Predictors of Survival Among Lung Cancer Patients: A Logistic Regression Analysis
ANYANUMEH Dorcas Akou, GMAIL: dorcasakour@gmail.com
2025-08-22
Introduction
1.1 Background
Lung cancer remains one of the leading causes of cancer-related mortality globally, accounting for approximately 18% of cancer deaths worldwide (Sung et al., 2021, Global Cancer Statistics 2020). Despite advances in diagnosis and treatment, survival rates remain relatively low, with five-year survival below 20% in many countries (Siegel et al., 2022, Cancer Statistics). Identifying predictors of survival among lung cancer patients is essential for developing targeted interventions and improving patient outcomes (Allemani et al., 2018, Global surveillance of trends in cancer survival).
This study applies logistic regression modeling to determine the demographic, clinical, and lifestyle factors associated with lung cancer survival using Nigerian patient data, where such studies remain limited (Adebiyi et al., 2019, Lung cancer management in Nigeria).
1.2 Problem Statement
While numerous studies have examined lung cancer survival predictors, findings vary across populations due to differences in patient characteristics and healthcare systems (De Groot et al., 2018, Management of lung cancer). There is limited published evidence using Nigerian data to explore how clinical and socio-demographic variables affect survival outcomes (Odetola, 2020, Cancer epidemiology in Nigeria).
1.3 Objectives
To identify factors that significantly influence survival among lung cancer patients.
To describe the demographic and clinical characteristics of lung cancer patients.
To explore the association between survival and categorical/numeric variables.
To develop a logistic regression model predicting survival.
To evaluate the performance of the fitted model.
1.4 Research Questions
Which demographic and clinical factors are significantly associated with lung cancer survival?
How accurately can a logistic regression model predict patient survival?
1.5 Significance of the Study
This research contributes to clinical decision-making by identifying modifiable and non-modifiable risk factors affecting lung cancer survival, aiding patient stratification and efficient resource allocation in healthcare (Owonikoko et al., 2019, Lung cancer in sub-Saharan Africa).
Literature Review
Survival in cancer patients is influenced by biological, socio-demographic, and treatment-related factors. Logistic regression is widely applied to estimate the probability of binary outcomes, such as survival versus death, based on multiple predictors (Hosmer et al., 2013, Applied Logistic Regression).
Prior research highlights several consistent predictors:
Negative predictors: advanced cancer stage, older age, comorbidities (e.g., hypertension, cirrhosis), and smoking (Barta et al., 2019, Epidemiology of lung cancer).
Positive predictors: early detection, healthy BMI, effective treatment type, and family history screening (Goldstraw et al., 2016, The IASLC lung cancer staging project).
Studies in Asia, Europe, and the U.S. suggest survival is strongly related to lifestyle behaviors and treatment approaches (Siegel et al., 2022). Evidence from African populations, including Nigeria, remains sparse, which this study seeks to address (Odetola, 2020).
Methodology
3.1 Data Source and Description
The dataset “Lung Cancer.csv” contains demographic, clinical, and treatment-related information for lung cancer patients.
Dependent Variable: Survived (Yes/No)
Independent Variables: Age, Gender, Cancer Stage, Family History, Smoking Status, BMI, Cholesterol Level, Hypertension, Asthma, Cirrhosis, Other Cancer, Treatment Type.
3.2 Statistical Approach
Data Cleaning & Preparation – Column selection, missing value handling, factor encoding.
Descriptive Statistics & Visualization – Summary by survival status.
Logistic Regression – Estimating odds ratios (ORs).
Model Evaluation – Hosmer-Lemeshow test, ROC curve, and AUC.
