NOEC

Extract the tested NOEC immediately below the first significant concentration from caller-supplied effect tests; report nonmonotone significance, and no-effect series remain right-censored errors.

Description

Select the concentration immediately below the first significant supplied effect test and flag later significance reversals.

A no observed effect concentration, or NOEC, is tied to a study design and a statistical comparison with control. Failure to detect an effect is not evidence that the true effect is zero; test sensitivity, replication, and the chosen concentration spacing influence the result.^[1]

This tool does not perform those statistical comparisons. It uses p-values you have already calculated, an alpha threshold, and an increasing concentration series beginning with a zero control. It returns the concentration immediately before the first significant treated concentration.

The monotoneSignificancePattern flag records whether every higher tested concentration remains significant after that first significant result. A later nonsignificant result gives false, while the selected endpoint still remains below the first significant concentration.

When to use NOEC

Use it to audit a prepared concentration-and-p-value series when this selection rule matches the analysis plan. Treat the output as an endpoint summary of supplied tests.

How to use NOEC and interpret its calculation

Enter at least two concentrations beginning with a zero control and increasing strictly, using one consistent concentration unit.
Enter aligned effectPValues between 0 and 1, including a control placeholder, and alpha strictly between 0 and 1. The control p-value is validated but excluded from significance selection.
Run the tool and read noEffectConcentration, firstSignificantConcentration, and monotoneSignificancePattern together. If no treated test is significant, report that situation separately rather than forcing an endpoint.

The implementation marks treated concentrations significant only when p < alpha. It finds the first significant treated entry, returns the preceding concentration, and checks whether all entries from the first significant result onward are significant.

significant_i = p_i < alpha for treated entries; selected concentration = the entry immediately before the first significant treated entry

A p-value equal to alpha is nonsignificant under this implementation.

json

{
  "input": {
    "concentrations": [
      0,
      1,
      2,
      4
    ],
    "effectPValues": [
      1,
      0.8,
      0.3,
      0.01
    ],
    "alpha": 0.05
  },
  "output": {
    "noEffectConcentration": 2,
    "firstSignificantConcentration": 4,
    "monotoneSignificancePattern": true
  }
}

Pattern	Behavior
First treated concentration significant	The returned preceding concentration is zero, the control reference.
A later concentration becomes nonsignificant	The endpoint stays below the first significant entry; the monotonicity flag is false.
No significant treated concentration	The tool returns an error because the selection rule has no first significant entry.

Limitations and assumptions

At least a control and one treated concentration are required; a control-only list is rejected before endpoint selection. It does not compute p-values, choose a test, correct multiple comparisons, assess effect direction or biological importance, or fit a concentration-response curve. The user must supply appropriately justified effect tests.

The selected value is not the highest nonsignificant concentration anywhere in a nonmonotone series. A returned zero is not a positive treated concentration shown to be without effects. No-significance data may imply an endpoint beyond the tested range rather than an invalid experiment.

Alternative or Complementary methods

A benchmark-dose approach can use a fitted response model rather than a tested-concentration endpoint. If using any point of departure in an exposure margin, independently justify the endpoint and align its dose or concentration basis with exposure.

References

Test No. 211: Daphnia magna Reproduction Test (2012) — Organisation for Economic Co-operation and Development

Similar or alternative tools

Linear Dose Probit Extra Risk BMD
Calculate a model-based benchmark dose from supplied probit parameters.
Margin of Exposure
Compare a separately justified point of departure with an exposure range.