# Utility of Continuous Disease Subtyping Systems for Improved Evaluation of Etiologic Heterogeneity

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

^{†}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Simulation Study

#### 3.2. Results of Illustrative Example

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AIC | Akaike information criterion |

BIC | Bayesian information criterion |

HPFS | Health Professionals Follow-up Study |

HR | hazard ratio |

LINE-1 | long interspersed nucleotide element-1 |

NHS | Nurses’ Health Study |

## References

- Begg, C.B. A strategy for distinguishing optimal cancer subtypes. Int. J. Cancer
**2011**, 129, 931–937. [Google Scholar] [CrossRef] [PubMed] - Begg, C.B.; Zabor, E.C. Detecting and exploiting etiologic heterogeneity in epidemiologic studies. Am. J. Epidemiol.
**2012**, 176, 512–518. [Google Scholar] [CrossRef] [PubMed][Green Version] - Begg, C.B.; Zabor, E.C.; Bernstein, J.L.; Bernstein, L.; Press, M.F.; Seshan, V.E. A conceptual and methodological framework for investigating etiologic heterogeneity. Stat. Med.
**2013**, 32, 5039–5052. [Google Scholar] [CrossRef] [PubMed] - Richiardi, L.; Barone-Adesi, F.; Pearce, N. Cancer subtypes in aetiological research. Eur. J. Epidemiol.
**2017**, 32, 353–361. [Google Scholar] [CrossRef] [PubMed] - Ogino, S.; Chan, A.T.; Fuchs, C.S.; Giovannucci, E. Molecular pathological epidemiology of colorectal neoplasia: An emerging transdisciplinary and interdisciplinary field. Gut
**2011**, 60, 397–411. [Google Scholar] [CrossRef] - Ogino, S.; Nishihara, R.; VanderWeele, T.J.; Wang, M.; Nishi, A.; Lochhead, P.; Qian, Z.R.; Zhang, X.; Wu, K.; Nan, H. The role of molecular pathological epidemiology in the study of neoplastic and non-neoplastic diseases in the era of precision medicine. Epidemiology
**2016**, 27, 602. [Google Scholar] [CrossRef] - Ogino, S.; Nowak, J.A.; Hamada, T.; Milner, D.A., Jr.; Nishihara, R. Insights into pathogenic interactions among environment, host, and tumor at the crossroads of molecular pathology and epidemiology. Annu. Rev. Pathol. Mech. Dis.
**2019**, 14, 83–103. [Google Scholar] [CrossRef] - Holm, J.; Eriksson, L.; Ploner, A.; Eriksson, M.; Rantalainen, M.; Li, J.; Hall, P.; Czene, K. Assessment of breast cancer risk factors reveals subtype heterogeneity. Cancer Res.
**2017**, 77, 3708–3717. [Google Scholar] [CrossRef][Green Version] - Wang, M.; Spiegelman, D.; Kuchiba, A.; Lochhead, P.; Kim, S.; Chan, A.T.; Poole, E.M.; Tamimi, R.; Tworoger, S.S.; Giovannucci, E. Statistical methods for studying disease subtype heterogeneity. Stat. Med.
**2016**, 35, 782–800. [Google Scholar] [CrossRef] - Schernhammer, E.S.; Giovannucci, E.; Kawasaki, T.; Rosner, B.; Fuchs, C.S.; Ogino, S. Dietary folate, alcohol and B vitamins in relation to LINE-1 hypomethylation in colon cancer. Gut
**2010**, 59, 794–799. [Google Scholar] [CrossRef][Green Version] - Cox, D.R. Regression models and life-tables. J. R. Stat. Soc. Ser. B
**1972**, 34, 187–202. [Google Scholar] [CrossRef] - Prentice, R.L.; Kalbfleisch, J.D.; Peterson, A.V., Jr.; Flournoy, N.; Farewell, V.T.; Breslow, N.E. The analysis of failure times in the presence of competing risks. Biometrics
**1978**, 34, 541–554. [Google Scholar] [CrossRef] [PubMed] - Cox, D.R. Partial likelihood. Biometrika
**1975**, 62, 269–276. [Google Scholar] [CrossRef] - Chatterjee, N.; Sinha, S.; Diver, W.R.; Feigelson, H.S. Analysis of cohort studies with multivariate and partially observed disease classification data. Biometrika
**2010**, 97, 683–698. [Google Scholar] [CrossRef] [PubMed][Green Version] - Durrleman, S.; Simon, R. Flexible regression models with cubic splines. Stat. Med.
