Optimal Allocation of Gold Standard Testing under Constrained Availability: Application to Assessment of HIV Treatment Failure

Abstract

The World Health Organization (WHO) guidelines for monitoring the effectiveness of HIV treatment in resource-limited settings (RLS) are mostly based on clinical and immunological markers (e.g., CD4 cell counts). Recent research indicates that the guidelines are inadequate and can result in high error rates. Viral load (VL) is considered the "gold standard", yet its widespread use is limited by cost and infrastructure. In this paper, we propose a diagnostic algorithm that uses information from routinely-collected clinical and immunological markers to guide a selective use of VL testing for diagnosing HIV treatment failure, under the assumption that VL testing is available only at a certain portion of patient visits. Our algorithm identifies the patient sub-population, such that the use of limited VL testing on them minimizes a pre-defined risk (e.g., misdiagnosis error rate). Diagnostic properties of our proposal algorithm are assessed by simulations. For illustration, data from the Miriam Hospital Immunology Clinic (RI, USA) are analyzed.

Keywords: Antiretroviral failure; HIV/AIDS; ROC; constrained optimization; resource limited; tripartite classification.

Figure 1

Risk score distributions and diagnosis actions.

Figure 2

Gamma distributions used for simulating CD4 count data. The gray step lines in the top-left subplot are histograms of the CD4 data from the Miriam Hospital Immunology Clinic. The smooth dashed (solid) lines are gamma densities for those with (without) treatment failure.

Figure 3

Large-sample convergence properties of estimated optimal cut-off boundaries. Horizontal lines are added to indicate the sample sizes needed to achieve σ_n = 25.

Figure 4

The optimal min-λ rules based on S₁ and associated FPR and FNR.

Figure 5

Empirical and semiparametric estimates of the cumulative densities of CD4 counts and log₁₀(CD4).

Figure 6

ROC curves for diagnostic rules using S₁ and S₂ (subplots (a) and (b)); the resulting AUC curves as functions of φ (subplot (c)); and the difference of the two AUC curves (S₂ “minus” S₁, subplot (d)). The point-wise 95% CI of the difference in AUC is calculated using the bootstrap method with 500 re-samples.