Meta-Analysis Ontology

flow "MetaAnalysisOntology" v4.0

# META-ANALYSIS ONTOLOGY
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/scientific-statistical-methods/meta-analysis-ontology.html"
  title: "Meta-Analysis Ontology"
  domain: "Probability and Statistics"
  category: "Scientific Statistical Methods"
  entity: META_ANALYSIS
  entity_type: SCIENTIFIC_STATISTICAL_ONTOLOGY

DEFINE:
  META_ANALYSIS :=
    STATISTICAL_EVIDENCE_SYNTHESIS_FRAMEWORK(
      STUDIES,
      EFFECT_SIZES,
      SAMPLING_VARIANCES,
      STUDY_WEIGHTS,
      HETEROGENEITY,
      FIXED_EFFECT_MODEL,
      RANDOM_EFFECTS_MODEL,
      MODERATOR_ANALYSIS,
      PUBLICATION_BIAS,
      SENSITIVITY_ANALYSIS
    )

PURPOSE:
  SYNTHESISE:
    RESULTS_FROM_MULTIPLE_STUDIES
    EFFECT_ESTIMATES
    UNCERTAINTY
    BETWEEN_STUDY_VARIATION
  ESTIMATE:
    POOLED_EFFECT
    HETEROGENEITY
    PREDICTION_INTERVAL
    MODERATOR_EFFECTS

FOUNDATION:
  STUDIES:
    i := 1,...,k
  STUDY_EFFECT:
    y_i
  WITHIN_STUDY_VARIANCE:
    v_i
  STUDY_STANDARD_ERROR:
    SE_i := sqrt(v_i)
  GENERIC_WEIGHTED_EFFECT:
    mu_hat := SUM_i w_i y_i / SUM_i w_i

ENTITIES:
  META_ANALYSIS: STATISTICAL_SYNTHESIS_OF_STUDY_RESULTS
  STUDY: INDIVIDUAL_EMPIRICAL_INVESTIGATION
  EFFECT_SIZE: STANDARDISED_OR_NATURAL_SCALE_STUDY_EFFECT
  SAMPLING_VARIANCE: WITHIN_STUDY_EFFECT_VARIANCE
  STUDY_WEIGHT: CONTRIBUTION_OF_STUDY_TO_POOLED_ESTIMATE
  POOLED_EFFECT: COMBINED_EFFECT_ESTIMATE
  HETEROGENEITY: BETWEEN_STUDY_EFFECT_VARIATION
  TAU_SQUARED: BETWEEN_STUDY_VARIANCE
  I_SQUARED: RELATIVE_HETEROGENEITY_MEASURE
  Q_STATISTIC: WEIGHTED_HETEROGENEITY_STATISTIC
  MODERATOR: STUDY_LEVEL_EXPLANATORY_VARIABLE
  PUBLICATION_BIAS: SELECTIVE_AVAILABILITY_RELATED_TO_RESULTS
  FOREST_PLOT: VISUALISATION_OF_STUDY_AND_POOLED_EFFECTS
  FUNNEL_PLOT: EFFECT_PRECISION_PATTERN_VISUALISATION

RELATIONSHIPS:
  STUDY -> PRODUCES -> EFFECT_SIZE
  EFFECT_SIZE -> HAS -> SAMPLING_VARIANCE
  SAMPLING_VARIANCE -> DETERMINES -> INVERSE_VARIANCE_WEIGHT
  STUDY_EFFECTS -> COMBINE_TO -> POOLED_EFFECT
  BETWEEN_STUDY_VARIATION -> REPRESENTED_BY -> TAU_SQUARED
  HETEROGENEITY -> ASSESSED_BY -> Q_STATISTIC
  HETEROGENEITY -> SUMMARISED_BY -> I_SQUARED
  MODERATOR -> MAY_EXPLAIN -> HETEROGENEITY
  PUBLICATION_BIAS -> MAY_DISTORT -> META_ANALYTIC_ESTIMATE
  SENSITIVITY_ANALYSIS -> ASSESSES -> ROBUSTNESS

