Circulating Sex Hormone Levels and Risk of Gastrointestinal Cancer: Systematic Review and Meta-Analysis of Prospective Studies

Gastrointestinal cancer occurred in 4.8 million individuals and caused 3.4 million deaths worldwide in 2018, corresponding to 26.3% of the global cancer incidence and 35.4% of all cancer-related deaths (1). Cancer of the esophagus, stomach, liver, pancreas, and colorectum are the five major types of gastrointestinal cancer (1). Men have a higher risk of gastrointestinal cancer than women, with an overall male-to-female incidence ratio between 1.31:1 and 2.71:1, which is highest (up to 9:1) in esophageal adenocarcinoma (2, 3). The male predominance is largely unexplained, but may be partly attributable to intrinsic sex-related exposures (4), and sex hormone levels have been hypothesized to play a role (3). Specifically, estrogens are hypothesized to prevent gastrointestinal cancer, while androgens might increase the risk.

Some reproductive factors seem to influence risk of gastrointestinal cancer, supporting a role of sex hormones (5–10). Studies have assessed associations between circulating levels of sex hormones and gastrointestinal cancer risk, but many have used a cross-sectional design, that is, the sex hormone levels were measured in blood samples collected at or after cancer diagnosis, which could distort associations (11–13). Prospective studies measuring prediagnostic circulating levels of sex hormones can avoid influence of the tumor on sex hormone levels and determine temporal relations. Prospective studies have examined associations between prediagnostic circulating levels of sex hormones and risk of cancer of the esophagus (14–18), stomach (14, 15, 17–19), liver (14, 18, 20–28), pancreas (14, 18, 28, 29), and colorectum (14, 17, 18, 30–42), but the findings are inconsistent.

We aimed to help clarify how prediagnostic circulating levels of sex hormones influence the risk of gastrointestinal cancer by conducting a comprehensive systematic review and meta-analysis of prospective studies.

This study was conducted and reported in accordance with the guidelines provided by PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses) and MOOSE (Meta-analysis Of Observational Studies in Epidemiology; refs. 43, 44). The protocol was registered at PROSPERO (CRD42022346909, available at: https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42022346909).

We systematically searched the MEDLINE and Embase databases to identify relevant studies from inception until February 20, 2023. The detailed search strategies are presented in the Supplementary Materials and Methods. Briefly, we used a combination of keywords for sex hormones and gastrointestinal cancer, including esophageal, gastric, liver, pancreatic, colon, and rectal (colorectal) cancer, to retrieve relevant articles written in English. In addition, the reference lists of the included studies and relevant review articles were checked manually to identify possible additional studies.

Articles that met all of the following criteria were eligible: (i) prospective study design, that is, cohort, nested case–control, or case–cohort studies; (ii) exposure being sex hormone levels measured in blood samples collected before the onset of the studied gastrointestinal cancer; (iii) outcome being incidence of gastrointestinal cancer (rather than mortality); (iv) measures of association being OR, rate ratio (RR) or HR, and their 95% confidence interval (CI), or with the necessary information to calculate these effect sizes and their 95% CI; and (v) full-text articles written in the English language. Whenever more than one article was based on the same study population, only the one with the largest sample size was included.

Two authors (Z. Liu and Y. Zhang) independently screened each article and extracted data from eligible studies. Uncertainties were resolved through reevaluation and verified by a senior investigator (S.-H. Xie). The extracted information included: (i) publication information (first author and year of publication); (ii) study characteristics (study design, study period, and duration of follow-up); (iii) participants’ characteristics (country, sample size, age and sex distribution, and source of controls); (iv) exposure assessment (studied sex hormones, type of blood sample, and laboratory methods); (v) primary outcome (cancer site and histology); (vi) effect sizes and their 95% CI based on the highest versus lowest categories or per SD increase of sex hormones; and (vii) adjusted or matched covariates. When more than one effect size was reported for one association, we used only the results adjusting for the maximum number of covariates. For studies examining liver cancer, whenever available, we also extracted information on hepatitis B surface antigen (HBsAg) status, adjustment for HBsAg status, and adjustment for antibody to hepatitis C virus (anti-HCV) positivity.

