Linkage of viral sequences among HIV-infected village residents in Botswana: estimation of linkage rates in the presence of missing data

Abstract

Linkage analysis is useful in investigating disease transmission dynamics and the effect of interventions on them, but estimates of probabilities of linkage between infected people from observed data can be biased downward when missingness is informative. We investigate variation in the rates at which subjects' viral genotypes link across groups defined by viral load (low/high) and antiretroviral treatment (ART) status using blood samples from household surveys in the Northeast sector of Mochudi, Botswana. The probability of obtaining a sequence from a sample varies with viral load; samples with low viral load are harder to amplify. Pairwise genetic distances were estimated from aligned nucleotide sequences of HIV-1C env gp120. It is first shown that the probability that randomly selected sequences are linked can be estimated consistently from observed data. This is then used to develop estimates of the probability that a sequence from one group links to at least one sequence from another group under the assumption of independence across pairs. Furthermore, a resampling approach is developed that accounts for the presence of correlation across pairs, with diagnostics for assessing the reliability of the method. Sequences were obtained for 65% of subjects with high viral load (HVL, n = 117), 54% of subjects with low viral load but not on ART (LVL, n = 180), and 45% of subjects on ART (ART, n = 126). The probability of linkage between two individuals is highest if both have HVL, and lowest if one has LVL and the other has LVL or is on ART. Linkage across groups is high for HVL and lower for LVL and ART. Adjustment for missing data increases the group-wise linkage rates by 40-100%, and changes the relative rates between groups. Bias in inferences regarding HIV viral linkage that arise from differential ability to genotype samples can be reduced by appropriate methods for accommodating missing data.

Figure 1. Average relative bias of adjusted (red) and unadjusted (black) estimators of group-wise linkage rates over general time-reversible evolutionary model simulations.

Figure 2. Estimates of individual-to-individual probability of linkage by groups, , for the full Mochudi data.

Figure 3. Estimates of conditional probability of linkage by groups, , for a 70% sample of the full Mochudi data.

Red line represents the “truth” as observed in the full data.

Figure 4. Estimates of conditional probability of linkage by groups, , for the full Mochudi data.

Figure 5. Realized values of for subsamples of 5 to 95% of Mochudi data.

Red line indicates the observed value of for the full data.

Figure 6. Distribution of unadjusted and bootstrap-adjusted estimators of group-wise linkage probabilities, using proportionate subsampling for a 70% sample of Mochudi data.

Figure 7. Distribution of unadjusted and bootstrap-adjusted estimators of group-wise linkage probabilities, using proportionate subsampling for a 30% sample of Mochudi data.

Figure 8. Diagnostic plots of subsample correlations by group, .

Figure 9. Point estimates and 95% confidence intervals for unadjusted and bootstrap-adjusted estimates of groupwise linkage rates in Mochudi.

The distance cutoff defining linkage between sequences ranges from 0.085 to 0.12.