META_ANALYSIS_FLOW:
  flow:
    DEFINE_RESEARCH_QUESTION
      -> DEFINE_ELIGIBILITY_CRITERIA
      -> IDENTIFY_STUDIES
      -> EXTRACT_EFFECT_DATA
      -> HARMONISE_EFFECT_MEASURES
      -> COMPUTE_EFFECT_SIZES_AND_VARIANCES
      -> ASSESS_STUDY_COMPARABILITY
      -> SELECT_META_ANALYTIC_MODEL
      -> ESTIMATE_POOLED_EFFECT
      -> ASSESS_HETEROGENEITY
      -> INVESTIGATE_MODERATORS
      -> ASSESS_SMALL_STUDY_AND_REPORTING_BIAS
      -> RUN_SENSITIVITY_ANALYSES
      -> REPORT_RESULTS_AND_LIMITATIONS

SYSTEMATIC_REVIEW_CONNECTION:
  systematic_review:
    STRUCTURED_IDENTIFICATION_APPRAISAL_AND_SYNTHESIS_OF_EVIDENCE
  meta_analysis:
    STATISTICAL_COMBINATION_OF_COMPATIBLE_QUANTITATIVE_RESULTS
  rule:
    SYSTEMATIC_REVIEW != META_ANALYSIS

ELIGIBILITY_CRITERIA:
  define:
    - POPULATION
    - INTERVENTION_OR_EXPOSURE
    - COMPARATOR
    - OUTCOME
    - STUDY_DESIGN
    - TIME_HORIZON
  requirement:
    PREDEFINE_BEFORE_RESULT_DRIVEN_SELECTION

EFFECT_SIZE:
  common_types:
    - MEAN_DIFFERENCE
    - STANDARDISED_MEAN_DIFFERENCE
    - RISK_RATIO
    - ODDS_RATIO
    - RISK_DIFFERENCE
    - HAZARD_RATIO
    - CORRELATION
    - LOG_RESPONSE_RATIO
  requirement:
    EFFECT_MEASURE_MUST_BE_COMPARABLE_ACROSS_INCLUDED_STUDIES

INVERSE_VARIANCE_WEIGHTING:
  fixed_effect_weight:
    w_i := 1/v_i
  implication:
    MORE_PRECISE_STUDIES_RECEIVE_GREATER_WEIGHT

FIXED_EFFECT_MODEL:
  model:
    y_i := theta+epsilon_i
  sampling_error:
    epsilon_i ~ approximately Normal(0,v_i)
  assumption:
    ALL_STUDIES_ESTIMATE_COMMON_UNDERLYING_EFFECT
    APART_FROM:
      SAMPLING_ERROR
  pooled_effect:
    theta_hat_FE := SUM_i w_i y_i / SUM_i w_i
  weights:
    w_i := 1/v_i

RANDOM_EFFECTS_MODEL:
  hierarchical:
    y_i := theta_i+epsilon_i
    theta_i := mu+u_i
  within_study:
    epsilon_i ~ approximately Normal(0,v_i)
  between_study:
    u_i ~ approximately Normal(0,tau_squared)
  marginal:
    y_i ~ approximately Normal(mu,v_i+tau_squared)
  weight:
    w_i_star := 1/(v_i+tau_squared)
  pooled_effect:
    mu_hat_RE := SUM_i w_i_star y_i / SUM_i w_i_star

FIXED_VS_RANDOM_EFFECTS:
  fixed_effect:
    TARGETS_COMMON_EFFECT_UNDER_MODEL
  random_effects:
    TARGETS_MEAN_OF_EFFECT_DISTRIBUTION_UNDER_MODEL
  rule:
    RANDOM_EFFECTS_MODEL_IS_NOT_JUST_A_RESPONSE_TO_SIGNIFICANT_HETEROGENEITY

HETEROGENEITY:
  sources:
    - POPULATION_DIFFERENCE
    - INTERVENTION_DIFFERENCE
    - OUTCOME_DEFINITION
    - FOLLOW_UP_TIME
    - STUDY_DESIGN
    - MEASUREMENT_METHOD
    - BIAS
    - RANDOM_VARIATION

