Building on existing experimental and epidemiological evidence, we designed a study to assess the effect of elevation-dependent ambient oxygen on cancer incidence. We focused on the elevation-varying western United States, maximizing variation in our exposure of interest while minimizing potential confounding. Recent proliferation of high-resolution, publicly-available data enabled a precise ecological evaluation of our hypothesis. We relied on county-level incidence rather than mortality to minimize quality of care and disease progression biases. To accurately assess oxygen exposure, we incorporated subcounty population dispersion into county elevation calculation. We accounted for potential confounding effects by including important risk and demographic factors and evaluating a range of environmental variables that covary with elevation. We compared the association of elevation with lung cancer versus its association with breast, colon, and prostate cancers to discriminate between atmosphere dependent and independent elevation effects. These steps combined with a robust and conservative statistical framework provided a rigorous assessment of our hypothesis: cancer incidence decreases as elevation rises, a trend most pronounced in tissue with direct atmospheric exposure.

Despite the inability to perform controlled experiments of oxygen toxicity in a human setting, elevation provides a natural experimental platform for examining the effects of oxygen on carcinogenesis. The relation between elevation and barometric pressure, and hence oxygen, is roughly linear at habitable altitudes. Across United States counties, elevation accounts for a 34.9% decrease in oxygen from Imperial County, California (−11 m) to San Juan County, Colorado (3,473 m). From its partial pressure at sea level, oxygen is reduced to 88.7% at 1,000 m, 78.5% at 2,000 m, and 69.2% at 3,000 m ( Berberan-Santos, 1997 ). Taking advantage of this natural dosage gradient, we asked whether atmospheric oxygen, assessed via elevation, associates with carcinogenesis.

Inspired molecular oxygen (O 2 ) leads to intracellular formation of reactive oxygen species (ROS). This occurs either by spontaneous ionizing radiation or by incomplete reduction of O 2 during normal cellular respiration ( Fridovich, 1988 ). ROS are highly unstable and undergo damaging redox reactions with a range of cellular components ( Jackson, 1985 ). A variety of antioxidant enzymes and pathways exist to eliminate ROS ( Matés, Pérez-Gómez & Núñez de Castro, 1999 ). However, formation and elimination of ROS is a stochastic process during which cells accumulate damage, including mutations from reactions with nucleic acids ( Cooke et al., 2003 ).

At present, four types of cancer—prostate, breast, lung, and colorectal—exceed 100,000 new cases per year in the United States. Of these cancers, lung cancer carries the worst prognosis and will claim an estimated 159,260 lives in 2014 ( Siegel et al., 2014 ). While lung cancer primarily afflicts smokers, 10–15% of cases arise in nonsmokers ( Samet et al., 2009 ), and over 80% of smokers never develop lung cancer ( Bilello, Murin & Matthay, 2002 , p. 5). Additional characterized risk factors include genetic susceptibility as well as environmental exposure to carcinogens such as radon, asbestos, and fine-particulate matter ( Subramanian & Govindan, 2007 ). This multifactorial etiology for lung cancer could include long-term exposure to an inhaled carcinogen.

The county-level dataset compiled for this study is available ( Data S1 ). The project GitHub repository ( https://github.com/dhimmel/elevcan ) contains the code used to perform analyses as well as all intermediate files.

Analyses were performed using the statistical-computing language R . County elevation computation relied on the GIS packages raster and rgdal . The best-subset regression analysis used the leaps package, which efficiently identifies top performing models from the complete search space. The glmnet package implemented the lasso ( Friedman, Hastie & Tibshirani, 2010 ). The state-specific lung cancer elevation coefficients were meta-analyzed using the metafor package ( Viechtbauer, 2010 ). Tables were exported using the Hmisc package. Plots were created with the ggplot2 package. Correlation plots were ordered using Ward’s hierarchical clustering.

