# Dose response curve fits

## Viability curve fits

Viability is the cell count relative to control at a specific time point (usually 72 hours). As a ratio of two positive numbers, it cannot go below zero.

Thunor fits viability data to a three parameter log-logistic model. The three parameters are E_{max},
EC_{50}, and Hill coefficient. A constrained fit is used: E_{max} is constrained to be between 0 and
1, and the Hill coefficient (slope) is constrained to be non-negative.

Equation: Three parameter Hill curve (log-logistic curve)

## DIP rate curve fits

The drug-induced proliferation rate (DIP rate) is defined as the steady-state rate of proliferation in the presence of a particular concentration of drug. It is quantified as the slope of the line on a plot of population doublings versus time. Unlike viability, DIP rate can go negative, indicating a cytotoxic drug effect.

Thunor fits DIP data to a four parameter log-logistic model. The four parameters are E_{min}, E_{max},
EC_{50}, and the Hill coefficient. For ease of comparison, the relative DIP rate is often used, where the
effect is shown relative to the minimum. Thus, on the relative scale, DIP curve fits will start from 1 on the y-axis.

Equation: Four parameter Hill curve (log-logistic curve)

## Curve fit parameters

For details on derived metrics like IC_{50}, see dose response parameters.