# Statistical terms

Understand the terms sensitivity, specificity, positive and negative predictive value and how these are affected by the prevalence of the disease in question

Describe bias, types of error, confounding factors and sample size calculations, and the factors that influence them

All these terms refer to characteristics of diagnostic tests. The easiest way to approach this is via a 2x2 table, and has been recommended in previous exams as an approach to questions on this topic.

## Types of Error

Draw a 2x2 table of disease state versus test outcome:

Disease Positive Disease Negative Total
Test Positive True Positives False Positives All Test Positives
Test Negative False Negatives True Negatives All Test Negatives
Total All Disease Positives All Disease Negatives
• True or false refers to whether the test was correct
• Positive or negative refers to the test result
• A Type I error is a false positive, when we incorrectly reject the null hypothesis
• The type I error rate can be decreased by decreasing α
• A Type II error is a false negative, when we incorrectly accept the null hypothesis
• The type II error rate can be decreased by decreasing β, usually expressed as increasing power
Power is the chance of detecting a difference if it exists. Power is equal to 1-β.

## Sensitivity and Specificity

### Sensitivity

• Sensitivity is the probability those with the disease test positive, i.e. the true positive rate, and expressed mathematically as:
• It refers to the ability of a test to detect the condition
• A highly sensitive test will likely be positive if the condition is present
• Therefore, a negative result on a sensitive test gives a high likelihood the disease is not present
• The mnemonic for this is SNOUT - Sensitive, Negative, rule OUT

### Specificity

• Specificity is the probability those without the disease test negative, i.e. the true negative rate ,and expressed mathematically as:
• It refers to the ability of a test to detect absence of the condition
• A highly specific test will likely be negative if the condition is not present
• Therefore a positive result on a specific test gives a high likelihood the disease is present
• The mnemonic for this is SPIN - Sensitive, Positive, rule IN

## Positive and Negative Predictive Values

• Positive and negative predictive values describe the proportion of test results which are true
• A high value indicates accuracy of the test
• Because of how they are derived, they are dependent on population prevalence of the disease
• Positive Predictive Value (PPV) is the probability that the disease is present when the test is positive:
• Negative Predictive Value (NPV) is the probability that the disease is absent when the test is negative:

### Remembering the Difference

• Rote learning these formulas is hard
• Remember that:
• Sensitivity and specificity are the same for any given prevalence of disease
Therefore they look at columns (disease positive or disease negative).
• PPV and NPV are not
Therefore they look at rows (test positive or test negative).

## Likelihood Ratios

The weakness of PPV and NPV as tools of evaluating the utility of a test in clinical practice is that they do not take into account the population prevalence, i.e. the prior probability, of a condition.

A classic example is the urine bHCG, which has a high positive predictive value for pregnancy. Tested on an exclusively male group however, the true positive rate will be 0 (since there are no pregnancies), and so all test positives will be false positives.

Therefore:

• The actual utility of a test in decision making is dependent upon the prior probability of the disease being present
• Likelihood Ratios relate the pre-test odds to the post-test odds
They are useful because (unlike the above values) they do not assume that the patient you are applying them to is identical to the sample from which the statistic was derived.
• The likelihood ratio multiplied by the pre-test odds gives the post-test odds of the disease being present
• A positive likelihood ratio is used when the test is positive:
• A negative likelihood ratio is used when the test is negative:

1. Myles PS, Gin T. Statistical methods for anaesthesia and intensive care. 1st ed. Oxford: Butterworth-Heinemann, 2001.
2. Course notes from "Introduction to Biostats", University of Sydney, School of Public Health, circa 2013.
Last updated 2019-11-02