Discrimination between recent and non-recent HIV infections using routine diagnostic serological assays

Abstract

The suitability of routine diagnostic HIV assays to accurately discriminate between recent and non-recent HIV infections has not been fully investigated. The aim of this study was to compare an established HIV recency assay, the Sedia limiting antigen HIV avidity assay (LAg), with the diagnostic assays; Abbott ARCHITECT HIV Ag/Ab Combo and INNO-LIA HIV line assays. Samples from all new HIV diagnoses in Ireland from January to December 2016 (n = 455) were tested. An extended logistic regression model, the Spiegelhalter–Knill–Jones method, was utilised to establish a scoring system to predict recency of HIV infection. As proof of concept, 50 well-characterised samples were obtained from the CEPHIA repository whose stage of infection was blinded to the authors, which were tested and analysed. The proportion of samples that were determined as recent was 18.1% for LAg, 6.4% with the ARCHITECT, and 14.5% in the INNO-LIA assay. There was a significant correlation between the ARCHITECT S/CO values and the LAg results, r = 0.717, p < 0.001. ROC analysis revealed that an ARCHITECT S/CO < 250 had a sensitivity and specificity of 90.32% and 89.83%, respectively. Combining the Abbott ARCHITECT HIV Ag/Ab Combo assay and INNO-LIA HIV assays resulted in an observed risk of being recent of 100%. Analysis of the CEPHIA samples revealed a strong agreement between the LAg assay and the combination of routine assays (κ = 0.908, p < 0.001). Our findings provide evidence that assays routinely employed to diagnose and confirm HIV infection may be utilised to determine the recency of HIV infection.

Appendix

A summary of the statistical techniques used to derive Spiegelhalter–Knill–Jones weightings is outlined by Seymour et al. [13].

To employ the Spiegelhalter–Knill–Jones method, which is an extension of logistic regression, all explanatory variables as well as the outcome variable must be binary. The LAg assay is the outcome variable and a cut-off of ODn ≤ 1.5 is used, with those ≤ 1.5 regarded as being recent infections. Algorithm 15.1 is presented in the data set as a binary variable (recent or non-recent), so no division or recoding is needed. A cut-off for the ARCHITECT S/CO of 250 was used in this study, with values < 250 regarded as recent infections.

Briefly as outlined by Seymour et al. [13], the mathematical derivation of Spiegelhalter–Knill–Jones weightings:

• The independence Bayes’ equation is:

$${\text{Posterior odds }}={\text{ prior odds }} \times {\text{ LR of variable 1 }} \times {\text{ LR of variable 2 }} \times {\text{ }} \cdots {\text{ }} \times {\text{ LR of variable }}n,$$

where

• (a) the posterior odds are the predicted odds of the outcome in an individual;

• (b) the prior odds are the odds of the outcome in the population under study;

• (c) LR is the likelihood ratio:

$${\text{LR }}={\text{ }}\left( {{\text{sensitivity}}} \right)/\left( {{\text{1}} - {\text{specificity}}} \right){\text{ for a positive test result }}\left( {{\text{in this study}},{\text{ recenct}}} \right),{\text{ OR}}$$

$${\text{LR }}={\text{ }}\left( {{\text{1}} - {\text{sensitivity}}} \right)/\left( {{\text{specificity}}} \right){\text{ for a negative test result }}\left( {{\text{in this study}},{\text{ non}} - {\text{recent}}} \right).$$

• Taking the natural logarithms and multiplying by 100, the independence Bayes’ equation becomes the following:

$${\text{1}}00 \times {\text{ln}}\left( {{\text{posterior odds}}} \right){\text{ }}={\text{ 1}}00 \times {\text{ln}}\left( {{\text{prior odds}}} \right){\text{ }}+{\text{ 1}}00 \times {\text{ln}}\left( {{\text{LR of variable 1}}} \right){\text{ }}+{\text{ 1}}00 \times {\text{ln}}\left( {{\text{LR of variable 2}}} \right){\text{ }}+{\text{ }} \ldots {\text{ }}+{\text{ 1}}00 \times {\text{ln}}\left( {{\text{LR of variable }}n} \right).$$

• In terms of the Spiegelhalter–Knill–Jones method, this equation becomes the following:

$${\text{Total score }}\left( T \right){\text{ }}={\text{ starting score }}+{\text{ weight of evidence of variable 1 }}+{\text{ weight of evidence of variable 2 }}+ \cdots +{\text{ weight of evidence of variable }}n.$$

• This equation assumes that the variables are independent of one another, which is unrealistic in many cases, so the Spiegelhalter–Knill–Jones method calculates adjusted weights to account for dependence. Adjusted weights are obtained by entering the raw weights of evidence as independent variables in a logistic regression equation. This produces the final form of the predictive equation:

$${\text{Total score }}\left( T \right){\text{ }}={\text{ starting score }}+{\text{ adjusted weight of evidence for variable 1 }}+{\text{ adjusted weight of evidence for variable 2 }}+ \cdots +{\text{ adjusted weight of evidence for variable }}n.$$

• Because T = 100 × ln(posterior odds) and because odds = probability/(1 − probability), the predicted probability can be calculated by the following:

$${\text{Predicted probability }}\left( \% \right)~={\text{ }}T{\text{ }}={\text{ 1}}00{\text{ln}}\left( {p/{\text{1}} - p} \right).$$

Therefore, Ln(p/1 − p) = T/100:

$$\begin{gathered} (p/p - 1)={e^{(T/100)}} \hfill \\ P={e^{(T/100)}}(1 - p)={e^{(T/100)}} - {e^{(T/100)}}p \hfill \\ P+{e^{(T/100)}}p={e^{(T/100)}} \hfill \\ P(1+{e^{(T/100)}})={e^{(T/100)}} \hfill \\ P={e^{(T/100)}}/(1+{e^{(T/100)}}) \hfill \\ {\text{Predicted}}\;{\text{probability}}\;(\% )={e^{(T/100)}}/(1+{e^{(T/100)}}) \times 100 \hfill \\ \end{gathered}$$

The application of the Spiegelhalter–Knill–Jones method for the two variables studied (Algorithm 15.1 and ARCHITECT S/CO) is shown below (Table 3).

