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Harvard University Harvard University Biostatistics Working Paper Series Year 2016 Paper 199 Leveraging Contact Network Structure in the Design of Cluster Randomized Trials Guy Harling Rui Wang Jukka-Pekka
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Harvard University Harvard University Biostatistics Working Paper Series Year 2016 Paper 199 Leveraging Contact Network Structure in the Design of Cluster Randomized Trials Guy Harling Rui Wang Jukka-Pekka Onnela Victor DeGruttola Harvard T.H. Chan School of Public Health, Harvard T.H. Chan School of Public Health and Brigham and Women s Hospital Harvard T.H. Chan School of Public Health Harvard T.H. Chan School of Public Health This working paper is hosted by The Berkeley Electronic Press (bepress) and may not be commercially reproduced without the permission of the copyright holder. Copyright c 2016 by the authors. Leveraging Contact Network Structure in the Design of Cluster Randomized Trials Guy Harling, Rui Wang, Jukka-Pekka Onnela, and Victor DeGruttola Abstract Background: In settings like the Ebola epidemic, where proof-of-principle trials have succeeded but questions remain about the effectiveness of different possible modes of implementation, it may be useful to develop trials that not only generate information about intervention effects but also themselves provide public health benefit. Cluster randomized trials are of particular value for infectious disease prevention research by virtue of their ability to capture both direct and indirect effects of intervention; the latter of which depends heavily on the nature of contact networks within and across clusters. By leveraging information about these networks in particular the degree of connection across randomized units we propose a novel class of connectivity-informed cluster trial designs that aim both to improve public health impact (speed of control l epidemics) while preserving the ability to detect intervention effects. Methods: We consider cluster randomized trials with staggered enrollment, in each of which the order of enrollment is based on the total number of ties (contacts) from individuals within a cluster to individuals in other clusters. These designs can accommodate connectivity based either on the total number of intercluster connections at baseline or on connections only to untreated clusters, and include options analogous both to traditional Parallel and Stepped Wedge designs. We further allow for control clusters to be held-back from re-randomization for some period. We investigate the performance of these designs in terms of epidemic control (time to end of epidemic and cumulative incidence) and power to detect vaccine effect by simulating vaccination trials during an SEIR-type epidemic outbreak using a network-structured agent-based model. Results: In our simulations, connectivity-informed designs lead to lower peak infectiousness than comparable traditional study designs and a 20% reduction in cumulative incidence, but have little impact on epidemic length. Power to detect differences in incidence across clusters is reduced in all connectivity-informed designs. However the inclusion of even a brief holdback restores most of the power lost in comparison to a traditional Stepped Wedge approach. Conclusions: Incorporating information about cluster connectivity in design of cluster randomized trials can increase their public health impact, especially in acute outbreak settings. Using this information helps control outbreaks by minimizing the number of cross-cluster infections with modest cost in power to detect an effective intervention. BACKGROUND Vaccine study designs typically focus on ensuring sufficient power to detect effects for the product under consideration [1]. In an epidemic setting, however, rapid disease control may also be of vital import. This imperative can be seen in use of a Ring vaccination trial a method previously employed to control smallpox and foot-and-mouth [2, 3] against Ebola in Guinea [4, 5]. In the Ebola trial, vaccination of all contacts was immediate in the intervention arm, and delayed for three weeks in the control arm [6]. While Ring Vaccination is likely to increase the speed of epidemic control, it requires considerable resources to conduct detailed contact tracing, and to maintain an active presence in all clusters. Conducting statistical inference in the context of vaccine (and other infectious disease) trials is complicated by dependent happenings where one s risk of infection depends on the health status of others which may lead to interference between treatment and control groups [7, 8]. Cluster randomized trials (CRTs) allow the estimation of combined direct (benefit of your vaccination) and indirect (benefit of others vaccination) effects. In the commonly-used Parallel design, clusters are pair-randomized to treatment or control, and then followed-up for a predetermined period of time; in settings where use of a control arm is considered unethical, an alternative Stepped