decision_threshold: Compute Optimal Decision Threshold

In mispitools: Missing Person Identification Tools

Compute Optimal Decision Threshold

Description

Calculates the optimal likelihood ratio (LR) threshold for classifying matches versus non-matches, based on the trade-off between false positive and false negative rates.

The optimal threshold minimizes a weighted Euclidean distance that balances the costs of different types of errors.

Usage

decision_threshold(datasim, weight = 10)

Arguments

datasim	A data.frame with columns Related and Unrelated containing LR values. Can be output from sim_lr_genetic, sim_lr_prelim, lr_to_dataframe, or lr_combine.
weight	Numeric. The relative weight of false positives compared to false negatives. A value > 1 penalizes false positives more heavily. Default: 10 (false positives are 10x worse than false negatives).

Details

If the input is a list (output from sim_lr_genetic), it is automatically converted to a data.frame using lr_to_dataframe.

Algorithm: The function computes the weighted Euclidean distance for each potential threshold value:

D = \sqrt{FNR^2 + (weight \times FPR)^2}

The threshold that minimizes this distance is returned as optimal.

Weight interpretation:

• weight = 1: Equal importance to FPR and FNR

• weight = 10: FPR is 10x more costly than FNR

• weight > 10: Very conservative (minimizes false positives)

• weight < 1: Aggressive (minimizes false negatives)

In missing person cases, false positives (wrongly identifying someone as the missing person) are typically considered more serious than false negatives (failing to identify a true match), justifying weight > 1.

Value

Prints and invisibly returns the suggested LR threshold value.

References

Marsico FL, Vigeland MD, Egeland T, Herrera Pinero F (2021). "Making decisions in missing person identification cases with low statistical power." Forensic Science International: Genetics, 52, 102519. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.fsigen.2021.102519")}

See Also

threshold_rates for computing error rates at a given threshold, plot_decision_curve for visualizing the FPR/FNR trade-off, plot_lr_distribution for LR distribution visualization.

Examples

# Simulate LRs
lr_sims <- sim_lr_prelim("sex", numsims = 500, seed = 123)

# Find optimal threshold (FP 10x worse than FN)
threshold <- decision_threshold(lr_sims, weight = 10)

# Check error rates at this threshold
threshold_rates(lr_sims, threshold)

# More conservative threshold (FP 20x worse)
decision_threshold(lr_sims, weight = 20)

mispitools documentation built on Aug. 26, 2026, 1:08 a.m.