  This paper presents a statistical combination of searches targeting final
states with two top quarks and invisible particles, characterised by the
presence of zero, one or two leptons, at least one jet originating from a
$b$-quark and missing transverse momentum. The analyses are searches for
phenomena beyond the Standard Model consistent with the direct production of
dark matter in $pp$ collisions at the LHC, using 139 fb$^{-\text{1}}$ of data
collected with the ATLAS detector at a centre-of-mass energy of 13 TeV. The
results are interpreted in terms of simplified dark matter models with a spin-0
scalar or pseudoscalar mediator particle. In addition, the results are
interpreted in terms of upper limits on the Higgs boson invisible branching
ratio, where the Higgs boson is produced according to the Standard Model in
association with a pair of top quarks. For scalar (pseudoscalar) dark matter
models, with all couplings set to unity, the statistical combination extends
the mass range excluded by the best of the individual channels by 50 (25) GeV,
excluding mediator masses up to 370 GeV. In addition, the statistical
combination improves the expected coupling exclusion reach by 14% (24%),
assuming a scalar (pseudoscalar) mediator mass of 10 GeV. An upper limit on the
Higgs boson invisible branching ratio of 0.38
(0.30$^{+\text{0.13}}_{-\text{0.09}}$) is observed (expected) at 95% confidence
level.
