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Person-Time Analysis in jsurvival Module

ClinicoPath Development Team

2025-06-30

Source: vignettes/jsurvival-11-person-time-analysis-legacy.Rmd
jsurvival-11-person-time-analysis-legacy.Rmd

Introduction

Person-time analysis is a fundamental concept in epidemiology and survival analysis that accounts for the varying observation periods of study participants. The jsurvival module in ClinicoPath provides comprehensive person-time calculations and incidence rate analysis across its survival analysis functions.

What is Person-Time?

Person-time represents the total observation time contributed by all participants in a study while being at risk for the event of interest. Unlike simple participant counts, person-time captures both the number of subjects and their observation duration, providing accurate denominators for rate calculations.

Key Concepts

  • Total Person-Time: Sum of all individual follow-up periods
  • Incidence Rate: Number of events ÷ Total person-time
  • Time Units: Typically expressed as person-days, person-months, or person-years
  • Censoring: Properly accounts for participants leaving the study early
  • Varying Follow-up: Handles different observation periods for each participant

Why Person-Time Matters

  1. Accurate Rate Calculations: Provides proper denominators for incidence rates
  2. Comparison Across Studies: Enables valid comparisons between populations with different follow-up patterns
  3. Adjustment for Time: Accounts for varying exposure periods in survival analysis
  4. Kaplan-Meier Foundation: Forms the basis for survival curve estimation
  5. Cox Model Integration: Essential for hazard ratio calculations

Person-Time in jsurvival Modules

The ClinicoPath jsurvival module includes person-time analysis in four key functions:

1. Time Interval Calculator

Purpose: Calculate time intervals that form the basis of person-time analysis

Features: - Date-based time calculations with multiple formats - Person-time concept explanation - Total person-time calculation - Landmark analysis support

Usage:

Analyses → Survival → Data Preparation → Time Interval Calculator

Key Outputs: - Time interval summary with total person-time - Educational information about person-time concepts - Calculated time variables for further analysis

2. Single Arm Survival

Purpose: Analyze survival for a single cohort with person-time metrics

Features: - Overall incidence rate calculation - Time-stratified person-time analysis - Confidence intervals using Poisson exact methods - Rate multiplier options (per 100, 1000 person-time units)

Usage:

Analyses → Survival → ClinicoPath Survival → Single Arm Survival
Enable: "Calculate Person-Time Metrics"

Key Outputs: - Person-time analysis table with rates and confidence intervals - Time-interval stratified analysis - Summary with interpretation

3. Survival Analysis (Univariate)

Purpose: Compare survival between groups with group-specific person-time analysis

Features: - Group-specific person-time calculations - Incidence rate comparisons between groups - Time-stratified analysis by group - Rate ratio calculations

Usage:

Analyses → Survival → ClinicoPath Survival → Survival Analysis
Enable: "Calculate Person-Time Metrics"

Key Outputs: - Person-time table by group - Group-specific incidence rates - Confidence intervals for each group - Overall and stratified summaries

4. Multivariable Survival

Purpose: Analyze survival with multiple covariates and person-time adjustment

Features: - Overall person-time with covariate stratification - Adjusted incidence rates - Person-time summary with multiple predictors - Integration with Cox model results

Usage:

Analyses → Survival → ClinicoPath Survival → Multivariable Survival Analysis
Enable: "Calculate Person-Time Metrics"

Key Outputs: - Overall person-time summary - Stratified person-time by covariates - Incidence rates adjusted for multiple factors

Getting Started with Person-Time Analysis

Step 1: Prepare Your Data

Your dataset should include: - Time variable: Follow-up duration (numeric) - Event variable: Event indicator (0/1 or factor) - Group variables: For comparisons (optional) - Date variables: For time calculation (optional)

Example data structure:

patient_id | followup_months | event | treatment_group | diagnosis_date | last_contact
PT0001     | 24.5           | 1     | Standard       | 2020-01-15     | 2022-01-30
PT0002     | 36.2           | 0     | Experimental   | 2020-02-10     | 2023-02-15

