docs: api: discussion & results obj.3 overhaul with regression, relat…

…ed: #1, #2, #5, #8, #9, #11, #12, #13, #14, #15

docs/api/abstract.tex

@@ -9,18 +9,18 @@
 non-linear compartmental models of sexual HIV transmission
 to simulate ART prevention impacts in Sub-Saharan Africa.
 We summarized data on model structure/assumptions (factors) related to risk and intervention heterogeneity,
-and explored crude associations of ART prevention impact with modelled factors.
+and explored multivariate ecological associations of ART prevention impact with modelled factors.
 \textbf{Results.}
 Of 1384 search hits, 94 studies were included,
 which primarily modelled medium/high prevalence epidemics in East/Southern Africa.
 64 studies considered sexual activity stratification and 39 modelled at least one key population.
 21 studies modelled faster/slower ART cascade transitions (HIV diagnosis, ART initiation, or cessation) by risk group,
 including 8 with faster and 4 with slower cascade transitions among key populations versus the wider population.
-Models without activity stratification predicted the largest ART prevention impacts,
-followed by models with key populations that had faster cascade transitions versus the wider population.
+In ecological analysis, activity stratification alone had minimal effect on projected ART prevention benefits,
+but turnover of higher risk groups, and ART cascade differences by sex both reduced projected benefits.
 \textbf{Conclusion.}
-Among compartmental transmission models applied to project ART prevention impacts,
-representations of risk heterogeneity and projected impacts varied considerably,
-where models with less heterogeneity tended to predict larger impacts.
-The potential influence of modelling assumptions about
-risk and intervention heterogeneity should be further explored.
+Among compartmental transmission models applied to project ART prevention impacts in Sub-Saharan Africa,
+representations of risk heterogeneity and projected impacts varied considerably.
+Future work should explore how assumptions about
+turnover and cascade differences amongst risk groups
+may influence projected ART prevention impacts.

