Non-inferiority analysis of subcutaneous versus intravenous 300 mg monthly natalizumab administration: A post hoc analysis of the REFINE study.

To quantify the probability that monthly intravenous (IV) and subcutaneous (SC) natalizumab (NTZ) had similar efficacy in relapsing-remitting multiple sclerosis (RRMS), non-inferiority of efficacy of NTZ-SC versus NTZ-IV on combined MRI unique active lesions number (CUAL) was explored re-analysing the REFINE data set. Non-inferiority margins were selected equal to 25%/33%/50% fractions of the effect size of NTZ-IV versus placebo observed in the AFFIRM study. Ninety-nine RRMS were included. NTZ-SC resulted not inferior to NTZ-IV on CUAL for all margins at 2.5% significance level, and, in worst-case scenario, its effect over NTZ-IV did not exceed 3.5% (or 2.8%) of the effect of NTZ-IV versus placebo.

Bayesian causal inference: a critical review.

This paper provides a critical review of the Bayesian perspective of causal inference based on the potential outcomes framework. We review the causal estimands, assignment mechanism, the general structure of Bayesian inference of causal effects and sensitivity analysis. We highlight issues that are unique to Bayesian causal inference, including the role of the propensity score, the definition of identifiability, the choice of priors in both low- and high-dimensional regimes. We point out the central role of covariate overlap and more generally the design stage in Bayesian causal inference. We extend the discussion to two complex assignment mechanisms: instrumental variable and time-varying treatments. We identify the strengths and weaknesses of the Bayesian approach to causal inference. Throughout, we illustrate the key concepts via examples. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

Sensitivity analyses for the principal ignorability assumption using multiple imputation.

In the context of clinical trials, there is interest in the treatment effect for subpopulations of patients defined by intercurrent events, namely disease-related events occurring after treatment initiation that affect either the interpretation or the existence of endpoints. With the principal stratum strategy, the ICH E9(R1) guideline introduces a formal framework in drug development for defining treatment effects in such subpopulations. Statistical estimation of the treatment effect can be performed based on the principal ignorability assumption using multiple imputation approaches. Principal ignorability is a conditional independence assumption that cannot be directly verified; therefore, it is crucial to evaluate the robustness of results to deviations from this assumption. As a sensitivity analysis, we propose a joint model that multiply imputes the principal stratum membership and the outcome variable while allowing different levels of violation of the principal ignorability assumption. We illustrate with a simulation study that the joint imputation model-based approaches are superior to naive subpopulation analyses. Motivated by an oncology clinical trial, we implement the sensitivity analysis on a time-to-event outcome to assess the treatment effect in the subpopulation of patients who discontinued due to adverse events using a synthetic dataset. Finally, we explore the potential usage and provide interpretation of such analyses in clinical settings, as well as possible extension of such models in more general cases.

Autologous haematopoietic stem cell transplantation versus low-dose immunosuppression in secondary-progressive multiple sclerosis.

BACKGROUND AND PURPOSE: Effectiveness of autologous haematopoietic stem cell transplantation (AHSCT) in relapsing-remitting multiple sclerosis (MS) is well known, but in secondary-progressive (SP)-MS it is still controversial. Therefore, AHSCT activity was evaluated in SP-MS using low-dose immunosuppression with cyclophosphamide (Cy) as a comparative treatment. METHODS: In this retrospective monocentric 1:2 matched study, SP-MS patients were treated with intermediate-intensity AHSCT (cases) or intravenous pulses of Cy (controls) at a single academic centre in Florence. Controls were selected according to baseline characteristics adopting cardinality matching after trimming on the estimated propensity score. Kaplan-Meier and Cox analyses were used to estimate survival free from relapses (R-FS), survival free from disability progression (P-FS), and no evidence of disease activity 2 (NEDA-2). RESULTS: A total of 93 SP-MS patients were included: 31 AHSCT, 62 Cy. Mean follow-up was 99 months in the AHSCT group and 91 months in the Cy group. R-FS was higher in AHSCT compared to Cy patients: at Year 5, 100% versus 52%, respectively (p < 0.0001). P-FS did not differ between the groups (at Year 5: 70% in AHSCT and 81% in Cy, p = 0.572), nor did NEDA-2 (p = 0.379). A sensitivity analysis including only the 31 "best-matched" controls confirmed these results. Three neoplasms (2 Cy, 1 AHSCT) and two fatalities (2 Cy) occurred. CONCLUSIONS: This study provides Class III evidence, in SP-MS, on the superior effectiveness of AHSCT compared to Cy on relapse activity, without differences on disability accrual. Although the suppression of relapses was observed in the AHSCT group only, AHSCT did not show advantages over Cy on disability, suggesting that in SP-MS disability progression becomes based more on noninflammatory neurodegeneration than on inflammation.

