Time-Dependent Covariates in Multisurvival Analysis

Introduction

Time-dependent covariates are variables that change their values over the course of follow-up time. In clinical research, many important variables can change during the study period, such as:

Treatment regimens (switching from standard to experimental therapy)
Disease status (remission, progression)
Performance status
Biomarker levels
Comorbidities

The multisurvival function in ClinicoPath now supports time-dependent covariates in both wide and long data formats, making it easier to analyze survival data where covariates change over time.

Data Format Options

Wide Format Data

In wide format, each subject has one row, with time-dependent variables represented as separate columns for different time points.

Example Wide Format Structure

# Example wide format data structure
wide_data <- data.frame(
  id = 1:3,
  age = c(65, 72, 58),
  sex = factor(c("Male", "Female", "Male")),
  time = c(24, 18, 30),
  status = c(1, 0, 1),
  
  # Baseline treatment (time 0)
  treatment_baseline = factor(c("Standard", "Standard", "Experimental")),
  
  # Treatment at 6 months
  treatment_t6 = factor(c("Standard", "Experimental", "Experimental")),
  
  # Treatment at 12 months  
  treatment_t12 = factor(c("Experimental", "Experimental", "Stopped")),
  
  # Treatment at 18 months
  treatment_t18 = factor(c("Experimental", "Stopped", "Stopped"))
)

print(wide_data)

##   id age    sex time status treatment_baseline treatment_t6 treatment_t12
## 1  1  65   Male   24      1           Standard     Standard  Experimental
## 2  2  72 Female   18      0           Standard Experimental  Experimental
## 3  3  58   Male   30      1       Experimental Experimental       Stopped
##   treatment_t18
## 1  Experimental
## 2       Stopped
## 3       Stopped

Wide Format Advantages: - One row per patient (easier to understand) - Common format in clinical databases - Easy to create from existing data

Wide Format Requirements: - Baseline variables: variable_baseline or just variable - Time-specific variables: variable_t6, variable_t12, etc. - Change times specified in options

Long Format Data

In long format, each subject can have multiple rows, with one row for each time interval where covariates remain constant.

Example Long Format Structure

# Example long format data structure  
long_data <- data.frame(
  id = c(1, 1, 1, 2, 2, 3, 3),
  age = c(65, 65, 65, 72, 72, 58, 58),
  sex = factor(c("Male", "Male", "Male", "Female", "Female", "Male", "Male")),
  tstart = c(0, 6, 12, 0, 6, 0, 12),
  tstop = c(6, 12, 24, 6, 18, 12, 30),
  status = c(0, 0, 1, 0, 0, 0, 1),
  treatment = factor(c("Standard", "Standard", "Experimental", 
                      "Standard", "Experimental", "Experimental", "Stopped"))
)

print(long_data)

##   id age    sex tstart tstop status    treatment
## 1  1  65   Male      0     6      0     Standard
## 2  1  65   Male      6    12      0     Standard
## 3  1  65   Male     12    24      1 Experimental
## 4  2  72 Female      0     6      0     Standard
## 5  2  72 Female      6    18      0 Experimental
## 6  3  58   Male      0    12      0 Experimental
## 7  3  58   Male     12    30      1      Stopped

Long Format Advantages: - More flexible for complex time patterns - Standard format for survival analysis packages - Can handle irregular time intervals

Long Format Requirements: - tstart and tstop variables for time intervals - Status = 1 only in final interval if event occurs - Time-dependent variables change between rows

Using Time-Dependent Covariates

Basic Wide Format Analysis

library(ClinicoPath)

# Load example wide format data
load("test_wide_time_dependent.rda")

result <- multisurvival(
  data = test_wide_time_dependent,
  elapsedtime = "time",
  outcome = "status", 
  outcomeLevel = "1",
  explanatory = c("sex", "stage"),
  contexpl = "age",
  
  # Time-dependent covariate options
  use_time_dependent = TRUE,
  td_format = "wide",
  time_dep_vars = c("treatment_baseline"),  # Base variable name
  change_times = "6, 12, 18",               # When changes occur
  td_suffix_pattern = "_t{time}",           # Naming pattern
  
  timetypeoutput = "months"
)

Basic Long Format Analysis

# Load example long format data
load("test_long_time_dependent.rda")

result <- multisurvival(
  data = test_long_time_dependent,
  
  # No elapsedtime needed - using tstart/tstop
  outcome = "status",
  outcomeLevel = "1", 
  explanatory = c("sex", "stage"),
  contexpl = "age",
  