The quality of the included studies was assessed in terms of selection bias, information bias, and confounding, and examined quantitatively using the Newcastle-Ottawa Scale. This scale includes eight items categorized into three domains, that is, selection, comparability, and exposure or outcome assessment, and results in an overall score ranging from 0 to 9, where higher scores represent higher study quality. The assessment of study quality was processed independently by two authors (Z. Liu. and Y. Zhang), and any discrepancies were dealt with by discussion or consultation with a senior investigator (S.-H. Xie).

We performed meta-analyses for associations between circulating sex hormone levels and the risk of gastrointestinal cancer types using random-effects models to calculate pooled OR and 95% CI. Because the incidence of the studied tumors is low in the general population, ORs were assumed to approximate RRs or HRs. Meta-analyses were performed for 13 sex hormone measures: testosterone, free testosterone, androstenedione, dehydroepiandrosterone (DHEA), dihydrotestosterone (DHT), estrone, estradiol, free estradiol, testosterone/estradiol ratio, estradiol/testosterone ratio, luteinizing hormone (LH), progesterone, and sex hormone binding globulin (SHBG) and for the five major types of gastrointestinal cancer: esophageal, gastric, liver, pancreatic, and colorectal cancer, wherever data were available in at least two studies. Effect sizes were transformed into a common scale of comparison, that is, the highest versus lowest tertiles of sex hormone levels, before conducting the meta-analysis, assuming that the circulating sex hormone level was normally distributed and had a log-linear association with the risk of outcome (45, 46). The logarithm of OR for the highest versus lowest tertiles was estimated to be 1.27 times that for the top versus bottom halves, 0.86 times the highest versus lowest quartiles, 0.78 times the highest versus lowest quintiles, and 2.18 times that for per SD increase (46). For example, if a study reported an OR of 0.60 for the highest versus lowest quartile of testosterone levels, we estimated the OR for the highest versus lowest tertile comparison by multiplying the lnOR by 0.86, that is, [ln(0.60) × 0.86], and exponentiating to obtain an OR of 0.64. Cochran Q test and I² statistics were used to assess heterogeneity across studies. A P value below 0.10 was considered statistically significant in Cochran Q test (47). I² statistics below 25% indicated low heterogeneity, 25%–49% moderate heterogeneity, and at least 50% represented high heterogeneity. To explore sources of heterogeneity, we performed subgroup analyses for each pair of exposure and outcome by study design, sex, geographic area, tumor histology (adenocarcinoma and squamous cell carcinoma for esophageal cancer; hepatocellular carcinoma, and intrahepatic cholangiocarcinoma for liver cancer), anatomic subsite of the tumor (cardia and non-cardia for gastric cancer, and colon and rectum separately), follow-up time, and for liver cancer also HBsAg status, adjustment for HBsAg status, and adjustment for anti-HCV positivity, wherever possible. We conducted sensitivity analyses by dropping individual primary studies one by one to examine the fluctuation of the pooled effect sizes. Publication bias was evaluated by visual inspection of funnel plots and quantitatively assessed by Begg and Egger tests (48, 49). At least three studies were required for analyses of subgroups, sensitivity, and publication bias. All analyses were performed using the statistical software Stata 15.0 (StataCorp), and all statistical tests were two sided.

The data generated in this study for the meta-analyses are available upon request from the corresponding author. The full texts of all included studies were retrieved from MEDLINE and Embase.

The detailed procedure of identification and selection of articles is presented in Fig. 1. The literature search identified 16,879 studies after duplicates were removed. Among these, 29 studies fulfilled the eligibility criteria and included 11 cohort studies (14, 17, 18, 22, 23, 27–29, 35, 36, 38), 15 nested case–control studies (15, 16, 19–21, 24–26, 31, 32, 34, 37, 40–42), and three case–cohort studies (30, 33, 39). Of all 29 studies, 11 were conducted in Europe (14, 16–18, 22, 25, 28, 29, 38, 41, 42), nine in the United States (15, 26, 30–34, 39, 40), seven in Asia (19–21, 23, 24, 27, 37), and two in Australia (35, 36). Nine studies included participants of both sexes (14, 17, 18, 25, 28, 29, 32, 38, 40), 12 studies included men only (15, 16, 19–24, 27, 35, 36, 42), and eight studies included postmenopausal women only (26, 30, 31, 33, 34, 37, 39, 41). Characteristics of each study are shown in Supplementary Tables S1 and S2. The overall quality of the included studies was high with Newcastle-Ottawa Scale scores ranging from 7 to 9 (Supplementary Table S3). The following subsections by cancer type present associations included in meta-analyses only.