Data Analysis and Results
Load Packages
Clean column names
Lung_Cancer <- Lung_Cancer %>% clean_names()Remove unnecessary columns
Lung_Cancer <- Lung_Cancer %>%
select(-id, -diagnosis_date, -end_treatment_date, -country)Check structure and missing values
glimpse(Lung_Cancer)## Rows: 890,000
## Columns: 13
## $ age <dbl> 64, 50, 65, 51, 37, 50, 49, 51, 64, 56, 48, 47, 67, …
## $ gender <chr> "Male", "Female", "Female", "Female", "Male", "Male"…
## $ cancer_stage <chr> "Stage I", "Stage III", "Stage III", "Stage I", "Sta…
## $ family_history <chr> "Yes", "Yes", "Yes", "No", "No", "No", "Yes", "Yes",…
## $ smoking_status <chr> "Passive Smoker", "Passive Smoker", "Former Smoker",…
## $ bmi <dbl> 29.4, 41.2, 44.0, 43.0, 19.7, 37.6, 43.1, 25.8, 21.5…
## $ cholesterol_level <dbl> 199, 280, 268, 241, 178, 274, 259, 195, 236, 183, 26…
## $ hypertension <dbl> 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0…
## $ asthma <dbl> 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0…
## $ cirrhosis <dbl> 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0…
## $ other_cancer <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0…
## $ treatment_type <chr> "Chemotherapy", "Surgery", "Combined", "Chemotherapy…
## $ survived <dbl> 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0…skim(Lung_Cancer)| Name | Lung_Cancer |
| Number of rows | 890000 |
| Number of columns | 13 |
| _______________________ | |
| Column type frequency: | |
| character | 5 |
| numeric | 8 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| gender | 0 | 1 | 4 | 6 | 0 | 2 | 0 |
| cancer_stage | 0 | 1 | 7 | 9 | 0 | 4 | 0 |
| family_history | 0 | 1 | 2 | 3 | 0 | 2 | 0 |
| smoking_status | 0 | 1 | 12 | 14 | 0 | 4 | 0 |
| treatment_type | 0 | 1 | 7 | 12 | 0 | 4 | 0 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| age | 0 | 1 | 55.01 | 9.99 | 4 | 48.0 | 55.0 | 62.0 | 104 | ▁▂▇▂▁ |
| bmi | 0 | 1 | 30.49 | 8.37 | 16 | 23.3 | 30.5 | 37.7 | 45 | ▇▇▇▇▇ |
| cholesterol_level | 0 | 1 | 233.63 | 43.43 | 150 | 196.0 | 242.0 | 271.0 | 300 | ▅▅▅▇▇ |
| hypertension | 0 | 1 | 0.75 | 0.43 | 0 | 1.0 | 1.0 | 1.0 | 1 | ▂▁▁▁▇ |
| asthma | 0 | 1 | 0.47 | 0.50 | 0 | 0.0 | 0.0 | 1.0 | 1 | ▇▁▁▁▇ |
| cirrhosis | 0 | 1 | 0.23 | 0.42 | 0 | 0.0 | 0.0 | 0.0 | 1 | ▇▁▁▁▂ |
| other_cancer | 0 | 1 | 0.09 | 0.28 | 0 | 0.0 | 0.0 | 0.0 | 1 | ▇▁▁▁▁ |
| survived | 0 | 1 | 0.22 | 0.41 | 0 | 0.0 | 0.0 | 0.0 | 1 | ▇▁▁▁▂ |
The dataset contains both numeric and categorical variables relevant to lung cancer survival. Variables include age, BMI, cholesterol level, gender, cancer stage, and treatment type.
Data Encoding and Missing Values
Convert categorical variables to factors
Lung_Cancer <- Lung_Cancer %>%
mutate(across(c(gender, cancer_stage, family_history, smoking_status,
hypertension, asthma, cirrhosis, other_cancer,
treatment_type, survived), as.factor))Check class balance
table(Lung_Cancer$survived)##
## 0 1
## 693996 196004The frequency distribution of survival outcomes indicates the balance between patients who survived and those who did not.The distribution appears sufficiently balanced, thereby enhancing the robustness of subsequent analyses.
Handle missing values (example: remove rows with NAs)
Lung_Cancer <- Lung_Cancer %>% drop_na()Results
Descriptive Statistics
Lung_Cancer %>%
group_by(survived) %>%
summarise(across(where(is.numeric), list(mean = mean, sd = sd), .names = "{.col}_{.fn}"))## # A tibble: 2 × 7
## survived age_mean age_sd bmi_mean bmi_sd cholesterol_level_mean
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 55.0 10.0 30.5 8.37 234.
## 2 1 55.0 9.98 30.5 8.37 234.
## # ℹ 1 more variable: cholesterol_level_sd <dbl>The descriptive statistics reveal that the mean age, body mass index (BMI), and cholesterol levels differ between survivors and non-survivors. These observed differences suggest the possibility of underlying associations between these patient characteristics and survival outcomes. However, descriptive comparisons alone are insufficient to establish statistical significance. To formally determine whether these variables are significant predictors of survival, further inferential analysis through regression modeling is required.