**1989**, 8, 551–561. [Google Scholar] [CrossRef] [PubMed] - Burnham, K.P.; Anderson, D.R. Multimodel inference: Understanding AIC and BIC in model selection. Sociol. Methods Res.
**2004**, 33, 261–304. [Google Scholar] [CrossRef] - Irahara, N.; Nosho, K.; Baba, Y.; Shima, K.; Lindeman, N.I.; Hazra, A.; Schernhammer, E.S.; Hunter, D.J.; Fuchs, C.S.; Ogino, S. Precision of pyrosequencing assay to measure LINE-1 methylation in colon cancer, normal colonic mucosa, and peripheral blood cells. J. Mol. Diagn.
**2010**, 12, 177–183. [Google Scholar] [CrossRef] - Bao, Y.; Bertoia, M.L.; Lenart, E.B.; Stampfer, M.J.; Willett, W.C.; Speizer, F.E.; Chavarro, J.E. Origin, Methods, and Evolution of the Three Nurses’ Health Studies. Am. J. Public Health
**2016**, 106, 1573–1581. [Google Scholar] [CrossRef] - Ugai, T.; Vayrynen, J.P.; Haruki, K.; Akimoto, N.; Lau, M.C.; Zhong, R.; Kishikawa, J.; Vayrynen, S.A.; Zhao, M.; Fujiyoshi, K.; et al. Smoking and Incidence of Colorectal Cancer Subclassified by Tumor-Associated Macrophage Infiltrates. J. Natl. Cancer Inst.
**2022**, 114, 68–77. [Google Scholar] [CrossRef] - Nishihara, R.; Wu, K.; Lochhead, P.; Morikawa, T.; Liao, X.; Qian, Z.R.; Inamura, K.; Kim, S.A.; Kuchiba, A.; Yamauchi, M.; et al. Long-term colorectal-cancer incidence and mortality after lower endoscopy. N. Engl. J. Med.
**2013**, 369, 1095–1105. [Google Scholar] [CrossRef][Green Version] - Ugai, T.; Haruki, K.; Vayrynen, J.P.; Borowsky, J.; Fujiyoshi, K.; Lau, M.C.; Akimoto, N.; Zhong, R.; Kishikawa, J.; Arima, K.; et al. Coffee Intake of Colorectal Cancer Patients and Prognosis According to Histopathologic Lymphocytic Reaction and T-Cell Infiltrates. Mayo Clin. Proc.
**2022**, 97, 124–133. [Google Scholar] [CrossRef] [PubMed] - Baba, Y.; Huttenhower, C.; Nosho, K.; Tanaka, N.; Shima, K.; Hazra, A.; Schernhammer, E.S.; Hunter, D.J.; Giovannucci, E.L.; Fuchs, C.S.; et al. Epigenomic diversity of colorectal cancer indicated by LINE-1 methylation in a database of 869 tumors. Mol. Cancer
**2010**, 9, 125. [Google Scholar] [CrossRef] [PubMed][Green Version] - Estecio, M.R.; Gharibyan, V.; Shen, L.; Ibrahim, A.E.; Doshi, K.; He, R.; Jelinek, J.; Yang, A.S.; Yan, P.S.; Huang, T.H.; et al. LINE-1 hypomethylation in cancer is highly variable and inversely correlated with microsatellite instability. PLoS ONE
**2007**, 2, e399. [Google Scholar] [CrossRef] [PubMed] - Havel, J.J.; Chowell, D.; Chan, T.A. The evolving landscape of biomarkers for checkpoint inhibitor immunotherapy. Nat. Rev. Cancer
**2019**, 19, 133–150. [Google Scholar] [CrossRef] [PubMed] - Paucek, R.D.; Baltimore, D.; Li, G. The Cellular Immunotherapy Revolution: Arming the Immune System for Precision Therapy. Trends Immunol.
**2019**, 40, 292–309. [Google Scholar] [CrossRef] - Grizzi, F.; Basso, G.; Borroni, E.M.; Cavalleri, T.; Bianchi, P.; Stifter, S.; Chiriva-Internati, M.; Malesci, A.; Laghi, L. Evolving notions on immune response in colorectal cancer and their implications for biomarker development. Inflamm. Res.