Five studies (three cohort and two nested case–control studies) examined associations between circulating levels of six sex hormone measures (testosterone, free testosterone, androstenedione, estradiol, testosterone/estradiol ratio, and SHBG) and risk of esophageal cancer (14–18). Meta-analyses showed no associations between levels of these six sex hormones and risk of total esophageal cancer (Fig. 2; Supplementary Fig. S1). In the subgroup analyses, higher testosterone levels were associated with a decreased risk of esophageal cancer in analyses limited to nested case–control studies (two studies; OR, 0.60; 95% CI, 0.36–0.99; Supplementary Table S4). There were no other associations in subgroup analyses by study design, participants’ sex, tumor histology (adenocarcinoma and squamous cell carcinoma), or duration of follow-up.

Five studies (three cohort and two nested case–control studies) reported associations between levels of six sex hormones (testosterone, free testosterone, androstenedione, estrone, estradiol, and SHBG) and risk of gastric cancer (14, 15, 17–19). Meta-analysis showed that higher SHBG levels were associated with an increased risk of gastric cancer (three studies; OR, 1.35; 95% CI, 1.06–1.72; I² = 0%; Figs. 2 and 3; Supplementary Fig. S2). Subgroup analyses showed that this association remained in men (OR, 1.43; 95% CI, 1.10–1.85) but not in postmenopausal women (OR, 0.97; 95% CI, 0.51–1.84), in studies with longer follow-up time (≥10 years; OR, 1.71; 95% CI, 1.01–2.90) and was slightly stronger in Asian populations (OR, 1.71; 95% CI, 1.01–2.90) compared with other populations (Table 1; Supplementary Table S5). No associations were found between the other five sex hormones and risk of gastric cancer (Fig. 2; Supplementary Fig. S2).

Eleven studies (six cohort and five nested case–control studies) investigated associations between levels of five sex hormones (testosterone, free testosterone, estradiol, testosterone/estradiol ratio, and SHBG) and risk of liver cancer (14, 18, 20–28). Meta-analysis showed that higher levels of testosterone (nine studies; OR, 2.10; 95% CI, 1.48–2.96; I² = 69.5%) and SHBG (five studies; OR, 2.07; 95% CI, 1.40–3.06; I² = 52.8%) were associated with an increased risk of liver cancer (Figs. 2 and 3; Supplementary Fig. S3). Subgroup analyses showed that the association between testosterone levels and risk of liver cancer was restricted to men (OR, 2.63; 95% CI, 1.65–4.18), Asian populations (OR, 3.27; 95% CI, 1.57–6.83), HBsAg-positive individuals (OR, 3.90; 95% CI, 1.43–10.64), hepatocellular carcinoma (OR, 2.72; 95% CI, 1.52–4.87), and in studies with shorter follow-up time (<10 years; OR, 2.55; 95% CI, 1.60–4.08). Subgroup analyses showed that the association between SHBG levels and risk of liver cancer was restricted to postmenopausal women (OR, 1.58; 95% CI, 1.09–2.29), hepatocellular carcinoma (OR, 2.92; 95% CI, 1.19–7.14), and in studies with shorter follow-up time (<10 years; OR, 2.20; 95% CI, 1.34–3.63; Table 1; Supplementary Table S6). A cohort study in Japan found that a higher testosterone/estradiol ratio was associated with an increased risk of hepatocellular carcinoma in men (OR, 25.40; 95% CI, 3.10–208.11), but the risk estimate was lack of precision (23). No associations were found between free testosterone or estradiol levels and risk of liver cancer (Supplementary Table S6).

Three cohort studies assessed the associations between levels of five sex hormones (testosterone, free testosterone, estradiol, free estradiol, and SHBG) and the risk of pancreatic cancer (14, 28, 29). The results showed that free estradiol levels were associated with a decreased risk of pancreatic cancer (OR, 0.68; 95% CI, 0.49–0.93; Supplementary Fig. S4). Meta-analysis showed no association between testosterone levels and risk of pancreatic cancer (two studies; OR, 0.94; 95% CI, 0.72–1.22; Fig. 2; Supplementary Fig. S4). One cohort study reported no overall association between free testosterone or SHBG levels and risk of pancreatic cancer (Supplementary Fig. S4), but higher free testosterone levels were associated with a borderline decreased risk of pancreatic cancer in women (OR, 0.58; 95% CI, 0.33–1.02; Supplementary Table S7; ref. 29).

