Fractional polynomial network meta-analysis of survival data
This method compares different treatments over time by modeling how the risk of an event (like death) changes, instead of assuming the risk stays constant. It's useful when treatments have different effects early versus late in time, which standard methods can't capture well.
At a glance
Use when
Comparing treatments with non-proportional hazards (e.g., survival curves cross), conducting cost-effectiveness analysis requiring accurate survival extrapolation, or when standard hazard ratio assumptions are implausible
Avoid when
Only simple, constant hazard ratio effects are of interest; when only hazard ratios (without survival curves) are available; or when data are too sparse to fit hazard functions
Inputs
Aggregate survival data (e.g., Kaplan-Meier curves, reported summary statistics) and trial-level hazard function estimates modeled via fractional polynomials
Outputs
Synthesized hazard functions for each treatment, estimated differences in survival outcomes, and treatment rankings based on time-varying effects
How it works
This method extends network meta-analysis for aggregate survival data by replacing the constant hazard ratio assumption with a multi-parameter representation of treatment effects using fractional polynomials. It models hazard functions from randomized trials with fractional polynomials, synthesizes differences in polynomial parameters across trials, and enables indirect comparisons even when proportional hazards do not hold.
- HTA domains
- Clinical Effectiveness, Costs & Economic Evaluation
- Assumptions
- Hazard functions can be adequately modeled using fractional polynomials of first or second order; trial-level differences in polynomial parameters are estimable and synthesizable across studies
- Strengths
- Does not rely on proportional hazards assumption; allows flexible modeling of time-varying treatment effects; improves fit to observed survival data; enables more accurate cost-effectiveness analyses
- Limitations
- Requires detailed survival data for modeling; increased complexity compared to standard NMA; potential overfitting with higher-order polynomials; limited availability of published survival data in usable form
- Also known as
- Fractional polynomial NMA, FP-NMA of survival data
Questions this answers
- › How do treatment effects on survival differ over time when proportional hazards do not hold?
- › Which treatment has the best long-term survival profile in a network of interventions?
- › How can survival curves be accurately reconstructed from aggregate data without assuming constant hazard ratios?
- › What is the magnitude and shape of the difference in hazard functions between treatments?
- › How can indirect comparisons be made when hazard ratios cross over time?
References & sources
Similar by meaning
- Change-point survival models for relative treatment effect extrapolation
- Two-stage network meta-regression for heterogeneous treatment effects
- Conducting Indirect-Treatment-Comparison and Network-Meta-Analysis Studies
- Three-stage network meta-regression for heterogeneous treatment effects
- Cranmer et al. comparison of partitioned survival analysis and state-transition multi-state modelling (oncology case study)
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