docs/api/discussion.tex

@@ -1,73 +1,98 @@
 \section{Discussion}
 \label{s:disc}
-Via scoping review, we found that representations of risk heterogeneity varied widely across
-transmission modelling studies of ART intervention in SSA, with
-stratification by sexual activity and key populations considered in approximately
-2/3 and 2/5 of models, respectively.
-We also found that the projected proportions of infections averted due to ART scale-up were
-larger under assumptions of homogeneous risk or prioritized ART to key populations,
-as compared to heterogeneous risk or without prioritized ART to key populations.
-Three notable themes emerged from our review.
+Model-based evidence continues to support
+evaluation and mechanistic understanding of ART prevention impacts.
+Such evidence may be sensitive to modelling assumptions about risk heterogeneity.
+Via scoping review, we found that stratification by sexual activity and key population(s)
+was considered in approximately 2/3 and 2/5 of studies to date, respectively;
+1/3 considered risk group turnover and 1/4 considered differential ART cascade by any risk group.
+In multivariate ecological analysis, we found that
+projected incidence reductions and propoportions of infections averted
+were minimally affected by risk heterogeneity directly,
+but were reduced by risk group turnover and differential ART cascade.
 \par
-First, modelling studies have an opportunity to keep pace with growing epidemiological data on risk heterogeneity.
-For example, 41\% of the modelling studies reviewed included at least one key population, such as FSW and or MSM.
-Key populations continue to experience disproportionate risk of HIV, even in high-prevalence epidemics \cite{AIDSinfo},
-and models examining the unmet needs of key populations suggest that
-these unmet needs play an important role in overall epidemic dynamics \cite{Stone2021,Bekker2015}.
-Furthermore, the we found that the number of modelled clients per female sex worker, and
-the relative rate of partnership formation among female sex workers versus other women
-did not always reflect the available data \cite{Watts2010,Scorgie2012}.
-Similarly, among studies with different partnership types, only 20\% modelled
-main/spousal partnerships---with more sex acts/lower condom use---between two higher risk individuals,
-while 80\% modelled only casual/commercial partnerships among higher risk individuals.
-However, data suggest female sex workers may form main/spousal partnerships
-with regular clients and boyfriends/spouses from higher risk groups \cite{Scorgie2012}.
-Thus, future models can continue to include emerging data on these and other factors of heterogeneity,
-while nested model comparison studies can study how
-multiple factors might act together to influence projections of ART impact \cite{Dodd2010,Hontelez2013}.
+Within-person variability in sexual risk has been illustrated among key populations,
+including MSM, FSW, and clients of FSW \cite{Fazito2012,Romero-Severson2012,Roberts2020},
+as well as in the wider population \cite{Houle2018}.
+This risk variability is often reflected in compartmental models as risk group turnover.
+Previous modelling suggested that
+turnover could make treatment as prevention \emph{more} feasible \cite{Henry2015};
+however, the model in \cite{Henry2015} was calibrated to overall equilibrium prevalence,
+allowing the reproduction number to decrease with increasing turnover.
+By contrast, when calibrating to group-specific prevalence with turnover,
+greater risk heterogeneity is inferred than without turnover,
+and the reproduction number may actually increase \cite{Knight2020}.
+Turnover of higher risk groups can also reduce ART coverage in those groups through
+net outflow of treated individuals, and net inflow of susceptible individuals,
+some of whom then become infected \cite{Knight2020}.
+The proportion of onward transmission prevented through ART may thus be reduced via turnover.
+Consistent inclusion of turnover in HIV transmission models would be supported by
+additional data on individual-level trajectories of sexual risk behaviour \cite{Watts2010}.
 \par
-Second, most models assumed equal ART cascade transition rates across subgroups,
+Most models assumed equal ART cascade transition rates across subgroups,
 including diagnosis, ART initiation, and retention.
-Recent data suggest differential ART cascade by sex, age, and key populations
+However, recent data suggest differential ART cascade by sex, age, and key populations
 \cite{Lancaster2016,Schwartz2017,Ma2020,Green2020}.
 These differences may stem from the unique needs of subpopulations
 and is one reason why differentiated ART services are a core component of HIV programs
 \cite{Chikwari2018,Ehrenkranz2019}.
 Moreover, barriers to ART may intersect with transmission risk, particularly among key populations,
 due to issues of stigma, discrimination, and criminalization \cite{Ortblad2019,Baral2019}.
-Thus, further opportunities exist to incorporate differentiated cascade data,
+Our ecological analysis estimated that
+differences in cascade by sex (lower among men) or risk (key populations prioritized)
+had a large influence on projected ART prevention benefits.
+Thus, opportunities exist to incorporate differentiated cascade data,
 examine the intersections of intervention and risk heterogeneity, and
 to consider the impact of HIV services as delivered on the ground.
 Similar opportunities were noted regarding modelling of pre-exposure prophylaxis in SSA \cite{Case2019}.
-Finally, depending on the research question, the modelled treatment cascade may need
+Depending on the research question, the modelled treatment cascade may need
