Logit Slope Calculator

OLSof actual fitted logit response slope against actual independently defined log-dose coordinates, not maximum-likelihood binomial dose-response fit, automatic link transformation or statistical uncertainty.

Description

A logit slope relates independently transformed response scores to a defined dose coordinate.

A logit slope relates independently transformed response scores to a defined dose coordinate.^[1]

Least squares on those scores does not fit the binomial likelihood of raw response counts.

When to use Logit Slope Calculator

Use this tool to calculate or review the supplied observations under the stated rules. Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.

How to use Logit Slope Calculator and understand its results

Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.
Enter actualLogDoseCoordinates, actualIndependentlyEstablishedLogitScores, using the field meanings and rules below, then run the tool.
Read result.observedLeastSquaresLinkSlope, result.observedLeastSquaresLinkIntercept. Use the units and subtraction order below to interpret each value; retain negative differences where returned.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
actualLogDoseCoordinates	Actual log dose coordinates	list of number	Required
actualIndependentlyEstablishedLogitScores	Actual independently established logit scores	list of number	Required

Supply at least two aligned finite predictor and response coordinates, already transformed into the declared logarithmic and response-link scales. Predictor variance must be nonzero; sorting is not required. Fit ordinary least squares with a free intercept. No transformation, binomial likelihood fit, weighting, uncertainty or endpoint estimate is added.

slope=Σ((x_i−mean(x))(y_i−mean(y)))/Σ((x_i−mean(x))²); intercept=mean(y)−slope×mean(x)

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.observedLeastSquaresLinkSlope	Ordinary least-squares slope of the supplied response-link coordinate versus log-dose coordinate.	number
result.observedLeastSquaresLinkIntercept	Free-intercept ordinary least-squares fit intercept on the supplied response-link scale.	number

json

{
  "input": {
    "actualLogDoseCoordinates": [
      0,
      1,
      2
    ],
    "actualIndependentlyEstablishedLogitScores": [
      1,
      3,
      5
    ]
  },
  "output": {
    "result": {
      "observedLeastSquaresLinkSlope": 2,
      "observedLeastSquaresLinkIntercept": 1
    }
  }
}

Limitations and assumptions

Chemical identity, route, assay, exposure basis and reference applicability are caller-established. The output supplies no causal conclusion, universal toxicity threshold or authoritative regulatory determination.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Probit Slope Calculator: A probit slope describes a relationship between independently transformed response scores and a stated dose coordinate. For a complementary comparison, use Probit Analysis Calculator: A probit-analysis record needs the fitted link, dose transformation and endpoint context.

References

Logit Slope Calculator — tool.io

Similar or alternative tools

Probit Slope Calculator
A probit slope describes a relationship between independently transformed response scores and a stated dose coordinate.
Probit Analysis Calculator
A probit-analysis record needs the fitted link, dose transformation and endpoint context.