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. Author manuscript; available in PMC: 2023 Mar 16.
Published in final edited form as: Ear Hear. 2022 Mar 16;43(5):1447–1455. doi: 10.1097/AUD.0000000000001216

TABLE 3:

Comparison of Alternative Analytic Methods for the Analysis of Audiometric Data: Simulation Study Scenario 2a

Both-ear Methodb Worse-ear Methodc Better-ear Methodd Left-ear Methode
Relative biasf (%) Empirical standard deviationg Estimated standard errorh Converge ratei (%) Relative bias (%) Empirical standard deviation Estimated standard error Converge rate (%) Relative bias (%) Empirical standard deviation Estimated standard error Converge rate (%) Relative bias (%) Empirical standard deviation Estimated standard error Converge rate (%)
x1,1 −2.06 0.11 0.11 0.95 −12.48 0.11 0.11 0.94 −143.41 0.34 0.35 0.84 −1.18 0.15 0.15 0.94
x1,2 0.36 0.11 0.11 0.94 −1.00 0.12 0.12 0.95 30.64 0.35 0.35 0.96 1.45 0.15 0.15 0.95
x1,3 −0.87 0.10 0.11 0.95 6.45 0.11 0.11 0.94 −67.34 0.32 0.32 0.91 0.13 0.15 0.14 0.96
x2 0.28 −0.09 0.09 0.94 2.86 0.09 0.10 0.93 37.71 0.26 0.26 0.71 0.68 0.13 0.13 0.96
x3 −0.06 0.09 0.09 0.94 7.69 0.10 0.10 0.75 42.97 0.25 0.25 0.24 0.11 0.13 0.13 0.96
x1,1×x2 −1.86 0.13 0.14 0.95 −10.85 0.14 0.14 0.94 −129.65 0.38 0.40 0.87 1.86 0.18 0.19 0.95
x1,2×x2 5.32 0.12 0.12 0.94 4.38 0.13 0.14 0.94 64.38 0.38 0.38 0.95 −9.85 0.17 0.18 0.95
x1,3×x2 0.76 0.12 0.13 0.94 −13.68 0.13 0.13 0.94 −118.55 0.36 0.37 0.92 4.18 0.17 0.17 0.95
x1,1×x3 10.00 0.13 0.14 0.94 −39.86 0.14 0.15 0.94 269.03 0.37 0.38 0.94 34.17 0.18 0.19 0.94
x1,2×x3 0.35 0.13 0.13 0.95 34.94 0.15 0.15 0.94 1159.58 0.39 0.38 0.96 0.57 0.18 0.18 0.95
x1,3×x3 1.48 0.12 0.12 0.94 98.149 0.13 0.14 0.93 −111.93 0.34 0.35 0.93 −9.17 0.17 0.17 0.95
x4 −0.43 0.02 0.02 0.96 −4.05 0.02 0.02 0.95 38.25 0.04 0.03 0.96 8.94 0.02 0.02 0.95
a

Simulation Study Scenario with a 4-level categorical exposure, a 20% event rate and a sample size of 5000, based on 1000 simulation replicates; using exchangeable working covariance-covariance matrix.

b

Both-ear method: logistic regression with hearing data of both ears at three frequency categories as correlated outcome.

c

Worse-ear method: logistic regression with hearing data of the worse ear at three frequency categories as the outcome.

d

Better-ear method: logistic regression with hearing data of the better ear at three frequency categories as the outcome.

e

Left ear method: logistic regression with hearing data of the left ear at three frequency categories as the outcome; the generalized estimating equation approach was used in all the methods for estimation.

f

Relative Bias is 100 × (the mean of the estimated log (OR) over simulation replicates – the true log (OR))/the true log (OR) ), where OR stands for odds ratio.

g

Empirical standard deviation (SD) is the empirical SD of the log(OR) estimates from simulation replicates.

h

Estimated standard error (SE) is the average of the sandwich SE over the simulation replications.

i

Coverage Rate is the 95% confidence interval coverage rate based on the sandwich SE.

x1,1, x1,2, and x1,3: indicators for a categorical exposure; x2: dummy variable for mid-frequency; x3: dummy variable for high-frequency; x4 continuous ear-level baseline measurement.