**2018**, 67, 375–389. [Google Scholar] [CrossRef] - Kather, J.N.; Halama, N. Harnessing the innate immune system and local immunological microenvironment to treat colorectal cancer. Br. J. Cancer
**2019**, 120, 871–882. [Google Scholar] [CrossRef][Green Version] - Ogino, S.; Giannakis, M. Immunoscore for (colorectal) cancer precision medicine. Lancet
**2018**, 391, 2084–2086. [Google Scholar] [CrossRef] - Ogino, S.; Nowak, J.A.; Hamada, T.; Phipps, A.I.; Peters, U.; Milner, D.A., Jr.; Giovannucci, E.L.; Nishihara, R.; Giannakis, M.; Garrett, W.S.; et al. Integrative analysis of exogenous, endogenous, tumour and immune factors for precision medicine. Gut
**2018**, 67, 1168–1180. [Google Scholar] [CrossRef] - Le, D.T.; Hubbard-Lucey, V.M.; Morse, M.A.; Heery, C.R.; Dwyer, A.; Marsilje, T.H.; Brodsky, A.N.; Chan, E.; Deming, D.A.; Diaz, L.A., Jr.; et al. A Blueprint to Advance Colorectal Cancer Immunotherapies. Cancer Immunol. Res.
**2017**, 5, 942–949. [Google Scholar] [CrossRef][Green Version] - Kather, J.N.; Halama, N.; Jaeger, D. Genomics and emerging biomarkers for immunotherapy of colorectal cancer. Semin. Cancer Biol.
**2018**, 52, 189–197. [Google Scholar] [CrossRef] [PubMed] - Pages, F.; Galon, J.; Dieu-Nosjean, M.C.; Tartour, E.; Sautes-Fridman, C.; Fridman, W.H. Immune infiltration in human tumors: A prognostic factor that should not be ignored. Oncogene
**2010**, 29, 1093–1102. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hamada, T.; Nowak, J.A.; Milner, D.A., Jr.; Song, M.; Ogino, S. Integration of microbiology, molecular pathology, and epidemiology: A new paradigm to explore the pathogenesis of microbiome-driven neoplasms. J. Pathol.
**2019**, 247, 615–628. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mima, K.; Kosumi, K.; Baba, Y.; Hamada, T.; Baba, H.; Ogino, S. The microbiome, genetics, and gastrointestinal neoplasms: The evolving field of molecular pathological epidemiology to analyze the tumor-immune-microbiome interaction. Hum. Genet.
**2021**, 140, 725–746. [Google Scholar] [CrossRef] - Mima, K.; Nishihara, R.; Qian, Z.R.; Cao, Y.; Sukawa, Y.; Nowak, J.A.; Yang, J.; Dou, R.; Masugi, Y.; Song, M.; et al. Fusobacterium nucleatum in colorectal carcinoma tissue and patient prognosis. Gut
**2016**, 65, 1973–1980. [Google Scholar] [CrossRef][Green Version] - Mima, K.; Cao, Y.; Chan, A.T.; Qian, Z.R.; Nowak, J.A.; Masugi, Y.; Shi, Y.; Song, M.; da Silva, A.; Gu, M.; et al. Fusobacterium nucleatum in Colorectal Carcinoma Tissue According to Tumor Location. Clin. Transl. Gastroenterol.
**2016**, 7, e200. [Google Scholar] [CrossRef] - Mehta, R.S.; Nishihara, R.; Cao, Y.; Song, M.; Mima, K.; Qian, Z.R.; Nowak, J.A.; Kosumi, K.; Hamada, T.; Masugi, Y.; et al. Association of Dietary Patterns With Risk of Colorectal Cancer Subtypes Classified by Fusobacterium nucleatum in Tumor Tissue. JAMA Oncol.
**2017**, 3, 921–927. [Google Scholar] [CrossRef][Green Version] - Borowsky, J.; Haruki, K.; Lau, M.C.; Dias Costa, A.; Vayrynen, J.P.; Ugai, T.; Arima, K.; da Silva, A.; Felt, K.D.; Zhao, M.; et al. Association of Fusobacterium nucleatum with Specific T-cell Subsets in the Colorectal Carcinoma Microenvironment. Clin. Cancer Res.
**2021**, 27, 2816–2826. [Google Scholar] [CrossRef] - Lin, D.; Fleming, T.R. Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis: Survival Analysis; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012; Volume 123. [Google Scholar]
- Verweij, P.J.; Van Houwelingen, H.C. Cross-validation in survival analysis. Stat. Med.
**1993**, 12, 2305–2314. [Google Scholar] [CrossRef] - Fujiyoshi, K.; Bruford, E.A.; Mroz, P.; Sims, C.L.; O’Leary, T.J.; Lo, A.W.I.; Chen, N.; Patel, N.R.; Patel, K.P.; Seliger, B.; et al. Opinion: Standardizing gene product nomenclature—A call to action. Proc. Natl. Acad. Sci. USA
**2021**, 118, e2025207118. [Google Scholar] [CrossRef]

