runs per scenario: 10000; n = 6 per group; seed 20261110

rate 3 per mm2, theta 2, true ratio 1
  poisson        22.1%
  quasipoisson    4.3%
  nb_wald         9.4%
  nb_lrt          7.7%
  log1p_welch     4.7%
  rate_welch      3.5%
  NB fits failed: 0

rate 15 per mm2, theta 2, true ratio 1
  poisson        53.7%
  quasipoisson    4.8%
  nb_wald        10.7%
  nb_lrt          8.1%
  log1p_welch     4.1%
  rate_welch      3.7%
  NB fits failed: 0

rate 3 per mm2, theta 1000, true ratio 1
  poisson         4.8%
  quasipoisson    4.9%
  nb_wald         4.3%
  nb_lrt          4.3%
  log1p_welch     4.3%
  rate_welch      4.7%
  NB fits failed: 0

rate 15 per mm2, theta 1000, true ratio 1
  poisson         5.1%
  quasipoisson    4.9%
  nb_wald         4.5%
  nb_lrt          3.9%
  log1p_welch     4.7%
  rate_welch      4.6%
  NB fits failed: 0

rate 3 per mm2, theta 2, true ratio 2
  poisson        63.2%
  quasipoisson   20.8%
  nb_wald        36.3%
  nb_lrt         31.3%
  log1p_welch    19.7%
  rate_welch     15.5%
  NB fits failed: 0
  median estimated ratio: NB 1.98; log(count+1) back-transformed 1.72

rate 15 per mm2, theta 2, true ratio 2
  poisson        87.3%
  quasipoisson   28.0%
  nb_wald        45.5%
  nb_lrt         39.7%
  log1p_welch    23.7%
  rate_welch     20.5%
  NB fits failed: 0
  median estimated ratio: NB 2.01; log(count+1) back-transformed 1.94

rate 3 per mm2, theta 1000, true ratio 2
  poisson        75.0%
  quasipoisson   64.8%
  nb_wald        72.4%
  nb_lrt         70.7%
  log1p_welch    52.0%
  rate_welch     61.4%
  NB fits failed: 0
  median estimated ratio: NB 2.01; log(count+1) back-transformed 1.83

rate 15 per mm2, theta 1000, true ratio 2
  poisson       100.0%
  quasipoisson   99.9%
  nb_wald       100.0%
  nb_lrt        100.0%
  log1p_welch    91.9%
  rate_welch     99.8%
  NB fits failed: 0
  median estimated ratio: NB 2.00; log(count+1) back-transformed 1.96