Wedge design treats all clusters sequentially in a randomized order. In this latter design effect can be measured through some combination of between- and within-cluster comparisons, accounting for the presence of temporal effects [9]. Standard Parallel and Stepped Wedge designs benefit from cluster randomization to prevent possible confounding by underlying differences among clusters [10], and in the case of Stepped Wedge designs also over time [11]. Concerns regarding risk factor imbalance in CRTs have historically led to matching designs, in which pairs or groups of clusters are chosen at baseline and then randomized to treatment or control, as potentially providing some increase in study efficiency [12]. Such designs are particularly attractive in the context of infectious diseases, given the likelihood of considerable heterogeneity in outcomes across clusters [13]. CRT study designs generally minimize contamination between study arms that arises when individuals in different arms have contact with one another [10], but this is not also feasible. For example, in CRTs for HIV prevention, individuals in one cluster may have partners in another [14]; in Ebola vaccine trials, infected individuals may travel for care to homes or hospitals within another trial cluster [15]. In an epidemic setting, the degree of connection between clusters is likely to Page 1 Hosted by The Berkeley Electronic Press predict outcomes of interest, including outbreak timing within a cluster and epidemic size. Taking between-cluster connectivity into account can therefore aid in matching. The purpose of a vaccine is to convert potentially-infectious network ties (i.e. the direct connection between infectious person i and susceptible person s) into non-functional ones [16-18]. This conversion can be achieved by successfully vaccinating either end of the tie. Hence, vaccination acts by removing ties from a graph that represent potentially infecting pathways within a population. Contamination can be also conceptualized as a network problem since ties between individuals across clusters can lead to the spread of either infections or behaviors from one study arm to another, thereby attenuating the impact of randomization. We propose a novel class of CRT study designs that make use of information about the network connectivity between study clusters; we show that these designs can reduce the number of new infections more rapidly than standard designs while still allowing for the evaluation of intervention effectiveness. Our approach requires less intensive follow-up than does a Ring Vaccination approach. We focus exclusively on trials with staggered implementation in order to mimic urgent settings in which epidemic control is a priority. We investigate the performance of these designs by simulating vaccination trials during an Ebola-like epidemic and evaluate both epidemic parameter values and power to detect an effect of the vaccine under various designs. METHODS A class of connectivity-informed cluster trial designs Connectivity defines how individuals or groups in a network are linked to one-another. For sexually transmitted infections, ties are sexual acts; for hemorrhagic fevers, physical contacts; for behavior change interventions, conversations. In our study, we consider ties measured prior to study commencement; for each cluster we calculate the absolute number of ties from members of the cluster to members of all other clusters. We then rank clusters from most- to least-connected in one of two ways: the Static Rank approach, where the ranking is conducted only once at baseline; and the Adaptive Rank approach, where untreated clusters are re-ranked at each vaccination time point based only on their connectedness to remaining untreated clusters. Both approaches are based on the idea that a cluster s connectivity to all other clusters is related to its tendency to transmit Page 2 infections; hence treating more connected clusters earlier may slow epidemic spread. We outline the proposed study designs in Table 1. Within the Static Rank approach, we consider several different designs: First, a Strict Order design which rolls-out treatment from most- to least-connected cluster; this non-randomized approach provides an upper bound on how fast the epidemic might be controlled using between-cluster connectivity information. Second, a Fuzzy Order design which randomizes the two mostconnected clusters to treatment and control status at the time of study origin (step 1). At the next time of randomization, the control cluster from step 1 and the next most-connected cluster are randomized. This process is repeated until the final untreated cluster remains, which is then assigned to treatment. The Fuzzy Order design can be generalized to a Fuzzy Order Holdback-h design, in which the control cluster at each time point is held-back from randomization for h vaccination time points: if h=1, the control cluster from step 1 would be re-eligible for randomization at step 3; for h=2, at step 4, etc. The only difference between Static Rank