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Data Pipeline & Statistical Methodology

data_flow.Rmd

Data Pipeline & Statistical Methodology

This document details the mathematical models, long-format data schemas, variance partitioning algorithm, ANCOVA, and longitudinal time-series handling in foundr.

1. Long-Format Data Model

All primary data input objects must be organized in tidy long format containing:

# Core input schema:
tibble(
  dataset   = "DietStudy",        # Optional dataset tag
  strain    = "AJ",               # One of 8 CC strains (AJ, B6, 129, NOD, NZO, CAST, PWK, WSB)
  sex       = "F",                # Biological sex ("M" or "F")
  animal    = "1024",             # Subject identifier
  condition = "HF",               # Experimental condition/diet (optional)
  trait     = "Glucose_12wk",     # Trait name
  value     = 142.5               # Measured value
)

2. Orthogonal Variance Partitioning

The partition() function (R/partition.R) separates phenotypic variance into three mutually orthogonal components:

value=signal+rest+noise\text{value} = \text{signal} + \text{rest} + \text{noise}

Two-Step Linear Model Decomposition

  1. Reduced Model (Rest Estimation): Fit a reduced linear model predicting trait value from nuisance/experimental control factors (rest\text{rest}): value∼rest\text{value} \sim \text{rest}rest̂=predict(fitred),ered=value−rest̂\widehat{\text{rest}} = \text{predict}(\text{fit}_{\text{red}}), \quad e_{\text{red}} = \text{value} - \widehat{\text{rest}}

  2. Full Model (Signal Estimation): Fit the residuals from the reduced model (erede_{\text{red}}) against the signal factors (signal\text{signal}): ered∼signale_{\text{red}} \sim \text{signal}signal̂=predict(fitfull)\widehat{\text{signal}} = \text{predict}(\text{fit}_{\text{full}})

  3. Cell Mean Calculation: cellmean=signal̂+rest̂\text{cellmean} = \widehat{\text{signal}} + \widehat{\text{rest}}

By default: - When condition is present: signal = "strain * sex * condition", rest = "strain * sex + sex * condition". - When condition is absent: signal = "strain * sex", rest = "sex".

3. Statistical Summaries & ANCOVA

Strain Statistics & ANOVA F-Tests

strainstats() computes linear models for each trait to evaluate founder strain main effects and strain-by-sex interactions.

  • Cell means: Mean trait value within each strain x sex x condition cell.
  • Cell SDs: Standard deviations computed within each strain cell.
  • F-statistics and p-values: Evaluated via broom::glance() and broom::tidy().

ANCOVA Modeling

traitAncova() extends linear modeling by conditioning founder strain effects on continuous physiological covariates:

trait∼covariate+strain×sex\text{trait} \sim \text{covariate} + \text{strain} \times \text{sex}

4. Longitudinal Trait & AUC Integration

For time-series measurements (e.g. weekly body weights or glucose tolerance test curves), foundr provides:

  1. timetraits(): Parses trait strings containing embedded time suffixes (e.g. Weight_t1, Weight_t2).
  2. area_under_curve(): Computes trapezoidal Area Under the Curve (AUC) over time trajectories.
  3. traitTimes: S3 object wrapping longitudinal trajectories with custom autoplot() methods for visual curve comparisons across founder strains.