Environmental variables without established cancer risk were not evaluated in the previous regression analyses to avoid problems of collinearity. For lung and breast cancer, we investigated whether substituting elevation with each of seven environmental variables produced a more likely model, which could indicate an indirect elevation-cancer association. For each environmental variable, we performed best subset regression to find the BIC-minimizing set of predictors. The covariates evaluated for each cancer matched those from before ( Table 1 ) with the exception of radon and fine particulate, which were excluded as lung cancer covariates and instead included as elevation replacements. For both cancers, the increase in minimum-BIC for each substitution compared to elevation was recorded. Change in BIC was converted to a Bayes factor, K ≈ e − 1 2 Δ B I C ( Raftery, 1995 , p. 139). K > 1 provides evidence favoring replacement whereas K < 1 provides evidence against.

We evaluated the association between elevation and lung cancer incidence measured for the following population subgroups: under 65 years old, 65 or older, males, and females. These subgroups were chosen because exposure to risk factors, such as occupational or lifestyle hazards, often segregates by sex or age. For this analysis, we created a dataset with counties that had no missing data for the four subgroup outcomes and the predictors from the optimal best subset model. Proceeding with the best subset covariates, we fit a separate regression model for each population subgroup. We used sex-specific smoking prevalence for the male and female models.

To mitigate uncontrolled confounding (i.e., omitted-variable bias), we stratified the lung cancer dataset by state. Health policy and data collection are often enacted at the state level, making stratification by state a sensible choice for maximizing within-strata homogeneity. Within each stratum, lung cancer incidence was regressed against elevation and smoking prevalence. The elevation effect size was estimated across the eleven state-specific models using a fixed-effects meta-analysis, which averaged elevation coefficients weighted by their inverse variances.

To investigate the potential of a smoking-elevation interaction affecting lung cancer, we partitioned counties into smoking prevalence terciles as follows: high-smoking (49.9–61.9), mid-smoking (44.9–49.9), low-smoking (28.2–44.9). Within each tercile, we regressed lung cancer incidence against elevation for visual examination. For statistical evaluation, we refitted the optimal best subset model with an added interaction term (standardized smoking prevalence × standardized elevation).

To display the relationship between elevation and cancer incidence while accounting for the effect of covariates, we employed partial regression plots. The x -axis represents the residual from regressing elevation against the remaining covariates. The y -axis represents the residual from regressing cancer incidence versus the included covariates absent elevation. The partial regression refers to the simple weighted regression of the cancer incidence residuals ( y -axis) against the elevation residuals ( x -axis). Underlying elevation and incidence values for each county are not discernable in the partial regression plots. However, the slope of the partial regression equals the multivariate elevation coefficient, and the residuals along the partial regression line are equivalent to the multivariate regression residuals. The partial coefficient of determination for elevation, computed as the partial R 2 , signifies the proportion of cancer variance explained by elevation.

We fit a single model for each cancer using lasso regression ( Tibshirani, 1996 ). Lasso requires a single regularization parameter. We optimized this parameter separately for each cancer using 10-fold cross-validation. To prevent overfitting, we adopted the ‘one-standard-error’ rule for determining the optimal parameter value ( Friedman, Hastie & Tibshirani, 2010 ).

For each cancer, we performed best subset regression by evaluating all predictor subsets that included elevation. Subset sizes ranged from one, where elevation was the sole predictor, up to the total number of included variables. For a given size, the predictor set minimizing the residual weighted sum of squares was computed. To identify an optimal model across subset sizes, we chose the subset whose model minimized the Bayesian Information Criterion (BIC) ( Schwarz, 1978 ). The BIC aims to balance the competing objectives of model parsimony and goodness of fit. Compared to alternative criteria, the BIC more harshly penalizes complexity, which is favorable in situations where extra terms risk exacerbating the effects of collinearity. To assess whether elevation was negatively correlated with incidence for each cancer, we applied a one-tailed t -test to the elevation coefficient in the optimal best subset model. A Bonferroni-adjusted significance cutoff of p = 0.0125 was adopted corresponding to a familywise error rate threshold of 5%.

Predictors displayed expected correlations such as a strong positive correlation between obesity and diabetes. Collinearity was moderate but pervasive. Elevation covaried with most variables including cancers indicating the need to adjust for covariates while carefully considering collinearity. Besides radon, the correlation of elevation with other predictors did not exceed | ρ | = 0.55.

