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
In most study designs, rows designate a grouping of the data, for instance, into treatment or exposure groups, while the columns indicate a dichotomous outcome, usually with the first column representing the outcome of interest. This designation of rows and columns may not be relevant in all study designs, please see the introduction to chapter 4 for details.
# 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
#> ----------------------------------------------------------------