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Clinical Trials

The Clinical Trials module covers Phase III superiority, non-inferiority, equivalence, oncology two-stage, cluster RCT, survival, and count endpoints.

Phase III superiority

power_compute(
  "rct_superiority_continuous",
  analysis = "post_hoc",
  d = 0.4,
  alpha = 0.025,
  n1 = 120,
  n2 = 120
)
#> ggpower result
#> Test: Clinical: RCT superiority (continuous endpoint)
#> Analysis: post_hoc
#> 
#> Input parameters
#>   tails: greater
#>   effect_size_d: 0.4
#>   alpha: 0.025
#>   sample_size_group_1: 120
#>   sample_size_group_2: 120
#> 
#> 
#> Output parameters
#>   noncentrality_parameter: 3.098387
#>   critical_t: 1.969982
#>   df: 238
#>   total_sample_size: 240
#>   power: 0.8698953
power_compute(
  "rct_superiority_binary",
  analysis = "a_priori",
  p0 = 0.3,
  p1 = 0.45,
  alpha = 0.025,
  power = 0.9,
  n1 = 50,
  n2 = 50
)
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> Warning: Large Fisher exact grids use Cohen's h normal approximation for speed.
#> ggpower result
#> Test: Clinical: RCT superiority (binary endpoint)
#> Analysis: a_priori
#> 
#> Input parameters
#>   tails: less
#>   p_group_1: 0.3
#>   p_group_2: 0.45
#>   alpha: 0.025
#>   sample_size_group_1: 217
#>   sample_size_group_2: 217
#>   target_power: 0.9
#> 
#> 
#> Output parameters
#>   effect_size_h: 0.3113494
#>   total_sample_size: 434
#>   actual_power: 0.9002812
#> 
#> 
#> Notes
#> - Fisher exact power enumerates all two-binomial outcome pairs and sums outcomes rejected by Fisher's exact test.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.
power_compute("multi_arm_superiority", "a_priori", f = 0.25, groups = 3,
              alpha = 0.05, power = 0.8)
#> ggpower result
#> Test: Clinical: Multi-arm superiority (ANOVA)
#> Analysis: a_priori
#> 
#> Input parameters
#>   effect_size_f: 0.25
#>   alpha: 0.05
#>   total_sample_size: 158
#>   groups: 3
#>   target_power: 0.8
#> 
#> 
#> Output parameters
#>   noncentrality_parameter: 9.875
#>   critical_f: 3.054385
#>   numerator_df: 2
#>   denominator_df: 155
#>   actual_power: 0.8021998
#> 
#> 
#> Notes
#> - Consider Dunnett adjustment for pairwise comparisons.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.

Non-inferiority

power_compute("rct_noninferiority_continuous", "a_priori", d = 0.1,
              ni_margin = 0.2, alpha = 0.025, power = 0.8, n1 = 100, n2 = 100)
#> ggpower result
#> Test: Clinical: Non-inferiority trial (continuous)
#> Analysis: a_priori
#> 
#> Input parameters
#>   tails: one
#>   effect_size_d: 0.1
#>   ni_margin: 0.2
#>   sample_size_group_1: 175
#>   sample_size_group_2: 176
#>   alpha: 0.025
#>   target_power: 0.8
#> 
#> 
#> Output parameters
#>   noncentrality_parameter: 2.810238
#>   critical_t: 1.966785
#>   df: 349
#>   total_sample_size: 351
#>   actual_power: 0.800255
#> 
#> 
#> Notes
#> - One-sided NI test: H0 difference <= -margin vs H1 difference > -margin.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.
power_compute("rct_noninferiority_binary", "post_hoc", p0 = 0.5, p1 = 0.55,
              ni_margin = 0.1, alpha = 0.025, n1 = 200, n2 = 200)
#> ggpower result
#> Test: Clinical: Non-inferiority trial (binary)
#> Analysis: post_hoc
#> 
#> Input parameters
#>   tails: one
#>   p_treatment: 0.55
#>   p_control: 0.5
#>   ni_margin: 0.1
#>   sample_size_group_1: 200
#>   sample_size_group_2: 200
#>   alpha: 0.025
#> 
#> 
#> Output parameters
#>   z_statistic: 3.007528
#>   total_sample_size: 400
#>   power: 0.8525803
#> 
#> 
#> Notes
#> - Normal approximation for NI on proportions (one-sided).

Equivalence (TOST)

power_compute("rct_equivalence_continuous", "a_priori", d = 0,
              eq_margin = 0.2, alpha = 0.05, power = 0.8, n1 = 80, n2 = 80)
#> ggpower result
#> Test: Clinical: Equivalence trial (continuous, TOST)
#> Analysis: a_priori
#> 
#> Input parameters
#>   effect_size_d: 0
#>   eq_margin: 0.2
#>   sample_size_group_1: 420
#>   sample_size_group_2: 420
#>   alpha: 0.05
#>   target_power: 0.8
#> 
#> 
#> Output parameters
#>   power_upper: 0.8945475
#>   power_lower: 0.8945475
#>   total_sample_size: 840
#>   actual_power: 0.8002153
#> 
#> 
#> Notes
#> - Two one-sided t tests (TOST); overall power is the product of both one-sided powers.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.
power_compute("rct_equivalence_proportion", "post_hoc", p0 = 0.5, p1 = 0.52,
              eq_margin = 0.1, alpha = 0.05, n1 = 150, n2 = 150)
#> ggpower result
#> Test: Clinical: Equivalence trial (proportions, TOST)
#> Analysis: post_hoc
#> 
#> Input parameters
#>   p_treatment: 0.52
#>   p_control: 0.5
#>   eq_margin: 0.1
#>   sample_size_group_1: 150
#>   sample_size_group_2: 150
#>   alpha: 0.05
#> 
#> 
#> Output parameters
#>   power_upper: 0.3979494
#>   power_lower: 0.6680152
#>   total_sample_size: 300
#>   power: 0.2658363
#> 
#> 
#> Notes
#> - TOST on proportion difference using normal approximation.

