Adjusting wheal size measures to correct atopy misclassification

Figures & data

Table 1 Comparison between gender of atopy prevalence and percentage of atopic cases having eczema based on 3 mm cutoff (405 males and 445 females)

Allergen	Sensitization prevalence (%)			% of atopic cases with eczema
	Males	Females	P-value	Males	Females	P-value
HDM	35.06	23.37	0.00087	14.08 (142)	21.15 (104)	0.073
Grass	26.73	21.34	0.033	13.89 (108)	18.95 (97)	0.16
Dog dander	12.35	8.99	0.056	26.00 (50)	25.00 (40)	0.46
Alternaria	9.63	6.74	0.062	17.95 (39)	20.00 (30)	0.41
All above	46.53	34.61	0.00013	12.23 (188)	20.13 (154)	0.023

Notes: The numbers of positive sensitization are included in the parentheses. Two-sided two sample proportion tests are used to test gender differences between percentages for each allergen. For tests in columns 4 and 7, respectively, multiple testing adjusted significance level is 0.0125 (0.05/5 = 0.01) using the Bonferroni method. P-values are listed to show the significance of percentage differences between gender.

Figure 1 Conceptual structure of the joint model.

Note: Squares represent constant (fixed) and ovals represent stochastic variables.

Appendix Figure 1 The detailed structure of the Bayesian joint model.

Appendix Figure 2 The WinBUGS program corresponding model structure in Appendix Figure 1.

Table 2 Summary of observed and inferred wheal sizes and proposed cutoff values (The unit of each variable is in millimeters. Standard deviations are in the parentheses)

Gender	Oj	T̂j	F̂j	$C_j^o$
HDM
Males	2.08 (2.78)	1.66 (0.98)	−0.43	3.43
Females	1.36 (2.37)	1.48 (0.97)	0.10	2.90
P-value	0.000065	0.0061
Grass
Males	1.80 (3.03)	1.33 (0.89)	−0.51	3.51
Females	1.23 (2.36)	1.25 (0.86)	0.01	2.99
P-value	0.0023	0.14
Dog dander
Males	0.77 (1.54)	0.59 (0.36)	−0.18	3.18
Females	0.55 (1.27)	0.57 (0.35)	0.02	2.98
P-value	0.021	0.31
Alternaria
Males	0.61 (1.66)	0.39 (0.26)	−0.22	3.22
Females	0.39 (1.31)	0.38 (0.25)	0.01	2.99
P-value	0.036	0.42

Notes: j = 1, 2 denotes two genders. O_j: the average of observed wheal sizes. T̂_j: the average of inferred true wheal sizes. F̂_j: estimate of the adjusting factor $C_j^o$ is the revised cutoff point. Two F sample t-tests were performed to test the differences of means between gender. In columns 2 and 3, respectively, multiple testing adjusted significance level is 0.0125 (0.05/4 = 0.0125) using the Bonferroni method. P-values are listed to show the significance of mean difference of wheal sizes between genders.

Figure 2 The relationship between sensitization prevalence of wheat and cutoff value based on T_ij.

Table 3 Cutoff values and sensitization prevalence comparison between gender based on T_ij

Allergen	Cutoff value (mm)	Sensitization prevalence (%)
		Males	Females	P-value
HDM	2.4	28.89	22.92	0.023
Grass	1.97	25.68	21.80	0.09
Dog dander	1.28	8.40	9.21	0.34
Alternaria	0.99	6.17	6.97	0.32

Notes: Two-sided two sample proportion tests are used to test gender differences between percentage for each allergen. Multiple testing adjusted significance level is 0.0125 (0.05/4) using the Bonferroni method. P-values are listed to show the significance of prevalence differences between gender.

Table 4 Eczema cases with positive sensitization based on T_ij

Allergen	% of atopic cases with eczema
	Males	Females	P-value
HDM	16.24 (117)	22.55 (102)	0.12
Grass	13.72 (102)	19.59 (97)	0.13
Dog dander	41.18 (34)	29.26 (41)	0.14
Alternaria	16.00 (25)	19.35 (31)	0.37

Notes: The numbers of positive sensitization are included in the parentheses. Two-sided two sample proportion tests are used to test gender differences between percentage for each allergen. Multiple testing adjusted significance level is 0.0125 (0.05/4) using the Bonferroni method. P-values are listed to show the significance of percentage differences between gender.

Table 5 Comparison of prevalence between gender based on $C_j^o$ of sensitization and percentage of atopic cases having eczema

Allergen	Sensitization prevalence (%)			Prevalence of eczema among atopic cases (%)
	Males	Females	P-value	Males	Females	P-value
HDM	32.35	23.37	0.0017	15.27	21.15	0.12
Grass	24.75	21.35	0.12	14.00	18.95	0.18
Dog dander	10.62	8.99	0.21	27.91	25.00	0.38
Alternaria	8.89	6.74	0.12	19.44	20.00	0.47

Notes: Two-sided two sample proportion tests are used to test gender differences between percentages for each allergen. For tests in columns 4 and 7, respectively, multiple testing adjusted significance level is 0.0125 (0.05/4 = 0.0125) using the Bonferroni method. P-values are listed to show the significance of percentage differences between gender.

Table 6 Comparison of prevalence between gender of atopy and percentage of atopic cases having eczema based on different cutoffs on all allergens

Allergen	Sensitization prevalence (%)			Prevalence of eczema among atopic cases (%)
	Males	Females	P-value	Males	Females	P-value
3 mm (males and females)	47.89	35.36	0.00011	11.92	20.38	0.00010
3.5 mm (males), 3 mm (females)	45.91	35.36	0.00089	11.89	20.38	0.00023

Notes: Two-sided two sample proportion tests are used to test gender differences between percentages for each allergen. For tests in columns 4 and 7, respectively, multiple testing adjusted significance level is 0.0125 (0.05/4 = 0.0125) using the Bonferroni method. P-values are listed to show the significance of percentage differences between gender.