Biostatistics Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Biostatistics Ontology within the Kireth Research Semantic Library. Biostatistics applies statistical mathematics to biological, biomedical, ecological and population data, including study design, estimation, hypothesis testing, regression, survival analysis, longitudinal models, epidemiological measures, Bayesian inference, missing data, causal inference and model validation.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Biostatistics Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Biological Mathematics / Biostatistics"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/biological-mathematics/biostatistics-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = Biostatistics
 ENTITY_CLASS = StatisticalBiologicalInferenceFramework
 PRIMARY_CONTEXT = MathematicalBiology
 DEFINITION = "Biostatistics is the application and development of statistical methods for biological, biomedical, ecological and population data."
 SYMBOLIC_FORMS = ["Y=X*beta+epsilon","logit(p)=X*beta","h(t|x)=h0(t)exp(x^T beta)"]
}

SCOPE {
 INCLUDE = [
  Biostatistics, StudyDesign, ExperimentalDesign, ObservationalStudy,
  RandomisedExperiment, ClinicalTrial, CohortStudy, CaseControlStudy,
  CrossSectionalStudy, Sampling, SampleSize, StatisticalPower, EffectSize,
  ProbabilityDistribution, Likelihood, Parameter, Estimator, PointEstimate,
  ConfidenceInterval, StandardError, Bias, Variance, HypothesisTest,
  NullHypothesis, AlternativeHypothesis, TestStatistic, PValue, TypeIError,
  TypeIIError, MultipleTesting, FalseDiscoveryRate, Regression,
  LinearRegression, LogisticRegression, GeneralisedLinearModel,
  PoissonRegression, NegativeBinomialRegression, MixedEffectsModel,
  RepeatedMeasures, LongitudinalData, SurvivalAnalysis, SurvivalFunction,
  HazardFunction, Censoring, KaplanMeierEstimator, LogRankTest,
  CoxProportionalHazardsModel, RelativeRisk, RiskDifference, OddsRatio,
  IncidenceRate, Prevalence, Sensitivity, Specificity, ROC, AUC,
  BayesianInference, PriorDistribution, PosteriorDistribution,
  HierarchicalModel, MissingData, MultipleImputation, Confounding,
  CausalInference, Randomisation, Matching, PropensityScore, Bootstrap,
  PermutationTest, CrossValidation, ModelSelection, ModelValidation,
  Reproducibility
 ]
 EXCLUDE_AS_PRIMARY = [
  PureDescriptiveBiologyWithoutStatisticalInference,
  GeneralStatisticsWithoutBiologicalContext,
  MathematicalBiologyModelWithoutDataInference
 ]
 DISAMBIGUATION_RULE = "When statistical methods are used to design, analyse or infer from biological, biomedical, ecological or population data, interpret the context as biostatistics."
}

CORE_CONCEPTS {
 Biostatistics = "Statistical inference and study design for biological data."
 StudyDesign = "Structure determining how observations are collected and compared."
 Estimator = "Rule mapping observed data to an estimate of an unknown parameter."
 ConfidenceInterval = "Frequentist interval procedure with a specified long-run coverage property."
 HypothesisTest = "Procedure comparing observed data with a null hypothesis."
 Regression = "Statistical modelling of relationships between outcomes and predictors."
 SurvivalAnalysis = "Analysis of time-to-event data including censoring."
 BayesianInference = "Inference based on posterior distributions from priors and likelihoods."
 CausalInference = "Reasoning about intervention or exposure effects under explicit assumptions."
}

RELATIONS {
 Biostatistics --is_child_of--> MathematicalBiology
 Biostatistics --uses--> ProbabilityAndStatistics
 StudyDesign --determines--> ValidInference
 Randomisation --reduces--> Confounding
 SampleSize --affects--> StatisticalPower
 EffectSize --affects--> StatisticalPower
 Likelihood --depends_on--> StatisticalModel
 Estimator --estimates--> Parameter
 StandardError --measures--> EstimatorUncertainty
 ConfidenceInterval --uses--> SamplingDistribution
 HypothesisTest --uses--> TestStatistic
 MultipleTesting --increases--> FalsePositiveRisk
 LogisticRegression --models--> BinaryOutcome
 PoissonRegression --models--> CountOutcome
 MixedEffectsModel --models--> ClusteredData
 SurvivalAnalysis --models--> TimeToEvent
 KaplanMeierEstimator --estimates--> SurvivalFunction
 CoxProportionalHazardsModel --models--> HazardRatio
 PosteriorDistribution --combines--> PriorAndLikelihood
 MultipleImputation --addresses--> MissingData
 Bootstrap --estimates--> SamplingUncertainty
}