[Analysis and future scenarios of the SARS-CoV-2 epidemic in Tuscany Region (Central Italy)]. / Analisi e previsioni dell'epidemia da SARS-CoV-2 in Toscana.

OBJECTIVES: about two months after the end of the lockdown imposed for the containment of the SARS-CoV-2 epidemic, the contagion dynamics in the Tuscany Region (Central Italy) have been assessed from the beginning of the emergency to the end of June through a compartmental model, and future medium-long term projections have been produced. DATA AND METHODS: this study used a SIRD model in which the infection reproduction number R0 varied over time, according to a piecewise constant function. The fatality parameter and the time from contagion to infection resolution (death or recovery) were fixed to ensure parameter identifiability, and the model was calibrated on the Covid-19 deaths notified from March 9th to June 30th 2020. The uncertainty around the estimates was quantified through parametric bootstrap. Finally, the resulting model was used to produce medium-long term projections of the epidemic dynamics. RESULTS: the date of the first infection in Tuscany was estimated as February 21st 2020. The value of R0(t) ranged from 7.78 (95%CI 7.55-7.89), at the beginning of the outbreak, to a value very close to 0 between April 27th and May 17th. Finally, R0(t) rose, reaching an average of 0.66 (0.32, 0.88) between May 18th and June 30th. At the epidemic peak, estimated at the beginning of April, the notified infected people circulating in the region were just 22% of those predicted by the model. According to the estimated SIRD, under the hypothetical scenario that R0(t) slightly exceeds 1 from the beginning of October 2020, a new wave of contagion could arise by next spring. CONCLUSIONS: the estimated trend of R0(t) is suggestive of a strong effect of the lockdown in Tuscany and of a mild increase of the contagion potentially attributable to the easing of the containment measures. Medium-long term projections unequivocally indicate that the danger of a new epidemic wave has not been averted.

Evaluating a SARS-CoV-2 screening strategy based on serological tests.

BACKGROUND: facing the SARS-CoV-2 epidemic requires intensive testing on the population to early identify and isolate infected subjects. Although RT-PCR is the most reliable technique to detect ongoing infections, serological tests are frequently proposed as tools in heterogeneous screening strategies. OBJECTIVES: to analyse the performance of a screening strategy proposed by the local government of Tuscany (Central Italy), which first uses qualitative rapid tests for antibody detection, and then RT-PCR tests on the positive subjects. METHODS: a simulation study is conducted to investigate the number of RT-PCR tests required by the screening strategy and the undetected ongoing infections in a pseudo-population of 500,000 subjects, under different prevalence scenarios and assuming a sensitivity of the serological test ranging from 0.50 to 0.80 (specificity 0.98). A compartmental model is used to predict the number of new infections generated by the false negatives two months after the screening, under different values of the infection reproduction number. RESULTS: assuming a sensitivity equal to 0.80 and a prevalence of 0.3%, the screening procedure would require on average 11,167 RT-PCR tests and would produce 300 false negatives, responsible after two months of a number of contagions ranging from 526 to 1,132, under the optimistic scenario of a reproduction number between 0.5 to 1. Resources and false negatives increase with the prevalence. CONCLUSIONS: the analysed screening procedure should be avoided unless the prevalence and the rate of contagion are very low. The cost and effectiveness of the screening strategies should be evaluated in the actual context of the epidemic, accounting for the fact that it may change over time.

Causal inference with interfering units for cluster and population level treatment allocation programs.

Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define new estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs, extending existing estimands to take into consideration the units' covariates and dependence between units' treatment assignment. We further propose entirely new estimands for population-level interventions over the collection of clusters, which correspond in the motivating setting to regulations at the federal (vs. cluster or regional) level. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. For a small number of observed clusters, a bootstrap approach for confidence intervals is proposed. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.

Bayesian inference for causal mechanisms with application to a randomized study for postoperative pain control.

We conduct principal stratification and mediation analysis to investigate to what extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients in a prospective, randomized, double-blind study. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification, as well as natural effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions, and involve different sets of structural assumptions.

Assessing the short term impact of air pollution on mortality: a matching approach.

BACKGROUND: The opportunity to assess short term impact of air pollution relies on the causal interpretation of the exposure-response association. However, up to now few studies explicitly faced this issue within a causal inference framework. In this paper, we reformulated the problem of assessing the short term impact of air pollution on health using the potential outcome approach to causal inference. We considered the impact of high daily levels of particulate matter ≤10 µm in diameter (PM10) on mortality within two days from the exposure in the metropolitan area of Milan (Italy), during the period 2003-2006. Our research focus was the causal impact of a hypothetical intervention setting daily air pollution levels under a pre-fixed threshold. METHODS: We applied a matching procedure based on propensity score to estimate the total number of attributable deaths (AD) during the study period. After defining the number of attributable deaths in terms of difference between potential outcomes, we used the estimated propensity score to match each high exposure day, namely each day with a level of exposure higher than 40 µg/m3, with a day with similar background characteristics but a level of exposure lower than 40 µg/m3. Then, we estimated the impact by comparing mortality between matched days. RESULTS: During the study period daily exposures larger than 40 µg/m3 were responsible for 1079 deaths (90% CI: 116; 2042). The impact was more evident among the elderly than in the younger age classes. Exposures ≥ 40 µg/m3 were responsible, among the elderly, for 1102 deaths (90% CI: 388, 1816), of which 797 from cardiovascular causes and 243 from respiratory causes. Clear evidence of an impact on respiratory mortality was found also in the age class 65-74, with 87 AD (90% CI: 11, 163). CONCLUSIONS: The propensity score matching turned out to be an appealing method to assess historical impacts in this field, which guarantees that the estimated total number of AD can be derived directly as sum of either age-specific or cause-specific AD, unlike the standard model-based procedure. For this reason, it is a promising approach to perform surveillance focusing on very specific causes of death or diseases, or on susceptible subpopulations. Finally, the propensity score matching is free from issues concerning the exposure-confounders-mortality modeling and does not involve extrapolation. On the one hand this enhances the internal validity of our results; on the other, it makes the approach scarcely appropriate for estimating future impacts.

Identification of causal effects in the presence of nonignorable missing outcome values.

We consider a new approach to identify the causal effects of a binary treatment when the outcome is missing on a subset of units and dependence of nonresponse on the outcome cannot be ruled out even after conditioning on observed covariates. We provide sufficient conditions under which the availability of a binary instrument for nonresponse allows us to derive tighter identification intervals for causal effects in the whole population and to partially identify causal effects in some latent subgroups of units, named Principal Strata, defined by the nonresponse behavior in all possible combinations of treatment and instrument. A simulation study is used to assess the benefits of the presence versus the absence of an instrument for nonresponse. The simulation design is based on real health data, coming from a randomized trial on breast self-examination (BSE) affected by a large proportion of missing outcome data. An instrument for nonresponse is simulated considering alternative scenarios to discuss the key role of the instrument for nonresponse in identifying average causal effects in presence of nonignorable missing outcomes. We also investigate the potential inferential gains from using an instrument for nonresponse adopting a Bayesian approach for inference. In virtue of our theoretical and empirical results, we provide some recommendations on study designs for causal inference.

Comparative efficacy of subcutaneous versus intravenous natalizumab on annualized relapse rate: A post-hoc analysis of the REFINE study.

