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jSurvival 01: Introduction to Survival Analysis for Pathologists

ClinicoPath Development Team

2025-06-30

Source: vignettes/jsurvival-01-introduction.Rmd
jsurvival-01-introduction.Rmd

Introduction

jsurvival provides comprehensive survival analysis tools specifically designed for clinical research and oncology studies. This module offers user-friendly interfaces for time-to-event analysis, from basic Kaplan-Meier curves to advanced competing risks and multivariate Cox regression models.

Learning Objectives:

  • Master fundamental survival analysis concepts and methods
  • Learn Kaplan-Meier survival curve construction and interpretation
  • Apply Cox proportional hazards regression for multivariable analysis
  • Understand competing risks analysis for complex clinical scenarios
  • Implement molecular biomarker survival analysis workflows
  • Create publication-ready survival plots and tables

Module Overview

jsurvival encompasses four main areas of survival analysis:

1. Basic Survival Analysis

  • Kaplan-Meier Curves: Non-parametric survival estimation
  • Log-rank Tests: Compare survival between groups
  • Median Survival: Time-to-event summary statistics
  • Confidence Intervals: Uncertainty quantification for survival estimates

2. Regression Models

  • Cox Proportional Hazards: Multivariable time-to-event modeling
  • Stratified Cox Models: Account for non-proportional hazards
  • Time-dependent Covariates: Dynamic risk factor modeling
  • Model Diagnostics: Assumption testing and validation

3. Advanced Methods

  • Competing Risks: Multiple event types analysis
  • Multistate Models: Disease progression modeling
  • Parametric Survival: Weibull, exponential, and other distributions
  • Frailty Models: Unobserved heterogeneity modeling

4. Clinical Applications

  • Biomarker Analysis: Molecular predictor evaluation
  • Treatment Comparisons: Therapeutic intervention assessment
  • Prognostic Models: Risk stratification tools
  • Real-World Evidence: Population-based survival studies

Getting Started

Sample Data Overview 

# Load molecular pathology survival data
data(ihc_molecular_comprehensive)

# Survival data structure
cat("Survival dataset dimensions:", nrow(ihc_molecular_comprehensive), "×", ncol(ihc_molecular_comprehensive), "\n")

# Key survival variables
survival_vars <- c("Overall_Survival_Months", "Death_Event", "PFS_Months", "Progression_Event")
cat("Survival variables:", paste(survival_vars, collapse = ", "), "\n")

# Molecular biomarkers for stratification
biomarker_vars <- c("EGFR_Mutation", "MSI_Status", "HER2_IHC", "PD_L1_TPS")
cat("Biomarker variables:", paste(biomarker_vars, collapse = ", "), "\n")

# Basic survival summary
survival_summary <- ihc_molecular_comprehensive %>%
  summarise(
    n = n(),
    median_os = median(Overall_Survival_Months),
    death_rate = round(mean(Death_Event) * 100, 1),
    median_pfs = median(PFS_Months),
    progression_rate = round(mean(Progression_Event) * 100, 1)
  )

cat("\nSurvival Summary:\n")
cat("Patients:", survival_summary$n, "\n")
cat("Median OS:", survival_summary$median_os, "months\n")
cat("Death rate:", survival_summary$death_rate, "%\n")
cat("Median PFS:", survival_summary$median_pfs, "months\n")
cat("Progression rate:", survival_summary$progression_rate, "%\n")

Core Survival Analysis

1. Kaplan-Meier Survival Analysis

Foundation of survival analysis for time-to-event data.

# Kaplan-Meier Analysis Example
# In jamovi: jsurvival > Survival Analysis

cat("Kaplan-Meier Survival Analysis\n")
cat("==============================\n\n")

if(requireNamespace("survival", quietly = TRUE)) {
  library(survival)
  
  # Create survival object
  surv_obj <- Surv(ihc_molecular_comprehensive$Overall_Survival_Months,
                   ihc_molecular_comprehensive$Death_Event)
  
  # Overall survival curve
  km_overall <- survfit(surv_obj ~ 1, data = ihc_molecular_comprehensive)
  
  cat("Overall Survival Analysis:\n")
  print(summary(km_overall, times = c(12, 24, 36, 60))$table)
  
  # Survival by EGFR mutation status
  km_egfr <- survfit(surv_obj ~ EGFR_Mutation, data = ihc_molecular_comprehensive)
  
  cat("\nSurvival by EGFR Status:\n")
  egfr_summary <- summary(km_egfr)$table
  print(egfr_summary)
  
  # Log-rank test
  logrank_egfr <- survdiff(surv_obj ~ EGFR_Mutation, data = ihc_molecular_comprehensive)
  p_value <- 1 - pchisq(logrank_egfr$chisq, 1)
  
  cat("\nLog-rank test p-value:", round(p_value, 4), "\n")
  
  if(p_value < 0.05) {
    cat("Conclusion: Significant difference in survival by EGFR status\n")
  } else {
    cat("Conclusion: No significant difference in survival by EGFR status\n")
  }
}

2. Cox Proportional Hazards Regression

Multivariable analysis accounting for multiple prognostic factors.

