Medical statistics

Applications of statistics to medicine and the health sciences

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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.[1] 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.[2] However, "biostatistics" more commonly connotes all applications of statistics to biology.[2] 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.[3]

## Use in medical hypothesis testing

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In medical hypothesis testing, the medical research is often evaluated by means of the confidence interval, the P value, or both.[4]

### Confidence interval

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This probability distribution presents two different confidence intervals.[1]

Frequently reported in medical research studies is the confidence interval (CI), which indicates the consistency and variability of the medical results of repeated medical trials. In other words, the confidence interval shows the range of values where the expected true estimate would exist within this specific range, if the study was performed many times.[1]

Most biomedical research is not able to use a total population for a study. Instead, samples of the total population are what are often used for a study. From the sample, inferences can be made of the total population by means of a sample statistic and the estimation of error, presented as a range of values.[1][4]

### P value

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Frequently used in medical studies is the statistical significance of P < 0.05.[4]

The P value is the probability of no effect or no difference (null hypothesis) of obtaining a result essentially equal to what was actually observed. The P stands for probability and measures how likely it is that any observed difference between groups is due to chance. The P value function between 0 and 1. The closer to 0, the less likely the results are due to chance. The closer to 1, the higher the probability that the results are actually due to chance.[4]

## Pharmaceutical statistics

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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.[1]

There are many professional bodies concerned with this field including:

* European Federation of Statisticians in the Pharmaceutical Industry
* Statisticians In The Pharmaceutical Industry

## Clinical biostatistics

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Clinical biostatistics is concerned with research into the principles and methodology used in the design and analysis of clinical research and to apply statistical theory to clinical medicine.[1][5]

Clinical biostatistics is taught in postgraduate biostatistical and applied statistical degrees, for example as part of the BCA Master of Biostatistics program in Australia.

## Basic concepts

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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.
* 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

* Absolute risk reduction
* Control event rate
* Experimental event rate
* Number needed to harm
* Number needed to treat
* Odds ratio
* Relative risk reduction
* Relative risk
* Relative survival
* Minimal clinically important difference

## Related statistical theory

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* 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.[6]
* Actuarial statistics: the statistics used by actuaries to calculate liabilities, evaluate risks and plan the financial course of insurance, pensions, etc.[7]

## See also

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* 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

## References

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1. ^ a b c d e f "Finding and Using Health Statistics". US National Library of Medicine. Retrieved 2024-03-15.
2. ^ a b Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-850994-4
3. ^ Kirkwood, Betty R. (2003). Essential Medical Statistics. Malden, Massachusetts: Blackwell. ISBN 978-0-86542-871-3.
4. ^ a b c d Shreffler, Jacob; Huecker, Martin R. (2024). "Hypothesis Testing, P Values, Confidence Intervals, and Significance". StatPearls. Treasure Island (FL): StatPearls Publishing. PMID 32491353. Retrieved 2024-03-16.
5. ^ "Our aims". International Society For Clinical Biostatistics. 22 February 2015. Retrieved 15 March 2024.
6. ^ 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.
7. ^ Benjamin, Bernard (1993). The analysis of mortality and other actuarial statistics. England, Institute of Actuaries: Oxford. ISBN 0521077494.

## Further reading

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* 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

## External links

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* Health-EU Portal EU health statistics

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Statistics

* Outline
* Index

Descriptive statistics

| Continuous data|

| Center|

* Mean
* Arithmetic
* Arithmetic-Geometric
* Contraharmonic
* Cubic
* Generalized/power
* Geometric
* Harmonic
* Heronian
* Heinz
* Lehmer
* Median
* Mode

|

Dispersion|

* Average absolute deviation
* Coefficient of variation
* Interquartile range
* Percentile
* Range
* Standard deviation
* Variance

Shape|

* Central limit theorem
* Moments
* Kurtosis
* L-moments
* Skewness

Count data|

* Index of dispersion

Summary tables|

* Contingency table
* Frequency distribution
* Grouped data

Dependence|

* Partial correlation
* Pearson product-moment correlation
* Rank correlation
* Kendall's τ
* Spearman's ρ
* Scatter plot

Graphics|

* Bar chart
* Biplot
* Box plot
* Control chart
* Correlogram
* Fan chart
* Forest plot
* Histogram
* Pie chart
* Q–Q plot
* Radar chart
* Run chart
* Scatter plot
* Stem-and-leaf display
* Violin plot

Data collection

| Study design|

* Effect size
* Missing data
* Optimal design
* Population
* Replication
* Sample size determination
* Statistic
* Statistical power

|

Survey methodology|

* Sampling
* Cluster
* Stratified
* Opinion poll
* Questionnaire
* Standard error

Controlled experiments|

* Blocking
* Factorial experiment
* Interaction
* Random assignment
* Randomized controlled trial
* Randomized experiment
* Scientific control