Fifteen studies (five cohort, seven nested case–control, and three case–cohort studies) reported associations between levels of 12 sex hormones (testosterone, free testosterone, androstenedione, DHEA, DHT, estrone, estradiol, free estradiol, estradiol/testosterone ratio, LH, progesterone, and SHBG) and the risk of colorectal cancer (14, 17, 30–42). Meta-analysis showed no overall associations between levels of these sex hormones and risk of total colorectal cancer (Fig. 2; Supplementary Fig. S5). Subgroup analyses confined to men indicated higher levels of testosterone (six studies; OR, 0.88; 95% CI, 0.80–0.97) and SHBG (five studies; OR, 0.89; 95% CI, 0.80–0.98) to be associated with a slightly reduced risk of colorectal cancer (Supplementary Table S8).

Eight studies assessed associations between levels of 10 sex hormones (testosterone, free testosterone, androstenedione, DHEA, estrone, estradiol, free estradiol, estradiol/testosterone ratio, progesterone, and SHBG) and risk of colon cancer (14, 17, 31, 34, 38, 40–42). Meta-analysis of five studies showed no overall association between higher testosterone levels and risk of colon cancer (OR, 0.93; 95% CI, 0.84–1.04; Supplementary Fig. S6), but subgroup analysis found an inverse association in men (three studies; OR, 0.86; 95% CI, 0.75–0.97; Supplementary Table S9). No associations were found for the other nine examined sex hormones and risk of colon cancer.

Four studies investigated associations between levels of five sex hormones (testosterone, free testosterone, estrone, estradiol, and SHBG) and risk of rectal cancer (Supplementary Fig. S7; refs. 17, 31, 34, 38). Meta-analysis found no overall associations for any of these sex hormones, although an increased risk associated with higher SHBG levels in postmenopausal women was reported in a nested case–control study in the United States (OR, 3.02; 95% CI, 1.31–6.96; Supplementary Table S10; ref. 34).

Some associations were examined in one study only, for which meta-analysis was not performed. Additional associations of statistical significance from individual studies are summarized in Supplementary Table S11. A nested case–control study in the United States found a decreased risk of gastric cardia adenocarcinoma associated with higher levels of dehydroepiandrosterone (OR, 0.34 highest vs. lowest quartiles; 95% CI, 0.14–0.81) and free estradiol (OR, 0.42 highest vs. lowest quartiles; 95% CI, 0.21–0.86) in men (15). Another nested case–control study in the United States found a decreased risk of liver cancer associated with higher 4-androstenedione levels (OR, 0.27 highest vs. lowest quartiles; 95% CI, 0.09–0.80) and androstenedione/estrone ratio (OR, 0.27 highest vs. lowest quartiles; 95% CI, 0.08–0.91) in postmenopausal women (26). A recent study based on the UK Biobank cohort found an increased risk of liver cancer associated with higher free estradiol levels (OR, 2.54 per SD increase; 95% CI, 2.19–2.93) in men, and the associations varied by sex and histologic subtype (28).

Sensitivity analyses by omitting one individual study at a time showed no substantial changes in the pooled estimates (Supplementary Figs. S1–S7).

No obvious publication bias was revealed by visual inspection of funnel plots (Supplementary Figs. S1–S7) or Begg and Egger tests (all P values >0.05; Table 2).

This systematic review and meta-analysis found that higher SHBG levels were associated with an increased risk of gastric cancer in men, an increased risk of liver cancer, and a decreased risk of colorectal cancer in men; and higher testosterone levels were associated with an increased risk of liver cancer, particularly in men, Asian populations, and HBsAg-positive individuals, and a decreased risk of colorectal cancer in men. No other associations were found between up to 13 examined sex hormones and the risk of developing any of the five studied gastrointestinal cancer types.