COCHRAN_Q:
  statistic:
    Q := SUM_i w_i (y_i-theta_hat_FE)^2
  degrees_of_freedom:
    k-1
  caution:
    Q_TEST_HAS_LOW_POWER_WITH_FEW_STUDIES_AND_HIGH_POWER_WITH_MANY_STUDIES

I_SQUARED:
  common_estimator:
    I_squared := max(0,(Q-(k-1))/Q)*100_percent
  caution:
    I_SQUARED_IS_NOT_ABSOLUTE_BETWEEN_STUDY_VARIANCE

TAU_SQUARED:
  meaning:
    ESTIMATED_BETWEEN_STUDY_VARIANCE
  estimators:
    - DER_SIMONIAN_LAIRD
    - REML
    - PAULE_MANDEL
    - MAXIMUM_LIKELIHOOD
    - BAYESIAN_ESTIMATION
  caution:
    TAU_SQUARED_ESTIMATE_CAN_BE_IMPRECISE_WITH_FEW_STUDIES

PREDICTION_INTERVAL:
  purpose:
    ESTIMATE_RANGE_FOR_UNDERLYING_EFFECT_IN_NEW_COMPARABLE_STUDY
  caution:
    CONFIDENCE_INTERVAL_FOR_MEAN_EFFECT != PREDICTION_INTERVAL_FOR_NEW_STUDY_EFFECT

META_REGRESSION:
  model:
    y_i := beta_0 + SUM_j beta_j X_ij + u_i + epsilon_i
  purpose:
    EXPLAIN_BETWEEN_STUDY_HETEROGENEITY_WITH_MODERATORS
  caution:
    STUDY_LEVEL_ASSOCIATIONS_MAY_BE_CONFOUNDED

SUBGROUP_ANALYSIS:
  flow:
    PARTITION_STUDIES_BY_MODERATOR
      -> ESTIMATE_EFFECT_WITHIN_SUBGROUP
      -> TEST_BETWEEN_SUBGROUP_DIFFERENCE
  caution:
    SIGNIFICANT_IN_ONE_SUBGROUP_AND_NOT_ANOTHER_DOES_NOT_PROVE_SUBGROUP_DIFFERENCE

DEPENDENT_EFFECT_SIZES:
  sources:
    - MULTIPLE_OUTCOMES_PER_STUDY
    - MULTIPLE_TIME_POINTS
    - MULTIPLE_TREATMENT_ARMS
    - SHARED_CONTROL_GROUP
    - CLUSTERED_EFFECTS
  methods:
    - MULTILEVEL_META_ANALYSIS
    - ROBUST_VARIANCE_ESTIMATION
    - MULTIVARIATE_META_ANALYSIS
    - EFFECT_AGGREGATION_WITH_JUSTIFICATION

FOREST_PLOT:
  displays:
    STUDY_EFFECT
    CONFIDENCE_INTERVAL
    STUDY_WEIGHT
    POOLED_EFFECT
    OPTIONAL_PREDICTION_INTERVAL

FUNNEL_PLOT:
  purpose:
    EXPLORE_SMALL_STUDY_EFFECTS_AND_ASYMMETRY
  caution:
    FUNNEL_ASYMMETRY != PUBLICATION_BIAS_BY_IDENTITY

PUBLICATION_BIAS:
  definition:
    PROBABILITY_OF_STUDY_AVAILABILITY_OR_PUBLICATION_DEPENDS_ON_RESULTS
  consequence:
    AVAILABLE_EVIDENCE_MAY_NOT_REPRESENT_ALL_CONDUCTED_STUDIES

SMALL_STUDY_EFFECTS:
  possible_causes:
    - PUBLICATION_BIAS
    - STUDY_QUALITY
    - TRUE_HETEROGENEITY
    - SAMPLING_VARIATION
    - SELECTIVE_REPORTING
  rule:
    SMALL_STUDY_EFFECTS != PUBLICATION_BIAS_BY_DEFAULT

