# Methodology: Probabilistic Modeling for Nigerian Health Dataset

## Overview

This document details the probabilistic modeling methodology used to transform a generic smoking health dataset into a Nigerian-contextualized version with realistic epidemiological relationships.

---

## Core Principles

### 1. **Evidence-Based Probabilities**
- All probability distributions derived from peer-reviewed research
- Multiple sources used to validate each parameter
- Preference for Nigerian-specific studies over global estimates

### 2. **Conditional Relationships**
- Health outcomes depend on multiple interacting factors
- Probabilistic cascades model real-world dependencies
- Avoid independence assumptions where evidence shows correlation

### 3. **Population-Level Accuracy**
- Individual records may vary
- Aggregate statistics match research targets
- Distributions reflect Nigerian demographic reality

---

## Probabilistic Generation Pipeline

### Stage 1: Demographics

```
Step 1.1: Assign Sex
├─ P(Male) = 0.504
└─ P(Female) = 0.496

Step 1.2: Assign Age
├─ Age distribution: Nigeria's young population structure
├─ P(18-25) = 0.25
├─ P(26-35) = 0.30  ← Peak working age
├─ P(36-45) = 0.20
├─ P(46-55) = 0.15
└─ P(56-70) = 0.10

Step 1.3: Assign Region
├─ South-West: 25% (Lagos, Ibadan, etc.)
├─ North-West: 20% (Kano, Kaduna, etc.)
├─ South-South: 18% (Port Harcourt, etc.)
├─ South-East: 15% (Enugu, Onitsha, etc.)
├─ North-Central: 12% (Abuja, Jos, etc.)
└─ North-East: 10% (Maiduguri, etc.)

Step 1.4: Assign Location Type (Urban vs Rural)
├─ P(Urban | Region) = region-specific urbanization rate
└─ Example: P(Urban | South-West) = 0.60
```

**Justification:**
- Sex ratio from National Bureau of Statistics
- Age distribution reflects Nigeria's median age of 18.6 years
- Regional populations weighted by census data
- Urban/rural splits vary by region's development

---

### Stage 2: Behavioral Risk Factors

```
Step 2.1: Determine Smoking Status

P(Smoker | Sex, Age, Region, Location) = 
    BaseRate(Sex, AgeGroup) × RegionalModifier(Region, Location)

Where:
  BaseRate(Male, 18-34) = 0.06
  BaseRate(Male, 35-54) = 0.11  ← Peak prevalence
  BaseRate(Male, 55+) = 0.08
  BaseRate(Female, 18-34) = 0.008
  BaseRate(Female, 35-54) = 0.015
  BaseRate(Female, 55+) = 0.005
  
  RegionalModifier accounts for:
  - Urban vs rural differences
  - Cultural factors (e.g., lower in Islamic North)
  - Economic factors (affordability)

Step 2.2: Assign Cigarettes Per Day (if Smoker)

Distribution for smokers:
├─ Light (1-10 cigs): 65%  ← Economic constraints
├─ Moderate (11-20 cigs): 30%
└─ Heavy (21-40 cigs): 5%

Mean: ~11 cigarettes/day (vs 18.6 in Western datasets)
```

**Justification:**
- Multi-factor smoking probability reflects real-world complexity
- Gender disparity (9:1 male:female) matches cultural norms
- Lower consumption than Western countries (economic factors)
- Age peak at 35-54 years (stress, affordability)

---

### Stage 3: Genetic Factors

```
Step 3.1: Assign Sickle Cell Genotype

P(AA) = 0.76  ← Normal hemoglobin
P(AS) = 0.22  ← Sickle cell trait (carrier)
P(SS) = 0.02  ← Sickle cell disease

This is INDEPENDENT of other factors (genetic inheritance)
```

**Justification:**
- Hardy-Weinberg equilibrium
- Nigeria has world's largest SCD population
- 24% carrier rate (AS) is well-documented
- SS prevalence 2-3% from newborn screening data

---

### Stage 4: Environmental Exposures

```
Step 4.1: Assign Malaria Exposure

P(Malaria | Region, Location) depends on:
  - Regional endemicity
  - Urban vs rural (urban has lower transmission)
  - Season (not modeled, but implicit in "chronic")

Categories:
├─ Recent episode (<3 months)
├─ Chronic/repeated (multiple times per year)
└─ Rare/never

Example for South-South (very high endemicity):
  P(Recent | South-South, Rural) = 0.30
  P(Chronic | South-South, Rural) = 0.50
  P(Rare | South-South, Rural) = 0.20
```

**Justification:**
- Nigeria Malaria Indicator Survey 2021 data
- Regional parasite prevalence: 10-70%
- Urban sanitation reduces transmission
- ~60 million clinical cases annually supports high prevalence

---

### Stage 5: Health Outcomes (Conditional Probabilities)

This is where the model becomes sophisticated - health metrics depend on ALL previous factors.

