  Sensitivity analysis helps identify which model inputs convey the most
uncertainty to the model output. One of the most authoritative measures in
global sensitivity analysis is the Sobol' total-order index, which can be
computed with several different estimators. Although previous comparisons
exist, it is hard to know which estimator performs best since the results are
contingent on the benchmark setting defined by the analyst (the sampling
method, the distribution of the model inputs, the number of model runs, the
test function or model and its dimensionality, the weight of higher order
effects or the performance measure selected). Here we compare several
total-order estimators in an eight-dimension hypercube where these benchmark
parameters are treated as random parameters. This arrangement significantly
relaxes the dependency of the results on the benchmark design. We observe that
the most accurate estimators are Razavi and Gupta's, Jansen's or Janon/Monod's
for factor prioritization, and Jansen's, Janon/Monod's or Azzini and Rosati's
for approaching the "true" total-order indices. The rest lag considerably
behind. Our work helps analysts navigate the myriad of total-order formulae by
reducing the uncertainty in the selection of the most appropriate estimator.
