Chapter 1 The role of biostatistics in clinical research

Under development

From clinical inquiry book - not sure where this may apply in this text; maybe as a review in an appendix since they should know this (it is entry level material for most clinicians)

1.1 Preliminaries

1.1.1 Contingency Table

\(D\) \(\neg D\)
\(S\) True Positive (TP) (a) False Positive (FP) (b)
\(\neg S\) False Negative (FN) (c) True Negative (TN) (d)

1.1.2 Sensitivity / Specificity

Sensitivity: \(P(S|D)=\dfrac{a}{a+c}\) (Rate of True Positives)

Specificity: \(P(\neg S|\neg D)=\dfrac{d}{b+d}\) (Rate of True Negatives)

1 - Sensitivity: \(P(\neg S|D)=\dfrac{c}{a+c}\) (Rate of False Negatives)

1 - Specificity: \(P(S|\neg D)=\dfrac{b}{b+d}\) (Rate of False Positives)

1.1.3 Positive Likelihood Ratio


\(+LR=\dfrac{P(S|D)}{P(S|\neg D)}\)

\(+LR= \dfrac{P(TP)}{P(FP)}\)

\(+LR= \dfrac{a(b+d)}{b(a+c)}\)

1.1.4 Negative Likelihood Ratio


\(-LR=\dfrac{P(\neg S|D)}{P(\neg S|\neg D)}\)

\(-LR= \dfrac{P(FN)}{P(TN)}\)

\(-LR= \dfrac{c(b+d)}{d(a+c)}\)

1.2 Bayes Formula

\(P(D|S)=\dfrac{P(S|D)\cdot P(D)}{P(S)}\)

The \(P(D)\) and \(P(S)\) are the “priors” - or “baseline” probabilities of the disease and the sign

1.2.1 Alternative format

\(P(\neg D|\neg S)=\dfrac{P(\neg S|\neg D)\cdot P(\neg D)}{P(\neg S)}\)

The \(P(\neg D)\) and \(P(\neg S)\) are the “priors” - or “baseline” probabilities of not having the disease or the sign