Quantal Dose-Response

Some endpoints aren't graded - a subject either responds or it doesn't: dead or alive, protected or not. Quantal analysis fits the fraction responding as a function of dose and reads off the dose that affects half the population.

What it measures

The dose at which a defined fraction of subjects cross the all-or-nothing threshold. Depending on the endpoint this is reported as:

• LD₅₀ - the lethal dose for 50% of subjects.
• ED₅₀ - the effective dose in 50%.
• TD₅₀ - the toxic dose in 50%.

Any percentile (LD₁₀, LD₉₀) can be requested from the same fit.

Data you upload

• A dose column.
• The number responding and the number tested at each dose (or a fraction with a group size). The response is a count, not a continuous signal.

What you get back

• The fitted dose-response curve on a probit (or logit) scale.
• LD₅₀/ED₅₀/TD₅₀ with a 95% confidence interval.
• The slope of the probit line, which reflects how steeply response rises with dose.
• A goodness-of-fit check on the binomial counts.

Method note

Quantal data are binomial, not continuous, so the fit maximizes a binomial likelihood rather than minimizing least squares. Probit analysis transforms the response fraction through the inverse normal CDF so the dose-response relationship becomes linear in log-dose; the logit link is offered as an alternative. Confidence limits on the median effective dose follow Fieller's theorem, which is why they can be asymmetric.

Related

For graded (continuous) dose-response, see Dose-Response. For two-drug combinations, see Drug Synergy.