Background
Randomised controlled trials assess the efficacy and safety of interventions [
1,
2]. When it is difficult to allocate interventions at the individual level, for example due to logistical or financial restrictions, randomisation and allocation of interventions at a group level may be preferred, this is a cluster randomised trial (CRT) [
3]. CRTs also allow for estimation of spillover and herd effects; the apparent treatment effect on individuals who do not receive the intervention [
4]. Failure to account for spillover effects can result in biases that reduce the quality of trials and mean that absence of bias is no longer guaranteed by the randomisation, especially when the relationship between intervention and outcome is complex [
5,
6].
Spatial effects are effects stemming from locational variation in the distribution of phenomena of interest or in the intensity of interaction between phenomena of interest. Such effects manifest as local variation in the estimated treatment effect over a study area. The existence of spatial effects suggests that global effects estimates are uncertain, and may under- or over-estimate the true effect dependent on location. When values of a single variable are related to nearby values of the same variable this is called spatial dependence, the existence of which is usually captured using spatial autocorrelation measures [
7]. Spatial dependence is a fundamental concept in spatial statistics [
8] and stems from Tobler’s [
9] 1st law of geography that “everything is related to everything else, but near things are more related than distant things.” In agricultural field trials it is long established that the location of the data can impact on trial results [
10]. Incorporation of spatial methodology in agricultural trials is common, [
11] but the impact of spatial effects in human CRTs have not been researched extensively.
Clusters in CRTs are often defined geographically and valid inference relies on the assumption that the clusters are independent irrespective of their nearness to one another [
3]. There is frequently an assumption of an absence of spillover; that movement of people and diseases occurs freely within a cluster but movement between clusters is negligible, non-existent, or not relevant [
12]. This assumption can be violated when there is movement of people or diseases across borders, such as mosquitoes flying between control and intervention households. If an intervention such as insecticide-treated bed nets provide a protective effect to nearby control households then ignoring mosquito mobility will result in underestimating the intervention effect of the trial. This could result in trials discarding effective interventions because the control and intervention are both receiving the benefit of the treatment.
Spillover may also be due to connections in social networks, [
13] also violating the assumption of independence. In this paper, we consider spillover that can be estimated using GPS data which is often collected as part of trials and therefore do not consider social networks. Spillovers are more likely in trials that have spatially close clusters, and the effect is especially important when an individual’s outcome is affected by their proximity to other individuals with different exposure statuses.
One way to minimise the potential for spillover is to design a trial with well-separated clusters. In practice this may not be logistically or financially feasible as spatial effects can be present over distances of several kilometres [
14]. Furthermore, greater distances between clusters removes our ability to measure spillover spatial effects. To be able to measure spatial effects we need to have data on people nearby to one another and by separating the clusters we may no longer have such information. If proximity to an intervention affects non-treated individuals this is of usually scientific interest and something we should measure. There is a need to control for and estimate spatial effects in the analysis of a trial without adding extra complexity to the design.
We therefore focus only on spatial analysis methods used in CRTs in this review and do not consider alternative trial designs. A further reason for focusing on analysis methods is that this may enable analysis of existing and previous CRTs where redesign is not possible. This review is a diagnostic review of spatial analysis methods that have been used in CRTs. As such, it does not attempt to pose statistical solutions or determine the best way to account for spatial effects within CRTs. We will describe the state of the literature and aim to improve understanding and help inform further research into spatial effects within CRTs by (1) Identifying spatial analysis methods used in CRTs. (2) Summarising and grouping spatial methods (3) Assessing the impact of spatial effects.
Methods
Search terms and review process
The PRISMA guidelines [
15] for systematic reviews and meta-analyses were followed for this review. It was conducted between January 2016 and September 2016. Ovid/Medline, Pubmed, and Web of Science databases were electronically searched and Mendeley was used to store articles. Search terms for CRTs and spatial effects are detailed in Table
1. Studies up to end of 2015 were included and only English language articles and search terms were considered.
Pubmed | Randomi*ed Trial | Spatial* | (Randomi*ed trial) AND (group OR community OR cluster OR place) AND (spatial* OR indirect effect* OR spillover* OR contamination* OR externalit*) |
Medline/Ovid | Group | Indirect effect* |
WebOfScience | Community | Spillover* |
| Cluster | Contamination* |
| Place | Externalit* |
Papers from each database were combined into a single spreadsheet containing the title, authors, journal, and year. Duplicates were removed automatically within the software and then manually during the title screen. The titles were screened to remove irrelevant papers such as individually randomised trials. Following this, abstracts were screened and the full texts of potentially relevant papers were independently reviewed by two reviewers and disagreements resolved. After selecting relevant papers the references of the articles were screened.
Inclusion and exclusion criteria
The inclusion criteria for studies were: (1) the study is a cluster randomised trial. (2) Spatial methods are used in the analysis of the study. We categorised a spatial method as one which accounts for the structure, location, or relative distances of the data. This includes direct estimation of an effect such as, the change in risk for those within 100 m of an intervention household or the use of a spatial model which account for spatial structure.