We employed two regression methods, best subset and lasso, in parallel. The best subset approach allowed us to force elevation into the model and exhaustively evaluate all possible models while remaining amenable to statistical interpretation. However, evaluating all possible subsets creates the potential for overfitting. Lasso addresses this concern by introducing coefficient shrinkage and variable selection ( Tibshirani, 1996 ). Despite efforts to exclude redundant predictors, variables were characterized by moderate yet pervasive collinearity ( Fig. 1 ). In the best subset method, severe collinearity could cause unstable and unreliable coefficient estimates with inflated standard errors. In addition to scrutinizing best subset results, we adopted the lasso, whose variable selection mechanism tends to include a single member from a group of correlated predictors. This characteristic makes the lasso effective at identifying truly associated predictors in the presence of high collinearity ( Dormann et al., 2013 ).

To minimize confounding effects, we selected well-established factors to include as covariates with elevation. We avoided excessive collinearity ( Dormann et al., 2013 ) by carefully identifying major cancer-specific risk factors with available county-level estimates. Smoking, radon, fine particulate matter, and percent male were identified for lung cancer; female smoking, mammogram, and drinking for breast cancer; smoking, drinking, diabetes, meat consumption, and percent male for colorectal cancer; and meat consumption for prostate cancer. We included six additional covariates—metro, white, black, education, income, and obesity—for all cancers to indirectly account for unknown or immeasurable risk factors or biases. Since a large degree of risk is shared between cancers ( Danaei et al., 2005 ), for each cancer we included the incidence of all other cancer. In addition to elevation, a total of 11 covariates were included for lung, 10 for breast, 12 for colorectal, and 8 for prostate ( Table 1 ). We created cancer-specific datasets by removing counties with any missing data for included variables. Standardized versions of each dataset were created by converting cancer incidence and all predictors to weighted z -scores.

We evaluated the association between elevation and cancer incidence using multivariate linear regression. Counties were weighted by their population square root up to a maximum population of 250,000 where measurement uncertainty leveled off to minimal levels. The weighting scheme accounted for increasing measurement uncertainty among low population counties without granting heavily populated counties an overwhelming influence.

We restricted the analysis to states in the contiguous United States with elevation spans exceeding 3,000 m. The selected states—AZ, CA, CO, ID, MT, NV, NM, OR, UT, WA, WY—contained 414 counties composing the Western United States. Next, counties were filtered for quality control. Counties with populations below 10,000 were excluded due to high missingness (values were missing for many of the variables) and observational error (values were present but subject to large margins of error, evidenced by source-reported confidence intervals). Counties with high Native American composition or immigration rates were considered potentially problematic: cancer rates among Native Americans are prone to misestimation ( Puukka, Stehr-Green & Becker, 2005 ); and immigrants accumulate cancer risk prior to migration, outside of their destination county. Accordingly, we found that predictions of all-site cancer incidence, based on eight general demographic and health predictors, diverged from reported incidence for Native American and immigration-rich counties ( Fig. S1 ). Selecting exclusion thresholds corresponding to this divergence, we omitted counties with five-year immigration rates exceeding 40% or Native American population exceeding 25%. After filtering, 260 counties remained.

We calculated county elevation by subdividing a county into census blockgroups, computing the mean elevation for each blockgroup, and calculating the population-weighted average of the blockgroup elevations. On average, US counties contained 66.5 blockgroups with an average population of 1348.3 persons per blockgroup. By accounting for population dispersion within counties, this method better assesses the inhabitants’ exposure to elevation than population agnostic methods. With greater computational resources, future researchers may choose to use census blocks as a finer subdivision combined with higher resolution elevation data. This framework can be generalized for measuring exposure to any topological variable across a geographical area.

Absolute barometric pressure provides a more direct measure of oxygen than does elevation, albeit marginally. However, barometric pressure data is collected at land stations, which are not universally distributed, and frequently reported relative to sea level for weather forecasting. Therefore, we relied on population-weighted elevation to assess atmospheric oxygen exposure.