 to include more cascade steps and states related to treatment failure/discontinuation.
 \par
-Third, based on ecological analysis of scenarios, we found that
-modelling assumptions about risk and intervention heterogeneity
-may influence the projected proportion of infections averted by ART.
-We did not find similar evidence for relative incidence reduction due to ART,
-but studies reporting these outcomes were largely distinct.
-Among studies reporting both, the overall pattern was consistent
-\cite{Salomon2005,Abbas2006,Pretorius2010,Nichols2014,Barnighausen2016,Maheu-Giroux2017,Akudibillah2018}.
-These findings highlight the limitations of ecological analysis to estimate
-the potential influence of modelling assumptions on projected ART prevention benefits,
-and motivate additional model comparison studies to better quantify this influence,
-such as \cite{Dodd2010,Hontelez2013}.
-Our ecological analysis also suggested that the anticipated ART prevention impacts from homogeneous models
-may be achievable in the context of risk heterogeneity
-if testing/treatment resources are prioritized to higher risk groups.
+Key populations often reflect intersections of risk heterogeneity, turnover, and cascade differences.
+For example, a sexual network comprising FSW with high turnover and FSW clients with low ART coverage
+could remain outside the reach of ART as prevention.
+Key populations continue to experience disproportionate risk of HIV,
+even in high-prevalence epidemics \cite{AIDSinfo},
+and models suggest that unmet needs of key populations
+play an important role in overall epidemic dynamics \cite{Bekker2015,Stone2021}.
+Although recent and/or context-specific key populations data are often lacking \cite{Rao2018},
+further opportunities exist to include key populations more consistenly in transmission models,
+and to improve modelling assumptions in the absence of such data.
+For example, we found that the number of modelled clients per female sex worker, and
+the relative rate of partnership formation among female sex workers versus other women
+did not always reflect available data syntheses for sex work \cite{Watts2010,Scorgie2012}.
+Similarly, among studies with different partnership types, only 1/5 modelled
+main/spousal partnerships---with more sex acts/lower condom use---between two higher risk individuals,
+while 4/5 modelled only casual/commercial partnerships among higher risk individuals.
+However, data suggest that female sex workers form main/spousal partnerships
+with regular clients and boyfriends/spouses from higher risk groups \cite{Scorgie2012}.
+Such modelling assumptions may influence the overall epidemic dynamics
+and the predicted ability of treatment to prevent population-level transmission.
 \par
-Limitations of our scoping review include our examination of only a few key populations.
-In our conceptual framework for risk heterogeneity, we did not explicitly examine heterogeneity
-by type of sex act (i.e. anal sex) which is associated with higher probability of HIV transmission,
+Our scoping review has several limitations.
+First, we focused on classically defined key populations,
+although other priority groups like mobile populations and adolescent girls and young women
+will remain important for treatment as prevention.
+Second, our conceptual framework for risk heterogeneity did not explicitly examine
+heterogeneity related to anal sex, which is associated with higher probability of HIV transmission,
 nor structural risk factors like violence \cite{Silverman2011,Baggaley2013}.
-The large number of differences between scenarios in the scoping review context
-also limited our ability to infer the influence of risk heterogeneity across scenarios.
+Third, we did not extract data on model fitting,
+which could explain some counterintuitive effect estimates.
+For example, modelling increased infectiousness in late-stage HIV reduced ART prevention impacts.
+However, in most studies, newly ART-eligible patients via scale-up had earlier stage HIV;
+therefore, such patients would have lower modelled infectiousness than late-stage HIV,
+and lower infectiousness than in a model with uniform infectiousness fitted to the same data.
+A similar mechanism could explain increased ART prevention impacts when including acute infection.
+Finally, the strength of our multivariate analysis was limited by
+the small number of studies/scenarios relative to the number of factors explored.
 \par
-In conclusion, representations of risk heterogeneity vary widely
-among models used to project the prevention impacts of ART in SSA.
-Such differences may partially explain the large variability in projected impacts.
-Opportunities exist to incorporate new and existing data on
-the intersections of risk and intervention heterogeneity.
-Moving forward, systematic model comparison studies are needed to
-estimate and understand the influence of various modelling assumptions on ART prevention impacts.
+In conclusion, model-based evidence of ART prevention impacts could likely be improved by:
+1) consistenly including risk group turnover,
+   to reflect prevention challenges associated with the dynamic nature of sexual risk;
+2) integrating emerging data on differences in ART cascade between sexual risk groups,
+   to reflect services as delivered on the ground; and
+3) routinely incorporating key populations,
+   to reflect intersections of transmission risk and barriers to care
+   that may undermine treatment as prevention.
+Model comparison studies like \cite{Dodd2010,Hontelez2013} that explore
+the influence of these factors in detail would also be welcome.