# Cox Regression Analysis Example
# In jamovi: jsurvival > Cox Diagnostics

cat("\nCox Proportional Hazards Regression\n")
cat("===================================\n\n")

if(requireNamespace("survival", quietly = TRUE)) {
  # Multivariable Cox model
  cox_model <- coxph(Surv(Overall_Survival_Months, Death_Event) ~ 
                     EGFR_Mutation + MSI_Status + Age + Grade + Tumor_Mutational_Burden,
                     data = ihc_molecular_comprehensive)
  
  cat("Cox Regression Results:\n")
  cox_summary <- summary(cox_model)
  print(cox_summary$coefficients[, c("coef", "exp(coef)", "Pr(>|z|)")])
  
  # Model performance
  cat("\nModel Performance:\n")
  cat("Concordance:", round(cox_summary$concordance[1], 3), "\n")
  cat("R-squared:", round(cox_summary$rsq[1], 3), "\n")
  cat("Likelihood ratio test p-value:", round(cox_summary$logtest[3], 4), "\n")
  
  # Hazard ratios with confidence intervals
  cat("\nHazard Ratios (95% CI):\n")
  hr_ci <- exp(confint(cox_model))
  hr_estimates <- exp(cox_model$coefficients)
  
  for(i in 1:length(hr_estimates)) {
    var_name <- names(hr_estimates)[i]
    hr <- round(hr_estimates[i], 2)
    ci_lower <- round(hr_ci[i, 1], 2)
    ci_upper <- round(hr_ci[i, 2], 2)
    p_val <- round(cox_summary$coefficients[i, "Pr(>|z|)"], 3)
    
    cat(paste0(var_name, ": HR = ", hr, " (", ci_lower, "-", ci_upper, "), p = ", p_val, "\n"))
  }
}

3. Competing Risks Analysis

Handle situations where multiple types of events can occur.

# Competing Risks Analysis Example
# In jamovi: jsurvival > Competing Survival

cat("\nCompeting Risks Analysis\n")
cat("=======================\n\n")

# Create competing events data
# Death from disease vs death from other causes
competing_data <- ihc_molecular_comprehensive %>%
  mutate(
    # Simulate competing events
    death_cause = case_when(
      Death_Event == 0 ~ "Alive",
      Death_Event == 1 & Grade == 3 ~ "Disease",
      Death_Event == 1 & Age > 75 ~ "Other",
      Death_Event == 1 ~ sample(c("Disease", "Other"), 1, prob = c(0.7, 0.3)),
      TRUE ~ "Alive"
    ),
    
    # Competing event indicator
    event_type = case_when(
      death_cause == "Disease" ~ 1,
      death_cause == "Other" ~ 2,
      TRUE ~ 0
    )
  )

# Competing risks summary
competing_summary <- competing_data %>%
  group_by(death_cause) %>%
  summarise(
    n = n(),
    percentage = round(n() / nrow(competing_data) * 100, 1),
    median_time = median(Overall_Survival_Months),
    .groups = 'drop'
  )

cat("Competing Events Summary:\n")
print(competing_summary)

# Event rates by biomarker status
biomarker_events <- competing_data %>%
  group_by(EGFR_Mutation, death_cause) %>%
  summarise(n = n(), .groups = 'drop') %>%
  group_by(EGFR_Mutation) %>%
  mutate(percentage = round(n / sum(n) * 100, 1))

cat("\nEvent Rates by EGFR Status:\n")
print(biomarker_events)

# Clinical interpretation
disease_death_rate <- mean(competing_data$death_cause == "Disease") * 100
cat("\nClinical Interpretation:\n")
cat("Disease-specific death rate:", round(disease_death_rate, 1), "%\n")

if(disease_death_rate > 50) {
  cat("Conclusion: Disease is the predominant cause of death\n")
} else {
  cat("Conclusion: Competing causes of death are significant\n")
}

Biomarker Survival Analysis

Molecular Stratification

Evaluate prognostic impact of molecular biomarkers.

cat("Molecular Biomarker Survival Analysis\n")
cat("====================================\n\n")

