exact.md
In basket: Basket Trial Analysis

Full Bayes can be calculated correctly.

Code
  unclass(summary(exact_res))
Output
  $call
  mem_exact(responses = vemu_wide1$responders, size = vemu_wide1$evaluable, 
      name = vemu_wide1$baskets, p0 = 0.25, cluster_analysis = TRUE)

  $basket

  The Null Response Rates (alternative is greater):
                 NSCLC CRC (vemu) CRC (vemu+cetu)
  Null           0.250      0.250            0.25
  Posterior Prob 0.951      0.002            0.00

  Posterior Mean and Median Response Rates:
         NSCLC CRC (vemu) CRC (vemu+cetu)
  Mean   0.425      0.041           0.042
  Median 0.422      0.032           0.033

  Highest Posterior Density Interval with Coverage Probability 0.95:
        NSCLC CRC (vemu) CRC (vemu+cetu)
  lower 0.208      0.000           0.000
  upper 0.628      0.105           0.109

  Posterior Effective Sample Size:
   NSCLC CRC (vemu) CRC (vemu+cetu)
   19.93     55.647          50.867


  $cluster

  Cluster 1        
   "NSCLC"
  Cluster 2                               
   "CRC (vemu)" "CRC (vemu+cetu)"

  The Null Response Rates (alternative is greater):
                             Cluster 1 Cluster 2
  Posterior for null of 0.25     0.951     0.001

  Posterior Mean and Median Response Rates:
         Cluster 1 Cluster 2
  Mean       0.425     0.041
  Median     0.422     0.033

  Highest Posterior Density Interval with Coverage Probability 0.95:
              Cluster 1 Cluster 2
  Lower Bound     0.214     0.000
  Upper Bound     0.631     0.107

  Posterior Effective Sample Size:
   Cluster 1 Cluster 2
       20.28     52.91

Exact corner case models

Code
  summary(basket(responses = vemu_wide1$responders, size = vemu_wide1$evaluable,
  name = vemu_wide1$baskets, cluster_analysis = TRUE, p0 = 0.25, method = "exact"))
Output

  -- The MEM Model Call ----------------------------------------------------------

  mem_exact(responses = responses, size = size, name = name, p0 = p0, 
      shape1 = shape1, shape2 = shape2, prior = prior, hpd_alpha = hpd_alpha, 
      alternative = alternative, seed = seed, cluster_analysis = cluster_analysis, 
      call = call, cluster_function = cluster_function)

  -- The Basket Summary ----------------------------------------------------------

  The Null Response Rates (alternative is greater):
                 NSCLC CRC (vemu) CRC (vemu+cetu)
  Null           0.250      0.250            0.25
  Posterior Prob 0.951      0.002            0.00

  Posterior Mean and Median Response Rates:
         NSCLC CRC (vemu) CRC (vemu+cetu)
  Mean   0.424      0.041           0.042
  Median 0.422      0.032           0.033

  Highest Posterior Density Interval with Coverage Probability 0.95:
        NSCLC CRC (vemu) CRC (vemu+cetu)
  lower 0.215      0.000           0.000
  upper 0.625      0.107           0.105

  Posterior Effective Sample Size:
    NSCLC CRC (vemu) CRC (vemu+cetu)
   20.933     52.153          55.786

  -- The Cluster Summary ---------------------------------------------------------

  Cluster 1        
   "NSCLC"
  Cluster 2                               
   "CRC (vemu)" "CRC (vemu+cetu)"

  The Null Response Rates (alternative is greater):
                             Cluster 1 Cluster 2
  Posterior for null of 0.25     0.951     0.001

  Posterior Mean and Median Response Rates:
         Cluster 1 Cluster 2
  Mean       0.424     0.041
  Median     0.422     0.033

  Highest Posterior Density Interval with Coverage Probability 0.95:
              Cluster 1 Cluster 2
  Lower Bound     0.219     0.000
  Upper Bound     0.637     0.107

  Posterior Effective Sample Size:
   Cluster 1 Cluster 2
      20.091    52.918

Code
  summary(mem_exact(responses = c(4, 3, 0), size = c(10, 3, 0), name = letters[1:
  3], cluster_analysis = TRUE, p0 = 0.25))
Output

  -- The MEM Model Call ----------------------------------------------------------

  mem_exact(responses = c(4, 3, 0), size = c(10, 3, 0), name = letters[1:3], 
      p0 = 0.25, cluster_analysis = TRUE)

  -- The Basket Summary ----------------------------------------------------------

  The Null Response Rates (alternative is greater):
                     a     b     c
  Null           0.250 0.250 0.250
  Posterior Prob 0.873 0.997 0.855

  Posterior Mean and Median Response Rates:
             a     b     c
  Mean   0.420 0.848 0.590
  Median 0.415 0.919 0.574

  Highest Posterior Density Interval with Coverage Probability 0.95:
            a     b     c
  lower 0.146 0.473 0.067
  upper 0.693 1.000 1.000

  Posterior Effective Sample Size:
        a     b     c
   11.073 5.199 2.187

  -- The Cluster Summary ---------------------------------------------------------

  Cluster 1    
   "a"
  Cluster 2    
   "b"
  Cluster 3    
   "c"

  The Null Response Rates (alternative is greater):
                             Cluster 1 Cluster 2 Cluster 3
  Posterior for null of 0.25     0.873     0.997     0.855

  Posterior Mean and Median Response Rates:
         Cluster 1 Cluster 2 Cluster 3
  Mean       0.420     0.848     0.590
  Median     0.415     0.919     0.574

  Highest Posterior Density Interval with Coverage Probability 0.95:
              Cluster 1 Cluster 2 Cluster 3
  Lower Bound     0.147     0.472     0.063
  Upper Bound     0.699     1.000     1.000

  Posterior Effective Sample Size:
   Cluster 1 Cluster 2 Cluster 3
      10.817     5.171      2.12

Code
  summary(mem_exact(responses = c(4, 3), size = c(10, 3), name = letters[1:2],
  cluster_analysis = TRUE, p0 = 0.25))
Output

  -- The MEM Model Call ----------------------------------------------------------

  mem_exact(responses = c(4, 3), size = c(10, 3), name = letters[1:2], 
      p0 = 0.25, cluster_analysis = TRUE)

  -- The Basket Summary ----------------------------------------------------------

  The Null Response Rates (alternative is greater):
                     a     b
  Null           0.250 0.250
  Posterior Prob 0.873 0.997

  Posterior Mean and Median Response Rates:
             a     b
  Mean   0.419 0.847
  Median 0.414 0.918

  Highest Posterior Density Interval with Coverage Probability 0.95:
            a     b
  lower 0.148 0.474
  upper 0.699 1.000

  Posterior Effective Sample Size:
        a     b
   10.816 5.251

  -- The Cluster Summary ---------------------------------------------------------

  Cluster 1    
   "a"
  Cluster 2    
   "b"

  The Null Response Rates (alternative is greater):
                             Cluster 1 Cluster 2
  Posterior for null of 0.25     0.872     0.997

  Posterior Mean and Median Response Rates:
         Cluster 1 Cluster 2
  Mean       0.419     0.847
  Median     0.414     0.918

  Highest Posterior Density Interval with Coverage Probability 0.95:
              Cluster 1 Cluster 2
  Lower Bound     0.148     0.471
  Upper Bound     0.699     1.000

  Posterior Effective Sample Size:
   Cluster 1 Cluster 2
      10.841     5.188