Table 3 Derivation of scoring system based on Spiegelhalter–Knill–Jones method

LR and Crude weights were calculated as shown below. Logistic coefficients were obtained by logistic regression analysis of the raw data using SPSS 22.

Individual markers

ARCHITECT S/CO versus LAg as the gold standard

Sensitivity = 21/30 = 70%.

Specificity = 112/118 = 94.9%.

The observed risk of being recent when ARCHITECT < 250 (suggests recency) is 21/27 = 77.8% (as shown in Table 2 in the manuscript).

Likelihood ratios for recency:

Sensitivity/100 − Specificity = 70.0/100 − 94.9 = 70.0/5.1 = 13.73.

Ln13.73 = 2.62.

2.62 × 100 = 262 = weighting to be applied to a recent test.

Likelihood ratios for non- recency:

100 − Sensitivity/Specificity = 100 − 70.0/94.9 = 30.0/94.9 = 0.316.

Ln0.316 = − 1.152.

− 1.152 × 100 = − 115.2 = weighting to be applied to a non-recent test.

Algorithm 15.1 versus LAg as the gold standard

Sensitivity = 39/76 = 51.3%.

Specificity = 323/345 = 93.6%.

The observed risk of being recent when Algorithm 15.1 suggests that recency is 39/61 = 63.9% (as shown in Table 2 in the manuscript).

Likelihood ratios for recency:

Sensitivity/100 − Specificity = 51.3/100 − 93.6 = 51.3/6.4 = 8.016.

Ln8.016= 2.081.

2.081 × 100 = 208 = weighting to be applied to a recent test.

Likelihood ratios for non-recency:

100 − sensitivity/specificity = 100 − 51.3/93.6 = 48.7/93.6 = 0.520.

Ln0.520= − 0.654.

− 0.654 × 100 = − 65.4 = weighting to be applied to a non-recent test.

Predictive analysis for the two markers—ARCHITECT S/CO and Algorithm 15.1

ARCHITECT S/CO (recent) and Algorithm 15.1 (recent) versus LAg as the gold standard

See Table 4.

$$\begin{gathered} {\text{Predicted probability }}\left( \% \right)~={\text{ 1}}00{\text{ln}}\left( {p/{\text{1}} - p} \right){\text{ }}={\text{ }} - {\text{117 }}+{\text{ }}\left( {0.00{\text{9}} \times {\text{1}}00} \right){\text{ }}\left( {{\text{262}}} \right){\text{ }}+{\text{ }}\left( {0.0{\text{12}} \times {\text{1}}00} \right){\text{ }}\left( {{\text{2}}0{\text{8}}} \right) \hfill \\ ~={\text{ }} - {\text{117 }}+{\text{ 235}}.{\text{8 }}+{\text{ 249}}.{\text{6 }}={\text{ 368}}.{\text{4}} \hfill \\ \end{gathered}$$

$$\begin{gathered} {\text{Ln}}\left( {p/{\text{1}} - p} \right)~~~={\text{ 3}}.{\text{684}} \hfill \\ \left( {p/{\text{1}} - p} \right)~~~~~~~={\text{ 39}}.{\text{815}}. \hfill \\ \end{gathered}$$

Table 4 Crosstabulation of LAg with ARCHITECT (S/CO < 250)

Predicted risk of being recent (as measured by the LAg as gold standard) if both tests suggest the recent infection = 39.815/1 + 39.805 = 39.815/40.815 = 97.6% (as shown in Table 2 in the manuscript).

ARCHITECT S/CO (non-recent) and Algorithm 15.1 (non-recent) versus LAg as the gold standard

See Table 5.

$$\begin{gathered} {\text{Predicted probability }}\left( \% \right)~={\text{ 1}}00{\text{ln}}\left( {p/{\text{1}} - p} \right){\text{ }}={\text{ }} - {\text{117 }}+{\text{ }}\left( {0.00{\text{9 }} \times {\text{1}}00} \right){\text{ }}\left( { - {\text{115}}} \right){\text{ }}+{\text{ }}\left( {0.0{\text{12 }} \times {\text{ 1}}00} \right){\text{ }}\left( { - {\text{65}}} \right) \hfill \\ ={\text{ }} - {\text{117 }}+{\text{ }}\left( { - {\text{1}}0{\text{3}}.{\text{5}}} \right){\text{ }}+{\text{ }}\left( { - {\text{78}}} \right){\text{ }}={\text{ }} - {\text{298}}.{\text{5}} \hfill \\ {\text{Ln}}\left( {p/{\text{1}} - p} \right)~~~={\text{ }} - {\text{2}}.{\text{985}} \hfill \\ \left( {p/{\text{1}} - p} \right)~~~~~~~={\text{ }}0.0{\text{5}}0{\text{5}}. \hfill \\ \end{gathered}$$

Table 5 Crosstabulation of LAg with Algorithm 15.1

Predicted risk of being non-recent (as measured by the LAg as gold standard) if both tests suggest non-recent infection = 0.0505/1 + 0.0505 = 0.0505/1.0505 = 4.8% (as shown in Table 2 in the manuscript).