Part 2 Sources of Spatial Autocorrelation
Summary: This blog presents several of the sources of spatial autocorrelation in health event data. Many of these could plausibly lead to clusters of health events, others (such as interpolation autocorrelation) may act to “smooth out” true clusters. How can one identify the cause(s) of a cluster of health events from among these competing explanations? Part of the solution is the use of neutral models, and that is the topic of my next blog.
This is the second of a two part blog on spatial autocorrelation and clusters of health events. The first part presented a framework for analyzing disease clusters that builds on the principles of strong inference. Strong inference involves enumeration of all of the possible explanations of a disease cluster, some may be causal (such as an environmental hazard or exposure linked aetiologically to the health outcome), some may not (such as geographic variation in proportion of cases reported). Each of them may result in spatial autocorrelation in health events – spatial patterns such that some areas are higher, and some are lower, and arranged in a manner that is non-random. One possible arrangement of high values is a cluster – a geographically localized area of elevated risk for the health event. Hence many of the sources of spatial autocorrelation in health events are potential causes of clusters, or may act to “smooth out” and obscure true clusters.
This raises a very important question. What are the sources of spatial autocorrelation in health events? These may need to be included in the set of explanatory hypotheses for an observed pattern, and include spatial autocorrelation in underlying risk factors, covariates, reporting, diagnosis, health care policies, physician behaviors, and interpolation autocorrelation, among others, as summarized below. This is by no means an exhaustive list, but includes factors that likely should be considered in many spatial analyses of health events.
Multifactorial causes of disease: It is important to recognize that many health outcomes may be caused by several different disease processes, and that a given exposure mechanism may result in different disease outcomes. For example, risk factors for myocardial infarction include genetic predispositions, diet, body weight, exercise habits, medication compliance, and access to care, among others. And specific exposures, such as smoking, are associated with elevated risk for a host of health outcomes, including bladder, throat, and lung cancers; asthma, pneumonia, and emphysema, among others. Spatial autocorrelation in health events may arise whenever the host of factors underlying disease expression are themselves spatially structured. Genetic predispositions for disease may be inherited, giving rise to spatial autocorrelation in disease risk whenever family members cohabitate and tend to live near one another; ambient air pollutant concentrations tend to be highly spatially autocorrelated, and so on.
Comorbidity and competing causes of death: It is unusual for chronic diseases to be the sole disease process occurring in a patient, especially as the age of the subject increases. This makes sense when one considers the multifactorial nature of most diseases. At the population level smoking will increase the risk of both lung and bladder cancers; at the individual level a smoker may have comorbid conditions such as emphysema and lung cancer. The expression of infection processes is often mediated by immune response and the health status of the individual. Hence risk of infection increases as the physical condition of the individual declines. Individuals and populations are thus both subject to competing causes of death. Prior to the advent of antibiotics in the 1940’s respiratory and childhood infections were major sources of mortality in most developed countries. As antibiotics became widely available the major source of mortality became chronic diseases such as heart conditions and cancer. These were “unmasked” once respiratory and childhood infections were removed as a competing cause of death. Spatial autocorrelation in health events thus may arise when there is underlying geographic variation in comorbid conditions and/or risks for competing causes of death.
Geographic variation in exposure and behaviors that mediate exposure: Health events associated with environmental exposures are mediated by exposure routes including eating, drinking, breathing, dermal exposures and ionizing radiation. When considering health outcomes associated with exposure to specific risk factors, such as arsenic, one needs to consider relevant exposure routes and mechanisms, such as consumption of foods and beverages containing biologically active forms of arsenic. Exposure-mediating behaviors are often modifiable risk factors, since what one smokes, drinks and eats are to a certain extent individual choices that can be changed. When evaluating spatial patterns in health outcomes associated with environmental exposures one needs to consider both environmental concentrations as well as the exposure routes whereby the compound under consideration enters the body. Both of these (environmental concentrations and exposure routes and mechanisms) may themselves be spatially structured. For example, the amount of water people drink varies with age, decreasing as one gets older, with occupation (farm workers requiring more water than office workers), with altitude and other factors.
