On the proportional hazards model for occupational and environmental case-control analyses

Table 5 Estimated effect of occupational asbestos exposure in males ever exposed (1041 cases and 1425 controls), using the WC models and logistic regression and assuming linear effects of quantitative exposure variables

Model	Exposure variables (a)	Unit	Method (b)	$exp (\hat{β})$ (c)	95% CI
1	Intensity	1.0 fiber/ml	WC1	1.75	1.66	1.84
			WC2	-	1.65	1.85
			CLR	2.55	2.29	2.83
			ULR	2.33	2.14	2.54
	Duration	14 years	WC1	1.32	1.24	1.40
			WC2	-	1.23	1.41
			CLR	1.18	1.12	1.24
			ULR	1.17	1.12	1.23
2	Intensity	1.0 fiber/ml	WC1	1.73	1.64	1.82
			WC2	-	1.63	1.83
			CLR	2.49	2.24	2.76
			ULR	2.31	2.12	2.52
	Duration	14 years	WC1	1.19	1.12	1.27
			WC2	-	1.11	1.28
			CLR	1.08	1.02	1.14
			ULR	1.10	1.05	1.15
	Age at first exposure	8 years	WC1	0.63	0.58	0.68
			WC2	-	0.57	0.70
			CLR	0.66	0.61	0.72
			ULR	0.77	0.73	0.82
3	Intensity	1.0 fiber/ml	WC1	1.74	1.65	1.83
			WC2	-	1.64	1.84
			CLR	2.53	2.28	2.82
			ULR	2.33	2.14	2.53
	Duration	14 years	WC1	1.90	1.68	2.14
			WC2	-	1.64	2.19
			CLR	1.41	1.27	1.57
			ULR	1.41	1.29	1.53
	Time since last exposure	14 years	WC1	1.55	1.37	1.75
			WC2	-	1.34	1.79
			CLR	1.24	1.11	1.39
			ULR	1.25	1.14	1.37

Results from the French case-control study on mesothelioma, 1987–2006.
(a) All the exposure variables were time-dependent in WC1 and WC2 models, and fixed at their value at diagnosis/interview in CLR and ULR. Intensity was measured by the mean index of exposure (MIE).
(b) WC1, weighted Cox models with robust sandwich variance; WC2, weighted Cox model with superpopulation variance; Both WC1 and WC2 used age as the time axis and included birth year as a quantitative covariate; ULR, unconditional logistic regression including age at diagnosis/interview and birth year as quantitative covariates; CLR, conditional logistic regression stratified on birth year group (5 years), and including age at diagnosis/interview as a quantitative covariate.
(c) Hazard ratio estimates for WC1 and WC2 (same value for WC1 and WC2) and odds ratio estimates for CLR and ULR, adjusted for age and birth year, and corresponding 95% confidence interval (CI).

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