SENSITIVITY_ANALYSIS:
  analyses:
    - LEAVE_ONE_OUT
    - ALTERNATIVE_EFFECT_MEASURE
    - ALTERNATIVE_TAU_SQUARED_ESTIMATOR
    - FIXED_VS_RANDOM_EFFECTS
    - EXCLUDE_HIGH_RISK_OF_BIAS_STUDIES
    - ALTERNATIVE_CORRELATION_ASSUMPTIONS
    - ALTERNATIVE_PUBLICATION_BIAS_MODEL


LEAVE_ONE_OUT:
  flow:
    REMOVE_STUDY_i
      -> REFIT_META_ANALYSIS
      -> RECORD_POOLED_EFFECT
      -> REPEAT_FOR_ALL_STUDIES
  purpose:
    IDENTIFY_INFLUENTIAL_STUDIES

INFLUENCE_DIAGNOSTICS:
  assess:
    - STANDARDISED_RESIDUALS
    - COOKS_DISTANCE
    - DFBETAS
    - LEAVE_ONE_OUT_CHANGE
  rule:
    INFLUENTIAL_STUDY != INVALID_STUDY_BY_DEFAULT

OUTLIER_STUDY:
  definition:
    STUDY_EFFECT_UNUSUAL_RELATIVE_TO_META_ANALYTIC_MODEL
  caution:
    OUTLYING_EFFECT_MAY_REFLECT_TRUE_HETEROGENEITY
    AND:
      SHOULD_NOT_BE_AUTOMATICALLY_EXCLUDED

CUMULATIVE_META_ANALYSIS:
  flow:
    ADD_STUDIES_SEQUENTIALLY
      -> RECALCULATE_POOLED_EFFECT
  purpose:
    EXAMINE_EVOLUTION_OF_EVIDENCE

RARE_EVENT_META_ANALYSIS:
  challenges:
    - ZERO_EVENTS
    - SPARSE_COUNTS
    - UNSTABLE_NORMAL_APPROXIMATIONS
  requirement:
    METHOD_SELECTION_MUST_MATCH_EVENT_FREQUENCY_AND_EFFECT_MEASURE

ZERO_EVENT_STUDIES:
  issue:
    SOME_EFFECT_MEASURES_UNDEFINED_WITH_ZERO_CELLS
  responses:
    - CONTINUITY_CORRECTION
    - EXACT_OR_LIKELIHOOD_METHOD
    - ALTERNATIVE_EFFECT_MEASURE
    - GENERALIZED_LINEAR_MIXED_MODEL
  caution:
    CONTINUITY_CORRECTIONS_CAN_AFFECT_RESULTS

MISSING_STUDY_DATA:
  examples:
    - MISSING_STANDARD_DEVIATION
    - INCOMPLETE_EFFECT_REPORTING
    - UNAVAILABLE_COVARIANCE
  responses:
    - CONTACT_AUTHORS
    - DERIVE_FROM_REPORTED_STATISTICS
    - IMPUTE_WITH_SENSITIVITY_ANALYSIS
  requirement:
    DERIVATION_OR_IMPUTATION_METHOD_MUST_BE_DOCUMENTED

STUDY_OVERLAP:
  issue:
    SAME_PARTICIPANTS_OR_DATA_SOURCE_APPEAR_IN_MULTIPLE_REPORTS
  consequence:
    DOUBLE_COUNTING_AND_DEPENDENCE
  response:
    IDENTIFY_REPORT_FAMILIES
      -> SELECT_OR_COMBINE_APPROPRIATELY

UNIT_OF_ANALYSIS:
  requirement:
    PRESERVE_INDEPENDENT_STATISTICAL_UNIT
  examples:
    PARTICIPANT
    CLUSTER
    STUDY
    EFFECT_WITHIN_STUDY

