Bayesian Belief Network
TransPlan offers Bayesian Belief Network inference as an alternative to Monte Carlo simulation. This approach uses exact probabilistic reasoning on a graphical model, providing faster query times and transparent causal assumptions.
The Problem with Independence
The standard Monte Carlo engine treats all factors as multiplicatively independent. Blood type multiplier times city factor times urgency multiplier times cause-of-death multiplier. But this misses important interactions.
The reality: the effect of blood type on wait time depends on regional donor supply. O-negative patients in a low-O-donor region face superlinearly disadvantaged outcomes. Age-organ mortality interactions vary dramatically across organs: heart mortality is far more age-sensitive than kidney. High-wait cities tend to have correlated high delisting rates, not independent ones.
A Bayesian Belief Network captures these causal dependencies as a directed acyclic graph with conditional probability tables.
Architecture
The TransPlan BBN is a 12-node DAG with 19 edges, built from existing SRTR data without introducing new parameters.
Nodes
- Evidence nodes (observed): Organ, BloodType, Age, Urgency, Region
- Intermediate nodes (latent): DonorSupply, WaitTimeCategory, GraftSurvival, MortalityRisk, DelistingRisk
- Outcome nodes (queried): TransplantOutcome (4 competing states)
Conditional Probability Tables (CPTs)
Each CPT is derived from:
- SRTR program-specific reports (organ-specific base rates)
- State-level donor registration data
- Regional cause-of-death distributions
- Hospital volume and center-specific survival outcomes
All CPTs are deterministic functions of existing public data — no free parameters are fitted to outcomes. That is a deliberate design property (the network is auditable end to end), not a claim that the numbers are arbitrary: the CompetingOutcome CPT is grounded in observed SRTR Table B7 rates rather than hand-set constants (#206), and the pediatric age group's mortality multipliers are measured per organ from SRTR pediatric waitlist data (#335).
Being deterministic also means the network is not learned: it cannot discover structure the CPT construction does not encode.
Query-Time Inference
When a patient profile is provided:
- Evidence is set on the five observable nodes (organ, blood type, age, urgency, region)
- VariableElimination (exact inference) computes marginal probabilities for all outcome nodes
- The network iterates over each of the 248 centers with region as the only changing evidence node
- Results are identical across multiple runs (deterministic)
Performance
A complete query across all 248 centers takes approximately 200-400ms on a typical laptop, compared to 2+ seconds for Monte Carlo. Results are not cached; inference is real-time.
Comparing MC and BBN
| Aspect | Monte Carlo | Bayesian Network |
|---|---|---|
| Query time | ~2000ms | ~300ms |
| Uncertainty | Sampling error (95% CI) | Deterministic (no sampling variance) |
| Interpretability | Black box simulation | Transparent DAG structure |
| Interactions | Multiplicative independence | Explicit conditional dependencies |
| Validation | Cross-validated rankings | Cross-validated with MC |
Cross-Validation Results
BBN and Monte Carlo were evaluated on 100 representative patient profiles across all organs. Spearman rank correlation between center rankings: 0.52 to 0.71 depending on organ. Mean absolute difference in 24-month transplant probability: 3 to 7 percentage points. Directional consistency on blood type, organ, and urgency effects: 100% agreement.
Access
Use the /simulate endpoint with ?inference_mode=bayesian to run BBN inference. The frontend includes a dropdown to select the inference engine. Results are returned in the same schema as Monte Carlo.
Limitations
The BBN assumes conditional independence between organ outcomes and causes-of-death given the intermediate nodes. In reality, some regional correlations exist. These are conservative assumptions that lean toward underestimating interactions.
The claim that the model "does not learn from regional variation" is no longer accurate. Evidence reaches the network at center granularity (248 regions in full mode), the competing-outcome split is grounded in each center's observed Table B7 rates, and patient factors now modulate that split rather than every patient at a center receiving the same average (#238). What remains true is the residual in L-072: the competing-risk split is still a center-level quantity modulated by patient factors, not a genuinely patient-specific estimate.
The competing-risk probabilities from the BBN do not have frequentist confidence intervals in the sampling sense — the network is deterministic, so repeated runs give identical answers. The interval shown instead reflects data uncertainty: a binomial standard error on the center's observed cohort, so a center with 20 observed candidates gets a visibly wider band than one with 400 (#226).
Those intervals were found to be under-covered against held-out releases and are now inflated by a measured factor rather than reported raw (#311). An interval that says 95% should contain the truth 95% of the time; before that correction it did not.