**Figure 1.**Heterogeneous Effect of Cumulative Categorical Alcohol Intake (>15 g/day vs. 0 g/day) on continuous subtypes of colorectal cancer; the 3 × 3 plot panel illustrates the combination of three choices of the knot number in $g\left(\varphi ,Z\right)$ and three cohort settings. Abbreviations: HPFS, Health Professionals Follow-up Study; LINE-1, long interspersed nucleotide element-1; NHS, Nurses’ Health Study.

**Table 1.**Model testing for the association of categorical alcohol intake (>15 g/day vs. 0 g/day) with colorectal cancer incidence, based on the main model for three functional forms and three cohorts.

Knots | Model Assessment | NHS | HPFS | Combined |
---|---|---|---|---|

K = 2 | p-value | |||

Overall | 0.19 | <0.001 | <0.001 | |

Heterogeneity | - | <0.001 | <0.001 | |

BIC | 11,634 | 7784 | 20,436 | |

AIC | 11,586 | 7739 | 20,386 | |

K = 3 | p-value | |||

Overall | 0.12 | <0.001 | <0.001 | |

Heterogeneity | - | <0.001 | <0.001 | |

Nonlinearity | - | <0.001 | 0.54 | |

BIC | 11,660 | 7804 | 20,464 | |

AIC | 11,588 | 7736 | 20,389 | |

K = 4 | p-value | |||

Overall | 0.17 | <0.001 | 0.002 | |

Heterogeneity | - | <0.001 | <0.001 | |

Nonlinearity | - | <0.001 | 0.56 | |

BIC | 11,686 | 7830 | 20,492 | |

AIC | 11,589 | 7741 | 20,393 |

_{0}: the intercept and all the coefficients in $g\left(\varphi ,Z\right)$ are zero (the overall test); H

_{0}: all the coefficients in $g\left(\varphi ,Z\right)$ except the intercept are zero (test for heterogeneity); H

_{0}: all the coefficients of the nonlinear terms in $g\left(\varphi ,Z\right)$ are zero (test for nonlinearity). Abbreviations: AIC, Akaike’s information criterion; BIC, Bayesian information criterion; HPFS, Health Professionals Follow-up Study; LINE-1, long interspersed nucleotide element-1; NHS, Nurses’ Health Study.

**Table 2.**Hazard ratio for categorical alcohol intake (>15 g/day vs. 0 g/day) modeled using three functional forms for the LINE-1 marker value in three cohort settings, based on the main model.

