Table 4.

Estimated Effects of Birth Cohort on Hearing Impairment Derived From the Use of Different Regression Techniques (n = 10,159), Epidemiology of Hearing Loss Study (1993–2005) and Beaver Dam Offspring Study (2005–2008)^a

Model	βb	Standard Errorc	Odds Ratio	95% Confidence Interval	P Value
Men
Standard logistic regression	−0.158	0.029	0.85	0.81, 0.90	<0.0001
Autoregressive GEEd	−0.140	0.026	0.87	0.84, 0.92	<0.0001
Exchangeable GEEe	−0.138	0.026	0.87	0.83, 0.92	<0.0001
Unstructured GEEf	−0.142	0.026	0.87	0.83, 0.91	<0.0001
ALRg	−0.138	0.026	0.87	0.83, 0.92	<0.0001
Women
Standard logistic regression	−0.098	0.028	0.91	0.86, 0.96	0.0006
Autoregressive GEE	−0.069	0.025	0.93	0.89, 0.98	0.0061
Exchangeable GEE	−0.071	0.025	0.93	0.89, 0.98	0.0043
Unstructured GEE	−0.074	0.025	0.93	0.89, 0.98	0.0030
ALR	−0.066	0.024	0.94	0.89, 0.98	0.0068

Abbreviations: ALR, alternating logistic regression; GEE, generalized estimating equations.

^aThe main effects included in the model were age, age², age³, cohort, and the interaction between sex and cohort.

^bRegression coefficient for birth cohort. Birth cohort was centered at the year 1937 in the unit of 5-year increase.

^cThe standard error for GEE and ALR was the robust standard error.

^dGEE with an autoregressive structure assumes that observations that are further apart in time have a lower correlation with each other.

^eExchangeable GEE assumes that the observations within a subject are equally correlated.

^fUnstructured GEE assumes that correlations of repeated measurements are unconstrained.

^gIn the ALR analyses, regression coefficients for within-subcluster (α₁) and between-subcluster (α₂) associations were 4.794 (P < 0.0001) and 0.211 (P = 0.0435), respectively.