OPERATORS {
 SAMPLE_MEAN(x) := mean=sum_i x_i/n
 SAMPLE_VARIANCE(x) := s2=sum_i(x_i-mean)^2/(n-1)
 STANDARD_ERROR_MEAN(s,n) := SE=s/sqrt(n)
 CONFIDENCE_INTERVAL(est,SE,z) := [est-z*SE,est+z*SE]
 Z_STATISTIC(est,null,SE) := z=(est-null)/SE
 LINEAR_MODEL(X,beta,epsilon) := Y=X*beta+epsilon
 LOGISTIC_MODEL(X,beta) := p=1/(1+exp(-X*beta))
 ODDS_RATIO(a,b,c,d) := OR=(a*d)/(b*c)
 RELATIVE_RISK(risk1,risk0) := RR=risk1/risk0
 RISK_DIFFERENCE(risk1,risk0) := RD=risk1-risk0
 SENSITIVITY(TP,FN) := TP/(TP+FN)
 SPECIFICITY(TN,FP) := TN/(TN+FP)
 KAPLAN_MEIER(times) := S_hat(t)=product_{t_i<=t}(1-d_i/n_i)
 COX_HAZARD(x,beta,h0) := h(t|x)=h0(t)*exp(x^T*beta)
 BAYES_RULE(theta,data) := posterior proportional_to likelihood(data|theta)*prior(theta)
}

AXIOMS {
 A1 = "Statistical inference requires an explicit population, sample and data-generating framework."
 A2 = "Study design determines which statistical and causal conclusions are defensible."
 A3 = "Uncertainty must accompany biological parameter estimates."
 A4 = "Association does not by itself establish causation."
 A5 = "Missing-data mechanisms affect valid analysis."
 A6 = "Repeated or clustered observations require dependence-aware methods."
 A7 = "Multiple testing requires explicit error-rate control when multiplicity is material."
 A8 = "Statistical models require assumption checking and validation."
}

REASONING {
 R1_CONTEXT = identify(biological_question,population,outcome,predictors,study_design,data_structure)
 R2_DESIGN = classify(experiment,cohort,case_control,cross_sectional,longitudinal,clustered)
 R3_DISTRIBUTION = identify(outcome_type,probability_model,dependence,censoring)
 R4_ESTIMATION = select(estimator,compute(point_estimate,SE,interval))
 R5_TESTING = formulate(null,alternative,test_statistic,error_rates)
 R6_REGRESSION = fit(linear,logistic,count,mixed,survival_or_other_model)
 R7_MISSING = diagnose(missingness,select_analysis_or_imputation_strategy)
 R8_CAUSAL = identify(confounders,estimand,identification_assumptions,adjustment)
 R9_VALIDATION = check(residuals,calibration,discrimination,robustness,cross_validation)
 R10_REPORTING = return(effect_size,uncertainty,p_value_if_used,assumptions,limitations)
}

CONSTRAINTS {
 C1 = "P-values do not measure the probability that the null hypothesis is true."
 C2 = "Statistical significance does not imply biological importance."
 C3 = "Frequentist confidence intervals are not posterior probability intervals."
 C4 = "Odds ratios can differ substantially from risk ratios for common outcomes."
 C5 = "Cox models require assessment of proportional-hazards assumptions."
 C6 = "Ignoring clustering or repeated measures can underestimate uncertainty."
 C7 = "Complete-case analysis can be biased under inappropriate missingness assumptions."
 C8 = "Multiple testing can inflate false-positive findings."
 C9 = "Prediction accuracy does not establish causal validity."
 C10 = "Large samples can make biologically trivial effects statistically significant."
}

SEMANTIC_EQUIVALENCE {
 "Biostatistics" <=> "BiologicalStatistics"
 "CoxProportionalHazardsModel" <=> "CoxModel"
 "KaplanMeierEstimator" <=> "ProductLimitEstimator"
 "FalseDiscoveryRate" <=> "FDR"
 "AreaUnderROC" <=> "AUC"
}