BAYESIAN_META_ANALYSIS:
  likelihood:
    y_i ~ Normal(theta_i,v_i)
  hierarchy:
    theta_i ~ Normal(mu,tau_squared)
  priors:
    p(mu)
    p(tau)
  posterior:
    p(mu,tau,theta_1,...,theta_k|D)
  outputs:
    - POSTERIOR_MEAN_EFFECT
    - POSTERIOR_HETEROGENEITY
    - CREDIBLE_INTERVAL
    - PREDICTIVE_DISTRIBUTION

PRIOR_SENSITIVITY:
  vary:
    p(mu)
    p(tau)
  observe:
    POSTERIOR_POOLED_EFFECT
    HETEROGENEITY
    PREDICTION_INTERVAL

INDIVIDUAL_PARTICIPANT_DATA_META_ANALYSIS:
  alias:
    IPD_META_ANALYSIS
  data:
    PARTICIPANT_LEVEL_DATA_FROM_MULTIPLE_STUDIES
  approaches:
    - ONE_STAGE
    - TWO_STAGE
  advantages:
    HARMONISED_ANALYSIS
    FLEXIBLE_COVARIATE_MODELLING
  caution:
    DATA_AVAILABILITY_AND_HARMONISATION_CAN_INTRODUCE_SELECTION_ISSUES

ONE_STAGE_IPD:
  model:
    PARTICIPANTS_NESTED_WITHIN_STUDIES
  analysis:
    JOINT_HIERARCHICAL_MODEL

TWO_STAGE_IPD:
  stage_1:
    ESTIMATE_EFFECT_WITHIN_EACH_STUDY
  stage_2:
    META_ANALYSE_STUDY_EFFECTS

PROSPECTIVE_META_ANALYSIS:
  definition:
    STUDIES_IDENTIFIED_AND_ANALYSIS_PLANNED_BEFORE_RESULTS_KNOWN
  advantage:
    REDUCE_RESULT_DRIVEN_SELECTION_AND_HARMONISE_OUTCOMES

LIVING_META_ANALYSIS:
  definition:
    META_ANALYSIS_UPDATED_AS_NEW_ELIGIBLE_EVIDENCE_APPEARS
  requirement:
    VERSIONING
    SEARCH_UPDATE
    REPRODUCIBLE_PIPELINE

META_ANALYSIS_VALIDATION:
  checks:
    - EFFECT_SIZE_RECALCULATION
    - DATA_EXTRACTION_VERIFICATION
    - DUPLICATE_STUDY_CHECK
    - MODEL_REPRODUCTION
    - SENSITIVITY_ANALYSIS
    - CODE_REVIEW

DATA_QUALITY_CONNECTION:
  assess:
    - EXTRACTION_ACCURACY
    - MISSING_DATA
    - DUPLICATE_REPORTS
    - OUTCOME_HARMONISATION
    - STUDY_PROVENANCE
  rule:
    META_ANALYSIS_QUALITY_DEPENDS_ON_INCLUDED_EVIDENCE_AND_EXTRACTION_QUALITY

STATISTICAL_VALIDATION_CONNECTION:
  validate:
    - MODEL_ASSUMPTIONS
    - HETEROGENEITY_ESTIMATION
    - INFLUENCE
    - PREDICTION
    - SENSITIVITY

SCIENTIFIC_STATISTICS_CONNECTION:
  meta_analysis:
    EXTENDS_STATISTICAL_INFERENCE_ACROSS_MULTIPLE_STUDIES
  requirement:
    STUDY_DESIGN_AND_EFFECT_ESTIMATION_CONTEXT_MUST_BE_PRESERVED

REPRODUCIBILITY:
  preserve:
    - SEARCH_DATE
    - SEARCH_STRATEGY
    - ELIGIBILITY_CRITERIA
    - STUDY_IDENTIFIERS
    - EXTRACTED_DATA
    - EFFECT_SIZE_FORMULAS
    - MODEL_TYPE
    - TAU_SQUARED_ESTIMATOR
    - SOFTWARE_VERSION
    - ANALYSIS_CODE
    - RANDOM_SEED_WHEN_RELEVANT