Simon two-stage (Phase II)

simon_two_stage supports post_hoc and sensitivity only.

power_compute("simon_two_stage", "post_hoc", p0 = 0.2, p1 = 0.4,
              r1 = 4, r = 10, n1 = 20, n2 = 20, alpha = 0.05)
#> ggpower result
#> Test: Clinical: Simon two-stage Phase II design
#> Analysis: post_hoc
#> 
#> Input parameters
#>   p0: 0.2
#>   p1: 0.4
#>   alpha: 0.05
#>   target_power: 0.8
#>   stage1_n: 20
#>   stage1_r: 4
#>   stage2_n: 20
#>   total_r: 10
#> 
#> 
#> Output parameters
#>   power: 0.9156202
#>   type_i_error: 0.05954113
#>   total_sample_size: 40
#>   expected_sample_size: 38.98096
#> 
#> 
#> Notes
#> - Simon optimal/minimax design power for specified (n1,r1,n2,r).

Cluster RCT

power_compute("cluster_rct", "a_priori", d = 0.4, icc = 0.05,
              cluster_size = 10, n_clusters = 20, alpha = 0.05, power = 0.8)
#> ggpower result
#> Test: Clinical: Cluster-randomized trial
#> Analysis: a_priori
#> 
#> Input parameters
#>   tails: two
#>   effect_size_d: 0.4
#>   icc: 0.05
#>   cluster_size: 10
#>   n_clusters_per_arm: 16
#>   alpha: 0.05
#>   target_power: 0.8
#> 
#> 
#> Output parameters
#>   design_effect: 1.45
#>   effective_n_per_arm: 110.3448
#>   noncentrality_parameter: 2.971125
#>   total_sample_size: 320
#>   actual_power: 0.8198668
#> 
#> 
#> Notes
#> - Design effect DE = 1 + (m-1)*ICC applied to two-arm cluster RCT.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.

Survival endpoints

power_compute("survival_pmu", "a_priori", hazard_ratio = 0.65,
              event_rate = 0.5, alpha = 0.05, power = 0.8)
#> ggpower result
#> Test: Clinical: Survival endpoint (log-rank / Cox framework)
#> Analysis: a_priori
#> 
#> Input parameters
#>   tails: two
#>   hazard_ratio: 0.65
#>   event_rate: 0.5
#>   allocation_ratio: 1
#>   total_sample_size: 339
#>   alpha: 0.05
#>   target_power: 0.8
#> 
#> 
#> Output parameters
#>   expected_events: 169.5
#>   z_statistic: 2.804228
#>   actual_power: 0.80074
#> 
#> 
#> Notes
#> - Schoenfeld/Freedman log-rank approximation for equal follow-up.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.

Binary and count endpoints

power_compute("rct_superiority_binary", "post_hoc", p0 = 0.3, p1 = 0.45,
              alpha = 0.025, n1 = 120, n2 = 120)
#> ggpower result
#> Test: Clinical: RCT superiority (binary endpoint)
#> Analysis: post_hoc
#> 
#> Input parameters
#>   tails: less
#>   p_group_1: 0.3
#>   p_group_2: 0.45
#>   alpha: 0.025
#>   sample_size_group_1: 120
#>   sample_size_group_2: 120
#> 
#> 
#> Output parameters
#>   effect_size_h: 0.3113494
#>   total_sample_size: 240
#>   power: 0.6319254
#> 
#> 
#> Notes
#> - Fisher exact power enumerates all two-binomial outcome pairs and sums outcomes rejected by Fisher's exact test.
power_compute("count_endpoint_poisson", "a_priori", exp_beta1 = 1.3,
              base_rate = 0.85, exposure = 1, alpha = 0.05, power = 0.9,
              total_n = 250)
#> ggpower result
#> Test: Clinical: Count endpoint (Poisson regression)
#> Analysis: a_priori
#> 
#> Input parameters
#>   tails: two
#>   exp_beta1: 1.3
#>   base_rate: 0.85
#>   exposure: 1
#>   alpha: 0.05
#>   total_sample_size: 180
#>   r2_other_x: 0
#>   x_variance: 1
#>   target_power: 0.9
#> 
#> 
#> Output parameters
#>   critical_z: -1.959964,  1.959964
#>   beta1: 0.2623643
#>   actual_power: 0.9006568
#> 
#> 
#> Notes
#> - Poisson regression support uses a large-sample Wald approximation; exact enumeration is a future refinement.
#> - A priori sample sizes are rounded up to integer values and actual power is recomputed.

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.