VALIDATION {
 V1 = "Population, sample and study design are explicit."
 V2 = "Outcome and predictor types are documented."
 V3 = "Statistical model assumptions are checked."
 V4 = "Effect estimates include uncertainty."
 V5 = "Multiplicity is addressed where relevant."
 V6 = "Missing-data assumptions are documented."
 V7 = "Clustering and repeated measures are handled appropriately."
 V8 = "Survival censoring assumptions are documented."
 V9 = "Predictive models are validated out of sample where possible."
 V10 = "Causal claims state identification assumptions and limitations."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 BIOSTATISTICS_DEFINITION = 0.99
 STUDY_DESIGN_REASONING = 0.99
 ESTIMATION_REASONING = 0.99
 TESTING_REASONING = 0.99
 REGRESSION_REASONING = 0.99
 SURVIVAL_REASONING = 0.98
 MISSING_DATA_REASONING = 0.98
 CAUSAL_REASONING = 0.97
 MODEL_VALIDATION_REASONING = 0.98
 POLICY = "Reduce confidence when study design, sampling, outcome distribution, dependence, missingness, confounding, censoring, multiplicity or validation evidence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch, OntologyGrounding, BiostatisticsReasoning,
  StudyDesignReasoning, SamplingReasoning, PowerReasoning,
  EstimationReasoning, ConfidenceIntervalReasoning, HypothesisTestingReasoning,
  RegressionReasoning, LogisticRegressionReasoning, CountModelReasoning,
  MixedEffectsReasoning, LongitudinalReasoning, SurvivalAnalysisReasoning,
  EpidemiologicalMeasureReasoning, DiagnosticTestReasoning,
  MultipleTestingReasoning, BayesianReasoning, MissingDataReasoning,
  CausalInferenceReasoning, BootstrapReasoning, ModelValidationReasoning,
  KnowledgeGraphConstruction, RetrievalAugmentation, RecursiveInference
 ]
 NORMALISE {
  "biostatistics" -> Biostatistics
  "biological statistics" -> Biostatistics
  "false discovery rate" -> FalseDiscoveryRate
  "FDR" -> FalseDiscoveryRate
  "Cox model" -> CoxProportionalHazardsModel
  "Kaplan-Meier" -> KaplanMeierEstimator
  "odds ratio" -> OddsRatio
  "relative risk" -> RelativeRisk
 }
}

EXECUTION_RULES {
 E1 = "If biological data require statistical inference, activate BiostatisticsOntology."
 E2 = "If outcome is continuous, consider linear or suitable distributional models."
 E3 = "If outcome is binary, consider logistic or binomial models."
 E4 = "If outcome is count data, consider Poisson or negative-binomial models."
 E5 = "If observations are clustered or repeated, use dependence-aware models."
 E6 = "If outcome is time-to-event, route to Survival Analysis."
 E7 = "If many hypotheses are tested, apply multiplicity control."
 E8 = "If missing data are material, state and model the missingness mechanism."
 E9 = "If causal effects are requested, require explicit causal assumptions."
}

