Application of Bayesian decision-making to laboratory testing for Lyme disease and comparison with testing for HIV

Figures & data

Figure 1 Flow diagram of logical AND two-tier test methodology for Lyme disease.

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Figure 2 Flow diagram of logical OR test methodology for HIV.

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table 1 HIV “rapid” serology test performance

Test	Specimen	Sensitivity	95% CI	Specificity	95% CI
A	Whole blood	98.97%	98.07–99.87	99.70%	99.60–100.00
A	Serum	99.18%	98.38–99.98	99.70%	99.60–100.00
A	Plasma	98.77%	97.79–99.75	99.90%	99.60–100.00
B	Whole blood	99.39%	98.70–100.00	100.00%	99.70–100.00
B	Oral	98.17%	96.99–99.35	99.80%	99.60–99.90
C	Plasma	100.00%	100.00–100.00	99.90%	99.60–100.00
D	Plasma	100.00%	100.00–100.00	99.91%	99.77–100.00
E	Serum	100.00%	100.00–100.01	99.93%	99.79–100.00
F	Plasma	100.00%	100.00–100.02	98.60%	99.00–100.00
Average		99.36%	98.64–100.00	99.73%	99.46–100.00

Abbreviation: CI, confidence interval.

Table 2 Lyme disease serology test performance

Stage	Test	Sensitivity	Specificity
Single test	C6 peptide ELISA	53.9%	92.1%
First tier with equivocals	C6 peptide ELISA	60.1%	92.1%
Single test	ELISA	62.3%	96.8%
Single- or two-tier test	Western blot	62.4%	94.8%
Combined	Two tier	53.7%	99.7%
Average	All	59.4%	95.8%

Notes: When C6 ELISA is used as a single test, only positives are reported. When used as the first stage of a two-tier test, both positives and equivocal samples are submitted to the confirmatory Western blot.

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table 3 Probability of having Lyme disease given a positive test

Lyme disease/HIV test comparison			Disease prevalence in clinically diagnosed cases
			5%	10%	25%	50%	75%
	Sensitivity	Specificity	Probability of having disease given a positive test
C6 peptide ELISA	53.9%	92.1%	26.4%	43.1%	69.4%	87.2%	95.3%
ELISA	62.3%	96.8%	50.6%	68.4%	86.6%	95.1%	98.3%
Western blot	62.4%	94.8%	38.7%	57.1%	80.0%	92.3%	97.3%
6 rapid HIV tests	99.5%	99.7%	94.6%	97.4%	99.1%	99.7%	99.9%

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table 4 False-positive results from C6 ELISA and HIV tests with the probability of not having Lyme disease given a positive test

LD/HIV test comparison: best-case LD test			Disease prevalence in clinically diagnosed cases
			5%	10%	25%	50%	75%
	Sensitivity	Specificity	False positives
C6 peptide	53.9%	92.1%	73.6%	56.9%	30.6%	12.8%	4.7%
ELISA	99.5%	99.7%	5.4%	2.6%	0.9%	0.3%	0.1%
6 rapid HIV tests	LD/HIV false-positive ratio		14	22	34	43	46

Abbreviations: ELISA, enzyme-linked immunosorbent assay; LD, Lyme disease.

Table 5 Probability of disease with a single-test and the two-tier test method

Test	First tier	Second tier	Test dependence = 0.62
	Test specificity		Prevalence in clinically diagnosed cases
	92.1%	94.8%	5%	10%	25%	50%	75%
	Test sensitivity		Probability of having disease given a positive test
First-stage C6 ELISA	53.9%	–	26.4%	43.1%	69.4%	87.2%	95.3%
Two-tier test	60.1%	62.4%	67.2%	77.9%	87.2%	92.8%	96.6%

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table 6 False-positive probability for single-stage and two-tier testing

