Wrapper for _CI_OR_2x2 functions on Chapter 4.
the_2x2_table_CIs_OR(n, alpha = 0.05)NULL. This function should be called for its printed output
# Example: A lady tasting a cup of tea
the_2x2_table_CIs_OR(tea)
#> Estimate of pi_1: 3 / 4 = 0.750
#> Estimate of pi_2: 1 / 4 = 0.250
#> Estimate of theta = (pi_1 / (1-pi_1)) / (pi_2 / (1-pi_2)): 9.000
#>
#> Interval method 95% CI Log width
#> ----------------------------------------------------------------
#> Woolf logit 0.367 to 220.927 6.401
#> Gart adjusted logit 0.364 to 81.419 5.410
#> Independence-smoothed logit 0.364 to 81.419 5.410
#> Inverse sinh 0.740 to 109.455 4.997
#> Adjusted inverse sinh (0.45, 0.25) 0.544 to 58.957 4.686
#> Adjusted inverse sinh (0.6, 0.4) 0.525 to 48.822 4.533
#> MOVER-R Wilson 0.849 to 68.142 4.386
#> Miettinen-Nurminen asymptotic score 0.405 to 200.058 6.203
#> Uncorrected asymptotic score 0.480 to 168.742 5.862
#> Cornfield exact conditional 0.310 to 308.557 6.903
#> Baptista-Pike exact conditional 0.397 to 148.616 5.926
#> Cornfield mid-P 0.310 to 308.557 6.903
#> Baptista-Pike mid-P 0.397 to 148.616 5.926
#> ----------------------------------------------------------------
# Example: Perondi et al. (2004)
the_2x2_table_CIs_OR(perondi_2004)
#> Estimate of pi_1: 7 / 34 = 0.206
#> Estimate of pi_2: 1 / 34 = 0.029
#> Estimate of theta = (pi_1 / (1-pi_1)) / (pi_2 / (1-pi_2)): 8.556
#>
#> Interval method 95% CI Log width
#> ----------------------------------------------------------------
#> Woolf logit 0.990 to 73.900 4.312
#> Gart adjusted logit 0.983 to 37.749 3.648
#> Independence-smoothed logit 0.990 to 60.488 4.112
#> Inverse sinh 1.317 to 55.568 3.742
#> Adjusted inverse sinh (0.45, 0.25) 1.102 to 35.585 3.475
#> Adjusted inverse sinh (0.6, 0.4) 1.085 to 30.825 3.347
#> MOVER-R Wilson 1.304 to 50.644 3.659
#> Miettinen-Nurminen asymptotic score 1.247 to 56.462 3.813
#> Uncorrected asymptotic score 1.261 to 55.848 3.791
#> Cornfield exact conditional 1.189 to 199.617 5.124
#> Baptista-Pike exact conditional 1.328 to 98.836 4.310
#> Cornfield mid-P 1.189 to 199.617 5.124
#> Baptista-Pike mid-P 1.328 to 98.836 4.310
#> ----------------------------------------------------------------
# Example: Lampasona et al. (2013)
the_2x2_table_CIs_OR(lampasona_2013)
#> Estimate of pi_1: 9 / 13 = 0.692
#> Estimate of pi_2: 4 / 14 = 0.286
#> Estimate of theta = (pi_1 / (1-pi_1)) / (pi_2 / (1-pi_2)): 5.625
#>
#> Interval method 95% CI Log width
#> ----------------------------------------------------------------
#> Woolf logit 1.077 to 29.371 3.306
#> Gart adjusted logit 1.021 to 23.773 3.148
#> Independence-smoothed logit 1.021 to 23.778 3.148
#> Inverse sinh 1.247 to 25.369 3.013
#> Adjusted inverse sinh (0.45, 0.25) 1.141 to 21.787 2.949
#> Adjusted inverse sinh (0.6, 0.4) 1.121 to 20.636 2.913
#> MOVER-R Wilson 1.043 to 20.567 2.981
#> Miettinen-Nurminen asymptotic score 1.093 to 28.942 3.276
#> Uncorrected asymptotic score 1.126 to 28.113 3.218
#> Cornfield exact conditional 1.023 to 31.502 3.428
#> Baptista-Pike exact conditional 1.149 to 29.086 3.232
#> Cornfield mid-P 1.023 to 31.502 3.428
#> Baptista-Pike mid-P 1.149 to 29.086 3.232
#> ----------------------------------------------------------------
# Example: Ritland et al. (2007)
the_2x2_table_CIs_OR(ritland_2007)
#> Estimate of pi_1: 0 / 16 = 0.000
#> Estimate of pi_2: 15 / 72 = 0.208
#> Estimate of theta = (pi_1 / (1-pi_1)) / (pi_2 / (1-pi_2)): 0.000
#>
#> Interval method 95% CI Log width
#> ----------------------------------------------------------------
#> Woolf logit 0.000 to Inf Inf
#> Gart adjusted logit 0.006 to 1.980 5.738
#> Independence-smoothed logit 0.000 to 39.466 15.815
#> Inverse sinh 0.000 to 0.912 Inf
#> Adjusted inverse sinh (0.45, 0.25) 0.006 to 1.817 5.766
#> Adjusted inverse sinh (0.6, 0.4) 0.011 to 1.611 4.982
#> MOVER-R Wilson 0.000 to 0.852 Inf
#> Miettinen-Nurminen asymptotic score 0.000 to 0.965 Inf
#> Uncorrected asymptotic score 0.000 to 0.953 Inf
#> Cornfield exact conditional 0.000 to 0.886 Inf
#> Baptista-Pike exact conditional 0.000 to 0.868 Inf
#> Cornfield mid-P 0.000 to 0.886 Inf
#> Baptista-Pike mid-P 0.000 to 0.868 Inf
#> ----------------------------------------------------------------