REPORTING:
  include:
    - RESEARCH_QUESTION
    - ELIGIBILITY_CRITERIA
    - SEARCH_AND_SELECTION
    - INCLUDED_STUDIES
    - EFFECT_MEASURE
    - MODEL_TYPE
    - STUDY_WEIGHTS
    - POOLED_EFFECT
    - UNCERTAINTY_INTERVAL
    - HETEROGENEITY
    - PREDICTION_INTERVAL_WHEN_RELEVANT
    - RISK_OF_BIAS
    - SENSITIVITY_ANALYSES
    - PUBLICATION_BIAS_ASSESSMENT
    - LIMITATIONS

APPLICATIONS:
  META_ANALYSIS -> SUPPORTS -> SYSTEMATIC_REVIEW
  META_ANALYSIS -> SUPPORTS -> SCIENTIFIC_STATISTICS
  META_ANALYSIS -> SUPPORTS -> EVIDENCE_SYNTHESIS
  META_ANALYSIS -> SUPPORTS -> MEDICINE
  META_ANALYSIS -> SUPPORTS -> BIOLOGY
  META_ANALYSIS -> SUPPORTS -> SOCIAL_SCIENCE
  META_ANALYSIS -> SUPPORTS -> ENGINEERING
  META_ANALYSIS -> SUPPORTS -> DECISION_ANALYSIS

MODEL_CONNECTIONS:
  META_ANALYSIS -> CONNECTS_TO -> SCIENTIFIC_STATISTICS
  META_ANALYSIS -> CONNECTS_TO -> STATISTICAL_VALIDATION
  META_ANALYSIS -> CONNECTS_TO -> BAYESIAN_STATISTICS
  META_ANALYSIS -> CONNECTS_TO -> REGRESSION
  META_ANALYSIS -> CONNECTS_TO -> MULTIVARIATE_STATISTICS
  META_ANALYSIS -> CONNECTS_TO -> SENSITIVITY_ANALYSIS
  META_ANALYSIS -> CONNECTS_TO -> DATA_QUALITY

SEMANTIC_EQUIVALENCE:
  "meta-analysis"
    ~= "statistical synthesis of effect estimates from multiple studies"

  "pooled effect"
    ~= "combined effect estimate under specified meta-analytic model"

  "between-study variance"
    ~= "tau squared"
    IN:
      RANDOM_EFFECTS_META_ANALYSIS

  "prediction interval"
    ~= "interval for effect in a new comparable study under model"

  EXCLUDE_EQUIVALENCE:
    META_ANALYSIS != SYSTEMATIC_REVIEW
    FIXED_EFFECT_MODEL != RANDOM_EFFECTS_MODEL
    I_SQUARED != TAU_SQUARED
    CONFIDENCE_INTERVAL != PREDICTION_INTERVAL
    FUNNEL_ASYMMETRY != PUBLICATION_BIAS
    SMALL_STUDY_EFFECT != PUBLICATION_BIAS_BY_DEFAULT
    INFLUENTIAL_STUDY != INVALID_STUDY
    HETEROGENEITY != BIAS
    META_REGRESSION_ASSOCIATION != INDIVIDUAL_CAUSAL_EFFECT

VALIDATION_RULES:
  RULE_1:
    RESEARCH_QUESTION_ELIGIBILITY_AND_EFFECT_MEASURE_MUST_BE_DEFINED
  RULE_2:
    STUDY_EFFECTS_AND_SAMPLING_VARIANCES_MUST_BE_COMPUTED_ON_COMPATIBLE_SCALE
  RULE_3:
    DEPENDENT_EFFECT_SIZES_MUST_NOT_BE_TREATED_AS_INDEPENDENT_WITHOUT_JUSTIFICATION
  RULE_4:
    MODEL_TYPE_AND_HETEROGENEITY_ESTIMATOR_MUST_BE EXPLICIT
  RULE_5:
    HETEROGENEITY_SHOULD_BE_QUANTIFIED_AND_SCIENTIFICALLY_INTERPRETED
  RULE_6:
    PUBLICATION_BIAS_DIAGNOSTICS_MUST_NOT_BE_TREATED_AS_DEFINITIVE_PROOF
  RULE_7:
    SENSITIVITY_TO_INFLUENTIAL_STUDIES_MODEL_CHOICES_AND_RISK_OF_BIAS_SHOULD_BE_ASSESSED
  RULE_8:
    STUDY_PROVENANCE_AND_DUPLICATE_REPORTS_MUST_BE_TRACKED