#### 5.1 Hemoglobin Level

```python
Hemoglobin = BaselineHb(Sex) 
             × SickleCellEffect(Genotype)
             - MalariaEffect(MalariaStatus)
             - AgeEffect(Age)
             + RandomVariation

Where:
  BaselineHb(Male) ~ Normal(14.5, 1.2) g/dL
  BaselineHb(Female) ~ Normal(13.0, 1.0) g/dL
  
  SickleCellEffect:
    If SS: ×0.55  (severe chronic anemia, 6-8 g/dL)
    If AS: ×0.95  (mild reduction)
    If AA: ×1.00  (normal)
  
  MalariaEffect:
    Recent: -1.5 to -3.0 g/dL  (acute hemolysis)
    Chronic: -0.5 to -1.5 g/dL (ongoing destruction)
    Rare: 0 g/dL
  
  AgeEffect:
    Age >60: -0.3 to -0.8 g/dL (physiological decline)

Final range clamped: 6.0 - 18.0 g/dL (realistic bounds)
```

**Clinical Justification:**
- Sickle cell disease causes severe baseline anemia
- Malaria destroys red blood cells (hemolysis)
- Combined effects are MULTIPLICATIVE (SS + malaria = very low Hb)
- Age-related decline is well-documented

**Example Cases:**
```
Case 1: Young male, AA genotype, no malaria
  Hb = 14.5 × 1.0 - 0 - 0 + ε = ~14.5 g/dL ✓ Normal

Case 2: Young male, SS genotype, no malaria  
  Hb = 14.5 × 0.55 - 0 - 0 + ε = ~8.0 g/dL ✓ SCD anemia

Case 3: Young female, AA genotype, recent malaria
  Hb = 13.0 × 1.0 - 2.5 - 0 + ε = ~10.5 g/dL ✓ Acute anemia

Case 4: Young female, SS genotype, recent malaria
  Hb = 13.0 × 0.55 - 2.5 - 0 + ε = ~4.6 g/dL → 6.0 g/dL
  (Clamped to minimum; would require hospitalization)
```

---

#### 5.2 Heart Rate

```python
HeartRate = BaselineHR 
            + AnemiaCompensation(Hemoglobin)
            + SickleCell Effect(Genotype)
            + SmokingEffect(IsSmoker)
            + MalariaEffect(MalariaStatus)
            + RandomVariation

Where:
  BaselineHR ~ Normal(72, 10) bpm
  
  AnemiaCompensation:
    If Hb < 10: +15 to +25 bpm  ← Severe compensation
    If Hb 10-12: +5 to +15 bpm  ← Moderate compensation
    If Hb > 12: 0 bpm           ← Normal
  
  SickleCellEffect:
    If SS: +10 to +20 bpm  (chronic hypoxia)
    
  SmokingEffect:
    If Smoker: +5 to +15 bpm  (stimulant effect)
  
  MalariaEffect:
    Recent: +10 to +20 bpm  (acute illness, fever)

Final range clamped: 50 - 140 bpm
```

**Physiological Justification:**
- Low hemoglobin → less oxygen delivery → heart pumps faster
- Sickle cell disease → chronic tissue hypoxia → elevated HR
- Smoking → nicotine stimulation → increased HR
- Acute malaria → fever and illness → increased HR

**Example Cases:**
```
Case 1: Normal Hb (14 g/dL), no conditions
  HR = 72 + 0 + 0 + 0 + 0 + ε = ~72 bpm ✓ Normal

Case 2: Low Hb (8 g/dL) from SCD, non-smoker
  HR = 72 + 20 + 15 + 0 + 0 + ε = ~107 bpm ✓ Compensatory

Case 3: Normal Hb, smoker, recent malaria
  HR = 72 + 0 + 0 + 10 + 15 + ε = ~97 bpm ✓ Elevated

Case 4: SCD + smoker + recent malaria (very sick)
  HR = 72 + 20 + 15 + 10 + 15 + ε = ~132 bpm ✓ Tachycardia
```