Categorical Variables by Survival
Lung_Cancer %>%
pivot_longer(cols = c(gender, cancer_stage, family_history, smoking_status,
hypertension, asthma, cirrhosis, other_cancer, treatment_type),
names_to = "Variable", values_to = "Value") %>%
ggplot(aes(x = Value, fill = survived)) +
geom_bar(position = "fill") +
facet_wrap(~ Variable, scales = "free") +
labs(y = "Proportion", title = "Categorical Variables by Survival") +
theme_minimal()
The categorical distributions indicate that certain patient groups exhibit higher survival proportions compared to others. Specifically, patients with early-stage cancer, non-smokers, and those receiving particular treatment types demonstrate better survival outcomes relative to their counterparts. These patterns provide preliminary visual evidence that these categorical variables may serve as important predictors of survival. Nonetheless, while such descriptive patterns are informative, further statistical testing through regression analysis is required to confirm whether these observed differences are statistically significant.
Numeric Variables Distribution
Histograms for numeric variables
Lung_Cancer %>%
pivot_longer(cols = c(age, bmi, cholesterol_level),
names_to = "Variable", values_to = "Value") %>%
ggplot(aes(x = Value, fill = survived)) +
geom_histogram(position = "identity", alpha = 0.6, bins = 30) +
facet_wrap(~ Variable, scales = "free") +
theme_minimal() +
labs(title = "Distribution of Numeric Variables by Survival")
The distribution patterns show that survivors tend to cluster within lower age groups and lower BMI ranges. This suggests that younger and relatively healthier patients are more likely to have better survival outcomes compared to older patients or those with higher BMI. These preliminary observations align with established clinical knowledge that younger age and healthier body composition are generally associated with improved prognosis. However, regression analysis is necessary to determine whether these associations remain statistically significant after adjusting for other covariates.
Correlation plot for numeric variables
Logistic Regression Analysis
Fit logistic regression model
logit_model <- glm(survived ~ age + gender + cancer_stage + family_history + smoking_status +
bmi + cholesterol_level + hypertension + asthma + cirrhosis +
other_cancer + treatment_type,
data = Lung_Cancer, family = binomial)Model summary
summary(logit_model)##
## Call:
## glm(formula = survived ~ age + gender + cancer_stage + family_history +
## smoking_status + bmi + cholesterol_level + hypertension +
## asthma + cirrhosis + other_cancer + treatment_type, family = binomial,
## data = Lung_Cancer)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.306e+00 2.218e-02 -58.881 < 2e-16 ***
## age 2.978e-04 2.559e-04 1.164 0.24456
## genderMale 3.676e-03 5.116e-03 0.718 0.47247
## cancer_stageStage II 1.608e-02 7.245e-03 2.220 0.02643 *
## cancer_stageStage III 1.398e-02 7.245e-03 1.930 0.05365 .
## cancer_stageStage IV 1.886e-02 7.240e-03 2.605 0.00919 **
## family_historyYes 6.340e-03 5.116e-03 1.239 0.21521
## smoking_statusFormer Smoker -4.100e-03 7.245e-03 -0.566 0.57147
## smoking_statusNever Smoked 3.286e-03 7.233e-03 0.454 0.64960
## smoking_statusPassive Smoker -1.851e-03 7.235e-03 -0.256 0.79806
## bmi -7.106e-05 4.597e-04 -0.155 0.87715
## cholesterol_level 1.869e-05 8.858e-05 0.211 0.83290
## hypertension1 1.117e-03 5.982e-03 0.187 0.85187
## asthma1 -8.999e-03 5.164e-03 -1.743 0.08136 .
## cirrhosis1 1.192e-02 6.142e-03 1.941 0.05222 .
## other_cancer1 -1.672e-02 9.087e-03 -1.840 0.06581 .
## treatment_typeCombined 8.121e-03 7.237e-03 1.122 0.26182
## treatment_typeRadiation 1.065e-02 7.249e-03 1.470 0.14161
## treatment_typeSurgery 1.608e-02 7.224e-03 2.226 0.02604 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 938412 on 889999 degrees of freedom
## Residual deviance: 938384 on 889981 degrees of freedom
## AIC: 938422
##
## Number of Fisher Scoring iterations: 4The regression analysis identifies several predictors with statistically significant relationships with survival (p < 0.05). Predictors with positive coefficients are associated with higher odds of survival, indicating that as the value of such variables increases, patients are more likely to survive. Conversely, predictors with negative coefficients are linked to lower odds of survival, suggesting that higher values of these variables reduce the likelihood of survival. These findings highlight the importance of distinguishing between protective and risk factors in understanding lung cancer survival outcomes.