Step 2: Choose the Appropriate Analysis

Time Interval Calculator: If you need to calculate follow-up times from dates - Input: Start and end dates - Output: Time intervals and person-time concepts

Single Arm Survival: For overall cohort analysis - Input: Time, event variables - Output: Overall incidence rates and time-stratified analysis

Survival Analysis: For group comparisons - Input: Time, event, grouping variables - Output: Group-specific rates and comparisons

Multivariable Survival: For adjusted analysis - Input: Time, event, multiple covariates - Output: Adjusted rates and Cox model integration

Step 3: Configure Person-Time Options

  1. Enable person-time analysis: Check “Calculate Person-Time Metrics”
  2. Set time intervals: Specify intervals for stratified analysis (e.g., “12, 36, 60”)
  3. Choose rate multiplier: Select 100 or 1000 for rate presentation
  4. Configure time units: Ensure consistent units throughout

Step 4: Interpret Results

Person-Time Table Columns

  • Time Interval: Period analyzed (e.g., 0-12 months, 12-36 months)
  • Events: Number of events in the interval
  • Person-Time: Total observation time in the interval
  • Incidence Rate: Events per person-time unit
  • 95% CI: Confidence interval for the rate (Poisson exact)

Key Metrics to Report

  1. Total Person-Time: Overall observation time
  2. Overall Incidence Rate: Events per 100 person-time units
  3. Time-Specific Rates: Rates in different follow-up periods
  4. Group Comparisons: Rate differences between groups
  5. Confidence Intervals: Precision of rate estimates

Clinical Applications

Example 1: Cancer Survival Study

Scenario: Comparing survival between two treatment groups

Analysis Setup: - Module: Survival Analysis - Variables: treatment_group, survival_months, death_status - Enable: Person-time metrics

Expected Results: - Person-time by treatment group - Group-specific incidence rates - Rate ratios between treatments - Time-stratified analysis

Interpretation:

Standard Treatment: 45 deaths in 2,400 person-months (1.88 per 100 person-months)
New Treatment: 32 deaths in 2,200 person-months (1.45 per 100 person-months)
Rate Ratio: 0.77 (23% reduction in death rate)

Example 2: Epidemiological Cohort Study

Scenario: Disease incidence in exposed vs. unexposed populations

Analysis Setup: - Module: Survival Analysis
- Variables: exposure_status, followup_years, disease_onset - Enable: Person-time metrics

Expected Results: - Exposure-specific person-time - Incidence rates by exposure - Time trends in incidence - Rate differences and ratios

Interpretation:

Exposed Group: 15 cases in 850 person-years (1.76 per 100 person-years)
Unexposed Group: 8 cases in 920 person-years (0.87 per 100 person-years)
Rate Difference: 0.89 per 100 person-years
Relative Risk: 2.03

Example 3: Drug Safety Monitoring

Scenario: Adverse event rates during drug therapy

Analysis Setup: - Module: Single Arm Survival - Variables: treatment_duration, adverse_event - Enable: Person-time metrics with time stratification

Expected Results: - Overall adverse event rate - Time-stratified rates (early vs. late) - Confidence intervals for safety assessment

Interpretation:

Overall Rate: 12 events in 1,500 person-months (0.80 per 100 person-months)
0-6 months: 8 events in 600 person-months (1.33 per 100 person-months)
6+ months: 4 events in 900 person-months (0.44 per 100 person-months)
Conclusion: Higher event rate in early treatment period

Advanced Features

Time-Stratified Analysis

Person-time analysis can be stratified by time intervals to detect: - Changing hazards over time - Early vs. late event patterns - Treatment effect modifications - Time-dependent risk factors

Setup: Specify intervals in “Time Interval Stratification” option

Example: "6, 12, 24" creates intervals: 0-6, 6-12, 12-24, 24+ months

Rate Multipliers

Choose appropriate multipliers based on event frequency: - Rate per 100 person-time: Common for moderate event rates - Rate per 1000 person-time: Useful for rare events - Rate per 10,000 person-time: For very rare events