# Multiple biomarker analysis
biomarkers <- c("EGFR_Mutation", "MSI_Status", "HER2_IHC")

for(biomarker in biomarkers) {
  cat(paste0("Survival Analysis for ", biomarker, ":\n"))
  cat(paste0(rep("-", nchar(biomarker) + 25), collapse = ""), "\n")
  
  # Create survival object
  surv_obj <- Surv(ihc_molecular_comprehensive$Overall_Survival_Months,
                   ihc_molecular_comprehensive$Death_Event)
  
  # Survival by biomarker
  formula_str <- paste("surv_obj ~", biomarker)
  km_biomarker <- survfit(as.formula(formula_str), data = ihc_molecular_comprehensive)
  
  # Summary statistics
  biomarker_summary <- summary(km_biomarker)$table
  print(biomarker_summary)
  
  # Log-rank test
  logrank_test <- survdiff(as.formula(formula_str), data = ihc_molecular_comprehensive)
  p_value <- 1 - pchisq(logrank_test$chisq, length(unique(ihc_molecular_comprehensive[[biomarker]])) - 1)
  
  cat("Log-rank test p-value:", round(p_value, 4), "\n")
  
  if(p_value < 0.05) {
    cat("Result: Significant prognostic biomarker\n")
  } else {
    cat("Result: Not a significant prognostic biomarker\n")
  }
  cat("\n")
}

Continuous Biomarker Analysis

Evaluate continuous biomarkers like PD-L1 expression or tumor mutational burden.

cat("Continuous Biomarker Analysis\n")
cat("=============================\n\n")

# PD-L1 TPS analysis
pdl1_quartiles <- quantile(ihc_molecular_comprehensive$PD_L1_TPS, 
                          probs = c(0, 0.25, 0.5, 0.75, 1.0))

ihc_with_quartiles <- ihc_molecular_comprehensive %>%
  mutate(
    PD_L1_Quartile = cut(PD_L1_TPS, 
                        breaks = pdl1_quartiles,
                        labels = c("Q1 (Low)", "Q2", "Q3", "Q4 (High)"),
                        include.lowest = TRUE),
    
    PD_L1_Clinical = case_when(
      PD_L1_TPS < 1 ~ "Negative (<1%)",
      PD_L1_TPS < 50 ~ "Low Positive (1-49%)",
      TRUE ~ "High Positive (≥50%)"
    )
  )

cat("PD-L1 TPS Distribution:\n")
pdl1_dist <- table(ihc_with_quartiles$PD_L1_Clinical)
print(pdl1_dist)

# Survival by PD-L1 clinical categories
if(requireNamespace("survival", quietly = TRUE)) {
  surv_obj <- Surv(ihc_with_quartiles$Overall_Survival_Months,
                   ihc_with_quartiles$Death_Event)
  
  km_pdl1 <- survfit(surv_obj ~ PD_L1_Clinical, data = ihc_with_quartiles)
  
  cat("\nSurvival by PD-L1 Expression Level:\n")
  pdl1_summary <- summary(km_pdl1)$table
  print(pdl1_summary)
  
  # Test for trend
  logrank_pdl1 <- survdiff(surv_obj ~ PD_L1_Clinical, data = ihc_with_quartiles)
  p_value_pdl1 <- 1 - pchisq(logrank_pdl1$chisq, 2)
  
  cat("Log-rank test p-value:", round(p_value_pdl1, 4), "\n")
  
  # Tumor mutational burden analysis
  tmb_median <- median(ihc_molecular_comprehensive$Tumor_Mutational_Burden)
  tmb_high <- ihc_molecular_comprehensive$Tumor_Mutational_Burden >= tmb_median
  
  cat("\nTumor Mutational Burden Analysis:\n")
  cat("Median TMB:", tmb_median, "mutations/Mb\n")
  cat("TMB-High cases:", sum(tmb_high), "(", round(mean(tmb_high) * 100, 1), "%)\n")
  
  # TMB survival analysis
  km_tmb <- survfit(surv_obj ~ tmb_high, data = ihc_molecular_comprehensive)
  tmb_summary <- summary(km_tmb)$table
  
  cat("Survival by TMB Status:\n")
  print(tmb_summary)
}

Advanced Applications

Multivariable Prognostic Models

Develop comprehensive prognostic models incorporating multiple biomarkers.

cat("Multivariable Prognostic Model Development\n")
cat("=========================================\n\n")

if(requireNamespace("survival", quietly = TRUE)) {
  # Comprehensive prognostic model
  prog_model <- coxph(Surv(Overall_Survival_Months, Death_Event) ~ 
                      Age + Grade + 
                      EGFR_Mutation + MSI_Status + 
                      PD_L1_TPS + Tumor_Mutational_Burden,
                      data = ihc_molecular_comprehensive)
  