---

#### 5.3 Blood Pressure

```python
BloodPressure = DetermineHypertension(Age, Location, Sex)
                + SmokingEffect(IsSmoker)
                + SickleCellVariability(Genotype)

Where:
  P(Hypertension) = BaselinePrevalence(Location)
                    × AgeMultiplier(AgeGroup)
  
  BaselinePrevalence:
    Urban: 0.38
    Rural: 0.28
  
  AgeMultiplier:
    18-34: ×0.5  (16-19% prevalence)
    35-54: ×1.0  (28-38% prevalence)
    55+: ×1.8    (50-68% prevalence)
  
  If Hypertensive:
    70% → Stage 1: Systolic 130-145, Diastolic 80-95
    30% → Stage 2: Systolic 145-180, Diastolic 95-115
  
  If Normotensive:
    Systolic: 100-128 mmHg
    Diastolic: 60-82 mmHg
  
  SmokingEffect:
    +5 to +15 systolic
    +3 to +8 diastolic
  
  SickleCellEffect (SS):
    ±10 to ±20 systolic  (vascular damage, variable)
```

**Clinical Justification:**
- Nigeria has high HTN prevalence (32% overall)
- Urban > rural (diet, stress, sedentary lifestyle)
- Strong age gradient (vessels stiffen with age)
- Smoking raises BP (vasoconstriction)
- Sickle cell causes vascular damage (unpredictable BP)

---

#### 5.4 Cholesterol

```python
Cholesterol = BaselineChol(Location)
              + AgeEffect(Age)
              + SexEffect(Sex)
              + RandomVariation

Where:
  BaselineChol:
    Urban ~ Normal(230, 35) mg/dL  ← Western diet
    Rural ~ Normal(200, 30) mg/dL  ← Traditional diet
  
  AgeEffect: +(Age - 30) × 0.5 mg/dL
  
  SexEffect:
    Male: +0 to +10 mg/dL
    Female: +0 mg/dL

Final range: 120 - 400 mg/dL
```

**Justification:**
- Nutrition transition in urban Nigeria (more processed food)
- Traditional rural diets → lower cholesterol
- Age-related increase is universal
- Males slightly higher (hormonal differences)

---

## Special Interactions Modeled

### 1. Smoking × Sickle Cell Disease

```python
if Genotype == 'SS':
    P(Smoker) = 0.01  # Extremely rare (<1%)
    
Justification:
  - Smoking triggers vaso-occlusive crises
  - Reduced oxygen → sickling → pain crisis
  - Most SCD patients educated to avoid smoking
```

### 2. Sickle Cell Trait × Malaria (Protective Effect)

```python
if Genotype == 'AS' and MalariaExposure == 'high':
    Severity = 'mild'  # Trait provides protection
    
Justification:
  - Evolutionary advantage in malaria-endemic areas
  - AS genotype reduces parasite multiplication
  - 50-90% protection against severe/cerebral malaria
  - This is WHY sickle cell trait persists at 24%
```

### 3. Multiple Comorbidities (Multiplicative Risk)

```python
if Smoker and Genotype == 'SS':
    StrokeRisk = BaselineRisk × 15  # Catastrophic
    
if Smoker and Hypertensive and Age > 55:
    CVDRisk = BaselineRisk × 8      # Very high
    
if Genotype == 'SS' and MalariaRecent:
    CrisisRisk = BaselineRisk × 5   # Triggers crisis
    HospitalizationNeeded = True
```

---

## Validation Strategy

### 1. Population-Level Validation

After generation, verify aggregate statistics match targets:

```python
Target vs Achieved:
  Smoking prevalence: 5.0% ± 0.3%  ✓
  Male smoking: 9.0% ± 0.5%        ✓
  Female smoking: 1.0% ± 0.2%      ✓
  AS genotype: 22% ± 1%            ✓
  SS genotype: 2% ± 0.3%           ✓
  Hypertension: 32% ± 2%           ✓
  Mean age: 38-40 years            ✓
```

### 2. Conditional Relationship Validation

Verify expected correlations exist:

```python
Correlation tests:
  Hemoglobin vs Heart Rate: Negative ✓ (lower Hb → higher HR)
  Age vs Blood Pressure: Positive ✓   (older → higher BP)
  Smoking vs Heart Rate: Positive ✓   (smokers → higher HR)
  SCD vs Hemoglobin: Negative ✓       (SS → much lower Hb)
```

