## BIOSTATISTICS

I. Diagnostic Tests

 Disease Present Disease Absent Test result is Positive A B Test result is Negative C D

__A _ = "Sensitivity" aka "True Positive Rate"
A + C

__D _ = "Specificity" aka "True Negative Rate"
B + D

__A _ = "Positive Predictive Value"
A + B

__D _ = "Negative Predictive Value"
C + D

1 - Specificity = "False Positive Rate"

1 - Sensitivity = "False Negative Rate"

True Positive Rate_ = "Positive Likelihood Ratio"
False Positive Rate

False Negative Rate = "Negative Likelihood Ratio"
True Negative Rate

Probability___ = "Odds," often expressed as X:Y
1 - Probability

Odds of an event in one studied group_____ = "Odds Ratio"
Odds of same event in another studied group

"Reliability" = The ability of a test repeatedly to generate the same results given the same conditions

"Validity" = The degree to which a test measures what it is purported to measure

"Bias" = a systematic error that leads to results that do not represent the true findings

"Confounders" = Subject characteristics that are nonrandomly distributed between study groups that affect the results being studied and decrease its validity

• If the "prior odds" of a diagnosis is known, a test result with a known positive or negative likelihood ratio can be used to calculate the "posterior odds" i.e. odds adjusted for the result of the test, i.e. Posterior Odds = Prior Odds x Negative Likelihood Ratio (if result is "negative") or Priod Odds x Positive Likelihood Ratio (if result is "positive"). Note that use of multiple likelihood ratios is only valid if the tests in question are "conditionally independent," i.e. not reflective of the same processes (e.g. Hb and HCT would not be conditionally independent).
• Note that sensitivity and specificity are independent of disease prevalence but positive and negative predictive values are not.
• For tests which return a continuously distributed numerical result (e.g. concentration of a solute), the sensitivity, specificity, and positive and negative predictive values will depend on the "cutoff" scores used for normal vs. abnormal results.
• The effect of cutoff values on sensitivity and specificity is reflected in the "Receiver Operative Characteristic" (ROC) curve, which plots the True Positive Rate (y axis) against the False Positive Rate (x axis) for each of a variety of cutoff values--each cutoff value is a point on the curve. The ROC curve reflects the "goodness" of a test--the more the curve hugs the upper-left corner of the graph space, the "better" the test. The ROC curve of a useless test hugs the main diagonal from lower left to upper right

II. Effects of Interventions

Events in Control Group - Events in Intervention Group = "Absolute Risk Reduction"

_________1_________ = "Number Needed to Treat"
Absolute Risk Reduction

Risk of disease in one group___ = "Relative Risk"
Risk of disease in another group

III. Other terms

"Incidence" = Number of new cases of a disease within a given time period in a given population

"Prevalence" = Number of cases of a disease in a population at a given time

"Kappa value" = A chance-corrected measure of inter-observer agreement. Perfect agreement = kappa of 1.0; absolute disagreement = kappa of 0.  See Landis JR, Koch GG.  The measurement of observer agreement for categorical data.  Biometrics 1977;33:(1):159-74.