County averages for minimum and maximum daily temperature (°C), fine particulate matter with an aerodynamic diameter less than 2.5 micrometers (µg/m 3 ), precipitation (mm), and sunlight (kJ/m 3 ) were downloaded from the CDC WONDER database ( Centers for Disease Control and Prevention, 2013a ). The maximum data collection time intervals were specified: temperature, precipitation, and sunlight measurements were collected from 1979 to 2000, while fine particulate matter was collected from 2003 to 2008. We calculated average diurnal temperature variation by subtracting the average daily minimum temperature from the average daily maximum. Solar UVB exposure (kJ/m 2 ), erythemally weighted to correspond to vitamin-D induction, was obtained from a 2006 study ( Boscoe & Schymura, 2006 ). Indoor radon concentrations in picocuries per liter were obtained from the Lawrence Berkeley National Laboratory High-Radon Project ( Lawrence Berkeley National Laboratory, 2013 ). Their model-based approach explained 64% of variation in mean radon concentration across 5027 living-areas ( Apte, Nero & Revzan, 1998 ). Elevation data was downloaded from WorldClim at 30 arc-seconds (1 km) resolution ( Hijmans et al., 2005 ; WorldClim, 2013 ).

A classification of counties as metropolitan or nonmetropolitan produced in 2003 was obtained from the USDA Economic Research Service ( United States Department of Agriculture Economic Research Service , 2013 ). County race, population, and migration information was downloaded from the US Census Bureau for the 2000 census ( United States Census Bureau, 2013 ). To achieve subcounty data resolution, county blockgroup boundaries and populations were also downloaded from the Census Bureau. The percents white, black, and Native American for counties were determined by the Census as the percent of individuals claiming that race alone or in combination with another race. Census blockgroup boundaries and the corresponding populations were downloaded in the TIGER shapefile format. We calculated 5-year county immigration rates by dividing the difference between total movers and within-county movers by the total population. Percent male was calculated using 2000-census data prepared by the National Atlas ( National Atlas of the United States, 2004 ).

Age-adjusted model-based estimates for obesity and diabetes prevalence were downloaded from the Centers for Disease Control (CDC) ( Centers for Disease Control and Prevention, 2013b ). The estimates were calculated from BRFSS data spanning 2004–2008 for diabetes and 2003–2005 for obesity. Diabetes was reported annually, so we averaged its prevalence over the five available years. Obesity refers to the percent of individuals over 20 who reported a body mass index of 30 or higher.

The percent of individuals having reported smoking over 100 cigarettes in their lifetime was downloaded from NCI Small Area Estimates ( National Cancer Institute, 2013a ). This resource provides model-based lifetime smoking estimates from BRFSS and NHIS data for the periods 1997–1999 and 2000–2003 ( Raghunathan et al., 2007 ). We downloaded separate estimates for males, females, and all individuals and averaged the estimates over the two time periods. The percent of adults that reported binge drinking in the past 30 days, calculated from BRFSS data spanning 2002–2008, was obtained from the County Health Rankings 2010 release ( University of Wisconsin Population Health Institute, 2014 ). Pounds of meat purchased per household during 2006 was extracted from the 2011 Food Environment Atlas ( United States Department of Agriculture Economic Research Service, 2014 ).

County-level education, income, and mammogram data were obtained from State Cancer Profiles ( National Cancer Institute, 2013b ), which derived data as follows: median household income and percent of individuals over 25 with a bachelor’s degree were calculated from the American Community Survey data spanning 2006–2010; the percentage of women over 40 who received a mammogram in the past two years was calculated from the Behavioral Risk Factor Surveillance System (BRFSS) and the National Health Interview Survey (NHIS) for the period 2000–2003.

Total county cancer incidences (‘All Races (incl. Hisp)’, ‘Both Sexes’, ‘All Ages’) were obtained from the National Cancer Institute (NCI) State Cancer Profiles for the following categories: ‘Lung & Bronchus’, ‘Breast’, ‘Prostate’, ‘Colon & Rectum’, and ‘All Cancer Sites’ ( National Cancer Institute, 2013b ). For ‘All Cancer Sites’, incidence for ‘Sex Males’ and ‘Sex Females’ was downloaded. ‘Lung & Bronchus’ incidence was obtained for ‘Sex Males’, ‘Sex Females’, ‘Age 65+’, and ‘Age <65’. The data was collected from 2005 to 2009, age-adjusted to the 2000 US standard population, and converted to cases per 100,000 individuals per year. For each cancer, we calculated the incidence for ‘other cancer’ by subtracting the relevant cancer’s incidence from the incidence for all sites combined. Breast and prostate incidences were subtracted from the corresponding sex-specific all-sites incidences.