Test	First tier	Second tier	Test dependence = 0.62
	Test specificity		Prevalence in clinically diagnosed cases
	92%	95%	5%	10%	25%	50%	75%
	Test sensitivity		False-positive probability
First-stage C6 ELISA	53.9%	–	73.6%	56.9%	30.6%	12.8%	4.7%
Two-tier test	60.1%	62.4%	32.8%	22.1%	12.8%	7.2%	3.4%

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table 7 Comparison of false-negative results for LD and HIV testing methodologies

LD testing					HIV disease testing				False-negative ratio two-tier LD and two-stage HIV
Disease stage	Test dependence 0.63				Test dependence 0.950
	Test sensitivity		Probability of a false-negative result		Test sensitivity		Probability of a false-negative result
	First tier	Second tier test	First tier test	Two-tier test	First stage	Second stage	Single-stage HIV test	Two-stage HIV test
Early	33.2%	34.5%	66.8%	74.9%	98.6%	98.6%	1.40%	1.33%	56
Early intermediate	46.9%	48.7%	53.1%	62.0%	98.9%	98.9%	1.10%	1.05%	59
Convalescent	60.5%	62.9%	39.5%	47.8%	99.4%	99.4%	0.60%	0.57%	84
Late intermediate	75.1%	78.0%	24.9%	31.0%	99.7%	99.7%	0.30%	0.29%	109
Neuro/arthritis	86.5%	89.9%	13.5%	16.7%	99.9%	99.9%	0.100%	0.095%	176

Abbreviation: LD, Lyme disease; Neuro, neurological.

Figure 3 False-negative percentage based on sensitivities with positive samples.

Figure S1 Dependence of enzyme-linked immunosorbent assay and Western blot test.

Figure S2 False-negative percentage based on test sensitivities with “clinical” samples.

Table S1 Lyme disease serology test performance based on clinical samples

Stage	Test method	Sensitivity	Specificity
Single test	C6 ELISA	33.1%	92.1%
First tier with equivocals	C6 ELISA	36.9%	92.1%
Single test	ELISA	38.3%	96.8%
Single- or two-tier test	Western blot	38.3%	94.8%
Combined	Two tier	33.0%	99.7%
Average	All	36.5%	95.8%

Notes: When C6 ELISA is used as a single test, only positives are reported. When used as the first stage of a two-tier test, both positives and equivocals are included for the confirmatory Western blot.

Abbreviation: ELISA, enzyme-linked immunosorbent assay.

Table S2 Lyme disease test kit sensitivity for various disease stages based on clinical samples

Disease stage	Sensitivity	Sensitivity by stage
		C6 ELISA	WB
Acute	21.7%	20.4%	21.2%
Convalescent	39.6%	37.2%	38.6%
Neurological	53.6%	50.3%	52.3%
Arthritis	58.8%	55.2%	57.3%
Neuro/arthritis	56.6%	53.1%	55.2%

Abbreviations: ELISA, enzyme-linked immunosorbent assay; WB, Western blot.

Table S3 Comparison of false-negative probabilities for LD and HIV testing based on clinical samples

Lyme disease stage	LD testing				HIV disease testing				False-negative ratio two-tier LD and two-stage HIV
	Test dependence 0.63				Test dependence 0.950
	Test sensitivity		Probability of a false-negative result		Test sensitivity		Probability of a false-negative result
	First tier	Second tier test	First tier test	Two-tier test	First stage	Second stage	Single-stage HIV test	Two-stage HIV test
Acute	20.4%	21.2%	79.6%	85.6%	98.6%	98.6%	1.40%	1.33%	64
Intermediate	30.4%	31.5%	69.6%	77.3%	98.9%	98.9%	1.10%	1.05%	74
Convalescent	37.2%	38.6%	62.8%	71.3%	99.4%	99.4%	0.60%	0.57%	125
Intermediate	45.5%	47.3%	54.5%	63.3%	99.7%	99.7%	0.30%	0.29%	222
Neuro/arthritis	53.1%	55.2%	46.9%	55.7%	99.9%	99.9%	0.100%	0.095%	586

Abbreviation: LD, Lyme disease; Neuro, neurological.