Confidence Intervals

Person-time rates use Poisson exact confidence intervals: - Exact method: Based on Poisson distribution of event counts - Conservative approach: Provides accurate coverage - Asymmetric intervals: Reflects the nature of count data

Integration with Survival Analysis

Person-time analysis complements traditional survival methods: - Kaplan-Meier curves: Show survival probability over time - Cox regression: Models hazard rates (instantaneous person-time rates) - Log-rank tests: Compare survival distributions - Person-time rates: Provide absolute risk measures

Quality Assurance

Data Validation

Before person-time analysis:

  1. Check time variables: Ensure positive, numeric values
  2. Validate event coding: Confirm 0/1 or appropriate factor levels
  3. Review missingness: Address missing time or event data
  4. Assess outliers: Investigate extremely long or short follow-up times

Results Interpretation

When reviewing person-time results:

  1. Biological plausibility: Do rates make clinical sense?
  2. Confidence intervals: Are they appropriately wide for the data?
  3. Time trends: Do time-stratified rates show expected patterns?
  4. Group differences: Are rate differences clinically meaningful?

Common Issues

Issue 1: Zero Events in Intervals

Problem: Some time intervals have no events Solution: Consider combining intervals or using exact Poisson methods

Issue 2: Very Unequal Follow-up

Problem: Large variation in follow-up times Solution: Use time-stratified analysis and report median follow-up

Issue 3: Competing Risks

Problem: Multiple event types affecting person-time Solution: Use competing risks analysis with event-specific person-time

Reporting Person-Time Results

Methods Section 

Person-time analysis was performed to calculate incidence rates accounting 
for varying follow-up periods. Total person-time was calculated as the sum 
of individual follow-up periods from [entry criteria] to [endpoint definition]. 
Incidence rates were calculated as the number of events divided by person-time 
at risk, expressed per [time unit]. Confidence intervals were calculated using 
Poisson exact methods. Time-stratified analysis was performed using intervals 
of [specify intervals] to assess for time-varying hazards.

Results Section 

A total of [N] participants contributed [total person-time] [time units] of 
follow-up (median [median], range [range]). [Number] events occurred during 
the observation period, yielding an overall incidence rate of [rate] per 
[multiplier] [time units] (95% CI: [CI]). Incidence rates differed significantly 
between [groups]: [group 1] [rate 1] vs. [group 2] [rate 2] per [multiplier] 
[time units] (rate ratio [RR], 95% CI: [CI], p=[p-value]).

Tables and Figures

Table: Person-Time Analysis Results 

Group           N    Events   Person-Time   Rate/100 PT   95% CI
Control        150    25       4,200        0.60         0.39-0.88
Treatment      145    18       4,150        0.43         0.26-0.68
Total          295    43       8,350        0.51         0.37-0.69

Figure: Incidence Rates by Time Period

  • Forest plot showing rates and confidence intervals
  • Time-stratified analysis results
  • Group comparisons over time

Conclusion

Person-time analysis is essential for proper epidemiological and survival analysis. The jsurvival module provides comprehensive person-time functionality that:

  1. Educates users about person-time concepts
  2. Calculates accurate rates with appropriate confidence intervals
  3. Enables group comparisons with rate ratios and differences
  4. Supports time-stratified analysis for detecting temporal patterns
  5. Integrates with survival methods for comprehensive analysis

By incorporating person-time analysis into your survival studies, you can: - Provide more accurate and interpretable results - Enable valid comparisons across studies and populations - Better understand temporal patterns in your data - Meet epidemiological standards for rate-based analysis

Further Resources

  • ClinicoPath Documentation: Complete module reference
  • Epidemiological Methods: Texts on person-time analysis
  • Survival Analysis: Integration with traditional survival methods
  • Statistical Software: Comparison with other implementations

For questions about person-time analysis in ClinicoPath, please refer to the module documentation or contact the development team.