Sensitivity Analysis

Author

Ndoh Penn

Published

August 11, 2026

Why Sensitivity Analysis Is Required

The FDA’s 2026 draft guidance, Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products, calls for sensitivity analyses that demonstrate trial conclusions are robust to plausible variations in prior specification.

bayprior provides two dedicated functions:

sensitivity_grid() — evaluates posterior mean, SD, and efficacy probability
sensitivity_cri() — focuses on credible interval width and bounds

Sensitivity analysis is fully independent of conflict diagnostics. You can run it without first running prior_conflict() by supplying data_summary directly.

Supported Data Types

`type =`	Conjugate update	`param_grid` names
`"binary"`	Beta-Binomial	`alpha`, `beta`
`"continuous"`	Normal-Normal	`mu`, `sigma`
`"poisson"`	Gamma-Poisson	`shape`, `rate`
`"survival"`	Gamma-Exponential	`shape`, `rate`

Binary Data

prior    <- elicit_beta(mean = 0.30, sd = 0.10, method = "moments",
                        label = "Response rate")
data_obs <- list(type = "binary", x = 14, n = 40)

sa <- sensitivity_grid(
  prior        = prior,
  data_summary = data_obs,
  param_grid   = list(alpha = seq(1, 8, 1), beta = seq(2, 20, 2)),
  target       = c("posterior_mean", "prob_efficacy"),
  threshold    = 0.30
)
sa$influence_scores

posterior_mean  prob_efficacy 
     0.1940984      0.8184416

plot_tornado(sa)

plot_sensitivity(sa, target = "posterior_mean")

Credible Interval Sensitivity

cri_sa <- sensitivity_cri(
  prior        = prior,
  data_summary = data_obs,
  param_grid   = list(alpha = seq(1, 8, 1), beta = seq(2, 20, 2)),
  cri_level    = 0.95
)
cri_sa$influence_scores

     cri_lower      cri_upper      cri_width posterior_mean   posterior_sd 
    0.15946768     0.21751316     0.06678301     0.19409836     0.01716165

plot_sensitivity(cri_sa, target = "cri_width")

Poisson / Count Data

Sensitivity with Poisson data uses Gamma-Poisson conjugate updating.

prior_ae  <- elicit_gamma(mean = 0.15, sd = 0.06, method = "moments",
                           label = "AE rate (per person-year)")
data_pois <- list(type = "poisson", x = 18, n = 120)

sa_pois <- sensitivity_grid(
  prior        = prior_ae,
  data_summary = data_pois,
  param_grid   = list(shape = seq(2, 10, 1), rate = seq(5, 40, 5)),
  target       = c("posterior_mean", "prob_efficacy"),
  threshold    = 0.20
)
sa_pois$influence_scores

posterior_mean  prob_efficacy 
     0.0990000      0.6908443

plot_tornado(sa_pois)

plot_sensitivity(sa_pois, target = "posterior_mean")

Survival / Time-to-Event Data

Sensitivity with survival data uses Gamma-Exponential conjugate updating.

prior_hz  <- elicit_exponential(mean = 0.05, method = "moments",
                                 label = "OS hazard rate")
data_surv <- list(type = "survival", x = 30, n = 600)

sa_surv <- sensitivity_grid(
  prior        = prior_hz,
  data_summary = data_surv,
  param_grid   = list(shape = seq(1, 5, 0.5), rate = seq(5, 30, 5)),
  target       = c("posterior_mean", "prob_efficacy"),
  threshold    = 0.10
)
sa_surv$influence_scores

posterior_mean  prob_efficacy 
  2.033320e-03   8.021621e-06

plot_tornado(sa_surv)

cri_surv <- sensitivity_cri(
  prior        = prior_hz,
  data_summary = data_surv,
  param_grid   = list(shape = seq(1, 5, 0.5), rate = seq(5, 30, 5)),
  cri_level    = 0.95
)
plot_sensitivity(cri_surv, target = "cri_width")

Continuous Endpoints

prior_cont <- elicit_normal(mean = 0.0, sd = 0.3, method = "moments",
                             label = "Log odds ratio")
sa_cont <- sensitivity_grid(
  prior        = prior_cont,
  data_summary = list(type = "continuous", x = 0.20, sd = 0.25, n = 60),
  param_grid   = list(mu = seq(-0.5, 0.5, 0.1), sigma = seq(0.1, 0.8, 0.1)),
  target       = c("posterior_mean", "posterior_sd")
)
plot_tornado(sa_cont)

Interpreting Influence Scores

Score	Sensitivity	Implication
< 0.05	Not sensitive	Prior has negligible influence
0.05 – 0.15	Moderate	Report alongside primary estimate
> 0.15	Sensitive	Consider robust prior; emphasise data

Mixture Prior Sensitivity

e1  <- elicit_beta(mean = 0.25, sd = 0.08, method = "moments",
                   expert_id = "E1", label = "ORR")
e2  <- elicit_beta(mean = 0.40, sd = 0.10, method = "moments",
                   expert_id = "E2", label = "ORR")
mix <- aggregate_experts(list(E1 = e1, E2 = e2), weights = c(0.5, 0.5))

sa_mix <- sensitivity_grid(
  prior        = mix,
  data_summary = list(type = "binary", x = 14, n = 40),
  param_grid   = list(alpha = seq(1, 8, 1), beta = seq(2, 16, 2)),
  target       = "posterior_mean"
)
plot_tornado(sa_mix)

Note: for mixture priors, the grid varies the dominant component’s parameters. A compatibility warning is shown in the Shiny app.

Regulatory Reporting

Include in the clinical study report:

Influence score table — one row per posterior quantity
Tornado plot — ordered from most to least sensitive
Heatmap — for the primary efficacy quantity
Classification statement — sensitive / not sensitive per quantity

All three are generated automatically by prior_report() when a bayprior_sensitivity object is supplied.

References

FDA (2026). Use of Bayesian Methodology in Clinical Trials of Drug and Biological Products (Draft Guidance for Industry).
ICH E9(R1) (2019). Addendum on Estimands and Sensitivity Analysis.