounding covariates can be measured. Definition We consider a binary outcome variable such as case status (e.g. lung cancer) and a binary predictor such as treatment status (e.g. smoking). The observations are grouped in strata. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds Ratio
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1, i.e., the odds of one event are the same in either the presence or absence of the other event. If the OR is greater than 1, then A and B are associated (correlated) in the sense that, compared to the absence of B, the presence of B raises the odds of A, and symmetrically the presence of A raises the odds of B. Conversely, if the OR is less than 1, then A and B are negatively correlated, and the presence of one event reduces the odds of the other event occurring. Note that the odds ratio is symmetric in the two events, and no causa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Statistics
Medical statistics (also health 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.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. However, "biostatistics" more commonly connotes all applications of statistics to biology. 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 anecdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epidemiology
Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and Risk factor (epidemiology), determinants of health and disease conditions in a defined population, and application of this knowledge to prevent diseases. It is a cornerstone of public health, and shapes policy decisions and evidence-based practice by identifying Risk factor (epidemiology), risk factors for disease and targets for preventive healthcare. Epidemiologists help with study design, collection, and statistical analysis of data, amend interpretation and dissemination of results (including peer review and occasional systematic review). Epidemiology has helped develop methodology used in clinical research, public health studies, and, to a lesser extent, basic research in the biological sciences. Major areas of epidemiological study include disease causation, transmission (medicine), transmission, outbreak investigation, disease surveillance, environmental epidemiology, forensic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Tests For Contingency Tables
Statistics (from German: ', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Logistic Regression
Conditional logistic regression is an extension of logistic regression that allows one to account for stratification and matching. Its main field of application is observational studies and in particular epidemiology. It was devised in 1978 by Norman Breslow, Nicholas Day, Katherine Halvorsen, Ross L. Prentice and C. Sabai. It is the most flexible and general procedure for matched data. Background Observational studies use stratification or matching as a way to control for confounding. Logistic regression can account for stratification by having a different constant term for each stratum. Let us denote Y_\in\ the label (e.g. case status) of the \ellth observation of the ith stratum and X_\in\mathbb^p the values of the corresponding predictors. We then take the likelihood of one observation to be : \mathbb(Y_=1, X_)=\frac where \alpha_i is the constant term for the ith stratum. The parameters in this model can be estimated using maximum likelihood estimation. For exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Score Test
In statistics, the score test assesses constraints on statistical parameters based on the gradient of the likelihood function—known as the ''score''—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than sampling error. While the finite sample distributions of score tests are generally unknown, they have an asymptotic χ2-distribution under the null hypothesis as first proved by C. R. Rao in 1948, a fact that can be used to determine statistical significance. Since function maximization subject to equality constraints is most conveniently done using a Lagrangean expression of the problem, the score test can be equivalently understood as a test of the magnitude of the Lagrange multipliers associated with the constraints where, again, if the constraints are non-binding at the maximum likelihood, the vector of Lagrange m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Logistic Regression
Conditional logistic regression is an extension of logistic regression that allows one to account for stratification and matching. Its main field of application is observational studies and in particular epidemiology. It was devised in 1978 by Norman Breslow, Nicholas Day, Katherine Halvorsen, Ross L. Prentice and C. Sabai. It is the most flexible and general procedure for matched data. Background Observational studies use stratification or matching as a way to control for confounding. Logistic regression can account for stratification by having a different constant term for each stratum. Let us denote Y_\in\ the label (e.g. case status) of the \ellth observation of the ith stratum and X_\in\mathbb^p the values of the corresponding predictors. We then take the likelihood of one observation to be : \mathbb(Y_=1, X_)=\frac where \alpha_i is the constant term for the ith stratum. The parameters in this model can be estimated using maximum likelihood estimation. For exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ben Klemens
Ben Klemens (born April 10, 1975) is an Australian economist, author, and co-host of the podcast 'Pod, Paper, Scissors'. He works for the US Treasury Department and was previously a nonresident fellow at the Brookings Institution's Center on Social and Economic Dynamics. He holds a PhD in Social Sciences from Caltech. Klemens is the author of the proposal to the Unicode consortium for the Falafel emoji, which will be appearing across web platforms in 2019. Statistical computing In the realm of statistical computing, Klemens has done extensive work on statistical analysis for large data sets and non-traditional models such as agent-based models. He developed an innovative library of statistics functions for C, named Apophenia, and has written a textbook on statistical computing, ''Modeling with Data''. Software patent policy Klemens has also worked on the policy aspects of computing, and in particular the issue of software patents. He has argued in a book entitled ''Math You ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simpson's Paradox
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations. Judea Pearl. ''Causality: Models, Reasoning, and Inference'', Cambridge University Press (2000, 2nd edition 2009). . The paradox can be resolved when confounding variables and causal relations are appropriately addressed in the statistical modeling (e.g., through cluster analysis). Simpson's paradox has been used to illustrate the kind of misleading results that the misuse of statistics can generate. Edward H. Simpson first described this phenomenon in a technical paper in 1951; the statisticians Karl Pearson (in 1899) and Udny Yule (in 1903) had mentioned similar effects earlier. The name ''Simpson's paradox'' was introduced by Col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