  # Time-dependent covariate options
  use_time_dependent = TRUE,
  td_format = "long", 
  start_time_var = "tstart",
  stop_time_var = "tstop",
  time_dep_vars = c("treatment"),  # Time-varying variable
  
  timetypeoutput = "months"
)

Advanced Examples

Multiple Time-Dependent Variables

# Wide format with multiple time-dependent variables
result <- multisurvival(
  data = clinical_data,
  elapsedtime = "followup_months",
  outcome = "event_status",
  outcomeLevel = "Event",
  explanatory = c("sex", "initial_stage"),
  contexpl = "baseline_age",
  
  # Multiple time-dependent variables
  use_time_dependent = TRUE,
  td_format = "wide",
  time_dep_vars = c("treatment_baseline", "ps_baseline"),  # Multiple variables
  change_times = "3, 6, 12, 18",           # More frequent assessments
  td_suffix_pattern = "_month{time}",       # Different naming pattern
  
  # Additional analysis options
  calculateRiskScore = TRUE,
  numRiskGroups = "three",
  hr = TRUE
)

Combining Time-Dependent Covariates with Other Features

# Complex analysis with multiple advanced features
result <- multisurvival(
  data = oncology_data,
  elapsedtime = "survival_months", 
  outcome = "vital_status",
  outcomeLevel = "Dead",
  explanatory = c("histology", "grade"),
  contexpl = c("age_at_diagnosis", "tumor_size"),
  
  # Time-dependent covariates
  use_time_dependent = TRUE,
  td_format = "wide",
  time_dep_vars = c("treatment_baseline", "response_baseline"),
  change_times = "6, 12, 24",
  td_suffix_pattern = "_m{time}",
  
  # Frailty model for hospital clustering
  use_frailty = TRUE,
  frailty_var = "treatment_center",
  frailty_distribution = "gamma",
  
  # Splines for non-proportional hazards
  use_splines = TRUE,
  spline_vars = "age_at_diagnosis",
  spline_df = 3,
  spline_type = "pspline",
  
  # Model selection
  use_modelSelection = TRUE,
  modelSelection = "backward",
  selectionCriteria = "aic",
  
  # Risk stratification
  calculateRiskScore = TRUE,
  numRiskGroups = "four",
  plotRiskGroups = TRUE
)

Data Preparation Guidelines

Converting Long to Wide Format

# Example conversion from long to wide format
library(dplyr)
library(tidyr)

# Starting with long format data
long_format <- data.frame(
  patient_id = c(rep(1, 3), rep(2, 2), rep(3, 4)),
  visit_month = c(0, 6, 12, 0, 6, 0, 6, 12, 18),
  treatment = c("A", "A", "B", "A", "B", "A", "A", "A", "B"),
  performance_status = c(0, 1, 1, 0, 0, 0, 1, 2, 2)
)

# Convert to wide format
wide_format <- long_format %>%
  pivot_wider(
    id_cols = patient_id,
    names_from = visit_month,
    values_from = c(treatment, performance_status),
    names_sep = "_t"
  ) %>%
  # Rename baseline variables
  rename(
    treatment_baseline = treatment_t0,
    ps_baseline = performance_status_t0
  )

Converting Wide to Long Format

# Example conversion from wide to long format
wide_data <- data.frame(
  id = 1:100,
  age = rnorm(100, 65, 10),
  sex = factor(sample(c("M", "F"), 100, replace = TRUE)),
  survival_time = rexp(100, 0.01),
  status = rbinom(100, 1, 0.3),
  treatment_baseline = factor(sample(c("A", "B"), 100, replace = TRUE)),
  treatment_t6 = factor(sample(c("A", "B", "C"), 100, replace = TRUE)),
  treatment_t12 = factor(sample(c("A", "B", "C", "Stop"), 100, replace = TRUE))
)

# This conversion would typically be done by the multisurvival function
# when td_format = "wide" is specified

Clinical Applications

Cancer Treatment Switching

Time-dependent covariates are particularly useful in oncology:

# Analyze impact of treatment switching in cancer patients
cancer_analysis <- multisurvival(
  data = cancer_cohort,
  elapsedtime = "overall_survival_months",
  outcome = "death_status", 
  outcomeLevel = "Dead",
  explanatory = c("cancer_type", "stage_at_diagnosis"),
  contexpl = c("age_at_diagnosis", "baseline_performance_status"),
  
  # Treatment changes over time
  use_time_dependent = TRUE,
  td_format = "wide",
  time_dep_vars = c("primary_treatment_baseline"),
  change_times = "3, 6, 12, 18, 24",  # Quarterly assessments
  td_suffix_pattern = "_quarter{time}",
  