Socio-economic and demographic factors: One definition of “covariate” is a variable that has an effect (e.g. is associated with the outcome) that is not of direct interest. When modeling health events such as disease incidence, socio-economic and demographic factors such as age may be considered as covariates, since age (for example) does not of itself cause disease. Yet these are of considerable importance when evaluating spatial disease patterns, since the risk of most health outcomes including cancer, heart disease, and infections, is typically associated with socio-economic status, sex, race and age. One thus may need to account for spatial patterns in covariates when assessing the significance of a clustering of health events. Rather than asking “are the health events clustered?” one instead may ask “Is there significant clustering of health events above and beyond spatial patterns in covariates?” Neutral models (described later) have been developed to address this question.
Genetics: Micro-evolutionary processes such as selection, isolation-by-distance, and migration give rise to spatial autocorrelation in genetic structure and genetic variance in geographically distributed populations. While we often think of human populations as being very well mixed, interbreeding freely over large geographic distances, this is often not the case. Population genetics in North American, European and Asian populations have been demonstrated to be spatially autocorrelated, and associated with language and dialect (Sokal, Jacquez et al. 1993). This makes sense when one considers that children speak the language of their parents and family, and that family members tend to live in geographic proximity of one another, even though some may travel far from their homes. Familial clusters are often observed for many cancers, both because of behavioral factors mediating common exposures such as second hand smoking and diet, but also because of within-family genetic similarity in oncogenes and tumor suppressor genes. For example, one hypothesis for explaining the excess of breast cancer incidence on Long Island is the higher incidence of mutations of BRCA genes in local populations thought to be descended from European populations, where these BRCA mutations are more frequent. BRCA1 and BRCA2 are tumor suppressor genes, and mutations of these genes are been linked to breast and ovarian cancers.
For infectious diseases the pathogen, whether a virus or a bacteria, undergoes a population bottleneck whenever there is infection transmission to a new susceptible person. Only a few (e.g. several thousands) of the pathogen may be required for infection to take hold, and together these may have a genetic composition that is quite different from the overall pathogen population. A mutation that occurs during a bottleneck can become fixed in the pathogen population infecting that host (person). When this mutation is associated with changes in infection transmission or severity of the infection, it can have important consequences for the spread of infection, as well as for morbidity, mortality and resistance to treatment. Such mutations can give rise to new pathogen strains, and the occurrence of these strains may be observed as outbreaks of the new strain, initially occurring in localized populations. This has been documented for diverse infectious diseases including cholera, tuberculosis, HIV and influenza, among others.
Perhaps one of the best known instances of interactions between infection and genetics is selective pressures for the sickle cell trait that foster resistance to malaria infection (Livingstone 1958). In sickle cell disease the red blood cells are misshapen, leading to circulatory problems, and early death of red blood cells, resulting in anemia. The disease has a genetic basis, with alleles that code for the sickle cell trait and for abnormal hemoglobin resulting in different forms of the disease of varying severity. But when one sickle cell allele is present it confers some resistance to malaria infection. This confers a substantial selective pressure in populations residing in malarial regions. The sickle cell trait, and sickle cell anemia, thus vary geographically with higher penetration of the sickle cell gene in populations residing where malaria is endemic.
Vector-borne diseases and parasites often have complex life histories, involving infection transmission and amplification among humans and one or more host organisms. Well-known examples include malaria, Lyme disease, and West Nile virus, among others. Here, spatial structure in the genetics of the pathogen can arise due to the interactions between population bottlenecks and mutations, as noted above for infectious diseases. The genetics of the host species can also influence the origin and spread of different pathogen strains.
Environment/vector-pathogen ecology: Environmental patchiness in habitats suitable for vector and host organism survival are important determinants of where and when vector-borne and parasitic infections occur. In the northeastern and mid-western United States, the white-tailed deer (Odocoileus virginianus) is an important host species for Lyme disease, which is transmitted by a bite from infected blacklegged ticks. Infection transmission events can only occur where both infected ticks and susceptible people are present. Blacklegged tick habitat includes wooded, brushy areas that provide food and cover for intermediate host species such as white-footed mice, and white-tailed deer. But infection transmission to humans only occurs when people are in areas where infected ticks are present and feeding. Thus the occurrence of Lyme disease is highly associated with geographic overlap of human activity spaces with habitat suitable for both intermediate hosts and the tick itself. Infection transmission is highly structured temporally as well, occurring in those months when the tick is searching for blood meals in the spring and fall.
