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Methodology, Parameters, and Calculations

Parameter definitions, formulas, uncertainty ranges, and data sources.
Doi

10.5281/zenodo.18203376

Keywords

health economics methodology, clinical trial cost analysis, medical research ROI, cost-benefit analysis healthcare, sensitivity analysis, Monte Carlo simulation, DALY calculation, pragmatic clinical trials

Overview

This appendix documents all 10 parameters used in the analysis, organized by type:

  • External sources (peer-reviewed): 7
  • Calculated values: 2
  • Core definitions: 1

Quick Navigation

Calculated Values (2 parameters) β€’ External Data Sources (7 parameters) β€’ Core Definitions (1 parameters)

Calculated Values

Parameters derived from mathematical formulas and economic models.

Total Deaths from Historical Progress Delays: 98.4M deaths

Total deaths from delaying existing drugs over 8.2-year efficacy lag. One-time impact of eliminating Phase 2-4 testing delay for drugs already approved 1962-2024. Based on 12M deaths/year rate Γ— 8.2 years. Excludes innovation acceleration effects.

Inputs:

\[ \begin{gathered} Deaths_{lag,total} \\ = T_{lag} \times 12000000 \\ = 8.2 \times 12000000 \\ = 98.4M \end{gathered} \]

Methodology: ../appendix/regulatory-mortality-analysis#historical-progress

βœ“ High confidence

Sensitivity Analysis

Sensitivity Indices for Total Deaths from Historical Progress Delays

Regression-based sensitivity showing which inputs explain the most variance in the output.

Input Parameter Sensitivity Coefficient Interpretation
Efficacy Lag Years 1.0000 Strong driver

Interpretation: Standardized coefficients show the change in output (in SD units) per 1 SD change in input. Values near Β±1 indicate strong influence; values exceeding Β±1 may occur with correlated inputs.

Monte Carlo Distribution

Monte Carlo Distribution: Total Deaths from Historical Progress Delays (10,000 simulations)

Simulation Results Summary: Total Deaths from Historical Progress Delays

Statistic Value
Baseline (deterministic) 98.4M
Mean (expected value) 98.3M
Median (50th percentile) 98.1M
Standard Deviation 23.7M
90% Confidence Interval [58.2M, 138M]

The histogram shows the distribution of Total Deaths from Historical Progress Delays across 10,000 Monte Carlo simulations. The CDF (right) shows the probability of the outcome exceeding any given value, which is useful for risk assessment.

Exceedance Probability

Probability of Exceeding Threshold: Total Deaths from Historical Progress Delays

This exceedance probability chart shows the likelihood that Total Deaths from Historical Progress Delays will exceed any given threshold. Higher curves indicate more favorable outcomes with greater certainty.

RECOVERY Trial Cost Reduction Factor: 82x

Cost reduction factor demonstrated by RECOVERY trial ($41K traditional / $500 RECOVERY = 82x)

Inputs:

\[ \begin{gathered} k_{RECOVERY} \\ = \frac{Cost_{P3,pt}}{Cost_{RECOVERY,pt}} \\ = \frac{\$41K}{\$500} \\ = 82 \end{gathered} \]

Methodology: Manhattan Institute - RECOVERY trial 82Γ— cost reduction

βœ“ High confidence

Sensitivity Analysis

Sensitivity Indices for RECOVERY Trial Cost Reduction Factor

Regression-based sensitivity showing which inputs explain the most variance in the output.

Input Parameter Sensitivity Coefficient Interpretation
Recovery Trial Cost Per Patient -2.4783 Strong driver
Traditional Phase3 Cost Per Patient 2.4635 Strong driver

Interpretation: Standardized coefficients show the change in output (in SD units) per 1 SD change in input. Values near Β±1 indicate strong influence; values exceeding Β±1 may occur with correlated inputs.

Monte Carlo Distribution

Monte Carlo Distribution: RECOVERY Trial Cost Reduction Factor (10,000 simulations)

Simulation Results Summary: RECOVERY Trial Cost Reduction Factor

Statistic Value
Baseline (deterministic) 82x
Mean (expected value) 71.2x
Median (50th percentile) 72.4x
Standard Deviation 15.3x
90% Confidence Interval [50x, 94.1x]

The histogram shows the distribution of RECOVERY Trial Cost Reduction Factor across 10,000 Monte Carlo simulations. The CDF (right) shows the probability of the outcome exceeding any given value, which is useful for risk assessment.

Exceedance Probability

Probability of Exceeding Threshold: RECOVERY Trial Cost Reduction Factor

This exceedance probability chart shows the likelihood that RECOVERY Trial Cost Reduction Factor will exceed any given threshold. Higher curves indicate more favorable outcomes with greater certainty.

External Data Sources

Parameters sourced from peer-reviewed publications, institutional databases, and authoritative reports.

Annual Global Clinical Trial Participants: 1.90M patients/year

Annual global clinical trial participants (IQVIA 2022: 1.9M post-COVID normalization)

Source: IQVIA Report - Global trial capacity

Uncertainty Range

Technical: 95% CI: [1.50M patients/year, 2.30M patients/year] β€’ Distribution: Lognormal

What this means: This estimate has moderate uncertainty. The true value likely falls between 1.50M patients/year and 2.30M patients/year (Β±21%). This represents a reasonable range that our Monte Carlo simulations account for when calculating overall uncertainty in the results.