From 11 publicly-available databases, we compiled US county data on cancer risk factors, environmental features, demographics, and quality control metrics, while avoiding redundancy. When selecting resources, we balanced several considerations including coverage, precision, collection period, and accessibility. To capture the long latency period of cancers and minimize observational error, we preferred collection periods preceding the cancer incidence timeframe and spanning multiple years. Resources were integrated using county FIPS (Federal Information Processing Standards) codes if available and name matching otherwise. Variables collected as cancer incidence predictors are displayed in Table 1 . Variables were averaged over their entire collection periods. Unless otherwise noted, averaging was performed by the source databases.

As a consequence of elevation’s numerous environmental correlates, we speculated that previous ecological studies of lung cancer may have fallen prey to uncontrolled elevation confounding. Radon ( ρ = 0.71) and UVB ( ρ = 0.50) correlated highly with elevation in our data ( Fig. 7A ) and both had previously been reported to associate negatively with lung cancer ( Cohen, 1995 ; Hayes, 2010 ). To test for confounding, we fit three models of lung cancer incidence with either radon or UVB exposure plus the following predictors: (1) smoking alone; (2) smoking and elevation; and (3) the predictors from the optimal best subset model. Similar to previous studies, model 1, which excluded elevation, identified a negative association for both radon ( p < 10 −14 , one-tailed) and UVB ( p < 10 −3 ). However, models 2 and 3, which both included elevation, erased these associations ( Table 4 ), indicating high potential for erroneous lung cancer associations when not accounting for elevation.

We approximated the likelihood (as a Bayes factor, K ) that any correlated environmental variable could replace elevation in our models of lung and breast cancer ( Fig. 7B ). Remarkably, for lung cancer, all of the variables tested produced models between 10 8 and 10 13 times less likely than the elevation-including model. Among these, fine particulate matter was over one trillion times ( K < 10 −12 ) less likely than elevation. In contrast, breast cancer was more effectively explained by environmental correlates or secondary climatic changes, such as precipitation, UVB, and sunlight, than by elevation. For example, precipitation was 17 times more likely than elevation. Together, these results indicated that lung cancer but not breast cancer was directly associated with atmospheric pressure.

(A) Environmental variables were strongly collinear. Correlation with elevation was high, hence many environmental variables also covaried with lung and breast cancer. (B) To test whether elevation-association with lung and breast cancer was direct or indirect, we substituted each environmental correlate in place of elevation during best subset selection for each cancer. The optimal model for each elevation-replacement was compared to the unreplaced model by approximating a Bayes factor ( K ) from the change in BIC. The Bayes factor indicates the odds that the replacement is superior, thus K > 1 favors the substitution while K < 1 provides evidence against. Since the elevation model was compared to itself, Δ BIC = 0 and K = 1 (log 10 K = 0). The standardized coefficient for each environmental predictor is represented by a triangle, where size is scaled to the magnitude and orientation indicates the sign (upwards for positive). For breast cancer (red), three substitutions increased likelihood suggesting that any association observed with elevation was indirect. For lung cancer (blue), substituting elevation produced models that were many orders of magnitude less likely, suggesting that the elevation association was direct.

Rising elevation leads to lower atmospheric pressure, which helps drive a repertoire of interconnected climatic changes, including perturbations in sun exposure, temperature, and precipitation. This trend was apparent in our data, as many environmental variables correlated with elevation, and thus also with lung and breast cancer ( Fig. 7A ). If either cancer’s elevation association was indirect of atmospheric pressure but rather a product of secondary climatic changes, we expected that environmental correlates could outperform elevation in best subset regression. For example, vitamin D synthesis is stimulated by sunlight and UV exposure ( Gilchrest, 2008 ). The hormonally active form of vitamin D, calcitriol, potentially possesses anti-cancer properties ( Krishnan & Feldman, 2011 ). Sunlight and UVB exposure correlate positively with elevation in our data. Hence, a reasonable proposition would be that increased vitamin D synthesis is driving elevation’s association with lower cancer rates (as posited by Hayes, 2010 ) and that replacing elevation with UVB would improve model likelihood.