Heterogeneity in population density, rate stability, and the small numbers problem: Health events that occur in small areas may be expressed as a rate, such as an incidence or mortality rate. Rates are calculated from a numerator, such as the number of incident lung cancer cases in white males; and a denominator, such as the population at risk (e.g. white males) for lung cancer. The rate is calculated by dividing the numerator by the denominator, and this is where the “small numbers problem” arises. The variance in the rate depends critically on the size of the denominator. When the denominator is small, variance in the rate is high, when the denominator is large, variance in the rate is small. Hence the appearance of an apparently large rate might be due entirely or in part to the small numbers problem (e.g. a small denominator with a resulting large variance in the rate estimate), and the true, underlying risk might be entirely unremarkable. A simple protocol for evaluating whether the small numbers problem is having an impact on estimated rates is as follows. First, create a map of the rate and a scatterplot of the rate (on the x-axis) and the population at risk (on the y-axis). Next, inspect the scatterplot for the “Greater Than” signature (e.g. “>”) such that variance in the rate is larger at small population sizes. (Figure 1). Finally, brush select on the scatterplot to see where the areas with high rates and low population sizes appear on the map. These are the places with apparent high rates that may be unstable due to the small numbers problem.
A plot of the lung cancer mortality rate for white males (y-axis) versus the square root of the white male population (x-axis) demonstrates the “>” signature, with higher variance in the rate at small population sizes. Brush selection on the scatterplot (the 3 large red circles in dashed rectangular box) locates the areas with high mortality rates that may be unstable since they have small denominators. Calculated in BioMedware SpaceStat software.
Variability in rates due to the small numbers problem, if not corrected for, can give rise to artifactual spatial structure in the estimated rates. For example, the three areas with high rates in brush selected in Figure 1 are high spatial outliers. When clustering rates it therefore is important to use statistical techniques that either stabilize the rates by constructing local populations with similar denominator sizes, or that account for denominator size when assessing statistical significance.
Interpolation autocorrelation: Smoothing rates in an attempt to adjust for rate instability can introduce spatial autocorrelation due to interpolation. Smoothing introduces nuisance autocorrelation whenever the kernels used to accomplish the smoothing overlap. Examples include inverse distance smoothing, empirical Bayesian smoothing, and others. Here, the spatial scale of the autocorrelation introduced by smoothing will depend on the kernel size. When assessing clusters it may be inappropriate to cluster rates after first smoothing them, since the smoothing step can introduce the appearance of artifactual local similarity in rates that is attributable to interpolation rather than to underlying disease processes. One thus may wish to use smoothing when displaying maps of the rates, but employ techniques that explicitly account for denominator size to evaluate clustering.
Access to screening, care and treatment: Access to health care and screening facilities can give rise to spatial autocorrelation in health events since both screening and treatment influence health outcomes. For example, several studies have demonstrated that access to breast cancer screening facilities is significantly associated with geographic differences in stage at diagnosis, with late-stage cancers more frequent in populations distant from breast cancer screening facilities (Meliker, Goovaerts et al. 2009). Poorer populations are particularly impacted by access to screening, since availability of transport and travel times may pose barriers to seeking health screening. An example is the use of mosquito nets, malaria incidence and distance to clinics that distribute the nets (Enayati and Hemingway 2010). In agrarian rural areas of Malawai with poor roads a distance of 10 kilometers to the nearest clinic where mosquito nets are distributed may involve a full day round trip. Not surprisingly, studies have demonstrated that households nearer to clinics have higher mosquito net usage rates than households that are distant. A useful intervention then is to distribute the mosquito tents directly to the households.
Neighborhood/contextual effects: Neighborhood and related contextual effects can have negative impacts on human health status that exceed the impacts of covariates such as socio-economic status and access to care that themselves may vary dramatically from one neighborhood to another (Spielman and Yoo 2009). Hypotheses suggest that perception of personal safety and quality of the neighborhood living environment can result in chronic stress that leads to reduced immune function and increased disease susceptibility, elevated blood pressure, and heart disease. One mechanism is the interaction between chronic stress, elevated cortisol and immune system status, such that chronic stressors are associated with suppression of both cellular and humoral measures of immune system function. (Segerstrom and Miller 2004). Neighborhood s thus may be associated with spatial autocorrelation in health effects through direct effects such as socio-economic determinants (e.g. income and health insurance), environmental factors (such as air quality) as well as contextual effects that impact stress and immune function (Li and Chuang 2009).
