# Medical statistics

## 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

## 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;
• 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
χ2 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 (r2) 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

## Spearman correlation

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

## 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.

## 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 - 9th edition)
• Steve's attempt to teach statistics (or here)
• HyperStat Online Statistics Textbook
• Statistics jokes
• StatPages "Web pages that perform statistical calculations!" - claims (October) to have "Over 600 Links (including 380 Calculating Pages) -- And Growing!" (previously here, with the same claim)
• 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))