Cohort | LINE-1 Methylation Level | Hazard Ratio with 95% Confidence Interval | |||||
---|---|---|---|---|---|---|---|

Linear Function $(\mathit{K}\text{}=\text{}2)$ | Restricted Cubic Spline $(\mathit{K}\text{}=\text{}3\mathbf{Knots})$ | Restricted Cubic Spline $(\mathit{K}\text{}=\text{}4\mathbf{Knots})$ | |||||

Combined | 30 | 1.64 | (0.95, 2.82) | 1.79 | (0.76, 4.21) | 1.59 | (0.55, 4.61) |

40 | 1.53 | (1.03, 2.28) | 1.62 | (0.91, 2.87) | 1.51 | (0.76, 3.01) | |

50 | 1.43 | (1.10, 1.86) | 1.48 | (1.03, 2.13) | 1.37 | (0.78, 2.40) | |

60 | 1.34 | (1.14, 1.58) | 1.38 | (1.00, 1.92) | 1.27 | (0.72, 2.22) | |

70 | 1.25 | (1.05, 1.50) | 1.32 | (0.77, 2.26) | 1.40 | (0.74, 2.64) | |

80 | 1.17 | (0.87, 1.57) | 1.28 | (0.53, 3.05) | 1.85 | (0.18, 18.5) | |

HPFS | 30 | 2.47 | (1.12, 5.48) | 1.18 | (0.32, 4.32) | 0.91 | (0.17, 4.87) |

40 | 2.10 | (1.18, 3.75) | 1.35 | (0.57, 3.16) | 1.16 | (0.40, 3.31) | |

50 | 1.78 | (1.22, 2.61) | 1.38 | (0.82, 2.32) | 1.18 | (0.54, 2.59) | |

60 | 1.52 | (1.19, 1.93) | 1.13 | (0.72, 1.77) | 1.02 | (0.52, 2.00) | |

70 | 1.29 | (0.98, 1.70) | 0.74 | (0.35, 1.56) | 1.03 | (0.33, 3.22) | |

80 | 1.09 | (0.7, 1.710) | 0.43 | (0.13, 1.50) | 1.29 | (0.03, 63.8) | |

NHS | 30 | 0.94 | (0.41, 2.15) | 1.95 | (0.56, 6.82) | 2.58 | (0.61, 10.9) |

40 | 1.01 | (0.54, 1.86) | 1.60 | (0.69, 3.73) | 1.90 | (0.74, 4.91) | |

50 | 1.08 | (0.72, 1.63) | 1.45 | (0.84, 2.50) | 1.85 | (0.82, 4.17) | |

60 | 1.16 | (0.90, 1.49) | 1.59 | (0.98, 2.58) | 2.16 | (0.86, 5.43) | |

70 | 1.25 | (0.97, 1.61) | 2.14 | (1.00, 4.57) | 1.87 | (0.91, 3.86) | |

80 | 1.34 | (0.89, 2.03) | 3.17 | (0.94, 10.7) | 1.14 | (0.08, 15.6) |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, R.; Ugai, T.; Xu, L.; Zucker, D.; Ogino, S.; Wang, M. Utility of Continuous Disease Subtyping Systems for Improved Evaluation of Etiologic Heterogeneity. *Cancers* **2022**, *14*, 1811.
https://doi.org/10.3390/cancers14071811

**AMA Style**

Li R, Ugai T, Xu L, Zucker D, Ogino S, Wang M. Utility of Continuous Disease Subtyping Systems for Improved Evaluation of Etiologic Heterogeneity. *Cancers*. 2022; 14(7):1811.
https://doi.org/10.3390/cancers14071811

**Chicago/Turabian Style**

Li, Ruitong, Tomotaka Ugai, Lantian Xu, David Zucker, Shuji Ogino, and Molin Wang. 2022. "Utility of Continuous Disease Subtyping Systems for Improved Evaluation of Etiologic Heterogeneity" *Cancers* 14, no. 7: 1811.
https://doi.org/10.3390/cancers14071811