The lognormal distribution means values can’t go negative and have a longer tail toward higher values (common for costs and populations).

Input Distribution

Probability Distribution: Annual Global Clinical Trial Participants

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

βœ“ High confidence

Regulatory Delay for Efficacy Testing Post-Safety Verification: 8.2 years

Regulatory delay for efficacy testing (Phase II/III) post-safety verification. Based on BIO 2021 industry survey. Note: This is for drugs that COMPLETE the pipeline - survivor bias means actual delay for any given disease may be longer if candidates fail and must restart.

Source: Biotechnology Innovation Organization (BIO) (2021) - BIO Clinical Development Success Rates 2011-2020

Uncertainty Range

Technical: Distribution: Normal (SE: 2 years)

Input Distribution

Probability Distribution: Regulatory Delay for Efficacy Testing Post-Safety Verification

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

~ Medium confidence β€’ πŸ“Š Peer-reviewed β€’ Updated 2021

Annual Deaths from All Diseases and Aging Globally: 55.0M deaths/year

Annual deaths from all diseases and aging globally

Source: World Health Organization (2024) - WHO Global Health Estimates 2024

Uncertainty Range

Technical: Distribution: Normal (SE: 5.00M deaths/year)

Input Distribution

Probability Distribution: Annual Deaths from All Diseases and Aging Globally

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

βœ“ High confidence

Phase 3 Trial Total Cost (Minimum): $20M

Phase 3 trial total cost (minimum)

Source: SofproMed - Phase 3 cost per trial range

βœ“ High confidence

Recovery Trial Cost per Patient: $500

RECOVERY trial cost per patient. Note: RECOVERY was an outlier - hospital-based during COVID emergency, minimal extra procedures, existing NHS infrastructure, streamlined consent. Replicating this globally will be harder.

Source: Oren Cass, Manhattan Institute (2023) - RECOVERY Trial Cost per Patient

Uncertainty Range

Technical: 95% CI: [$400, $2.50K] β€’ Distribution: Lognormal

What this means: This estimate is highly uncertain. The true value likely falls between $400 and $2.50K (Β±210%). This represents a very wide range that our Monte Carlo simulations account for when calculating overall uncertainty in the results.

The lognormal distribution means values can’t go negative and have a longer tail toward higher values (common for costs and populations).

Input Distribution

Probability Distribution: Recovery Trial Cost per Patient

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

βœ“ High confidence

RECOVERY Trial Global Lives Saved: 1.00M lives

Estimated lives saved globally by RECOVERY trial’s dexamethasone discovery. NHS England estimate (March 2021). Based on Águas et al. Nature Communications 2021 methodology applying RECOVERY trial mortality reductions (36% ventilated, 18% oxygen) to global COVID hospitalizations. Wide uncertainty range reflects extrapolation assumptions.

Source: NHS England; Águas et al. (2021) - RECOVERY trial global lives saved (~1 million)

Uncertainty Range

Technical: 95% CI: [500k lives, 2.00M lives] β€’ Distribution: Lognormal

What this means: This estimate is highly uncertain. The true value likely falls between 500k lives and 2.00M lives (Β±75%). This represents a very wide range that our Monte Carlo simulations account for when calculating overall uncertainty in the results.

The lognormal distribution means values can’t go negative and have a longer tail toward higher values (common for costs and populations).

Input Distribution

Probability Distribution: RECOVERY Trial Global Lives Saved

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

~ Medium confidence

Phase 3 Cost per Patient: $41K

Phase 3 cost per patient (median from FDA study)

Source: FDA Study via NCBI - Trial Costs, FDA Study

Uncertainty Range

Technical: 95% CI: [$20K, $120K] β€’ Distribution: Lognormal

What this means: This estimate is highly uncertain. The true value likely falls between $20K and $120K (Β±122%). This represents a very wide range that our Monte Carlo simulations account for when calculating overall uncertainty in the results.

The lognormal distribution means values can’t go negative and have a longer tail toward higher values (common for costs and populations).

Input Distribution

Probability Distribution: Phase 3 Cost per Patient

This chart shows the assumed probability distribution for this parameter. The shaded region represents the 95% confidence interval where we expect the true value to fall.

βœ“ High confidence

Core Definitions

Fundamental parameters and constants used throughout the analysis.

Stage 1 Observational Analysis Cost per Patient: $0.100

Order-of-magnitude estimate for Stage 1 observational signal detection (PIS calculation). Validated by FDA Sentinel benchmark (~$1/patient/year for similar drug safety analysis at 100M+ scale). True cost varies with scale and complexity; exact value less important than order-of-magnitude difference vs pragmatic trials (~$500-929/patient) and traditional Phase 3 (~$41,000/patient).