  # Account for treatment center effects
  use_frailty = TRUE,
  frailty_var = "treatment_center",
  
  # Test proportional hazards assumption
  ph_cox = TRUE,
  
  # Generate comprehensive outputs
  hr = TRUE,
  calculateRiskScore = TRUE,
  person_time = TRUE
)

Cardiovascular Risk Factors

# Analyze changing cardiovascular risk factors
cv_analysis <- multisurvival(
  data = cardiovascular_study,
  tint = TRUE,
  dxdate = "enrollment_date",
  fudate = "last_contact_date",
  timetypedata = "ymd",
  timetypeoutput = "years",
  outcome = "cv_event",
  outcomeLevel = "Yes",
  explanatory = c("gender", "diabetes_baseline"),
  contexpl = c("baseline_age", "baseline_bmi"),
  
  # Time-varying medication and lab values
  use_time_dependent = TRUE,
  td_format = "wide", 
  time_dep_vars = c("statin_use_baseline", "bp_medication_baseline"),
  change_times = "0.5, 1, 2, 3, 4, 5",  # Annual visits
  td_suffix_pattern = "_year{time}",
  
  # Account for clinic clustering
  use_frailty = TRUE,
  frailty_var = "clinic_id",
  frailty_distribution = "gamma"
)

Interpretation Guidelines

Understanding Time-Dependent Effects

When interpreting results with time-dependent covariates:

Hazard Ratios: Represent the instantaneous risk at any given time, accounting for the current value of time-dependent variables.
Model Fit: Time-dependent models often fit better than static models but require more data and assumptions.
Causality: Time-dependent covariates help address time-varying confounding but don’t guarantee causal interpretation.

Common Pitfalls

Immortal Time Bias: Ensure time-dependent variables are properly aligned with risk periods.
Missing Data: Handle missing time-dependent measurements appropriately.
Measurement Timing: Consider whether variable changes are known at the time of measurement or retrospectively.

Technical Considerations

Wide Format Requirements

Consistent naming pattern for time-dependent variables
Complete specification of change times
Baseline values for all time-dependent variables

Long Format Requirements

Proper tstart/tstop intervals with no gaps
Status = 1 only in final interval for events
Consistent covariate values within intervals

Performance Considerations

Wide format is generally faster for simple patterns
Long format is more flexible but computationally intensive
Consider data size when choosing format

Advanced Features Integration

Time-dependent covariates work seamlessly with other advanced features:

# Comprehensive analysis combining all advanced features
comprehensive_analysis <- multisurvival(
  data = complex_dataset,
  elapsedtime = "time_to_event",
  outcome = "event_indicator",
  outcomeLevel = "1",
  explanatory = c("treatment_arm", "biomarker_status"),
  contexpl = c("age", "baseline_score"),
  
  # Time-dependent covariates
  use_time_dependent = TRUE,
  td_format = "wide",
  time_dep_vars = c("drug_dose_baseline", "toxicity_grade_baseline"),
  change_times = "4, 8, 12, 16, 20, 24",
  
  # Frailty for center effects
  use_frailty = TRUE,
  frailty_var = "study_center",
  frailty_distribution = "gamma",
  
  # Splines for non-linear age effects
  use_splines = TRUE,
  spline_vars = "age",
  spline_df = 4,
  spline_type = "ns",
  
  # Stratification for non-proportional hazards
  use_stratify = TRUE,
  stratvar = "biomarker_status",
  
  # Model selection
  use_modelSelection = TRUE,
  modelSelection = "both",
  selectionCriteria = "aic",
  
  # Risk assessment
  calculateRiskScore = TRUE,
  numRiskGroups = "four",
  plotRiskGroups = TRUE,
  
  # Comprehensive outputs
  hr = TRUE,
  km = TRUE,
  ac = TRUE,
  adjexplanatory = "treatment_arm",
  person_time = TRUE,
  ph_cox = TRUE,
  showNomogram = TRUE
)

Conclusion

Time-dependent covariates in multisurvival provide a powerful tool for analyzing survival data where important variables change over time. The support for both wide and long data formats makes this functionality accessible to researchers working with different data structures.

Key benefits include:

Realistic modeling of clinical scenarios where treatments and patient status change
Flexible data input supporting both wide and long formats
Integration with other advanced survival analysis features
Comprehensive output including plots, tables, and model diagnostics

For most clinical applications, wide format provides the most intuitive approach, while long format offers maximum flexibility for complex time patterns.

ClinicoPath Team

2025-07-13