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

$+LR=\dfrac{Sensitivity}{1-Specificity}$

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

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

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

1.1.4 Negative Likelihood Ratio

$-LR=\dfrac{1-Sensitivity}{Specificity}$

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

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

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

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