designs is the order in which clusters are treated. We illustrate how these Static Rank designs operate in Figure 1. We also propose a Ranked Parallel design, which randomizes the two most-connected clusters to treatment and control condition at study origin. At step 2, the randomization process is repeated using the third- and fourth-most connected clusters, and so on until half the clusters are assigned to treatment. At this point the collected data are analyzed, and if the treatment proves protective, it is rolled out to the untreated clusters, starting with the most connected. The Strict, Fuzzy and Holdback Ordered designs can all also use an Adaptive Rank approach, although the Ranked Parallel design cannot since all randomization pairs must be specified simultaneously. The Adaptive Rank approach minimizes the treatment of people already connected to treated subjects, by including only unvaccinated clusters in between-cluster connectivity: since successful vaccination removes ties between vaccinated and unvaccinated subjects, there is no further benefit to vaccinating the unvaccinated member of a connection. At the cluster level, this implies that vaccinating a cluster that is highly-connected to already-treated clusters is likely to provide less population-level benefit than vaccinating one largely connected to untreated clusters. Removing treated clusters from the set of potentially transmitting ties can lead to significant rerankings (see Figure 1B), and thus more rapid epidemic control. The cost of the Adaptive Rank approach is its requirement for more detailed data than the Strict Rank approach: the latter Page 3 Hosted by The Berkeley Electronic Press requires only an ordering of clusters by their overall connectivity (K quantities in a study of K clusters), whereas the former requires a measure of connectivity for every pair of clusters (( K 2 ) = 1 2 K(K 1) quantities). Simulation studies We generate a community-structured population using a standard stochastic block model with K blocks or clusters, each block consisting of N nodes (individuals) [19]. Mean degree for each individual is set at 5.5. In the baseline simulation, we assume that within each cluster, ties are distributed randomly. Half of all clusters are designated to have higher external connectivity: in these clusters individuals have a number of between-cluster ties drawn from a normal distribution with a mean of 1 versus 0.5; all clusters have a standard deviation of 0.5. We simulate an epidemic on the network graph of the structured population, based on Ebola as a recent example of a disease requiring urgent vaccine trials, and a member of the viral hemorrhagic fever group quite likely to cause future severe, acute outbreaks [20].We use a state transition model with six states: Susceptible, Exposed, Infectious, Hospitalized, Funeral, and Removed (see Supplementary Figure 1) [21]. Parameter values for the simulation are calibrated such that progression times between states and the basic reproductive number (R 0, the average number of new infections caused by an infectious individual in a fully susceptible population) are roughly equal to those observed for Ebola. These values were not optimized to historical data since the simulation is intended for design comparison, not Ebola epidemic prediction. To compare study designs, we first generate a network realization from the stochastic block model. We then simulate nine epidemics on the network using the above six-state epidemic model; one for each trial design. We initialize the epidemic model by randomly selecting four nodes at the beginning of the simulation to be infected and use the same initial condition for each study design (and for the reference simulation involving no intervention at all). In each case, the epidemic is propagated on the underlying network using daily time steps, and allowed to run for 42 days (six weeks) from initial introduction of infection. If all nine epidemics have substantial ongoing transmission at this point specifically the effective reproductive number (R e, the average number of new infections actually caused by each infectious person) is greater than one in week six then we begin the trial; otherwise we discard this network realization. Page 4 We simulate vaccinating one cluster every seven days; even in Parallel trials, roll-out is likely to be staggered for logistical reasons as for example in both Sierra Leone s and Liberia s Ebola vaccine trials [22, 23]. Parallel designs include a ten-week pause in the study after half of all clusters had been vaccinated to allow for statistical analyses to be completed. We assume 80% vaccine coverage of susceptible individuals in targeted clusters, and that vaccine immediately removes individuals from a susceptible state 95% of the time. We continue the simulation until each epidemic has died out. We repeat the network generation and epidemic simulation process until we have 1,000 complete iterations. Parameter values for network generation, epidemic model, and infection and vaccination models