Differences in response to health care policy: Policies related to health care, treatment, drug development and deployment, and others, can have substantial impacts on health outcomes that may differ from one geographic area to another. In the United States the states often have a fair amount of flexibility in how they implement national policies. For example, the Center for Disease Control (CDC) is required to conduct the Behavioral Risk Factor Surveillance System (BRFSS), which is an on-going telephone health survey system, tracking health conditions and risk behaviors in the United States annually since 1984. Data are collected monthly by all 50 states, the District of Columbia, Puerto Rico, the U.S. Virgin Islands, and Guam. A core portion of the health survey questions come from the CDC, but states can supplement the survey with their own optional modules, and the BRFSS variables may thus vary from one state to another.
In addition, health policies can have differential impacts on physician behaviors that are not immediately apparent when the policies are drafted. For example, a recent study explored geographic variation in use of physician-administered chemotherapeutic agents under Medicare Part B, in response to a major reform of Medicare’s reimbursement system (Jacobson, Earle et al. 2011) under a new health policy act. Physician prescription behavior in response to the payment change varied from state to state. Some states increased treatments with certain chemotherapeutic agents by 4%, and a few actually reduced treatment rates. The state-to-state differences are statistically significant, with the null hypothesis that the change in chemotherapy treatment was the same across states rejected at alpha<0.001 level.
Healthy worker and geographic attractors: The “healthy worker effect” describes the reduced disease risk observed among employed individuals in many industries, and that cuts across different diseases. This can give the false appearance of no differences in risk between workers employed in a given industry when compared to the larger population, even though substantial occupational risks may be present (Fornalski and Dobrzyński 2010). Workers tend to follow employment opportunities, and the establishment of large manufacturing facilities can attract a cohort of healthy workers resulting in an apparent deficit of disease risk in neighborhoods where these workers reside. A related phenomenon is that of the “geographic attractor” that arises after health conditions are diagnosed. Here, individuals decide to move nearer hospitals, clinics and treatment centers to ease health care access. When they die, the place of death is recorded as their last known residence, leading to an apparent excess of disease near treatment facilities.
Outbreaks/spread of infection: Infectious diseases transmitted through the air, through sexual contact, fomite transmission, by drinking water contaminated with pathogens, and through other means, often require infected and susceptible individuals to be in close proximity to one another. This is true for pathogens with limited life-spans outside the human body (e.g. influenza viruses), but is less true for those with a dormant phase that can survive outside the body for extended periods (such as anthrax spores). For highly infectious pathogens transmitted from person-to-person we may observe an initial outbreak from an index case (the first case to appear in a local population), that is followed by a spatial “wave” of infection that moves outward from the location of the index case. This may be followed by an endemic phase characterized by the maintenance of lower levels of infection in the population characterized by local outbreaks, or by the infection spreading rapidly and dying out. Geographic pattern in the spread of infection is mediated by complex interactions between the probability of infection transmission, the contacts between infected and susceptible individuals, the life history of infection including the duration and timing of the infective stage, mobility of infected and susceptible individuals, timing of the rise and waning of immunity, the virulence of infection, as well as other factors (Sattenspiel and Lloyd 2010).
Immunity: When considering spatial autocorrelation in the spread of infectious diseases the geography of immunity can be an important consideration (Gao and Hua 2010). Issues include the waning of immunity, herd immunity, vaccination behaviors, and vaccine availability and distribution (Funk, Salathé et al. 2010). When pathogens enter the body the immune system develops antibodies to fight the infection. Immune response is said to wane as the concentrations of antibodies specific to that pathogen decrease over time. When immunity has waned sufficiently, the person may then become infected once again. This process can result in the appearance of clusters where members of a local population are infected, become immune, and then a resurgence of infection as immunity wanes, resulting in space-time patterns in infection.
