Competing Risks
A transplant patient waiting on the list faces multiple possible outcomes, not just "transplant or keep waiting." TransPlan models three competing events.
The Problem
Standard survival analysis asks: "How long until the event?" But a transplant patient can experience one of three distinct outcomes. The first is transplant, the desired outcome. The second is mortality, specifically death while on the waiting list. The third is delisting, which means removal from the list due to clinical deterioration, improvement, or patient choice.
These are competing risks: experiencing one event precludes the others. A standard Kaplan-Meier estimator would treat mortality and delisting as censored observations, which overestimates transplant probability. Competing risks analysis correctly partitions the probability space.
Model
At 24 months, the four mutually exclusive outcomes must sum to 1.0:
P(transplant) + P(mortality) + P(delisting) + P(still waiting) = 1.0
Mortality Model
Mortality while on the waiting list is modeled as an exponential process:
P(mortality by t) = 1 - exp(-λ_mortality × t)
where λ_mortality is estimated from SRTR Table B7 (waiting list mortality rates) per organ and city.
Delisting Model
Delisting (removal for reasons other than transplant or death) is similarly modeled:
P(delisting by t) = 1 - exp(-λ_delisting × t)
λ_delisting is estimated from SRTR Table B7 (removal rates for "too sick," "condition improved," "patient decision").
Integration with Monte Carlo
During each Monte Carlo iteration, all three processes compete. The engine samples a transplant time t_tx from the log-normal wait distribution, a mortality time t_mort from the exponential mortality distribution, and a delisting time t_delist from the exponential delisting distribution. The outcome is whichever event occurs first, specifically min(t_tx, t_mort, t_delist). If all three times exceed the 36-month horizon, the outcome is recorded as "still waiting."
Output
The competing risks breakdown appears as a stacked horizontal bar in the app. Green represents transplant, red represents mortality while waiting, orange represents delisting, and gray represents still waiting at 24 months.
In the API response, the breakdown is returned as:
"competing_risks": {
"p_transplant": 0.61,
"p_mortality": 0.08,
"p_delisting": 0.11,
"p_still_waiting": 0.20
}
Organ-Specific Notes
| Organ | Mortality Risk | Notes |
|---|---|---|
| Heart | Highest | Status 1A patients have very high short-term mortality risk |
| Liver | High | MELD >25 patients have significant 6-month mortality |
| Lung | High | LAS incorporates mortality risk directly |
| Kidney | Lowest | Dialysis provides a survival bridge |
| Pancreas | Low | Rare; primarily type 1 diabetics with kidney disease |
| Intestine | Moderate | Very small candidate pool; significant morbidity risk |
Interactive: Competing Risk Rates by Organ
Annual mortality and delisting rates vary substantially across organs. Heart and liver patients face the highest mortality risk while waiting, while kidney patients benefit from dialysis as a survival bridge.
Annual Competing Risk Rates by Organ (National Average)
| Annual Mortality | Annual Delisting | Combined Annual Risk | |
|---|---|---|---|
| Kidney | 3.3% | 3.4% | 6.7% |
| Liver | 15.2% | 12.1% | 27.3% |
| Heart | 17.1% | 13.1% | 30.2% |
| Lung | 14.5% | 9.8% | 24.3% |
| Pancreas | 4.2% | 6.5% | 10.7% |
| Intestine | 8.9% | 10.2% | 19.1% |
Data Sources
Mortality and delisting rates are derived from SRTR Program-Specific Reports (Table B7: Waiting List Removal Reasons). These are parsed annually from SRTR Excel PSR files via scripts/parse-srtr-reports.py and stored in data/competing-risks.json.
Limitations
The exponential model assumes constant hazard (memoryless), whereas real mortality risk increases with time on the list. City-level variation in mortality and delisting rates is partially captured, but center-specific practices are not modeled. Interaction effects between clinical score trajectories (for example, rising MELD) and delisting or mortality are also not modeled. Data is updated biannually via SRTR PSR downloads.
See Wait Time Distributions for how the transplant wait model is calibrated.