Points represent counties shaded by their regression weight based on population. Partial regression plots are displayed for each subgroup with 99% confidence bands. Subgroups displayed similar strongly negative elevation associations, indicating that our findings were not the result of sex or age-based confounding. The elevation coefficient, standardized elevation coefficient, and partial R 2 are listed for each partial regression.

Disparate habits and lifestyles exist across age groups and sexes. Using subgroup-specific lung cancer incidences, we refit the best subset model asking whether elevation association would change ( Fig. 6 ). All four subgroupings showed significant, negative association with elevation: under 65 years old ( p < 10 −12 ), 65 and older ( p < 10 −17 ), males ( p < 10 −14 ), and females ( p < 10 −18 ). Standardized coefficients were large, ranging from −4.39 to −3.58. Subgroup confidence intervals all overlapped the confidence interval from the global model, showing no evidence for subgroup-specific effect mediation or confounding.

While focusing on the elevation-varying Western United States minimized the risk of regional confounding, possible differences in health policy or practice between higher and lower elevation states could still exist. State-specific models that accounted for smoking found negative elevation coefficients for ten of eleven states ( Fig. 5B ). Moreover, while small intrastate sample sizes created coefficient uncertainty, meta-analysis estimated that lung cancer incidence decreases by 10.8 99% CI [7.0–14.6] cases (per 100,000 individuals) per kilometer, matching the best subset regression confidence estimate of 7.2 99% CI [5.7–8.8] and indicating that state-based confounding did not underlie the negativity of the region-wide elevation association. To evaluate the consistency of state-specific elevation effects, we calculated I 2 , which equaled 71% 95% CI [35–90%]. Despite its uncertainty, the observed I 2 suggests moderate to high heterogeneity across states ( Higgins et al., 2003 ), which is unsurprising given the small sample sizes and limited covariate adjustment of the state-specific models.

Stratification analyses provide no evidence for a smoking-elevation interaction or state-based confounding. (A) Lung cancer incidence (age-adjusted per 100,000) and elevation (km) are plotted for counties stratified into terciles by smoking prevalence. Counties were shaded by their regression weight, and a bivariate regression was fit for each stratum. The non-overlapping confidence bands (95%) illustrate the strong effect of smoking on lung cancer, while the approximately parallel slopes demonstrate the lack of an observable smoking-elevation interaction. (B) Lung cancer was regressed against elevation and smoking for each state. State-specific elevation coefficients are plotted with 95% confidence intervals. Ten of eleven states displayed negative coefficients. State-specific elevation coefficients were meta-analyzed. The resulting 99% confidence interval overlaps the interval from the optimal best subset model shown in blue. The number of counties within each state analysis is indicated in parentheses.

Given the respiratory intersection of oxygen inhalation and smoking, we asked whether elevation associated differently across smoking prevalences. Stratifying counties into smoking terciles, the strong effect of smoking on lung cancer was illustrated by the non-overlapping confidence bands ( Fig. 5A ). Tercile slopes were approximately parallel providing no evidence for an interaction between smoking and elevation. Corroborating the lack of interaction, an added smoking × elevation term was not significant ( p = 0.47) when refitting the best subset model.

Points represent counties shaded by their regression weight based on population. Bivariate (red) and partial (blue) regression lines are displayed with 99% confidence bands. (A) Bivariate plot of county lung cancer incidence (age-adjusted per 100,000) and elevation (km). (B) Partial regression plot for elevation based on the optimal best subset lung model. Association sharpens after adjustment for covariates, illustrated by the tighter confidence band and higher R 2 in the partial plot.

For lung cancer, both regression methods found previously characterized positive associations with smoking prevalence, percent of black residents ( Greenlee et al., 2000 , p. 10), and rate of other cancer ( Ahlbom et al., 1997 ), as well as large negative associations with elevation and education. The lasso also found a small negative association with radon ( β z = −0.01), attributable to radon’s strong positive correlation with elevation ( Fig. 1 ). Including covariates sharpened the association between elevation and lung cancer, as evidenced by elevation’s higher partial R 2 = 0.252 in the multivariate model versus the bivariate R 2 = 0.202 ( Fig. 4 ). Of note, both best subset and lasso regression attributed the two largest effect sizes to smoking (best subset: 0.59 and lasso: 0.52) and elevation (−0.35 and −0.33). The best subset model also found that smoking ( p < 10 −35 ) and elevation ( p < 10 −16 ) were the two most significant associations with lung cancer incidence ( Table S1 ).

