# Gene Screening in High-Throughput Right-Censored Lung Cancer Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Description

#### 2.2. Sure Independence Screening for Right-Censored Data

#### 2.3. The Screening Index

#### 2.4. The Sreening Algorithm

- (1)
- Estimate the survival function by the Kaplan–Meier estimator as$${\widehat{F}}_{T}\left(t\right):=1-\prod _{i=1}^{n}{\left(1-\frac{1}{{\sum}_{l=1}^{n}I\{{Y}_{l}\ge {Y}_{i}\}}\right)}^{{\delta}_{i}I\{{Y}_{i}\le t\}}$$
- (2)
- Treat ${\{{\widehat{F}}_{{X}_{j}}\left({X}_{ij}\right),{\widehat{F}}_{T}\left({Y}_{i}\right)\}}_{i=1}^{n}$ as the observed data of $({U}_{{X}_{j}},{U}_{T})$ and compute the sample correlation ${\widehat{w}}_{j}:={\rho}_{K,G,n}\left({U}_{T}\right|{U}_{{X}_{j}})$ for $j=1,...,p$.
- (3)
- Let $\widehat{\mathcal{A}}:=\{1\le j\le p:{\widehat{w}}_{j}\phantom{\rule{3.33333pt}{0ex}}\mathrm{is}\phantom{\rule{4.pt}{0ex}}\mathrm{among}\phantom{\rule{4.pt}{0ex}}\mathrm{the}\phantom{\rule{4.pt}{0ex}}\mathrm{first}\phantom{\rule{3.33333pt}{0ex}}d\phantom{\rule{3.33333pt}{0ex}}\mathrm{largest}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{all}\}$.

`R`code to implement the proposed algorithm is available at https://github.com/cke23/GeneScreeningDemo1 (accessed on 30 September 2022).

#### 2.5. Application

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Kaplan–Meier curves of overall survival for test (TCGA) and validation (GEO) cohorts varying with the risk level determined by the four competing models. p-values were obtained from the log-rank tests contrasting the two risk groups.

**Figure 3.**Kaplan–Meier curves of disease-free survival for test (TCGA) and validation (GEO) cohorts varying with the risk level determined by the four competing models. p-values were obtained from the log-rank tests contrasting the two risk groups.

**Figure 4.**ROC curves of overall survival predicted by the four competing models on the external validation data.

Variables | Frequency (Percent) |
---|---|

Age | |

Less than 50 | 15 (3.2%) |

50–59 | 67 (14.2%) |

60–69 | 178 (37.6%) |

70–79 | 186 (39.3%) |

80 or greater | 27 (5.7%) |

Gender | |

Female | 125 (26.4%) |

Male | 348 (73.6%) |

Smoking History | |

Current reformed smoker for ≤ 15 years | 236 (49.9%) |

Current reformed smoker for > 15 years | 81 (17.1%) |

Current reformed smoker, duration not specified | 5 (1.1%) |

Current smoker | 133 (28.1%) |

Lifelong non-smoker | 18 (3.8%) |

Lymph Node Metastasis | |

N0 | 302 (63.8%) |

N1, N2, N3 | 165 (34.9%) |

NX | 6 (1.3%) |

Distant Metastasis | |

M0 | 386 (81.6%) |

M1, M1a, M1b | 7 (1.5%) |

MX | 80 (16.9%) |

Pathological Stage | |

I | 236 (49.9%) |

II | 150 (31.7%) |

III | 80 (16.9%) |

IV | 7 (1.5%) |

**Table 2.**Genes selected by the four competing models. A risk gene with a positive coefficient from the fitted PenCox model is denoted by “+”, while a protective gene with a negative coefficient is denoted by “−”.

Model (No. of Genes Selected) | Gene Names |
---|---|

Naive + PenCox (6) | PCDHA5(+), C9ORF131(+), PM20D1(+), PCDHA3(+), FAM196B(+), PITX3(−) |

CRIS + PenCox (10) | CCDC79(+), LCN1(+), GPR78(+), SSX1(+), CCKAR(+), SLC10A2(+), STARD6(−), GUCY2F(−), DPPA2(+), LINC00628(+) |

IPOD + PenCox (4) | TRIM58(+), C9ORF131(+), PKNOX2(+), PCDHGA11(+) |

ESIS + PenCox (6) | NACC2(+), FAM65A(+), LOC641845(−), MON1B(+), IBTK(+), SDHAF3(−) |

**Table 3.**Multivariable Cox regression analysis of the risk of death against the 6-gene signature identified by ESIS+PenCox and other clinical covariates. CI denotes confidence interval.

Variable | Hazard Ratio (95% CI) | p-Value |
---|---|---|

6-gene signature | 12.59 (4.11, 38.56) | <0.001 |

Age | 1.02 (1.01, 1.04) | 0.008 |

Gender | ||

Male | 0.92 (0.67, 1.28) | 0.629 |

Female | - | - |

Tumor stage | ||

I | 0.59 (0.42, 0.83) | 0.003 |

II | 0.63 (0.43, 0.92) | 0.018 |

III or IV | - | - |

Smoking history | ||

Lifelong non-smoker | 1.94 (0.83, 4.54) | 0.126 |

Current smoker | 1.54 (1.14, 2.07) | 0.005 |

Current reformed smoker | - | - |

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**MDPI and ACS Style**

Ke, C.; Bandyopadhyay, D.; Acunzo, M.; Winn, R.
Gene Screening in High-Throughput Right-Censored Lung Cancer Data. *Onco* **2022**, *2*, 305-318.
https://doi.org/10.3390/onco2040017

**AMA Style**

Ke C, Bandyopadhyay D, Acunzo M, Winn R.
Gene Screening in High-Throughput Right-Censored Lung Cancer Data. *Onco*. 2022; 2(4):305-318.
https://doi.org/10.3390/onco2040017

**Chicago/Turabian Style**

Ke, Chenlu, Dipankar Bandyopadhyay, Mario Acunzo, and Robert Winn.
2022. "Gene Screening in High-Throughput Right-Censored Lung Cancer Data" *Onco* 2, no. 4: 305-318.
https://doi.org/10.3390/onco2040017