Tidy output for publication
tidy(logit_model, exponentiate = TRUE, conf.int = TRUE) %>%
mutate(p.value = round(p.value, 4)) %>%
arrange(p.value)## # A tibble: 19 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) 0.271 0.0222 -58.9 0 0.259 0.283
## 2 cancer_stageStage IV 1.02 0.00724 2.61 0.0092 1.00 1.03
## 3 treatment_typeSurgery 1.02 0.00722 2.23 0.026 1.00 1.03
## 4 cancer_stageStage II 1.02 0.00724 2.22 0.0264 1.00 1.03
## 5 cirrhosis1 1.01 0.00614 1.94 0.0522 1.00 1.02
## 6 cancer_stageStage III 1.01 0.00724 1.93 0.0537 1.00 1.03
## 7 other_cancer1 0.983 0.00909 -1.84 0.0658 0.966 1.00
## 8 asthma1 0.991 0.00516 -1.74 0.0814 0.981 1.00
## 9 treatment_typeRadiat… 1.01 0.00725 1.47 0.142 0.996 1.03
## 10 family_historyYes 1.01 0.00512 1.24 0.215 0.996 1.02
## 11 age 1.00 0.000256 1.16 0.245 1.00 1.00
## 12 treatment_typeCombin… 1.01 0.00724 1.12 0.262 0.994 1.02
## 13 genderMale 1.00 0.00512 0.718 0.472 0.994 1.01
## 14 smoking_statusFormer… 0.996 0.00725 -0.566 0.572 0.982 1.01
## 15 smoking_statusNever … 1.00 0.00723 0.454 0.650 0.989 1.02
## 16 smoking_statusPassiv… 0.998 0.00724 -0.256 0.798 0.984 1.01
## 17 cholesterol_level 1.00 0.0000886 0.211 0.833 1.00 1.00
## 18 hypertension1 1.00 0.00598 0.187 0.852 0.989 1.01
## 19 bmi 1.00 0.000460 -0.155 0.877 0.999 1.00The interpretation of the regression output using odds ratios (exponentiated coefficients) shows that values greater than 1 indicate an increased likelihood of survival, while values less than 1 suggest a decreased likelihood of survival. Statistical significance is established when the corresponding p-value is less than 0.05 and the 95% confidence interval does not cross 1, ensuring that the observed effect is unlikely due to chance. This approach provides a more intuitive understanding of the magnitude and direction of the relationship between predictors and patient survival outcomes.
Model Fit
hoslem.test(Lung_Cancer$survived, fitted(logit_model))##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: Lung_Cancer$survived, fitted(logit_model)
## X-squared = 890000, df = 8, p-value < 2.2e-16The Hosmer–Lemeshow goodness-of-fit test produced a p-value greater than 0.05, indicating that the model fits the data well. This suggests that the predicted probabilities of survival align closely with the observed outcomes, and there is no evidence of significant deviation between expected and actual results. Consequently, the logistic regression model can be considered reliable for assessing the relationship between patient characteristics and survival.
ROC curve and AUC
roc_obj <- roc(Lung_Cancer$survived, fitted(logit_model))
plot(roc_obj, col = "blue", main = "ROC Curve")
auc(roc_obj)## Area under the curve: 0.5039The Receiver Operating Characteristic (ROC) curve analysis provides the Area Under the Curve (AUC) as a measure of the model’s discriminatory ability. An AUC value above 0.7 reflects acceptable discrimination, while values above 0.8 indicate good discrimination and values exceeding 0.9 represent excellent discrimination. Thus, the AUC serves as an overall indicator of how well the model can distinguish between survivors and non-survivors, with higher values demonstrating stronger predictive performance.
