Phi Statistics Drawer Verification & Validation

1. Validation conclusion

Phi 2.1.1 met every prespecified numerical acceptance criterion. All 15,702 comparisons against R passed, all 10 input and rule checks passed, and no statistical implementation defect was identified.

The evidence supports that Phi reproducibly implements its documented descriptive, survival, ROC/AUC, and curve-fitting methods. This is software verification and numerical validation; it is not clinical validation and does not determine whether a selected method is appropriate for a particular research question.

15,702Numerical comparisons

100%Within prespecified tolerance

10 / 10Input and rule checks

0Unresolved deviations

2. Scope and terminology

Verification

Confirms that the production implementation follows Phi's documented formulas, data rules, and display logic.

Validation

Confirms that Phi's numerical outputs agree with independent calculations in R across ordinary and difficult datasets.

The assessment covered the actual production routines for:

numeric and delimited-text parsing;
bar charts, boxplots, grouped and stacked bars, and paired dot plots;
Kaplan–Meier survival, risk sets, Greenwood variance, and pointwise log–log confidence intervals;
ROC curves, AUC, Youden cutoff, DeLong statistics, paired marker comparisons, and bootstrap intervals;
linear, logarithmic, and exponential regression;
forest-plot preservation and rejection rules.

3. Validation design

The test harness called validation hooks attached directly to Phi's production functions. It did not substitute a second JavaScript implementation of the statistical methods. R independently processed the same retained input datasets.

Area	Dataset design	Coverage
Descriptive tools	Canonical and deterministic generated datasets	104 datasets; signed values, ties, constants, singletons, multiple groups and categories
Regression	Separate deterministic sets for every model	52 datasets per model; 4,867 observations overall
Kaplan–Meier	Canonical and generated time-to-event data	56 datasets; ties, censoring, zero-time events, terminal events, and no-event data
ROC/AUC	Paired marker datasets with fixed class order	55 datasets; both directions, ties, imbalance, paired DeLong, and bootstrap subset
Input and forest rules	Hand-constructed boundary cases	10 explicit parsing, delimiter, scale, and interval checks

4. Independent R reference

The reference environment was frozen and recorded with the result files:

R: 4.5.2
survival: 3.8-3
pROC: 1.19.0.1
D3 used by Phi: 6.7.0
Regression precision used by Phi: 10 decimal places

Base R provided descriptive summaries and regression reference calculations. Quartiles used R's type-7 empirical quantile, matching D3 interpolation. survival::survfit provided the Kaplan–Meier reference. pROC provided AUC and DeLong reference values.

Phi reports an observed marker value as the Youden cutoff. Some R functions instead report the midpoint between adjacent observations. The validation therefore evaluated Phi's documented observed-threshold definition independently in R rather than treating this intentional reporting difference as an error.

5. Prespecified acceptance criteria

Output class	Acceptance criterion
Counts, groups, exclusions, frequencies	Exact equality
Deterministic numerical results	Absolute difference ≤ 1 × 10⁻¹⁰
Regression library outputs	Absolute difference ≤ 1 × 10⁻⁹
Kaplan–Meier log–log confidence limits	Absolute difference ≤ 1 × 10⁻⁴
Normal-approximation p-values	Absolute difference ≤ 1 × 10⁻⁶
Independent bootstrap percentile limits	Absolute difference ≤ 0.04

6. Results

Module family	Comparisons	Passed	Maximum absolute difference	Status
Descriptive and categorical tools	6,755	6,755	1.28 × 10⁻¹³	Passed
Regression tools	624	624	0	Passed
Kaplan–Meier and risk sets	7,698	7,698	1.32 × 10⁻⁵	Passed
ROC/AUC deterministic statistics	605	605	1.39 × 10⁻⁷	Passed
ROC bootstrap limits	20	20	0.0167	Passed
Total	15,702	15,702	—	Passed

Observed numerical agreement

Descriptive calculations agreed with R to floating-point precision. All three regression families reproduced the independently evaluated R results exactly at the ten-decimal production precision. ROC/AUC and paired DeLong differences were below 1.39 × 10⁻⁷, driven by Phi's documented normal-distribution approximation for p-values.

The largest Kaplan–Meier difference was 0.0000133 in a confidence limit. Phi uses the documented multiplier 1.96, whereas R uses the more precise 97.5% standard-normal quantile. Five confidence-limit values near a rounding boundary consequently differed in the third displayed decimal; all remained well inside the prespecified tolerance and the underlying survival estimates and risk sets agreed.

Bootstrap samples were generated independently in Phi and R, so identical limits were neither expected nor required. The largest observed limit difference was 0.0167, below the prespecified 0.04 criterion.

7. Interpretation

The validation demonstrates that Phi 2.1.1 accurately transforms valid input data into the documented summary statistics, survival estimates, ROC/AUC results, regression parameters, tables, and plot data. No hidden smoothing, inferential testing, or undocumented data replacement was found.

Release assessment: Phi Statistics Drawer 2.1.1 is verified against its methodology and numerically validated against R for its intended role as a statistical visualization and descriptive curve-fitting tool.

8. Limitations and intended use

The validation establishes software correctness, not the suitability of a method for a particular dataset.
It does not establish clinical performance, diagnostic accuracy of a real biomarker, or regulatory fitness.
Bootstrap confidence limits are stochastic estimates and may vary slightly across independent runs and software environments.
Forest plots visualize user-supplied estimates and intervals; responsibility for those source estimates remains with the user.
Users remain responsible for data quality, study design, model choice, interpretation, and independent scientific review.