Loss to Follow-Up Risk among HIV Patients on ART in Zimbabwe, 2009–2016: Hierarchical Bayesian Spatio-Temporal Modeling
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Design
2.2. Study Site
2.3. Data Source
2.4. Statistical Analysis
2.4.1. The Bayesian Spatio-Temporal Poisson Regression Model Specification
Likelihood Function
Linear Predictor Function
The Space-Time Interaction Terms
2.4.2. Bayesian Model Fitting and Model Comparison
3. Results
3.1. Loss to Follow-Up Trend and Descriptive Statistics
3.2. Factors Associated with LTFU
3.3. Spatio-Temporal Patterns of LTFU
3.4. Provinces with Exceedance LTFU Risk
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Parameter Definition | Prior Specification |
---|---|---|
This is the mean log overall LTFU risk over all regions. | The parameter was assumed to follow a flat distribution, i.e., to have a “sum to zero” constraint for the structured spatial parameter. | |
This denotes the fixed effects regression coefficients associated with explanatory variables . | The regression coefficients, , were assumed to follow a non-informative Gaussian distribution with a mean and a wide variance, i.e., , with precision . | |
The spatial random effects were partitioned into two components were defined as the structured spatial random effects that allow for smoothing amongst adjacent areas and defined as the unstructured spatial random effects to account for the extra-Poisson variability in the observed LTFU counts data [13]. | The unstructured spatial random effects were assumed Gaussian priors, , with precision . The BYM model assumes spatial dependence between neighbouring areas; hence, the spatial polygons were assumed to follow a Gaussian distribution, i.e., where is the mean parameter and is the part of the variance parameter of the structured spatial component. The represents the number of neighbours and represents the sets of neighbours for the region . | |
This parameter defined the temporal random effects common to all regions. | The temporal random effects were assumed first-order random walk priors and . | |
This component defined the space-time interaction random effects that explain differences in the time trend of LTFU risk for different regions. | To investigate the space-time interaction, the was modelled as a Gaussian parameter with a precision matrix where is an unknown scalar and is the correlation structure matrix defining the temporal and/or spatial dependence between the elements of . |
Provinces | Sex (Females) N (%) | Age at ART Initiation Mean ± SD | Tuberculosis Infection (Positive) N (%) | WHO Clinical Stage (Stage III/IV) N (%) | Duration on ART Median(IQR) |
---|---|---|---|---|---|
Harare | 9395 (65.77) | 37.8 ± 10.6 | 363 (2.54) | 7251 (50.76) | 2.6 (1.2–5.8) |
Bulawayo | 5059 (63.0) | 38.9 ± 10.9 | 297 (3.7) | 3699 (46.06) | 2.6 (1.1–5.6) |
Manicaland | 28,410 (66.07) | 37.6 ± 11.4 | 465 (1.08) | 25,872 (60.17) | 3.7 (2.1–6.5) |
Mashonaland Central | 23,829 (66.09) | 37.4 ± 11.5 | 225 (0.62) | 23,696 (65.68) | 3.1 (1.7–5.7) |
Mashonaland East | 36,584 (65.72) | 36.8 ± 11.2 | 625 (1.12) | 30,647 (54.99) | 3.6 (2.1–5.7) |
Mashonaland West | 33,812 (64.72) | 37.2 ± 11.1 | 583 (1.12) | 31,218 (59.75) | 2.8 (1.8–4.4) |
Masvingo | 39,614 (66.47) | 37.9 ± 11.6 | 669 (1.12) | 28,621 (48.02) | 3.3 (1.9–5.7) |
Matabeleland North | 22,677 (63.73) | 37.2 ± 11.8 | 436 (1.23) | 16,463 (46.27) | 3.6 (2.1–5.9) |
Matabeleland South | 25,977 (66.14) | 36.7 ± 11.8 | 562 (1.43) | 20,911 (53.24) | 3.3 (1.9–5.3) |
Midlands | 30,487 (64.95) | 37.6 ± 11.4 | 591 (1.26) | 23,439 (49.94) | 3.7 (2.1–6.2) |
Variables | Province-Level Spatial Unit | ||||
---|---|---|---|---|---|
Non-Spatio-Temporal Model RR (95%CI) | Spatio-Temporal Model RR (95%CI) | Type I Interaction Model RR (95%CI) | Type II Interaction Model RR (95%CI) | Type III Interaction Model RR (95%CI) | |
Sex | |||||
Male | Reference | Reference | Reference | Reference | Reference |
Female | 0.914 (0.91–0.92) | 0.975 (0.97–0.98) | 0.915 (0.81–1.04) | 0.976 (0.94–1.01) | 1.011 (1.97–1.05) |
Age at ART initiation | |||||
(mean age in years) | 0.601 (0.68–0.71) | 0.818 (0.79–0.84) | 1.092 (0.79–1.51) | 1.004 (1.00–1.01) | 1.014 (0.97–1.06) |
Tuberculosis co-infection | |||||
No | Reference | Reference | Reference | Reference | Reference |
Yes | 0.747 (0.74–0.76) | 0.616 (0.61–0.63) | 0.700 (0.59–0.83) | 0.895 (0.77–1.05) | 0.701 (0.61–0.81) |
WHO staging | |||||
I/II | Reference | Reference | Reference | Reference | Reference |
III/IV | 1.025 (1.02–1.03) | 1.014 (1.01–1.02) | 0.967 (0.93–1.00) | 0.993 (0.97–1.01) | 0.981 (0.96–1.00) |
Duration on ART | |||||
(average time since ART initiation | 0.601 (0.59–0.61) | 0.742 (0.71–0.77) | 0.618 (0.44–0.85) | 0.651 (0.59–0.71) | 0.736 (0.56–0.97) |
Information criterion | |||||
DIC | 9367.17 | 3079.93 | 787.33 | 784.08 | 789.36 |
WAIC | 21,338.73 | 6647.31 | 768.86 | 766.81 | 772.89 |
pD | 3677.72 | 1222.38 | 78.08 | 41.95 | 44.48 |
Marginal log-likelihood | −8520.78 | −2699.27 | −635.33 | −600.38 | −628.81 |
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Matsena Zingoni, Z.; Chirwa, T.; Todd, J.; Musenge, E. Loss to Follow-Up Risk among HIV Patients on ART in Zimbabwe, 2009–2016: Hierarchical Bayesian Spatio-Temporal Modeling. Int. J. Environ. Res. Public Health 2022, 19, 11013. https://doi.org/10.3390/ijerph191711013
Matsena Zingoni Z, Chirwa T, Todd J, Musenge E. Loss to Follow-Up Risk among HIV Patients on ART in Zimbabwe, 2009–2016: Hierarchical Bayesian Spatio-Temporal Modeling. International Journal of Environmental Research and Public Health. 2022; 19(17):11013. https://doi.org/10.3390/ijerph191711013
Chicago/Turabian StyleMatsena Zingoni, Zvifadzo, Tobias Chirwa, Jim Todd, and Eustasius Musenge. 2022. "Loss to Follow-Up Risk among HIV Patients on ART in Zimbabwe, 2009–2016: Hierarchical Bayesian Spatio-Temporal Modeling" International Journal of Environmental Research and Public Health 19, no. 17: 11013. https://doi.org/10.3390/ijerph191711013