Uncertainty Range

Technical: 95% CI: [$0.030, $1.00] β€’ Distribution: Lognormal

What this means: This estimate is highly uncertain. The true value likely falls between $0.030 and $1.00 (Β±485%). This represents a very wide range that our Monte Carlo simulations account for when calculating overall uncertainty in the results.

The lognormal distribution means values can’t go negative and have a longer tail toward higher values (common for costs and populations).

Core definition

References

1.
Report, I. Global trial capacity. IQVIA Report: Clinical Trial Subjects Number Drops Due to Decline in COVID-19 Enrollment https://gmdpacademy.org/news/iqvia-report-clinical-trial-subjects-number-drops-due-to-decline-in-covid-19-enrollment/
1.9M participants annually (2022, post-COVID normalization from 4M peak in 2021) Additional sources: https://gmdpacademy.org/news/iqvia-report-clinical-trial-subjects-number-drops-due-to-decline-in-covid-19-enrollment/
.
2.
(BIO), B. I. O. BIO clinical development success rates 2011-2020. Biotechnology Innovation Organization (BIO) https://go.bio.org/rs/490-EHZ-999/images/ClinicalDevelopmentSuccessRates2011_2020.pdf (2021)
Phase I duration: 2.3 years average Total time to market (Phase I-III + approval): 10.5 years average Phase transition success rates: Phase I→II: 63.2%, Phase II→III: 30.7%, Phase III→Approval: 58.1% Overall probability of approval from Phase I: 12% Note: Largest publicly available study of clinical trial success rates. Efficacy lag = 10.5 - 2.3 = 8.2 years post-safety verification. Additional sources: https://go.bio.org/rs/490-EHZ-999/images/ClinicalDevelopmentSuccessRates2011_2020.pdf
.
3.
Organization, W. H. WHO global health estimates 2024. World Health Organization https://www.who.int/data/gho/data/themes/mortality-and-global-health-estimates (2024)
Comprehensive mortality and morbidity data by cause, age, sex, country, and year Global mortality:  55-60 million deaths annually Lives saved by modern medicine (vaccines, cardiovascular drugs, oncology):  12M annually (conservative aggregate) Leading causes of death: Cardiovascular disease (17.9M), Cancer (10.3M), Respiratory disease (4.0M) Note: Baseline data for regulatory mortality analysis. Conservative estimate of pharmaceutical impact based on WHO immunization data (4.5M/year from vaccines) + cardiovascular interventions (3.3M/year) + oncology (1.5M/year) + other therapies. Additional sources: https://www.who.int/data/gho/data/themes/mortality-and-global-health-estimates
.
4.
SofproMed. Phase 3 cost per trial range. SofproMed https://www.sofpromed.com/how-much-does-a-clinical-trial-cost
Phase 3 clinical trials cost between $20 million and $282 million per trial, with significant variation by therapeutic area and trial complexity. Additional sources: https://www.sofpromed.com/how-much-does-a-clinical-trial-cost | https://www.cbo.gov/publication/57126
.
5.
Oren Cass, M. I. RECOVERY trial cost per patient. Oren Cass https://manhattan.institute/article/slow-costly-clinical-trials-drag-down-biomedical-breakthroughs (2023)
The RECOVERY trial, for example, cost only about
\(500 per patient... By contrast, the median per-patient cost of a pivotal trial for a new therapeutic is around \\\)41,000. Additional sources: https://manhattan.institute/article/slow-costly-clinical-trials-drag-down-biomedical-breakthroughs
.
6.
al., N. E. Á. et. RECOVERY trial global lives saved ( 1 million). NHS England: 1 Million Lives Saved https://www.england.nhs.uk/2021/03/covid-treatment-developed-in-the-nhs-saves-a-million-lives/ (2021)
Dexamethasone saved  1 million lives worldwide (NHS England estimate, March 2021, 9 months after discovery). UK alone: 22,000 lives saved. Methodology: Águas et al. Nature Communications 2021 estimated 650,000 lives (range: 240,000-1,400,000) for July-December 2020 alone, based on RECOVERY trial mortality reductions (36% for ventilated, 18% for oxygen-only patients) applied to global COVID hospitalizations. June 2020 announcement: Dexamethasone reduced deaths by up to 1/3 (ventilated patients), 1/5 (oxygen patients). Impact immediate: Adopted into standard care globally within hours of announcement. Additional sources: https://www.england.nhs.uk/2021/03/covid-treatment-developed-in-the-nhs-saves-a-million-lives/ | https://www.nature.com/articles/s41467-021-21134-2 | https://pharmaceutical-journal.com/article/news/steroid-has-saved-the-lives-of-one-million-covid-19-patients-worldwide-figures-show | https://www.recoverytrial.net/news/recovery-trial-celebrates-two-year-anniversary-of-life-saving-dexamethasone-result
.
7.
NCBI, F. S. via. Trial costs, FDA study. FDA Study via NCBI https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6248200/
Overall, the 138 clinical trials had an estimated median (IQR) cost of
\(19.0 million (\\\)12.2 million-
\(33.1 million)... The clinical trials cost a median (IQR) of \\\)41,117 (
\(31,802-\\\)82,362) per patient. Additional sources: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6248200/
.

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