BACKGROUND: The non-inferiority of the efficacy of subcutaneous (SC) vs intravenous (IV) administration of natalizumab (NTZ) once every 4 weeks in relapsing-remitting multiple sclerosis (RRMS) was recently demonstrated on the primary outcome of the REFINE study, i.e. MRI "combined unique active lesions number" (CUAL). To provide further evidence on the comparative efficacy of the two NTZ formulations, the effect of NTZ-SC vs NTZ-IV on annualized relapse rate (ARR) was investigated re-analysing the REFINE dataset. METHODS: Post-hoc analysis of the REFINE study dataset aimed at exploring the non-inferiority of the efficacy of NTZ-SC vs NTZ-IV on ARR, i.e. the main secondary outcome of the REFINE study. Robustness of the non-inferiority analysis on CUAL with respect to the presence of cases from the SC arm who received a rescue treatment, including NTZ-IV, was also assessed by sensitivity analyses. Three non-inferiority margins were selected, corresponding to 25 %, 33 %, and 50 % fractions of the effect size of NTZ-IV vs placebo observed in the AFFIRM study on ARR (i.e. 0.125, 0.170, and 0.250). RESULTS: Ninety-nine RRMS patients were included. The mean difference in the effect of NTZ-SC vs NTZ-IV on ARR was close to 0. The lower bound of the 95 % confidence interval (worst case scenario) was -0.119, corresponding to 25 % (p = 0.025) of the effect of NTZ-IV vs placebo on ARR. Sensitivity analyses confirmed the results of the primary non-inferiority analysis on the outcome CUAL. CONCLUSIONS: NTZ-SC resulted not inferior to NTZ-IV on ARR for all the non-inferiority margins. The non-inferiority analysis of the efficacy of NTZ-SC vs NTZ-IV on CUAL was demonstrated to be robust with respect to rescued patients.

Matching on Generalized Propensity Scores with Continuous Exposures.

In the context of a binary treatment, matching is a well-established approach in causal inference. However, in the context of a continuous treatment or exposure, matching is still underdeveloped. We propose an innovative matching approach to estimate an average causal exposure-response function under the setting of continuous exposures that relies on the generalized propensity score (GPS). Our approach maintains the following attractive features of matching: a) clear separation between the design and the analysis; b) robustness to model misspecification or to the presence of extreme values of the estimated GPS; c) straightforward assessments of covariate balance. We first introduce an assumption of identifiability, called local weak unconfoundedness. Under this assumption and mild smoothness conditions, we provide theoretical guarantees that our proposed matching estimator attains point-wise consistency and asymptotic normality. In simulations, our proposed matching approach outperforms existing methods under settings with model misspecification or in the presence of extreme values of the estimated GPS. We apply our proposed method to estimate the average causal exposure-response function between long-term PM2.5 exposure and all-cause mortality among 68.5 million Medicare enrollees, 2000-2016. We found strong evidence of a harmful effect of long-term PM2.5 exposure on mortality. Code for the proposed matching approach is provided in the CausalGPS R package, which is available on CRAN and provides a computationally efficient implementation.

Assessment of the feasibility of pool testing for SARS-CoV-2 infection screening.

BACKGROUND: SARS-CoV-2 pandemic represented a huge challenge for national health systems worldwide. Pooling nasopharyngeal (NP) swabs seems to be a promising strategy, saving time and resources, but it could reduce the sensitivity of the RT-PCR and exacerbate samples management in terms of automation and tracing. In this study, taking advantage of the routine implementation of a screening plan on health workers, we evaluated the feasibility of pool testing for SARS-CoV-2 infection diagnosis in the presence of low viral load samples. METHOD: Pools were prepared with an automated instrument, mixing 4, 6 or 20 NP specimens, including one, two or none positive samples. Ct values of positive samples were on average about 35 for the four genes analyzed. RESULTS: The overall sensitivity of 4-samples and 6-samples pools was 93.1 and 90.0%, respectively. Focussing on pools including one sample with Ct value ≥35 for all analyzed genes, sensitivity decreased to 77.8 and 75.0% for 4- and 6-samples, respectively; pools including two positive samples, resulted positive in any size as well as pools including positive samples with Ct values <35. CONCLUSION: Pool testing strategy should account the balance between cost-effectiveness, dilution effect and prevalence of the infection. Our study demonstrated the good performances in terms of sensitivity and saving resources of pool testing mixing 4 or 6 samples, even including low viral load specimens, in a real screening context possibly affected by prevalence fluctuation. In conclusion, pool testing strategy represents an efficient and resources saving surveillance and tracing tool, especially in specific context like schools, even for monitoring changes in prevalence associated to vaccination campaign.