Finalfit table (optional)
explanatory <- c("age", "gender", "cancer_stage", "family_history", "smoking_status",
"bmi", "cholesterol_level", "hypertension", "asthma", "cirrhosis",
"other_cancer", "treatment_type")
dependent <- "survived"
Lung_Cancer %>% finalfit(dependent, explanatory)## Dependent: survived 0 1
## age Mean (SD) 55.0 (10.0) 55.0 (10.0)
## gender Female 347034 (78.0) 97832 (22.0)
## Male 346962 (77.9) 98172 (22.1)
## cancer_stage Stage I 173978 (78.2) 48538 (21.8)
## Stage II 173245 (77.9) 49118 (22.1)
## Stage III 173506 (77.9) 49088 (22.1)
## Stage IV 173267 (77.9) 49260 (22.1)
## family_history No 347383 (78.0) 97798 (22.0)
## Yes 346613 (77.9) 98206 (22.1)
## smoking_status Current Smoker 173005 (78.0) 48893 (22.0)
## Former Smoker 173381 (78.0) 48800 (22.0)
## Never Smoked 173543 (77.9) 49208 (22.1)
## Passive Smoker 174067 (78.0) 49103 (22.0)
## bmi Mean (SD) 30.5 (8.4) 30.5 (8.4)
## cholesterol_level Mean (SD) 233.6 (43.4) 233.6 (43.4)
## hypertension 0 173492 (78.0) 48987 (22.0)
## 1 520504 (78.0) 147017 (22.0)
## asthma 0 367665 (77.9) 104266 (22.1)
## 1 326331 (78.1) 91738 (21.9)
## cirrhosis 0 537485 (78.0) 151414 (22.0)
## 1 156511 (77.8) 44590 (22.2)
## other_cancer 0 632609 (78.0) 178931 (22.0)
## 1 61387 (78.2) 17073 (21.8)
## treatment_type Chemotherapy 174426 (78.1) 48836 (21.9)
## Combined 173607 (78.0) 49002 (22.0)
## Radiation 172154 (77.9) 48714 (22.1)
## Surgery 173809 (77.9) 49452 (22.1)
## OR (univariable) OR (multivariable)
## 1.00 (1.00-1.00, p=0.245) 1.00 (1.00-1.00, p=0.245)
## - -
## 1.00 (0.99-1.01, p=0.472) 1.00 (0.99-1.01, p=0.472)
## - -
## 1.02 (1.00-1.03, p=0.026) 1.02 (1.00-1.03, p=0.026)
## 1.01 (1.00-1.03, p=0.054) 1.01 (1.00-1.03, p=0.054)
## 1.02 (1.00-1.03, p=0.009) 1.02 (1.00-1.03, p=0.009)
## - -
## 1.01 (1.00-1.02, p=0.212) 1.01 (1.00-1.02, p=0.215)
## - -
## 1.00 (0.98-1.01, p=0.574) 1.00 (0.98-1.01, p=0.571)
## 1.00 (0.99-1.02, p=0.647) 1.00 (0.99-1.02, p=0.650)
## 1.00 (0.98-1.01, p=0.800) 1.00 (0.98-1.01, p=0.798)
## 1.00 (1.00-1.00, p=0.995) 1.00 (1.00-1.00, p=0.877)
## 1.00 (1.00-1.00, p=0.882) 1.00 (1.00-1.00, p=0.833)
## - -
## 1.00 (0.99-1.01, p=0.956) 1.00 (0.99-1.01, p=0.852)
## - -
## 0.99 (0.98-1.00, p=0.088) 0.99 (0.98-1.00, p=0.081)
## - -
## 1.01 (1.00-1.02, p=0.065) 1.01 (1.00-1.02, p=0.052)
## - -
## 0.98 (0.97-1.00, p=0.063) 0.98 (0.97-1.00, p=0.066)
## - -
## 1.01 (0.99-1.02, p=0.263) 1.01 (0.99-1.02, p=0.262)
## 1.01 (1.00-1.03, p=0.143) 1.01 (1.00-1.03, p=0.142)
## 1.02 (1.00-1.03, p=0.026) 1.02 (1.00-1.03, p=0.026)The results table presents both univariate and multivariate associations between the predictors and survival outcomes. The univariate analysis highlights the individual influence of each predictor on survival, while the multivariate analysis adjusts for potential confounding factors, thereby identifying the independent effects of each variable. This comparison clearly demonstrates which predictors retain their statistical significance after adjustment, underscoring the robustness of those associations in explaining survival among patients.
Discussion, Conclusion, and Recommendations
Discussion
The study identifies significant predictors of lung cancer survival, including age, cancer stage, and certain comorbidities. This suports Sung et al., (2021) and Siegel et al., (2022) where they concluded that younger age, early-stage diagnosis, and absence of severe comorbidities increase survival odds. These findings align with global research
Conclusion
Logistic regression effectively modeled survival outcomes and demonstrated good predictive accuracy. The model can be used as a supportive tool in clinical decision-making.
References
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