### 3. Clinical Plausibility Checks

```python
Flag impossible combinations:
  - Hb > 18 g/dL → Polycythemia (rare, check)
  - Hb < 6 g/dL → Life-threatening (should be hospitalized)
  - BP > 200/120 → Hypertensive emergency
  - SS genotype + Hb > 12 → Implausible (investigate)
```

---

## Advantages of This Methodology

### 1. **Realistic Feature Interactions**
- Traditional synthetic data: Features generated independently
- This approach: Conditional probabilities model real biology
- ML models: Will learn actual disease relationships

### 2. **Population Heterogeneity**
- Not all smokers are unhealthy
- Not all non-smokers are healthy
- Sickle cell, malaria, hypertension create varied profiles
- Reflects real-world medical complexity

### 3. **Regional Variations**
- Urban Lagos ≠ Rural Sokoto
- Dataset captures geographic health disparities
- Useful for policy targeting and resource allocation

### 4. **Research Validity**
- Every parameter traceable to published research
- Transparent methodology enables critique and improvement
- Suitable for academic publication and peer review

### 5. **Educational Value**
- Teaches epidemiological thinking
- Shows how risk factors interact
- Demonstrates population vs individual risk

---

## Limitations & Assumptions

### 1. **Simplified Disease Models**
- Real biology is more complex
- We model major effects, not every pathway
- Chronic diseases (diabetes, TB, HIV) not yet included

### 2. **Static Snapshot**
- Dataset represents one point in time
- Doesn't model disease progression or aging
- No longitudinal follow-up

### 3. **Independence Assumptions**
- Some factors assumed independent when data unavailable
- Example: Cholesterol independent of sickle cell status
  (Real relationship unclear from literature)

### 4. **Regional Aggregation**
- Geopolitical zones aggregate many states
- Within-region variation exists but not modeled
- Assumes homogeneity within urban/rural categories

### 5. **Missing Confounders**
- Socioeconomic status (SES) affects health
- Education level correlates with smoking
- Occupation affects exposure risks
- These are not included (yet)

---

## Future Enhancements

### Potential Additions:

1. **Additional Comorbidities**
   - Diabetes prevalence (urban: 5-8%)
   - HIV/AIDS (1.3% overall, regional variation)
   - Tuberculosis co-infection with HIV
   - Chronic kidney disease

2. **Socioeconomic Factors**
   - Education level (affects health literacy)
   - Income quintile (affects healthcare access)
   - Occupation (exposure risks)

3. **Healthcare Access**
   - Distance to nearest hospital
   - Health insurance status (NHIS coverage: ~5%)
   - Traditional vs modern medicine use

4. **Temporal Dynamics**
   - Season (malaria seasonality)
   - Time since last medical visit
   - Disease progression trajectories

5. **Medication Effects**
   - Antihypertensive use (but adherence is low)
   - Antimalarial prophylaxis
   - Hydroxyurea for SCD (improves Hb)

---

## Technical Implementation Notes

### Random Seed
- Set to 42 for reproducibility
- All probabilistic steps use numpy.random with fixed seed
- Regenerating with same seed → identical dataset

### Performance
- Generates 3,900 records in ~5-10 seconds
- Scalable to millions of records
- Vectorization possible but not implemented (prioritized readability)

### Code Structure
```
nigerianize_smoking_health_dataset.py
├─ Constants (prevalence rates, names)
├─ Helper functions (one per factor)
├─ Main transformation function (orchestrates)
└─ Validation & summary statistics
```

### Output Formats
- CSV: Human-readable, universal compatibility
- Parquet: Compressed, efficient for analytics
- Both contain identical data

---

## Conclusion

This methodology demonstrates how to create **scientifically valid synthetic health data** using:
- ✅ Evidence-based probability distributions
- ✅ Conditional relationships from clinical research
- ✅ Multi-factor disease modeling
- ✅ Population-level validation
- ✅ Transparent, reproducible process

The result is a dataset that:
- Reflects Nigerian epidemiological reality
- Contains realistic feature interactions
- Supports both research and education
- Can be extended with additional factors
- Is fully documented and reproducible

---

**Document Version:** 1.0  
**Last Updated:** October 2025  
**Authors:** electricsheepafrica  
**License:** CC-BY-4.0 (documentation), MIT (dataset)