docs/api/results.tex

@@ -194,77 +194,56 @@ \subsection{ART Prevention Impact}
 \label{ss:res:api}
 Dataset~B comprised \x{n/n.a.api} studies,
 including \x{n/n.s.api} scenarios of ART scale-up.
-Relative incidence reduction with ART scale-up
-as compared to status quo
+Relative incidence reduction (IR) with ART scale-up as compared to status quo
 was reported in \x{n/n.a.api.inc} studies (\x{n/n.s.api.inc} scenarios);
-proportion of cumulative infections averted due to ART scale-up
+proportion of cumulative infections averted (CIA) due to ART scale-up
 was reported in \x{n/n.a.api.chi} (\x{n/n.s.api.chi});
 and \x{n/n.a.api.both} (\x{n/n.s.api.both}) reported both.
-Some scenarios reported these outcomes on multiple time horizons.
+Some scenarios included multiple time horizons.
 \par
 \begin{table}
   \centering
-  \caption{Projected ART prevention benefits,
+  \caption{Projected ART prevention impacts,
     stratified by factors of risk heterogeneity and contexts}
   \input{tab/api}
   \label{tab:api}
 \end{table}
-Figure~\ref{fig:api} summarizes each outcome versus time since ART scale-up,
-stratified by a composite index of modelled risk heterogeneity.
-Ecological-level analysis across scenarios by degree of risk heterogeneity
-identified differences in proportions of infections averted,
-but not in relative incidence reduction (Table~\ref{tab:api}).
-The largest proportions of infections averted were reported from
-scenarios without risk heterogeneity (median [IQR]\% = \xd{api/chi/Risk.None}), followed by
-scenarios with key populations prioritized for ART (\xd{api/chi/Risk.KP-(priority)}).
-The smallest impacts were observed in scenarios with
-key populations who were not prioritized for ART (\xd{api/chi/Risk.KP-(same)})
-and in models with risk heterogeneity but without key populations
-(\xd{api/chi/Risk.Activity-(No-KP)}).
-Among \x{n/n.s.api.both} scenarios from \x{n/n.a.api.both} studies that provided both outcomes
-\cite{Salomon2005,Abbas2006,Pretorius2010,Nichols2014,Barnighausen2016,Maheu-Giroux2017,Akudibillah2018}, % MAN
-the pattern of incidence reduction versus modelled heterogeneity
-was similar to the pattern of infections averted versus modelled heterogeneity
-(Figure~\ref{fig:api:both}).
 \begin{figure}
-  \begin{subfigure}{0.5\textwidth}
-    \centering
-    \includegraphics[width=\textwidth]{{inc.Risk}.pdf}
-    \caption{Reduction in HIV incidence}
-    \label{fig:api:inc}
-  \end{subfigure}%
-  \begin{subfigure}{0.5\textwidth}
-    \centering
-    \includegraphics[width=\textwidth]{{chi.Risk}.pdf}
-    \caption{Cumulative HIV infections averted}
-    \label{fig:api:chi}
-  \end{subfigure}
-  \caption{Projected ART prevention benefits over different time horizons,
-    stratified by levels of modelled risk heterogeneity: whether models considered
-    differences in sexual activity, key populations, and
-    ART cascade prioritized to key populations;
-    no scenarios considered lower cascade among key populations.}
-  \label{fig:api}
+  \centering
+  \includegraphics[width=0.75\linewidth]{effects-subset}
+  \caption{Effect estimates for selected factors of heterogeneity on
+    incidence reduction (\%, IR) and cumulative infections averted (\%, CHI)
+    from linear multivariate regression with generalized estimating equations.}
+  \label{fig:effects-sub}
   \floatfoot{
-    The numbers of unique scenario time-horizons
-    contributing to each box are given above it.
-    The number of studies (scenarios) reporting
-    incidence reduction, cumulative infections averted, both, and either was:
-    \x{n/n.a.api.inc}~(\x{n/n.s.api.inc}),
-    \x{n/n.a.api.chi}~(\x{n/n.s.api.chi}),
-    \x{n/n.a.api.both}~(\x{n/n.s.api.both}), and
-    \x{n/n.a.api}~(\x{n/n.s.api}), respectively (Dataset~B).
-    KP: key populations;
-    priority: cascade transitions were faster for at least one step among KP vs overall;
-    same: cascade transitions were assumed the same speed in KP as overall;
-    no scenarios in Dataset~B considered lower cascade among KP.}
+    Numerical results given in Table~\ref{tab:api}.
+    KP: key populations.
+    priority: modelled ART cascade transitions were faster in KP vs overall due to prioritized programs;
+    same: cascade transitions were assumed the same in KP as overall;
+    diff: cascade transitions were slower among men.
+    Factor definitions are given in Appendix~\ref{a:defs}.}
 \end{figure}
+Table~\ref{tab:api} summarizes projected ART prevention impacts (IR, CIA),
+stratified by heterogeneity and contextual factors,
+plus adjusted effect estimates for each factor from multivariate analysis.
+Figures~\ref{fig:api:Risk}--\ref{fig:api:art.rbeta.cat} illustrate
+unadjusted impacts stratified by factor levels, while
+Figures~\ref{fig:effects}~and~\ref{fig:effects-sub} (subset) illustrate effect estimates.
+Including activity groups without key populations
+slightly increased projected ART prevention impacts---adjusted effect (95\% CI):
+\x{api/inc/Risk.Activity-(no-KP).eff}\% IR, \x{api/chi/Risk.Activity-(no-KP).eff}\% CIA.
+Including key population(s) without prioritized ART cascade had a similar effect:
+\x{api/inc/Risk.KP-(same).eff}\% IR, \x{api/chi/Risk.KP-(same).eff}\% CIA.
+However, including turnover of one or more higher risk group(s) reduced ART prevention impacts:
+\x{api/inc/act.turn.any.TRUE.eff}\% IR, \x{api/chi/act.turn.any.TRUE.eff}\% CIA,
+such that overall, including activity groups and/or key population(s) with turnover
+reduced ART prevention impacts.
 \par
-ART prevention impacts were larger with
-longer time horizon,
-lower HIV prevalence (Figure~\ref{fig:api:api.prev.cat}), and
-greater ART eligibility (Figure~\ref{fig:api:art.cd4});
-however patterns were not consistent across
-epidemic phase (Figure~\ref{fig:api:api.phase}),
-ART coverage targets (Figure~\ref{fig:api:art.cov.cat}), or
-relative infectiousness on ART (Figure~\ref{fig:api:art.rbeta.cat}).
+Including ART cascade prioritized to any key population(s)
+increased the projected ART prevention impacts enough to overcome reductions due to turnover:
+\x{api/inc/Risk.KP-(priority).eff}\% IR, \x{api/chi/Risk.KP-(priority).eff}\% CIA.
+No studies in Dataset~B examined lower ART cascade among key population(s).
+Stratifying by sex, and considering lower ART cascade among men was estimated to reduce CIA:
+\x{api/chi/Sex.Yes-(same).eff}\% and \x{api/chi/Sex.Yes-(diff).eff}\%, respectively;
+although similar effects were not observed for IR:
+\x{api/inc/Sex.Yes-(same).eff}\% and \x{api/inc/Sex.Yes-(diff).eff}\%.