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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 2:

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

Both-ear methodb Worse-ear methodc
Relative biasd (%) Empirical standard deviatione Estimated standard errorf Converge rateg (%) Relative bias (%) Empirical standard Deviation Estimated standard error Converge rate (%)
x1,1 −3.51 0.24 0.25 0.95 −13.90 0.25 0.27 0.94
x1,2 2.51 0.24 0.25 0.95 −1.63 0.27 0.29 0.94
x1,3 5.62 0.23 0.24 0.95 −2.91 0.24 0.25 0.94
x2 1.76 0.20 0.21 0.95 3.93 0.21 0.22 0.93
x3 0.90 0.21 0.22 0.94 8.24 0.23 0.24 0.90
x1,1×x2 −2.04 0.30 0.31 0.94 −11.04 0.32 0.33 0.94
x1,2×x2 1.52 0.27 0.28 0.95 9.28 0.31 0.33 0.94
x1,3×x2 38.73 0.28 0.29 0.94 −1.09 0.30 0.31 0.95
x1,1×x3 23.29 0.30 0.32 0.94 −35.35 0.33 0.34 0.94
x1,2×x3 2.85 0.29 0.31 0.94 25.40 0.34 0.37 0.93
x1,3×x3 −7.50 0.26 0.28 0.94 127.11 0.30 0.31 0.93
x4 −6.67 0.04 0.04 0.95 −17.82 0.04 42.00 0.96
a

Simulation Study Scenario with a 4-level categorical exposure, a 20% event rate and a sample size of 1000, 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

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.

e

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

f

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

g

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.

The better-ear and left/right-ear methods have low convergence rates and thus the results are unavailable.