are provided in Supplementary Table 2. Statistical analyses For each simulation we compute three metrics to quantify the epidemic outcomes: (1) time from epidemic start (T 0 ) until R e first falls below one; (2) time from T 0 until the last infectious individual recovers; and (3) cumulative incidence for the entire epidemic. These metrics are intended to evaluate the: (i) speed of control; (ii) speed of elimination; and (iii) overall burden of the epidemic. For each metric, we calculate median and interquartile range across all 1,000 simulations. We compute statistical power to detect effectiveness of a vaccine using permutation tests based on pairwise comparisons of incidence across treatment and control clusters for the six study designs that involved randomization (Table 1). The test statistic for a null hypothesis of equal incidence rates in treatment and control clusters for week T after the treated cluster was vaccinated, is the sum of the differences in incidence rate between clusters in each simulation, in week T; null hypotheses of equal incidence cumulative from week T to week T + w are similar. For Parallel designs, the test statistic is the sum of K/2 differences in incidence rates; for Stepped Wedge designs, it involves (K h 1) differences. Each test involves 2000 permutations, and p-values are the proportion of test statistics greater or equal to the observed test statistic in absolute value. We calculate the probability of rejecting the null hypothesis at week T 2 (i.e. two weeks prior to vaccination) and at each subsequent week up to T Our designs differ from usual CRTs in that pairs are formed based on their connectivity, not matched on potential cluster characteristics that are predictive of the outcome. This connectivity-based matching means that pairs are not strictly exchangeable, and thus our pair-wise randomization may not fully protect us from confounding when estimating treatment effects, if factors are associated both with connectedness and infection likelihood within clusters. The validity of the permutation tests is, however, guaranteed by randomization. Page 5 Hosted by The Berkeley Electronic Press To assess sensitivity of results to key vaccine, trial and population characteristics, we conduct sensitivity analyses. First, we run a model for a vaccine with no effectiveness (for type-i error control). Second, we modeled vaccines that are: (i) perfect (100% reach and 100% protective); (ii) poor (70% reach and 70% effective); and (iii) able to protect those in the Exposed as well as the Susceptible state, moving them directly to the Removed state. Third, we began the vaccination program at 56 and 70 days post-initial infection. Fourth, we varied the heterogeneity in connectivity between clusters by decreasing and increasing the standard deviation of the betweencluster ties term from 0.5 to 0.25 and 0.75 contacts respectively. Finally, we considered clusters with skewed within-cluster ties by drawing each respondent s degree from a lognormal distribution with σ = 1. For each sensitivity analysis we summarized results in terms of the key metrics for epidemic outcomes. RESULTS In the absence of an intervention, the spreading process infects a median of 80.0% of the population (interquartile range [IQR] across 1,000 runs: %), peaks at a mean of incident cases per 1000 susceptible individuals per week, and dies out after a median of 290 days (IQR ). Mean R e declines slowly from a peak of 2.08 on day 36, falling below 1 after a median of 134 days (IQR: ). Temporal plots of mean values for all state variables are shown in Supplementary Figure 2. As intended, all study designs lead to substantial reductions in proportion of individuals ever infected, time to end of outbreak and time to R e 1, relative to no vaccination (Table 2). All connectivity-informed designs lead to lower peak infectiousness than with traditional study designs, with little discernable difference among them (Figure 2B). Both of the Parallel designs suffer from the pause for analysis prior to vaccinating the second half of clusters, leading to lower levels of overall vaccine coverage (an average of 44.4% for Standard and 47.4% for Ranked Parallel vs % for the Stepped Wedge designs) and higher overall mortality (an average of % for Parallel vs % for Stepped Wedge designs) (Figure 2C and D). The effectiveness of Parallel designs prior to the pause is however, identical to their Stepped Wedge analogues, since the designs are identical prior to this point. Connectivity-informed Stepped Wedge designs reduce the proportion of individuals ever infectious relative to the Standard Stepped Wedge by approximately 20%, but do not have meaningful impact on time to last infection or to infection Page 6 control (Table 2). The Ranked Parallel design similarly reduce the proportion ever infectious, compared to the Standard Parallel design, but is approximately one week slower to control the epidemic. Cluster-level mean incidence rates decline as each cluster is vaccin
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