RECURSION {
 ENTRY = Biostatistics
 EXPAND(Biostatistics) -> [
  StudyDesign, ExperimentalDesign, ObservationalStudy, RandomisedExperiment,
  ClinicalTrial, CohortStudy, CaseControlStudy, CrossSectionalStudy, Sampling,
  SampleSize, StatisticalPower, EffectSize, ProbabilityDistribution, Likelihood,
  Parameter, Estimator, PointEstimate, ConfidenceInterval, StandardError,
  Bias, Variance, HypothesisTest, NullHypothesis, AlternativeHypothesis,
  TestStatistic, PValue, TypeIError, TypeIIError, MultipleTesting,
  FalseDiscoveryRate, Regression, LinearRegression, LogisticRegression,
  GeneralisedLinearModel, PoissonRegression, NegativeBinomialRegression,
  MixedEffectsModel, RepeatedMeasures, LongitudinalData, SurvivalAnalysis,
  SurvivalFunction, HazardFunction, Censoring, KaplanMeierEstimator,
  LogRankTest, CoxProportionalHazardsModel, RelativeRisk, RiskDifference,
  OddsRatio, IncidenceRate, Prevalence, Sensitivity, Specificity, ROC, AUC,
  BayesianInference, PriorDistribution, PosteriorDistribution,
  HierarchicalModel, MissingData, MultipleImputation, Confounding,
  CausalInference, Randomisation, Matching, PropensityScore, Bootstrap,
  PermutationTest, CrossValidation, ModelSelection, ModelValidation,
  Reproducibility
 ]
 STOP_CONDITION = "Stop when study design, statistical model, effect estimate, uncertainty, assumptions, missingness, multiplicity and validation are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Mathematical Biology"
 RELATED_ONTOLOGIES = [
  "Mathematical Biology Ontology",
  "Biological Mathematics",
  "Probability & Statistics Ontologies",
  "Regression Ontologies",
  "Survival Analysis Ontologies",
  "Bayesian Statistics Ontologies",
  "Epidemic Modelling Ontology",
  "Ecological Modelling Ontology",
  "Population Dynamics Ontology",
  "Computational Mathematics Ontologies"
 ]
 ROUTE_RULES = [
  "Biostatistics -> Mathematical Biology for parent semantics",
  "Biostatistics -> Probability & Statistics for foundational inference",
  "Biostatistics -> Regression for predictor-outcome modelling",
  "Biostatistics -> Survival Analysis for time-to-event data",
  "Biostatistics -> Bayesian Statistics for posterior inference",
  "Biostatistics -> Epidemic Modelling for infectious-disease data",
  "Biostatistics -> Ecological Modelling for ecological observations",
  "Biostatistics -> Population Dynamics for demographic inference",
  "Biostatistics -> Computational Mathematics for numerical inference"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"
 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible study designs, statistical models or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"
 RULES = [
  "Preserve study-design semantics.",
  "Preserve estimate-versus-uncertainty distinction.",
  "Preserve association-versus-causation distinction.",
  "Preserve frequentist-versus-Bayesian interpretation.",
  "Preserve clustered-data semantics.",
  "Preserve missing-data semantics.",
  "Preserve multiplicity semantics.",
  "Preserve machine-readable biostatistics semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION = "Biostatistics applies statistical methods to biological, biomedical, ecological and population data."
 DESIGN_SUMMARY = "Study design, sampling and randomisation determine the inferential structure of biological data."
 INFERENCE_SUMMARY = "Estimation and hypothesis testing quantify effects together with sampling uncertainty."
 REGRESSION_SUMMARY = "Regression and generalised linear models relate biological outcomes to explanatory variables."
 SURVIVAL_SUMMARY = "Survival analysis models time-to-event outcomes while accounting for censoring."
 DIAGNOSTIC_SUMMARY = "Sensitivity, specificity, predictive values and ROC analysis quantify diagnostic performance."
 CAUSAL_SUMMARY = "Causal inference requires explicit assumptions about interventions, confounding and identification."
 VALIDATION_SUMMARY = "Biostatistical analyses should report assumptions, uncertainty, missing-data handling, multiplicity and model validation."
}

FLOW {
 INPUT
 -> detect_biostatistics_context
 -> identify_biological_question_population_sample_study_design_outcome_predictors_and_data_structure
 -> classify_experimental_observational_longitudinal_clustered_survival_or_diagnostic_design
 -> select_probability_model_and_statistical_method
 -> estimate_effects_and_uncertainty
 -> if_hypothesis_testing_define_null_alternative_and_error_control
 -> if_regression_fit_model_and_check_assumptions
 -> if_missing_data_assess_missingness_and_apply_valid_strategy
 -> if_multiple_testing_apply_error_rate_control
 -> if_causal_define_estimand_confounders_and_identification_assumptions
 -> validate_model_calibration_discrimination_robustness_and_reproducibility
 -> route_to_mathematical_biology_probability_statistics_regression_survival_analysis_Bayesian_statistics_epidemic_modelling_ecological_modelling_population_dynamics_or_computational_mathematics_ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Biostatistics Ontology defines statistical mathematics for biological and biomedical data. It supports study design, randomised and observational studies, sampling and power, likelihood and estimation, confidence intervals and hypothesis tests, multiple-testing control, linear, logistic, Poisson and negative-binomial regression, mixed-effects and longitudinal models, survival analysis, Kaplan-Meier estimation and Cox models, relative risks, odds ratios and incidence measures, diagnostic sensitivity and specificity, Bayesian inference, missing-data methods, causal inference, bootstrap and permutation methods, cross-validation, model selection, validation and reproducibility."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-BIOSTATISTICS-ONTOLOGY-V1"
}

}

END_FLOW