The findings showed higher SHBG levels were associated with an increased risk of gastric cancer in men. SHBG is a glycoprotein responsible for binding and transporting androgens and estrogens in the circulation and regulating sex hormone bioavailability (50). Thus, higher SHBG levels lower the bioavailable levels of androgens and estrogens. An in vitro study has suggested that estradiol inhibits gastric cancer growth by promoting apoptosis and reducing cell viability (51), whereas epidemiologic studies assessing associations between estrogen levels and gastric cancer risk are sparse. The observed associations between higher SHBG levels and gastric cancer may be explained by suppressed anticancer properties of estradiol related to its lowered bioavailable levels. None of the included studies examining gastric cancer adjusted for Helicobacter pylori infection, but this might not be very relevant because the associations between H. pylori infection and sex hormone levels are unclear (52, 53).

Higher testosterone levels were associated with an increased risk of liver cancer, particularly in men and HBsAg-positive individuals. Liver cancer is two to three times more common in men than in women in most parts of the world, with hepatocellular carcinoma as the dominant histologic type (2). The differences in the prevalence of established risk factors, including hepatitis viral infection, tobacco smoking, and alcohol overconsumption, between the sexes cannot fully explain the male predominance (26). Higher testosterone levels were associated with an increased risk of liver cancer in men, which might contribute to male predominance. Subgroup analyses indicated that the association was stronger in HBsAg-positive individuals. Hepatitis B virus infection is a primary risk factor for hepatocellular carcinoma and male carriers have higher viral loads and are more likely to remain HBsAg-positive over time (54, 55). Animal studies have found that the androgen pathway may enhance hepatitis B virus transcription and replication (54). In addition, the androgen receptor may mediate effects of testosterone on HBsAg levels and contribute to Hepatitis B virus–induced hepatocarcinogenesis by modulating the transcription of hepatitis B virus RNA (56, 57). All these lines of evidence support a role of interaction between androgen levels and hepatitis B virus infection in the etiology of liver cancer.

In this study, higher SHBG levels were associated with an increased risk of liver cancer. SHBG levels may be affected by liver diseases because SHBG is synthesized in the liver (50), and reports have shown that higher SHBG levels are associated with liver fibrosis, liver cirrhosis, and liver disease severity (58–60). The underlying mechanisms for these associations are largely unknown, but may include suppression of the anticancer properties of estrogens (61, 62).

Higher levels of testosterone and SHBG in men were associated with a decreased risk of colorectal cancer in this study. Similar findings have been reported in a previous meta-analysis (42), although the current updated meta-analysis included five more recent studies. On the contrary, a Mendelian randomization study found no associations between genetically predicted testosterone or SHBG levels and risk of colorectal cancer in men (63). Experimental evidence regarding the role of androgens in colorectal cancer is contradictory. Both in vitro and in vivo studies have demonstrated antitumorigenic properties of testosterone by activating the membrane androgen receptor in colon cancer tissue (64–66). In contrast, an animal study found that surgically castrated rats were markedly protected against colon adenomas, whereas testosterone supplementation increased susceptibility to adenomagenesis (67).

No overall associations of statistical significance were found between any of the studied sex hormones and risk of esophageal or pancreatic cancer, but this might be due to the low number of studies. Esophageal adenocarcinoma is featured by a striking male predominance with a male-to-female incidence ratio of up to 9:1 in some Western populations (3), and an influence of sex hormones is supported by a 16-year delayed onset in women compared with men (68), a duration-response inverse relation with breastfeeding (69), and a reduced risk in postmenopausal women using hormone replacement therapy (70, 71). However, only a few studies have directly measured associations between prediagnostic circulating levels of sex hormones and risk of esophageal adenocarcinoma and these have provided contradictory findings (15–18). A Mendelian randomization analysis of large international consortia data of genome-wide association studies revealed a potential role of follicle-stimulating hormone and luteinizing hormone in the development of esophageal adenocarcinoma (72). Esophageal squamous cell carcinoma and pancreatic cancer are also more common in men, though the sex difference is less striking compared with that in esophageal adenocarcinoma (2, 73). The role of sex hormones in these cancer types has also been indicated by a reduced risk in users of menopausal hormone therapy and antiandrogenic 5α-reductase inhibitors (74–76). Nevertheless, studies examining associations between endogenous sex hormone levels and risk of these cancer types have been limited.