CONFIDENCE:
  ontology_identity: 0.99
  effect_size_structure: 0.99
  fixed_effect_structure: 0.99
  random_effects_structure: 0.99
  heterogeneity_structure: 0.99
  publication_bias_structure: 0.98
  sensitivity_structure: 0.99
  semantic_distinctions: 0.99

UPDATE_MODEL:
  IF:
    NEW_ELIGIBLE_STUDY_ARRIVES
  THEN:
    UPDATE:
      STUDY_SET
      EFFECT_SIZE_DATA
      STUDY_WEIGHTS
      POOLED_EFFECT
      HETEROGENEITY
      PREDICTION_INTERVAL
    RERUN:
      SENSITIVITY_ANALYSES

  IF:
    EFFECT_SIZE_OR_VARIANCE_CORRECTION_OCCURS
  THEN:
    UPDATE:
      STUDY_EFFECT
      SAMPLING_VARIANCE
    RECOMPUTE:
      META_ANALYSIS
      HETEROGENEITY
      INFLUENCE

  IF:
    META_ANALYTIC_MODEL_CHANGES
  THEN:
    RECOMPUTE:
      WEIGHTS
      POOLED_EFFECT
      UNCERTAINTY
      PREDICTION_INTERVAL
    COMPARE:
      MODEL_SENSITIVITY

  PRESERVE:
    RESEARCH_QUESTION
    ELIGIBILITY_CRITERIA
    STUDY_IDENTIFIERS
    EFFECT_MEASURE
    EFFECT_SIZE_DATA
    SAMPLING_VARIANCES
    DEPENDENCE_STRUCTURE
    MODEL_TYPE
    HETEROGENEITY_ESTIMATOR
    RISK_OF_BIAS
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - DEFINE_RESEARCH_QUESTION_AND_ELIGIBILITY
    - IDENTIFY_UNIQUE_STUDIES_AND_REPORT_FAMILIES
    - SELECT_COMMON_EFFECT_MEASURE
    - COMPUTE_STUDY_EFFECTS_AND_VARIANCES
    - IDENTIFY_DEPENDENT_EFFECTS
    - SELECT_FIXED_OR_RANDOM_EFFECTS_MODEL_BY_SCIENTIFIC_TARGET
    - ESTIMATE_POOLED_EFFECT
    - ESTIMATE_HETEROGENEITY
    - COMPUTE_PREDICTION_INTERVAL_WHEN_RELEVANT
    - INVESTIGATE_MODERATORS
    - ASSESS_SMALL_STUDY_AND_REPORTING_BIAS
    - RUN_INFLUENCE_AND_SENSITIVITY_ANALYSES
    - RETURN_META_ANALYTIC_INTERPRETATION

  constraints:
    - PRESERVE_EFFECT_SIZE_SCALE
    - PRESERVE_STUDY_IDENTITY
    - MODEL_DEPENDENT_EFFECTS_WHEN_PRESENT
    - DISTINGUISH_FIXED_FROM_RANDOM_EFFECTS_TARGETS
    - DISTINGUISH_I_SQUARED_FROM_TAU_SQUARED
    - DISTINGUISH_CONFIDENCE_FROM_PREDICTION_INTERVAL
    - DISTINGUISH_FUNNEL_ASYMMETRY_FROM_PUBLICATION_BIAS
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "meta-analysis"
  namespace: "probability-statistics/scientific-statistical-methods"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - EFFECT_SIZE_SYNTHESIS
    - FIXED_AND_RANDOM_EFFECTS
    - HETEROGENEITY
    - PUBLICATION_BIAS_AND_SENSITIVITY

END_FLOW