  In Value of Information (VoI) analysis, the unit normal loss integral (UNLI)
frequently emerges as a solution for the computation of various VoI metrics.
However, one limitation of the UNLI has been that its closed-form solution is
available for only one dimension, and thus can be used for comparisons
involving only two strategies (where it is applied to the scalar incremental
net benefit). We derived a closed-form solution for the two-dimensional UNLI,
enabling closed-form VoI calculations for three strategies. We verified the
accuracy of this method via simulation studies. A case study based on a
three-arm clinical trial was used as an example. VoI methods based on the
closed-form solutions for the UNLI can now be extended to three-decision
comparisons, taking a fraction of a second to compute and not being subject to
Monte Carlo error. An R implementation of this method is provided as part of
the predtools package (https://github.com/resplab/predtools/).