Several methodologic issues merit attention when interpreting the findings. First, the statistical power has been limited in previous studies and even in this meta-analysis, particularly for cancer types of relatively low incidence and subgroup analyses. The lack of statistically significant findings does not rule out the role of sex hormone but highlight the need for additional studies. Second, the follow-up time, that is, the duration of blood drawn to cancer onset, was rather short in some previous studies and might have caused reverse causality problems. Considering the long latency period for cancer, longer follow-up is needed for evaluating the longitudinal changes in sex hormone levels and their relation to cancer risk. Third, due to the complex biosynthesis and function, particularly the correlations between sex hormones, associations for specific sex hormones do not necessarily imply causation. Some but not all previous studies included in this meta-analysis mutually adjusted for other hormones when assessing the associations for individual sex hormones. In our meta-analysis, we only used the results that adjusted for the maximum number of covariates when more than one effect size was reported for one association, which however might not be appropriate, particularly when the between-hormone correlations were strong. More advanced methods and techniques, for example, Mendelian randomization analysis, mediation analysis, and omics technologies, may be useful in further disentangling the mystery of sex difference in gastrointestinal cancer and the role of sex hormones.

This study has some strengths. First, the broad search strategy enabled a comprehensive identification of relevant publications covering a wide range of sex hormones (exposures) and risk of the five main gastrointestinal cancer types (outcomes). Second, the study only included prospective studies that examined circulating levels of sex hormones in blood samples collected before cancer diagnosis, thus allowing assessment of temporal relations and reducing the chance of reverse causality. Third, harmonizing the reported associations on different comparison scales into a common form, that is, comparing the highest versus lowest tertiles, reduced heterogeneity across studies. There are also several limitations. First, a low number of studies were identified for many of the examined associations and subgroup analyses. Second, heterogeneity across studies was observed for some associations, which might be due to differences in participants’ characteristics, exposure assessment, outcome identification, and the extent to which confounding was controlled for. Third, only a small proportion of the included studies (e.g., approximately one-third for testosterone) used the mass spectrum–based method for measuring sex hormone levels, while the majority used methods of relatively lower accuracy. Fourth, sex hormone levels were measured only once in the included studies, making it impossible to assess longitudinal changes of sex hormone levels in relation to gastrointestinal cancer risk.

In conclusion, this comprehensive systematic review and meta-analysis synthesized the existing evidence from prospective studies on associations between prediagnostic circulating levels of up to 13 sex hormones and the risk of five gastrointestinal cancer types. Higher SHBG levels were associated with an increased risk of gastric cancer in men, an increased risk of liver cancer, and a decreased risk of colorectal cancer in men. Higher testosterone levels were associated with an increased risk of liver cancer and a decreased risk of colorectal cancer in men. No other associations were found. More prospective studies are needed to further clarify associations between circulating sex hormone levels and the risk of gastrointestinal cancer, particularly for less commonly tested sex hormones and specific cancer types of lower incidence. International collaborations which combine data from multiple cohorts would be essential to increase study power and potentially enable investigations on relatively rare cancer types and subpopulations including women.

No disclosures were reported.

Z. Liu: Conceptualization, data curation, software, formal analysis, funding acquisition, investigation, visualization, methodology, writing–original draft, writing–review and editing. Y. Zhang: Data curation, investigation. J. Lagergren: Supervision, visualization, writing–review and editing. S. Li: Investigation. J. Li: Investigation. Z. Zhou: Investigation. Z. Hu: Resources, supervision, funding acquisition, methodology, project administration, writing–review and editing. S.-H. Xie: Conceptualization, resources, supervision, funding acquisition, visualization, methodology, project administration, writing–review and editing.

This study was supported by the Startup Fund for Scientific Research, Fujian Medical University (2019QH1297, to Z. Liu), the Scientific Foundation of Fuzhou City (2020-WS-57, to Z. Liu), the Scientific and Technological Innovation Joint Capital Projects of Fujian Province (2020Y9018, to Z. Hu), the Natural Science Foundation of Fujian Province (2021J01726 and 2021J01733, to Z. Hu), the Central Government-led Local Science and Technology Development Special Project (2020L3009, to Z. Hu), and the Swedish Cancer Society (190043 and 222038, to S.-H. Xie). The funding body had no role in the study design, the collection, analysis, and interpretation of data, or the writing of the article and the decision to submit it for publication.

The publication costs of this article were defrayed in part by the payment of publication fees. Therefore, and solely to indicate this fact, this article is hereby marked “advertisement” in accordance with 18 USC section 1734.