Vaccination confers immunity without having to undergo a full-blown infection. Herd immunity is the protection from infection that arises when a sufficiently large proportion of the population has been vaccinated. Infection transmission halts when enough individuals are vaccinated and immune, conferring protection even to those who have not been vaccinated. Vaccination itself often follows geographic distribution and adoption patterns. Hence the vaccine distribution strategy can impact the timing of when immunity is conferred by vaccination and thus the geographic spread of infection. Vaccination itself can have intriguing side effects in terms of disease ecology. The eradication of small pox is one of the great public health triumphs of our time, in which the global distribution and administration of the smallpox vaccine eradicated the disease (Alasdair M) in natural populations. Immunity to smallpox confers partial immunity to a related infection, monkey pox. Once smallpox was eradicated the smallpox vaccination program stopped, and outbreaks of monkey pox infections are now increasing. (Rimoin, Mulembakani et al. 2010)
Geographic variation in positional error: That errors in case ascertainment and incomplete reporting can complicate the detection of disease clusters is well known (Kingsley, Schmeichel et al. 2007). Positional error can also impact cluster detection, in at least two ways (Jacquez 2012). First, geographic confounding arises when geographic variation in risk factors is associated with geographic variability in positional error. The potential for this is larger than one might expect as positional error in geocoded place of residences is larger in rural areas, a gradient similar to certain environmental risk factors and socio-economic and demographic variates. Second, positional error decreases the power to detect true clusters. Hence our ability to detect clusters from place of residence data will vary geographically when gradients in positional errors are present.
Migration/Latency: Both chronic and infectious diseases have a latency between exposures that lead to the onset of disease and its diagnosis. For cancers this latency can be a decade or more, for infectious diseases such as influenza it may days. Because humans are mobile the geographic pattern of where individuals were when they were exposed may differ dramatically from where they are when they are diagnosed. Consider the example of breast cancer. A re-analysis of a case control study of breast cancer in Marin County, California, mapped incident cases and controls from 1997 to 1999 as they were enrolled in the study (Jacquez, Barlow et al. 2011). Breast cancer is a complex disease thought to have long latencies on the order of decades, although a small proportion of cases do appear in childhood and adolescence. The geographic pattern of where women lived over their life course differs dramatically from where they lived when they were diagnosed (Figure 2). For many health outcomes, geographic patterns in cases at time of diagnosis may differ dramatically from that observed at disease onset.
Geographic locations of place of residence may vary dramatically from that observed at time of diagnosis in Marin county (lower right) to where women lived over their life course in the US (top) and California (lower left). Source: Jacquez, Barlow et al. 2011.
References
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Enayati, A. and J. Hemingway (2010). “Malaria Management: Past, Present, and Future.” Annual Review of Entomology 55(1): 569-591.
Fornalski, K. W. and L. Dobrzyński ( 2010). “The healthy worker effect and nuclear industry workers.” Dose-Response 8(2): 125 – 147.
Funk, S., M. Salathé, et al. (2010). “Modelling the influence of human behaviour on the spread of infectious diseases: a review.” Journal of The Royal Society Interface 7(50): 1247-1256.
Gao, K. and D.-y. Hua (2010). “Effects of immunity on global oscillations in epidemic spreading in small-world networks.” Physics Procedia 3(5): 1801-1809.
Jacobson, M., C. C. Earle, et al. (2011). “Geographic Variation in Physicians’ Responses to a Reimbursement Change.” New England Journal of Medicine 365(22): 2049-2052.
Alasdair M, G. “The history of smallpox.” Clinics in Dermatology 24(3): 152-157.
Enayati, A. and J. Hemingway (2010). “Malaria Management: Past, Present, and Future.” Annual Review of Entomology 55(1): 569-591.
Fornalski, K. W. and L. Dobrzyński ( 2010). “The healthy worker effect and nuclear industry workers.” Dose-Response 8(2): 125 – 147.
Funk, S., M. Salathé, et al. (2010). “Modelling the influence of human behaviour on the spread of infectious diseases: a review.” Journal of The Royal Society Interface 7(50): 1247-1256.
Gao, K. and D.-y. Hua (2010). “Effects of immunity on global oscillations in epidemic spreading in small-world networks.” Physics Procedia 3(5): 1801-1809.
Jacobson, M., C. C. Earle, et al. (2011). “Geographic Variation in Physicians’ Responses to a Reimbursement Change.” New England Journal of Medicine 365(22): 2049-2052.
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