Combining CMFs and Evaluating Treatment Trade-Offs

Combining CMFs and Evaluating Treatment Trade-Offs

Start with compatible baselines and effects

A project can introduce several treatments and affect several crash types. Applying one total-crash percentage to every injury category can conceal trade-offs or overstate benefit. Define mutually exclusive baseline categories and select evidence for each relevant type and severity. Keep counts, periods, and comparison conditions consistent.

If one treatment only has evidence for angle injury crashes, do not assume it affects rear-end or PDO crashes identically. If another estimate concerns total crashes, it cannot automatically be applied uniformly to every severity stratum. An aggregate estimate can reflect a changed mix. Use disaggregated evidence where available or state the assumption and uncertainty.

Understand multiplicative combination

For treatments with suitably independent relative effects on the same defined population, a common simplifying approach multiplies CMFs:

$$CMF_c=CMF_1\times CMF_2$$

For hypothetical values 0.60 and 0.70, the product is 0.42, corresponding to an estimated 58% reduction under that assumption. Adding 40% and 30% to claim 70% treats each effect as acting on the full original baseline and can double count benefit. Adding two 60% reductions would even imply an impossible 120% reduction.

Multiplication is an assumption, not proof of the actual combined effect. Overlapping mechanisms, interaction, implementation order, or study definitions can make a simple product inappropriate. The fact that two estimates concern the same crash type does not alone prove they cannot be combined; the mechanisms and dependencies matter. Nor is there one universal legal ban on multiplying more than two or three factors.

The current TPCB reference list includes NCHRP Report 991, addressing combined CMFs. Consult the applicable combination guidance and available joint-treatment evidence rather than inventing an adjustment rule. TPCB reference materials

Work a fully specified hypothetical example

Assume a baseline of 12 crashes per year partitioned into angle injury 2.5, angle PDO 1.5, rear-end 5, and other 3. Treatment A has hypothetical CMFs of 0.70 for angle injury and 0.85 for angle PDO, with no assumed effect on the other categories. Treatment B is hypothetically assumed to have a CMF of 0.90 in each listed category and to act independently of A. These are arithmetic assumptions, not published values for a named device.

The treated total rounds to 9.92, the reduction to 2.08, and the percentage reduction to 17.3%. Adding rounded rows can produce a different displayed total, so retain unrounded intermediate values. The total combined CMF is $9.9225/12=0.826875$; it is not the angle-injury factor 0.63 applied to the entire intersection.

Test the assumptions

For an actual project, verify whether B's evidence supports each category rather than only an aggregate total. Review whether A and B target overlapping recognition failures, whether one study already included the other feature, and whether the combination changes user behavior. If evidence is limited, compare reasonable scenarios and state the assumption rather than hiding it in a formula.

A simpler estimate with transparent limits can be preferable to a precise-looking product built from mismatched studies. Consider joint-treatment studies, applicable guidance, or a conservative sensitivity range. Do not present the lowest combined CMF as a guaranteed result.

Evaluate collision and user trade-offs

A protected left-turn phase can reduce opposing-traffic conflicts and alter pedestrian interaction, waiting, and capacity. Examine permitted turns, right turns, pedestrian phases, and accessibility. The label “protected” does not establish that all pedestrian conflicts disappear.

A roundabout can reduce high-angle vehicle conflicts and operating speed while creating different crossing and navigation tasks. A barrier can reduce crossover exposure while introducing barrier strikes. A median change can shift access and turning to other locations. Evaluate affected users and nearby sites, not only the intended crash type at the installation.

Carry the result into economics and evaluation

Economic appraisal should value the category-specific changes using compatible cost units and base years. An increase in rear-end events is not automatically canceled by a reduction in angle events without considering numbers, severity, and uncertainty. Document nonmonetized effects such as accessibility, noise, community severance, or emergency access.

The evaluation plan should test the intended mechanisms and adverse outcomes. Record treatments, dates, maintenance, exposure, and comparison conditions. If multiple measures are installed together, the evaluation may estimate the package effect without separating each component. State that limit rather than attributing the whole change to whichever component is most visible.

Explain the conclusion clearly

A reviewable recommendation identifies the baseline, selected CMFs, applicability, combination assumptions, unrounded results, trade-offs, and sensitivity. It should say what the evidence supports and what remains uncertain. The purpose of the calculation is a defensible treatment decision, not a benchmark table with invented study ratings or a promise of an exact next-year crash count.