PM2.5 and hospital admissions among Medicare enrollees with chronic debilitating brain disorders.

BACKGROUND: Although long-term exposure to particulate matter<2.5 µm (PM2.5) has been linked to chronic debilitating brain disorders (CDBD), the role of short-term exposure in health care demand, and increased susceptibility for PM2.5-related health conditions, among Medicare enrollees with CDBD has received little attention. We used a causal modeling approach to assess the effect of short-term high PM2.5 exposure on all-cause admissions, and prevalent cause-specific admissions among Medicare enrollees with CDBD (Parkinson's disease-PD, Alzheimer's disease-AD and other dementia). METHODS: We constructed daily zipcode counts of hospital admissions of Medicare beneficiaries older than 65 across the United-States (2000-2014). We obtained daily PM2.5 estimates from a satellite-based model. A propensity score matching approach was applied to match high-pollution (PM2.5 > 17.4 µg/m3) to low-pollution zip code-days with similar background characteristics. Then, we estimated the percent change in admissions attributable to high pollution. We repeated the models restricting the analysis to zipcode-days with PM2.5 below of 35 µg/m3. RESULTS: We observed significant increases in all-cause hospital admissions (2.53% in PD and 2.49% in AD/dementia) attributable to high PM2.5 exposure. The largest observed effect for common causes was for pneumonia and urinary tract infection. All the effects were larger in CDBD compared to the general Medicare population, and similarly strong at levels of exposure considered safe by the EPA. CONCLUSION: We found Medicare beneficiaries with CDBD to be at higher risk of being admitted to the hospital following acute exposure to PM2.5 levels well below the National Ambient Air Quality Standard defined as safe by the EPA.

Pool testing on random and natural clusters of individuals: Optimisation of SARS-CoV-2 surveillance in the presence of low viral load samples.

Facing the SARS-CoV-2 epidemic requires intensive testing on the population to early identify and isolate infected subjects. During the first emergency phase of the epidemic, RT-qPCR on nasopharyngeal (NP) swabs, which is the most reliable technique to detect ongoing infections, exhibited limitations due to availability of reagents and budget constraints. This stressed the need to develop screening procedures that require fewer resources and are suitable to be extended to larger portions of the population. RT-qPCR on pooled samples from individual NP swabs seems to be a promising technique to improve surveillance. We performed preliminary experimental analyses aimed to investigate the performance of pool testing on samples with low viral load and we evaluated through Monte Carlo (MC) simulations alternative screening protocols based on sample pooling, tailored to contexts characterized by different infection prevalence. We focused on the role of pool size and the opportunity to develop strategies that take advantage of natural clustering structures in the population, e.g. families, school classes, hospital rooms. Despite the use of a limited number of specimens, our results suggest that, while high viral load samples seem to be detectable even in a pool with 29 negative samples, positive specimens with low viral load may be masked by the negative samples, unless smaller pools are used. The results of MC simulations confirm that pool testing is useful in contexts where the infection prevalence is low. The gain of pool testing in saving resources can be very high, and can be optimized by selecting appropriate group sizes. Exploiting natural groups makes the definition of larger pools convenient and potentially overcomes the issue of low viral load samples by increasing the probability of identifying more than one positive in the same pool.

Evaluation of the health impacts of the 1990 Clean Air Act Amendments using causal inference and machine learning.

We develop a causal inference approach to estimate the number of adverse health events that were prevented due to changes in exposure to multiple pollutants attributable to a large-scale air quality intervention/regulation, with a focus on the 1990 Clean Air Act Amendments (CAAA). We introduce a causal estimand called the Total Events Avoided (TEA) by the regulation, defined as the difference in the number of health events expected under the no-regulation pollution exposures and the number observed with-regulation. We propose matching and machine learning methods that leverage population-level pollution and health data to estimate the TEA. Our approach improves upon traditional methods for regulation health impact analyses by formalizing causal identifying assumptions, utilizing population-level data, minimizing parametric assumptions, and collectively analyzing multiple pollutants. To reduce model-dependence, our approach estimates cumulative health impacts in the subset of regions with projected no-regulation features lying within the support of the observed with-regulation data, thereby providing a conservative but data-driven assessment to complement traditional parametric approaches. We analyze the health impacts of the CAAA in the US Medicare population in the year 2000, and our estimates suggest that large numbers of cardiovascular and dementia-related hospitalizations were avoided due to CAAA-attributable changes in pollution exposure.