Adaptive designs|

* Adaptive clinical trial
* Stochastic approximation
* Up-and-down designs

Observational studies|

* Cohort study
* Cross-sectional study
* Natural experiment
* Quasi-experiment

Statistical inference

| Statistical theory|

* Population
* Statistic
* Probability distribution
* Sampling distribution
* Order statistic
* Empirical distribution
* Density estimation
* Statistical model
* Model specification
* Lp space
* Parameter
* location
* scale
* shape
* Parametric family
* Likelihood (monotone)
* Location–scale family
* Exponential family
* Completeness
* Sufficiency
* Statistical functional
* Bootstrap
* U
* V
* Optimal decision
* loss function
* Efficiency
* Statistical distance
* divergence
* Asymptotics
* Robustness

|

Frequentist inference|

| Point estimation|

* Estimating equations
* Maximum likelihood
* Method of moments
* M-estimator
* Minimum distance
* Unbiased estimators
* Mean-unbiased minimum-variance
* Rao–Blackwellization
* Lehmann–Scheffé theorem
* Median unbiased
* Plug-in

|

Interval estimation|

* Confidence interval
* Pivot
* Likelihood interval
* Prediction interval
* Tolerance interval
* Resampling
* Bootstrap
* Jackknife

Testing hypotheses|

* 1- & 2-tails
* Power
* Uniformly most powerful test
* Permutation test
* Randomization test
* Multiple comparisons

Parametric tests|

* Likelihood-ratio
* Score/Lagrange multiplier
* Wald

Specific tests|

* Z-test (normal)
* Student's t-test
* F-test

Goodness of fit|

* Chi-squared
* G-test
* Kolmogorov–Smirnov
* Anderson–Darling
* Lilliefors
* Jarque–Bera
* Normality (Shapiro–Wilk)
* Likelihood-ratio test
* Model selection
* Cross validation
* AIC
* BIC

Rank statistics|

* Sign
* Sample median
* Signed rank (Wilcoxon)
* Hodges–Lehmann estimator
* Rank sum (Mann–Whitney)
* Nonparametric anova
* 1-way (Kruskal–Wallis)
* 2-way (Friedman)
* Ordered alternative (Jonckheere–Terpstra)
* Van der Waerden test

Bayesian inference|

* Bayesian probability
* prior
* posterior
* Credible interval
* Bayes factor
* Bayesian estimator
* Maximum posterior estimator

* Correlation
* Regression analysis

| Correlation|

* Pearson product-moment
* Partial correlation
* Confounding variable
* Coefficient of determination

|

Regression analysis|

* Errors and residuals
* Regression validation
* Mixed effects models
* Simultaneous equations models
* Multivariate adaptive regression splines (MARS)

Linear regression|

* Simple linear regression
* Ordinary least squares
* General linear model
* Bayesian regression

Non-standard predictors|

* Nonlinear regression
* Nonparametric
* Semiparametric
* Isotonic
* Robust
* Homoscedasticity and Heteroscedasticity

Generalized linear model|

* Exponential families
* Logistic (Bernoulli) / Binomial / Poisson regressions

Partition of variance|

* Analysis of variance (ANOVA, anova)
* Analysis of covariance
* Multivariate ANOVA
* Degrees of freedom

Categorical / multivariate / time-series / survival analysis

| Categorical|

* Cohen's kappa
* Contingency table
* Graphical model
* Log-linear model
* McNemar's test
* Cochran–Mantel–Haenszel statistics

|

Multivariate|

* Regression
* Manova
* Principal components
* Canonical correlation
* Discriminant analysis
* Cluster analysis
* Classification
* Structural equation model
* Factor analysis
* Multivariate distributions
* Elliptical distributions
* Normal

Time-series|

| General|

* Decomposition
* Trend
* Stationarity
* Seasonal adjustment
* Exponential smoothing
* Cointegration
* Structural break
* Granger causality

|

Specific tests|

* Dickey–Fuller
* Johansen
* Q-statistic (Ljung–Box)
* Durbin–Watson
* Breusch–Godfrey

Time domain|

* Autocorrelation (ACF)
* partial (PACF)
* Cross-correlation (XCF)
* ARMA model
* ARIMA model (Box–Jenkins)
* Autoregressive conditional heteroskedasticity (ARCH)
* Vector autoregression (VAR)

Frequency domain|

* Spectral density estimation
* Fourier analysis
* Least-squares spectral analysis
* Wavelet
* Whittle likelihood

Survival|

| Survival function|

* Kaplan–Meier estimator (product limit)
* Proportional hazards models
* Accelerated failure time (AFT) model
* First hitting time

|

Hazard function|

* Nelson–Aalen estimator

Test|

* Log-rank test

Applications

| Biostatistics|

* Bioinformatics
* Clinical trials / studies
* Epidemiology
* Medical statistics

|

Engineering statistics|

* Chemometrics
* Methods engineering
* Probabilistic design
* Process / quality control
* Reliability
* System identification

Social statistics|

* Actuarial science
* Census
* Crime statistics
* Demography
* Econometrics
* Jurimetrics
* National accounts
* Official statistics
* Population statistics
* Psychometrics

Spatial statistics|

* Cartography
* Environmental statistics
* Geographic information system
* Geostatistics
* Kriging

* Category
* Mathematics portal
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* WikiProject

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