Effect of Smoking on Breast Cancer by Adjusting for Smoking Misclassification Bias and Confounders Using a Probabilistic Bias Analysis Method

Figures & data

Figure 1 Causal directed acyclic graph (cDAG) for the effect of smoking and breast cancer. Minimally sufficient adjustment set included age, alcohol, education, physical activity and socioeconomic status (SES).

Figure 2 LOWESS (A) and fractional polynomial plot (B) for the association between age and breast cancer.

Table 1 The Probability Distributions Parameters for Triangular, Beta and Logistic Distributions in Case and Control Groups

	Bias Parameters (95% CI)		Group	Triangular Distribution (Min; Max; Mode)	Beta Distribution (Alpha; Beta)	Logistic Distribution (Location; Scale)
Type of misclassification	Differential	Sensitivity 84% (73 to 95)	Case group	0.73; 0.95; 0.84	35.01; 6.67	0.84; 0.0309
		Specificity 94% (89 to 100)		0.89; 1; 0.94	33.82; 1.23	0.94; 0.0168
		Sensitivity 90% (83 to 97)	Control group	0.83; 0.97; 0.90	62.60; 6.96	0.90; 0.0197
		Specificity 98% (95 to 100)		0.95; 1; 0.98	183.50; 3.74	0.98; 0.0056
	Non-differential	Sensitivity 85% (76 to 94)	Both groups	0.76; 94; 0.85	52.67; 9.30	0.85; 0.0248
		Specificity 95% (91 to 99)		0.91; 99; 0.95	224.67; 11.83	0.95; 0.0110

Abbreviation: CI, confidence interval.

Table 2 Characteristics of Cases and Controls

Variables		Number (%)
		Control	Case
Marital status	Married	792 (79.2)	744 (79.8)
	Single	133 (13.3)	61 (6.5)
	Divorced	34 (3.4)	47 (5.0)
	Widow	41 (4.1)	80 (8.6)
Insurance	No	107 (10.7)	32 (3.4)
	Yes	893 (89.3)	900 (96.6)
Education	Illiterate	48 (4.8)	55 (5.9)
	Primary	108 (10.8)	163 (17.5)
	Secondary	158 (15.8)	148 (15.9)
	High school	342 (34.2)	316 (33.9)
	Bachelor	284 (28.4)	200 (21.5)
	More than bachelor	60 (6.0)	50 (5.4)
Job	Housekeeper	723 (72.3)	746 (80.0)
	Government employed	159 (15.9)	96 (10.3)
	Self-employed	108 (10.8)	48 (5.2)
	Retired	10 (1.0)	42 (4.5)
SES	Very low	11 (1.1)	25 (2.7)
	Low	68 (6.8)	187 (20.1)
	Middle	273 (27.3)	491 (52.7)
	High	638 (63.8)	198 (21.2)
	Very high	10 (1.0)	31 (3.3)
Alcohol	Yes	971 (97.1)	892 (95.7)
	No	29 (2.9)	40 (4.3)
Physical activity	Yes	891 (89.1)	833 (89.4)
	No	109 (10.9)	99 (10.6)
Age		42.16±9.49	50.40±9.70

Figure 3 The distribution of ORs adjusted for measurement bias and confounding, assuming non-differential (A, B and C) and differential (D, E and F) misclassification errors. The distribution of bias parameter was assumed to be triangular (A and D), beta (B and E) and logistic (C and F).

Table 3 Adjusted Odds Ratio with 95% Confidence Interval or MCSA Interval Using Conventional and Probabilistic Bias Analyses.

Conventional Analysis	Bias Parameter Distribution	Bias Analysis (MCSA 95%)
		Non-Differential	Differential
0.64 (95% CI: 0.36 to 1.13)	Triangular	2.63 (1.75 to 4.19)	1.73 (0.87 to 5.06)
	Beta	2.63 (1.83 to 3.88)	2.83 (1.20 to 15.98)
	Logistic	2.69 (1.36 to 6.31)	2.09 (1.05 to 10.15)

Notes: All estimates were adjusted for age, alcohol consumption, education level, physical activity and socioeconomic status.

Abbreviations: CI, confidence interval; MCSA, Monte Carlo sensitivity analysis.

Table 4 The Estimates of Population Attributable Fraction with 95% Confidence Intervals or MCSA Intervals Using Conventional and Bias Analyses

Conventional Analysis	Bias Parameter Distribution	Bias Analysis (MCSA 95%)
		Non-Differential	Differential
−2.53% (95% CI: −8.01 to 0.52)	Triangular	1.55% (0.56 to 2.89)	0.62% (−0.21 to 3.52)
	Beta	1.36% (0.41 to 2.50)	2.01% (0.05 to 5.12)
	Logistic	1.72% (0.25 to 4.07)	0.95% (0.01 to 4.35)

Abbreviations: CI, confidence interval; MCSA, Monte Carlo sensitivity analysis.

Table 5 E-Values for Alcohol Consumption Assuming No Adjustment Was Made for the Variable

Bias Parameter Distribution	Bias Analysis (MCSA 95%)
	E-value
	Non-Differential	Differential
Triangular	4.70 (2.90 to 7.85)	2.85 (1.00 to 9.59)
Beta	4.70 (3.06 to 7.22)	5.11 (1.69 to 31.45)
Logistic	4.82 (2.06 to 12.10)	3.60 (1.28 to 19.79)

Abbreviation: MCSA, Monte Carlo sensitivity analysis.