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Sensitivity Analysis

Ndoh Penn

2026-05-29

Why Sensitivity Analysis Is Required

Regulatory guidelines — including the FDA Draft Guidance on Bayesian Statistical Methods (2026) and ICH E9(R1) — require demonstrating that trial conclusions are robust to plausible variations in prior specification.

bayprior provides two dedicated functions:

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:

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

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

References

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.