(A) Summary of the predictors included in the optimal best subset model for each cancer (see Table S1 for more detail). (B) Summary of the models produced by lasso regression, displaying characteristic coefficient shrinkage. Both regression techniques produced similar sets of models that were sensible for lung, breast, and colorectal cancer. Elevation displayed a strong and consistent negative coefficient in lung cancer models.

Models produced for each cancer by best subset ( Fig. 3A ) and lasso ( Fig. 3B ) regression corresponded with the literature. The lasso (and best subset) models explained 67% (70%) of variation in lung cancer incidence, 51% (57%) in breast, 29% (34%) in colorectal, and 9% (19%) in prostate, ( Tables 3 and 2 ) mirroring a previously described trend in fraction of risk attributable to modifiable factors for each of the four cancers ( Danaei et al., 2005 ).

Lasso regression performs variable selection that operates well under moderate collinearity and coefficient shrinkage that prevents overfitting. Using a conservative setup of the lasso, we again observed a strong, negative association between elevation and lung cancer incidence with a standardized coefficient of −0.33, changing minimally from the best subset estimate ( β z = −0.35) despite the strong regularization of the lasso ( Table 3 ). For breast cancer, where the best subset model yielded an elevation coefficient with high uncertainty, the lasso reduced the estimate to a trivial level ( β z = −0.02) indicating that overfitting contributed to best subset negativity. Meanwhile, the elevation term was absent in the colorectal and prostate lasso models. Together the regression methods indicated a negative association with elevation that was unique to lung cancer in terms of strength, significance, and statistical robustness.

Elevation coefficients and 99% confidence intervals are plotted across a range of best subset model sizes for each cancer. As determined by BIC, more likely models are shaded darker. The optimal (BIC-minimizing) model for each cancer is denoted by a star. Lung cancer is the only cancer to display consistently negative coefficients and confidence intervals.

The optimal (BIC-minimizing) models contained five predictors for lung and colorectal cancers, six predictors for breast, and four predictors for prostate cancer ( Table 2 ). Within each cancer, we compared the elevation coefficients across a range of model sizes ( Fig. 2 ). Unique to lung cancer, elevation confidence intervals were consistent and wholly negative, indicating robustness to collinearity as well as to confounding by included covariates. Other cancers displayed greater coefficient variability and uncertainty, possibly due to covariate collinearity with elevation, which led us to implement lasso regression.

Performing best subset regression for each cancer, we found a highly significant, strong negative association between elevation and lung cancer incidence with a standardized coefficient ( β z ) of −0.35 99% CI [−0.46, −0.25] ( p < 10 −16 , one-tailed t -test) ( Table 2 ). Lung cancer incidence decreased by 7.23 [5.67–8.80] cases (per 100,000 individuals) per kilometer rise in elevation, equating to 12.7% [9.1%–16.4%] of the mean lung cancer incidence. For other cancers, we found a weak, negative association with breast cancer ( β z = −0.15, p < 10 −2 ) but not with colorectal ( p = 0.88) or prostate ( p = 0.97) cancer.

Discussion

We attributed a decrease of 25.2 99% CI [18.0–32.4] lung cancer cases per 100,000 individuals to the range of elevation of counties of the Western United States, equating to approximately 44% of the mean incidence (56.8). Were the entire United States situated at the elevation of San Juan County, CO (3,473 m), we estimate 65,496 99% CI [46,855–84,136] fewer new lung cancer cases would arise per year (ceteris paribus and assuming 2000-census county-populations). The causal factor behind the association appears to play a notable role in lung carcinogenesis, worthy of consideration by researchers, health providers, and the general public.