  # Model summary
  prog_summary <- summary(prog_model)
  
  cat("Comprehensive Prognostic Model:\n")
  print(prog_summary$coefficients[, c("coef", "exp(coef)", "Pr(>|z|)")])
  
  # Model performance metrics
  cat("\nModel Performance:\n")
  cat("Concordance index:", round(prog_summary$concordance[1], 3), "\n")
  cat("Standard error:", round(prog_summary$concordance[2], 3), "\n")
  
  # Risk score calculation
  risk_scores <- predict(prog_model, type = "risk")
  risk_tertiles <- cut(risk_scores, 
                      breaks = quantile(risk_scores, probs = c(0, 1/3, 2/3, 1)),
                      labels = c("Low Risk", "Intermediate Risk", "High Risk"),
                      include.lowest = TRUE)
  
  # Risk group validation
  risk_validation <- ihc_molecular_comprehensive %>%
    mutate(Risk_Group = risk_tertiles) %>%
    group_by(Risk_Group) %>%
    summarise(
      n = n(),
      events = sum(Death_Event),
      event_rate = round(mean(Death_Event) * 100, 1),
      median_survival = median(Overall_Survival_Months),
      .groups = 'drop'
    )
  
  cat("\nRisk Group Validation:\n")
  print(risk_validation)
  
  # Test risk stratification
  surv_risk <- Surv(ihc_molecular_comprehensive$Overall_Survival_Months,
                    ihc_molecular_comprehensive$Death_Event)
  
  km_risk <- survfit(surv_risk ~ risk_tertiles)
  logrank_risk <- survdiff(surv_risk ~ risk_tertiles)
  p_value_risk <- 1 - pchisq(logrank_risk$chisq, 2)
  
  cat("Risk stratification p-value:", round(p_value_risk, 4), "\n")
  
  if(p_value_risk < 0.001) {
    cat("Conclusion: Excellent risk stratification achieved\n")
  } else if(p_value_risk < 0.05) {
    cat("Conclusion: Significant risk stratification achieved\n")
  } else {
    cat("Conclusion: Risk stratification needs improvement\n")
  }
}

Integration with Other Modules

jsurvival works seamlessly with other ClinicoPath modules:

Connection to ClinicoPathDescriptives

  • Baseline characteristics inform survival model covariates
  • Quality metrics validate survival endpoint reliability
  • Descriptive statistics support survival study design

Connection to meddecide

  • Survival analysis provides time-to-event data for decision trees
  • Hazard ratios inform Markov model transition probabilities
  • Prognostic models support treatment decision algorithms

Connection to jjstatsplot

  • Survival curves and forest plots enhance presentation
  • Statistical visualization supports survival analysis interpretation
  • Publication-ready graphics for survival studies

Best Practices

Study Design Considerations

  1. Follow-up Time: Adequate duration to observe events of interest
  2. Censoring: Understand and appropriately handle censored observations
  3. Sample Size: Power calculations for survival studies
  4. Endpoint Definition: Clear, objective, and clinically meaningful endpoints
  5. Covariate Collection: Comprehensive baseline and time-dependent variables

Statistical Analysis Guidelines

  1. Proportional Hazards: Test and address violations when necessary
  2. Model Building: Use principled variable selection approaches
  3. Validation: Internal and external validation of prognostic models
  4. Missing Data: Appropriate handling of incomplete observations
  5. Multiple Testing: Adjust for multiple comparisons when appropriate

Reporting Standards

  1. STROBE Guidelines: Follow reporting guidelines for observational studies
  2. Complete Reporting: Include all relevant model diagnostics
  3. Clinical Interpretation: Translate statistical findings to clinical relevance
  4. Limitations: Discuss study limitations and potential biases
  5. Reproducibility: Provide sufficient detail for study replication

Conclusion

jsurvival provides comprehensive tools for modern survival analysis in clinical research, from basic Kaplan-Meier curves to sophisticated prognostic modeling. The integration with molecular biomarker data and other ClinicoPath modules makes it essential for contemporary oncology research and precision medicine applications.

Next Steps

To explore specific survival analysis techniques:

  • Advanced Methods: See detailed survival analysis vignettes
  • Biomarker Analysis: Explore molecular prognostic factor evaluation
  • Model Development: Learn comprehensive prognostic model building
  • Clinical Applications: Study real-world survival analysis examples

This introduction provides the foundation for using jsurvival in clinical research. Explore the detailed vignettes for specific techniques and advanced applications.