# Medical statistics

### From Ganfyd

See also Wiki page on "biostatistics" and links below.

## Hypothesis testing

Hypotheses are almost impossible to prove, much easier to disprove. Hypothesis testing usually attempts to disprove a **null hypothesis**. If p >= 0.05, then a study is generally considered to have failed to disprove the null hypothesis.

## Types of data

- Categorical, including nominal and ordinal
- Interval (3-2, 4-3…) or ratio (6 = 2*3, 9 = 3*3, 12 = 4*3 = 2*6).
- Continuous

## Estimates

Estimates.

- Precision (scatter of an estimate)
- accuracy (amount of bias)

## Describing a population

- μ (mu)
- = mean of population
- σ (sigma)
- = standard deviation of population
- μ ± 2σ
- = confidence interval for μ

Many biological variables are distributed with a *"normal distribution"*.

Rare events typically have a *"Poisson distribution"*.

## Causation

Features that suggest that a causal relationship include:

- the strength of the relationship;
- the consistency (in different trials etc. - inconsistency may indicate bias) of the relationship;
- its specificity (cause -> only one effect, effect due to single cause);
- the temporal relationship;
- the biologic gradient (dose-response);
- biological plausibility;
- coherence;
- evidence from experiments;
- analogy

## Interaction

American term "effect modification" may be preferable. Occurs when the effect is different in different groups, e.g if a drug is harmful in children, progressively less harmful in older age groups, and useful in the elderly. Age "interacts" with the effects of the drug.

## Common statistical tests

Trisha Greenhalgh has published a useful list of tests in her "how to read a paper" series in the BMJ - see below. The following table is based on one from this paper.

### Some commonly used statistical tests - table

Parametric test | Example of non-parametric | Purpose of test | Example |
---|---|---|---|

Two-sample (unpaired) t test | Mann-Whitney U test | Compares two independent samples drawn from the same population | To compare girls’ heights with boys’ heights |

One sample (paired) t test | Wilcoxon matched pairs test | Compares two sets of observations on a single sample | To compare weight of infants before and after a feed |

One way analysis of variance (F test) using total sum of squares | Kruskal-Wallis analysis of variance by ranks | Effectively, a generalisation of the paired t or Wilcoxon matched pairs test where three or more sets of observations are made on a single sample | To determine whether plasma glucose is higher one, two, or three hours after a meal |

Two way analysis of variance | Two way analysis of variance by ranks | As above, but tests the influence (and interaction) of two different covariates | In the above example, to determine whether the results differ in male and female subjects |

χ^{2} test
| Fisher’s exact test | Tests the null hypotheses that the distribution of a discontinuous variable is the same in two (or more) independent samples | To determine whether acceptance into medical school is more likely if the applicant was born in Britain |

Product moment correlation coefficient (Pearson’s r)
| Spearman’s rank coefficient (r^{2})
| Assesses the strength of the straight line association between two continuous variables | To assess whether and to what extent plasma HbA1 concentration is related to plasma triglyceride concentration in diabetic patients |

Regression by least squares method | Non-parametric regression (various tests) | Describes the numerical relation between two quantitative variables, allowing one value to be predicted from the other | To see how peak expiratory flow rate varies with height |

Multiple regression by least squares method | Non-parametric regression (various tests) | Describes the numerical relation between a dependent variable and several predictor variables (covariates) | To determine whether and to what extent a person’s age, body fat, and sodium intake determine their blood pressure |

## Variance, standard error of the mean

See Variance and standard error of the mean

## χ^{2} test

See Chi square test. See also Wiki page on Chi Square

## Student’s t-test

See Statistical tests for comparing means

## Mann-Whitney U Test

See Statistical tests for comparing means

## Paired t-test

See Statistical tests for paired or matched data - Paired t-test

## Wilcoxon test

See Statistical tests for paired or matched data - Wilcoxon test

## Pearson product moment coefficient

See Statistical tests for product moment coefficients - Pearson product moment coefficient.

## Spearman correlation

Spearman correlation coefficient is a non-parametric equivalent of Pearson product moment coefficient.

See Statistical tests for product moment coefficients - Spearman correlation.

## McNemar test

Used for proportions in matched groups. See McNemar test.

## Regression

Including analysis of variance. See Statistical tests for regression.

## Survival analysis

See Statistical tests for survival analysis. May include analysis of regression to identify risk factors.

## Kappa test

The kappa (κ) test is a test of agreement - e.g. between experts, sphygmomanometers.

See Statistical tests for agreement - Kappa test.

## Meta-analysis

This is a statistical technique which assumes the study populations in a number of clinical trials are similar and examines the pooled outcomes. It can be extremely useful when a number of randomised controlled trials have collected data on an issue, in which any one trial is under-powered to detect a clinically significant effect in the variable of interest. For a fuller account try What is meta-analysis?

## Internet resources on medical statistics

*Statistics at Square One*by T D V Swinscow, revised by M J Campbell, University of Southampton, published by BMJ is available online (currently - October 2007 - 9th edition)- Steve's attempt to teach statistics (or here)
- HyperStat Online Statistics Textbook
- Statistics jokes
- StatPages.net
*"Web pages that perform statistical calculations!"*- claims (October 2007) to have*"Over 600 Links (including 380 Calculating Pages) -- And Growing!"*(previously here, with the same claim) - Dr Robert Newcombe has lots of spreadsheets for downloading, for various statistical calculations at his website.
- Supercourse has lectures on "biostatistics".
*Medpage Guide to Biostatistics*- covering study design, research methods, and many aspects of medical statistics- Trisha Greenhalgh has written an excellent series of papers "How to read a paper" in the BMJ, including:

- The Medline database (BMJ 1997;315:180-183 (19 July))
- Getting your bearings (deciding what the paper is about) (BMJ 1997;315:243-246 (26 July))
- Assessing the methodological quality of published papers (BMJ 1997;315:305-308 (2 August))
- Statistics for the non-statistician. I: Different types of data need different statistical tests (BMJ 1997;315:364-366 (9 August))
- Statistics for the non-statistician. II: "Significant" relations and their pitfalls (BMJ 1997;315:422-425 (16 August))
- Papers that report drug trials (BMJ 1997;315:480-483 (23 August))
- Papers that report diagnostic or screening tests (BMJ 1997;315:540-543 (30 August))
- Papers that tell you what things cost (economic analyses) (BMJ 1997;315:596-599 (6 September))
- Papers that summarise other papers (systematic reviews and meta-analyses) (BMJ 1997;315:672-675 (13 September))
- Papers that go beyond numbers (qualitative research) (BMJ 1997;315:740-743 (20 September))