Prior to covariate adjustment, elevation correlated negatively with lung, breast, and colorectal cancer. Adjusting for demographic and risk factors using best subset and lasso regression, we produced sensible models for each cancer that captured known risk factors. Elevation’s negative association with colorectal cancer disappeared with adjustment for demographics, while association with breast cancer proved to be minimal and could be better represented by several other environmental variables. In contrast, lung cancer’s negative association with elevation was sharpened following multiple regression, failed to be captured by any other environmental variables, and had a remarkably strong effect size and significance. Lung-elevation association was robust to county stratification by smoking and state, as well as to population subgrouping by age and sex.

In summary, lung cancer associated with elevation over oxygen-independent environmental factors, and likewise elevation associated with lung cancer but not with non-respiratory cancers. Together these points provide substantial evidence for an inversely-linked inhaled carcinogen tied directly to elevation. Viewing our findings through the lens of the literature, atmospheric oxygen emerges as the most probable culprit.

Confounding effect of elevation Since elevation commonly covaries and its effect size on lung cancer is large, the potential for confounding is high. We identified two reported lung cancer associations—radon (Cohen, 1995) and UVB (Hayes, 2010)—that we attributed wholly to elevation in our analyses. Previously, Lagarde & Pershagen (1999) implicated ecological fallacy in the appearance of weak inverse associations between radon and lung cancer in Sweden. However, the plausibility of ecological fallacy resulting in the strong inverse association Cohen (1995) observed across American counties is less clear. Alternatively, Van Pelt (2003) attributed “some, but not all” of the Cohen (1995) radon association to elevation. Follow-up correspondences by each author revolved around the difficulty in assigning the effect wholly to elevation or radon when both of these highly-correlated predictors remained significant (Cohen, 2004; Van Pelt, 2004). We believe that our data quality improvements, including county-specific smoking prevalences and population-weighted elevations, were responsible for wholly attributing the effect to elevation. Studies where lung cancer is incorporated as a predictor rather than outcome may also be susceptible to confounding. Since the collection and availability of tobacco data has historically lagged behind lung cancer data, lung cancer rates have often been adopted as a proxy for smoking prevalence (Peto et al., 1992). Ezzati et al. (2012) evaluated whether elevation was associated with several mortality outcomes across US counties. Their study relied on “lung cancer as the indicator of accumulated population exposure to smoking. This adjustment for lung cancer in multivariable regressions may have over-adjusted, if altitude has a beneficial effect on lung cancer.” The confounding potential of elevation extends to any analysis of lung cancer across an elevation-varying region. To protect against this uncontrolled confounding, we urge future lung cancer studies to strongly consider adjusting for elevation. Fortunately, elevation is well-documented across the globe, and many existing epidemiological datasets contain locality information.

Limitations & future directions Cross-sectional study designs are susceptible to uncontrolled confounding where associations arise due to an unmeasured confounding factor. We designed the study to minimize this risk by focusing on a homogeneous and elevation-varying region, filtering error-prone counties, including established covariates, and performing multiple stratifications and subgroupings. Furthermore, while environmental correlates of elevation represented likely confounders, all seven pervasive environmental factors we investigated could not replace elevation in models of lung cancer. Therefore, our findings gave no indication of uncontrolled confounding for lung cancer. As relevant data becomes available, follow-up across different regions will provide additional assessment of uncontrolled confounding. Since we evaluated counties rather than individuals, ecological fallacy was also a concern. However, several of our methods and findings limit this possibility. By focusing on US counties, the smallest population grouping with systematic data available for the target region, we inherently reduced the risk of ecological fallacy. Moreover, further increases in group specificity through population subgrouping did not alter the elevation-lung association. Additionally, we reason that an exposure affecting only a portion of the population must confer a very large risk to produce the strong association observed. We find it unlikely that an extremely damaging risk factor on the individual level, such as smoking, would have evaded detection until now. Therefore, we speculate the causal factor is likely mild in carcinogenicity but universal in exposure and thus amenable to translation from the individual to population level. Follow-up biological and experimental analyses will be critical to understanding the causal factor and potential mechanisms underlying the observed elevation association. If future research confirms oxygen-driven tumorigenesis in the human lung, the present study will join the substantial list of ecological analyses that spurred new insights into cancer etiology (Pearce, 2000).