ESTIMATING POPULATION AVERAGE CAUSAL EFFECTS IN THE PRESENCE OF NON-OVERLAP: THE EFFECT OF NATURAL GAS COMPRESSOR STATION EXPOSURE ON CANCER MORTALITY.

Most causal inference studies rely on the assumption of overlap to estimate population or sample average causal effects. When data suffer from non-overlap, estimation of these estimands requires reliance on model specifications, due to poor data support. All existing methods to address non-overlap, such as trimming or down-weighting data in regions of poor data support, change the estimand so that inference cannot be made on the sample or the underlying population. In environmental health research settings, where study results are often intended to influence policy, population-level inference may be critical, and changes in the estimand can diminish the impact of the study results, because estimates may not be representative of effects in the population of interest to policymakers. Researchers may be willing to make additional, minimal modeling assumptions in order to preserve the ability to estimate population average causal effects. We seek to make two contributions on this topic. First, we propose a flexible, data-driven definition of propensity score overlap and non-overlap regions. Second, we develop a novel Bayesian framework to estimate population average causal effects with minor model dependence and appropriately large uncertainties in the presence of non-overlap and causal effect heterogeneity. In this approach, the tasks of estimating causal effects in the overlap and non-overlap regions are delegated to two distinct models, suited to the degree of data support in each region. Tree ensembles are used to non-parametrically estimate individual causal effects in the overlap region, where the data can speak for themselves. In the non-overlap region, where insufficient data support means reliance on model specification is necessary, individual causal effects are estimated by extrapolating trends from the overlap region via a spline model. The promising performance of our method is demonstrated in simulations. Finally, we utilize our method to perform a novel investigation of the causal effect of natural gas compressor station exposure on cancer outcomes. Code and data to implement the method and reproduce all simulations and analyses is available on Github (https://github.com/rachelnethery/overlap).

Identification and Estimation of Causal Mechanisms in Clustered Encouragement Designs: Disentangling Bed Nets using Bayesian Principal Stratification.

Exploration of causal mechanisms is often important for researchers and policymakers to understand how an intervention works and how it can be improved. This task can be crucial in clustered encouragement designs (CED). Encouragement design studies arise frequently when the treatment cannot be enforced because of ethical or practical constrains and an encouragement intervention (information campaigns, incentives, etc) is conceived with the purpose of increasing the uptake of the treatment of interest. By design, encouragements always entail the complication of non-compliance. Encouragements can also give rise to a variety of mechanisms, particularly when encouragement is assigned at cluster level. Social interactions among units within the same cluster can result in spillover effects. Disentangling the effect of encouragement through spillover effects from that through the enhancement of the treatment would give better insight into the intervention and it could be compelling for planning the scaling-up phase of the program. Building on previous works on CEDs and non-compliance, we use the principal stratification framework to define stratum-specific causal effects, that is, effects for specific latent subpopulations, defined by the joint potential compliance statuses under both encouragement conditions. We show how the latter stratum-specific causal effects are related to the decomposition commonly used in the literature and provide flexible homogeneity assumptions under which an extrapolation across principal strata allows one to disentangle the effects. Estimation of causal estimands can be performed with Bayesian inferential methods using hierarchical models to account for clustering. We illustrate the proposed methodology by analyzing a cluster randomized experiment implemented in Zambia and designed to evaluate the impact on malaria prevalence of an agricultural loan program intended to increase the bed net coverage. Farmer households assigned to the program could take advantage of a deferred payment and a discount in the purchase of new bed nets. Our analysis shows a lack of evidence of an effect of the offering of the program to a cluster of households through spillover effects, that is through a greater bed net coverage in the neighborhood.