Lung Transplantation: Parametric Weibull Survival Model and Cost-Utility Evaluation

HEOR case study using a Weibull survival model and cost-utility framework based on a synthetic lung transplant cohort.

Overview

Since the first heart–lung and lung transplants performed in France in the 1980s, over 3,700 procedures have been reported nationwide. The main indications for transplantation include cystic fibrosis, COPD, pulmonary fibrosis, and pulmonary arterial hypertension. Despite improved allocation systems and reduced waiting list mortality, long-term survival remains limited—approximately 70% at one year and below 50% at five years. While lung transplantation has proven effective in improving survival and quality of life, no cost-utility evaluation has been conducted in France. This projet therefore aims to assess the cost-effectiveness of lung and heart–lung transplantation compared with medical management.

Methodology Framework

Data sources

The study was based on data collected at Foch Hospital (Suresnes, France), a national reference center and pioneer in lung transplantation. The institutional database includes all patients followed for lung or heart–lung transplantation since 1989. For this analysis, only records with complete demographic and clinical information (date of birth, hospital identifier, transplant date) were retained.

The dataset comprised:

• Sociodemographic and occupational variables,

• Clinical and paraclinical data,

• Hospitalization and follow-up information

• Quality-of-life assessments using the Nottingham Health Profile (NHP) questionnaire.

Data summary

Between 1989 and January 2015, 631 patients were recorded in the Foch Hospital cohort, including 571 transplanted patients (90.5%) and 60 awaiting transplantation (9.5%). The sex ratio was balanced (≈50% female), with a mean age of 38.8 years at listing.

The primary indications for transplantation were:

• Cystic fibrosis (50%),

• Emphysema/COPD (21%),

• Interstitial lung disease (15%), and

• Other etiologies (12%).

As of May 2015, 42.5% of patients had died, and 19 patients (3%) underwent a second transplantation.

Quality-of-life data were available for 302 transplanted patients (pre- and post-transplant), assessed through the NHP dimensions: pain, mobility, sleep, energy, emotions, and social isolation. These scores were converted to EQ-5D utilities using a validated mapping algorithm to enable QALY computation for cost-utility analysis.

Methodology

A retrospective cohort design was used to evaluate the cost-utility of lung and heart–lung transplantation compared with continued medical management. The analysis integrated survival modeling, utility estimation, and cost evaluation from the French National Health Insurance (Assurance Maladie) perspective.

Study Groups

• Transplantation group (TP): All transplanted patients since 2005 with at least one pre- and post-transplant quality-of-life measure. Mean post-transplant survival was estimated using a parametric Weibull model (time origin = transplantation date).

• Medical management group: Because randomization is ethically infeasible and few patients die untransplanted, a direct control group could not be constructed.

Instead, pseudo-controls were generated using literature-derived hazard ratios to estimate counterfactual survival in the absence of transplantation.

Costing perspective

Costs were estimated from the payer perspective (Assurance Maladie) and included:

Hospital costs based on Diagnosis-Related Group [GHS/GHM] tariffs for transplantation),

Ambulatory care and potential post-acute care (SSR/HAD), and

Expert-based estimates or complementary data from Foch Hospital when necessary.

The final cost-utility analysis compared transplantation with medical management and expressed results as an Incremental Cost-Effectiveness Ratio (ICER), reported in cost per QALY gained.

Results Summary

Descriptive Overview

The synthetic cohort reproduced the demographic and clinical characteristics of the original Foch Hospital population.
The mean age at listing was 38.8 years (range 11–72), with an equal sex distribution (≈50% female).
Among 631 patients, 571 (90.5%) underwent transplantation and 60 (9.5%) remained on the waiting list.
The main indications for transplantation were cystic fibrosis (50%), COPD/emphysema (21%), and interstitial lung disease (15%).

df %>%
  summarize(
    mean_age = mean(AGE),
    sd_age = sd(AGE),
    prop_female = mean(SEX == 0),
    prop_transplanted = mean(TRANSPLANTED == 1)
  )

Survival Analysis

A parametric Weibull survival model was fitted to censored post-transplant data.

Parameter	Estimate	95% CI
Shape (k)	1.36	1.03 – 1.78
Scale (λ)	1670 days	1320 – 2010

The hazard function indicated an increasing risk of death over time (k > 1).

Predicted survival probabilities were:

Time since TP	Survival Probability (S(t))
1 year	0.90
2 years	0.76
3 years	0.61
4 years	0.47
5 years	0.34

The median survival was approximately 4.2 years, consistent with national registry data.

Quality of Life (QoL)

Quality of life, assessed with the Nottingham Health Profile (NHP) and mapped to EQ-5D utilities, showed clear improvement after transplantation:

Utility Measure	Mean (Pre-TP)	Mean (Post-TP)
EQ-5D Utility	0.30	0.60
Δ Utility (gain)	—	+0.30

Cost–Utility Analysis

From the Assurance Maladie (payer) perspective:

Parameter	Value
Time horizon	10 years
Discount rate	3%
Hazard ratio (non-TP vs TP)	1.8
Incremental QALYs	+1.2
Incremental Cost	€120,000
ICER	€100,000 per QALY gained

Although the ICER exceeded the typical French threshold (€50,000/QALY), the result reflects the high initial cost of transplantation balanced by substantial gains in survival and quality of life.

Sensitivity Analyses

• One-way sensitivity identified the hazard ratio and post-transplant utility as the most influential parameters on the ICER.

• Probabilistic Sensitivity Analysis (PSA) showed that transplantation was cost-effective in ~40% of simulations at a willingness-to-pay threshold of €100,000/QALY.

Key Insights

• The Weibull model accurately described post-transplant survival.

• Lung transplantation resulted in substantial QALY gains despite high upfront costs.

• The workflow demonstrates a complete HEOR pipeline: survival modeling, utility mapping, and cost-effectiveness evaluation, all with synthetic, ethically shareable data.

NoteEthical statement

The dataset used in this report is synthetic and was generated to replicate the structure and statistical characteristics of the Foch Hospital lung transplantation cohort.
No real patient information is included.
The study and analyses are presented for educational and methodological purposes only.

Ousmane Diallo, MPH-PhD – Biostatistician, Data Scientist & Epidemiologist based in Chicago, Illinois, USA. Specializing in SAS programming, CDISC standards, and real-world evidence for clinical research.