The exclusion criteria were (1) non-randomised studies (2) individual randomised trials and hybrid CRTs such as Double or pseudo-randomised studies as they were considered not to be cluster randomised trials (3) grey literature (4) studies where spillover effects are measured in a non-spatial way, for example comparison of vaccinated and non-vaccinated individuals within an intervention cluster. (5) Studies that account for spatial effects at the design stage only; for instance, using buffer zones or well-separated clusters (6) articles which were study protocols and therefore had not applied their methods yet.
The following variables were collected on each paper: title, year, journal, author, intervention, outcome, whether a map was presented, spatial analysis method.
Discussion
This review has found multiple approaches to incorporating or measuring spatial effects in the context of CRTs, however these stem from only a few examples in the literature. Further, no conventional or standard approach was found. The approaches differ by whether they directly analyse a spatial variable or model the spatial structure. Spatial variables were either straight-line distance from a participant to a place of interest or a measure of the density surrounding a participant. For instance, distance between a control participant and an intervention participant. Spatial models included spatial structure in the covariance of the random effects model using a distance parameter or spatial weights matrix. Accounting for spatial structure affects both the precision and point estimates of treatment effects and failure to do so could give inaccurate results [
25,
29].
The papers in this review are only a small proportion of the total number of CRTs that have been published. That only ten records were found suggests that spatial effects are not often considered in this area. Furthermore, despite evidence of spatial effects, they were rarely adjusted for in the primary analysis of the trial. It appears that the impact of location on analytical approach is at best an afterthought and in most cases ignored. The trials come from a variety of domains and although predominantly focused in infectious diseases, there may be implications for a broader range of trials particularly in trials of health services organisation [
29] which are becoming more common [
31]. Therefore, a wide range of trials may not be accounting for spatial effects that bias results, however it is presently unclear as to what extent this may be an issue.
Further research is required to determine how much spatial effects impact trial results. Simulation studies may allow exploration of how the magnitude and extent of spatial autocorrelation may bias trial results. There have been some attempts to quantify how important spatial effects may be in trials more generally [
32,
33]. Methods that allow for estimation of treatment effects whilst accounting for spatial effects could be investigated and also testing under simulation. However, there are several challenges to overcome such as whether we can estimate the true randomised intervention effect using a spatial model, and how such an effect estimate should be interpreted.
An alternative use of spatial data is to conduct additional analyses to complement analysis of the main trial. These analyses explore spatial component of the trial, and could improve understanding of the mechanism of the intervention effect. Spatial methods could be applied to previous trial data and a toolbox of standard approaches defined allowing future trials to predefine spatial analyses. This would allow for quantification of the distance over which spatial effects are present for different disease areas. A further area of research is in alternative CRT designs, although they are not the focus of this review this might include double randomisation or pseudo randomised trials where clusters are first randomised and subsequently individuals within clusters are randomised to allow for measurement of spillover effects [
34,
35].
Multiple terms in the literature refer to spillover effects and many of them could refer to spatial effects with differing terminology between fields and researchers in the same fields. To add to confusion, these terms can have dual meanings for instance, an indirect effect can be the effect on an individual who does not receive the intervention or the effect of an intervention through a mediating variable. The search strategy attempted to include a broad range of terms for CRTs and spatial effects but at present, there is no established standard for citing the use of spatial data in the analysis of CRTs. Consequently, it is possible that trials have been missed. Although this is a weakness, comparison with a larger more general systematic review on health-related spillover in impact evaluations [
13] did not result in the addition of any further trials. They had searched 19 databases and screened more than 34,000 records. Due to this the authors conclude the omission of further studies is likely to be minimal.
This review has focused only on the analysis stage of a CRT and it could be argued that adjusting for spatial effects is not necessary in a well-designed trial as clusters should be well-separated to minimise spillover effects [
4]. Trial designs such as the fried egg design [
3] which incorporates a buffer around clusters could be used to attempt to eliminate or measure spatial spillover. However, in cases where spatial correlation is present over large distances [
14] this may not be possible and could lead to the inability to detect the difference between no effect and everyone having an effect [
36]. Additionally, as spatial effects are rarely considered in trials, it may not be until after the design stage that the problem becomes apparent, if at all.
On the other hand, having clusters relatively close together could have advantages, because the measurement of spatial spillover effects is of scientific interest. Knowledge that an intervention provides indirect benefit based on proximity is useful to differentiate between interventions and to plan how to benefit the largest number of people. Furthermore, subjects who live further apart are more likely to be heterogeneous than those living close together due to cultural, geographical, and social differences which could make treatment differences harder to distinguish due to imbalance between clusters.
In conclusion although there have been a few attempts to control and estimate spatial effects within the context of human CRTs our understanding is limited. Although there are commonalities between approaches there is no consensus on how to account for spatial effects with in CRTs and more work needs to be done to evaluate and develop spatial methodology within the context of a range of CRTs.
Authors’ contributions
CJ, GLDT, and DL were involved in defining the search strategy. CJ and GLDT performed the search and screening of articles. CJ drafted the article with feedback, input and guidance from GLDT, DL, NA, and WJE. All authors read and approved the final manuscript.