Statistics for neurologists

K K Jain MD (Dr. Jain is a consultant in neurology and has no relevant financial relationships to disclose.)
Originally released July 13, 1999; last updated July 13, 2017; expires July 13, 2020


This article describes the role of statistics in the practice of medicine and, particularly, in neurology. Most of the applications are in clinical trials. Statistical methods are important for evaluating results of diagnostic tests and epidemiology of disease. They are also important in evaluating results of clinical trials, making diagnoses, and choosing appropriate treatment. Logistic regression can be used for outcome studies and estimation of risk factors as predictors of disease. Bayes' theorem has been applied to determine if a patent foramen ovale is incidental or causal in patients with cryptic stroke.

Key points


• Statistics has a broad application in medicine, including neurology.


• Statistical issues are important in evaluating results of clinical trials, making diagnoses, and choosing appropriate treatment.


• Bayesian analysis, a commonly used approach, begins with the observed differences between treatment A and treatment B and then asks how probable it is that treatment A is superior to treatment B.

Historical note and terminology

"Statistics" is defined as methodology for learning from experience, usually in the form of numbers derived from several separate measurements with individual variations. The scope of application in medicine is broad. Practicing physicians, including neurologists, encounter statistics in audits, resource allocations, publications, and hospital-utility data. Two basic terms used in describing disease epidemiology are “incidence” and “prevalence.” Incidence is the rate of new cases of the disease occurring within a period of time, eg, per month or per year, and should not be confused with prevalence, which is the proportion of cases in the population at a given time. Incidence conveys information about the risk of contracting the disease, whereas prevalence indicates how widespread the disease is. Consideration of incidence of a disease may be important for making decisions about recommending prophylactic therapy. Inadequate understanding of basic statistics may lead to errors, and an excellent example was given in article on straight and crooked thinking in medicine as follows (Asher 1954):


An investigator published an article showing that of 200 epileptic subjects, 24% had had infantile convulsions in the first two years of life, whereas of 200 normal subjects only 2% had had infantile convulsions. He went on to argue that the pronounced difference between the 24% in the epileptics and in the 2% in the control group made it clear that convulsions within the first two years of life ought to be taken as a manifestation of epilepsy and that any child having convulsions in infancy should be treated with anticonvulsant drugs for several years. The argument appears most convincing, doesn't it? The fallacy is not at all obvious. The incidence of epilepsy in the population has been left out. Now, this is about 1 in 400. So among 40,000 people there would be 100 epileptics, 24 of whom had infantile convulsions. But among 40,000 people there would be 800 normal people (2% of 40,000) who had suffered from infantile convulsions. So it would mean treating 800 people, of whom only 24 had epilepsy, in other words, submitting 32 normal children to prolonged anticonvulsant therapy in order to make sure of treating one epileptic early in life.

The most useful statistical procedure for assessing diagnostic tests is based on a theorem named after Reverend Thomas Bayes, who discovered it in 1763 (Bayes 1763). The ideas incorporated in this theorem are familiar to all clinicians making clinical diagnoses. The likelihood of a disease being present depends not only on the signs and symptoms, but also on the frequency of the disease in the community. The latter probability is termed as "prior probability." Application of statistics in clinical trials did not start until the mid-twentieth century (Hill 1951). Statistical issues are now important in evaluating results of clinical trials, making diagnoses, and choosing appropriate treatment. For those involved in clinical research, statistics cover all stages from planning and design of studies to data analysis and interpretation. This article will deal with a few important basics of statistics that are useful to neurologists in the interpretation of data from clinical trials and for evaluation of diagnostic procedures. Statistical programs can be installed on personal computers.

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