Probit Analysis

Probit Analysis is a specialized regression model of binomial response variables (variables with only two outcomes). It transforms the sigmoid dose-response curve to a straight line that can then be analyzed by regression either through least squares or maximum likelihood.

Applications of Probit Analysis

Probit Analysis is commonly used in toxicology to determine the relative toxicity of chemicals to living organisms. This is done by testing the response of an organism under various concentrations of chemicals, comparing the concentrations at which responses are encountered. The response is binomial (e.g., death/no death), and the relationship between the response and concentration is typically sigmoid. Probit analysis transforms the sigmoid relationship into a linear one and performs regression. The most commonly used outcome is LC50 (liquids) or LD50 (solids), representing the concentration or dose at which 50% of the population responds.

The Estimation of the Median Effective Dose

In Probit analysis, batches of subjects (e.g., insects) are exposed to different concentrations of a chemical, and after a suitable interval, the numbers dead and alive are recorded. The experimental results are transformed to estimate parameters using the probit transformation.

Probit Transformation and Equation

The probit of the proportion \(P\) is defined as the probability \(P\) in a normal distribution with a mean of 5 and a variance of 1. The relationship is expressed by the following linear equation:

Y = α + βX

Where \(Y\) is the probit and \(X\) is the logarithm of the dose.

Methods of Estimation

There are two methods for estimating the parameters in Probit analysis:

Method 1: Graphical Approach

  1. Determine the least tolerated and most tolerated doses.
  2. Select intermediate doses, observe mortality, and convert them to probit values.
  3. Apply correction factors to 0% and 100% mortality groups.
  4. Plot the probits against the logarithm of the dose and estimate the slope and intercept of the line.
  5. Perform a χ2 test to verify the adequacy of the regression line.

Method 2: Maximum Likelihood Estimation

  1. Calculate empirical proportions of responders for each dose and correct them using the Abbott equation.
  2. Convert the proportions to probit values and establish a provisional regression line.
  3. Iteratively refine the probit regression line using the maximum likelihood method until the χ2 statistic stabilizes.

The final result provides estimates of the lethal dose (LD50) and its 95% confidence limits.

Procedure to Perform Probit Analysis using OPSTAT

  1. Enter the data in the text area in the format: [dose] [total no. of subjects] [no. killed], as shown in the example below:
    2. 1.01 50 44
0.89 49 42
0.71 46 24
0.58 48 16
0.41 50 6
0 50 0
    Copy Data
  2. Submit the data using the Submit button.
  3. On the next page, enter the number of doses (excluding the control group) and press Analyze.
  4. The results will be displayed on a separate page and can be printed or saved.

References

Web hosting by Somee.com