Merge pull request #6 from openpharma/2_meta_analytic

2: Add meta_analytic Turing model

Project.toml

@@ -11,5 +11,7 @@ ExpectationMaximization = "e1fe09cc-5134-44c2-a941-50f4cd97986a"
 FreqTables = "da1fdf0e-e0ff-5433-a45f-9bb5ff651cb1"
 Pluto = "c3e4b0f8-55cb-11ea-2926-15256bba5781"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

src/BSSD.jl

@@ -0,0 +1,12 @@
+module BSSD
+
+using Turing
+using StatsPlots
+using Distributions
+
+export 
+    meta_analytic
+
+include("meta_analytic.jl")
+
+end 

src/meta_analytic.jl

@@ -0,0 +1,28 @@
+"""
+    Meta Analytic Prior Model
+
+This Turing model is used to generate posterior samples of the parameters `a` and `b`.
+"""
+@model function meta_analytic(
+    y::Vector{Bool}, 
+    time::Vector{Float64}, 
+    trialindex::Vector{Int64}, 
+    prior_a::Distribution, 
+    prior_b::Distribution)
+
+    n = length(y)
+    n_trials = maximum(trialindex)
+
+    a ~ prior_a
+    b ~ prior_b
+    pis ~ filldist(Beta(a * b * n, (1 - a) * b * n), n_trials)
+
+    for i in 1:n
+        pi = pis[trialindex[i]]
+        mu = log(-log(1 - pi))
+        x = mu + log(time[i])
+        prob = 1 - exp(-exp(x))
+        y[i] ~ Bernoulli(prob)
+    end
+
+end;

test/runtests.jl

@@ -0,0 +1,45 @@
+using Test
+using StableRNGs
+using Random
+using Distributions
+using DataFrames
+using Turing
+using BSSD
+
+# Helper function for numerical tests.
+# Taken from https://github.com/TuringLang/Turing.jl/blob/master/test/test_utils/numerical_tests.jl#L41 for now.
+function check_numerical(chain,
+    symbols::Vector,
+    exact_vals::Vector;
+    atol=0.2,
+    rtol=0.0)
+    for (sym, val) in zip(symbols, exact_vals)
+        E = val isa Real ?
+            mean(chain[sym]) :
+            vec(mean(chain[sym], dims=1))
+        @info (symbol=sym, exact=val, evaluated=E)
+        @test E ≈ val atol=atol rtol=rtol
+    end
+end
+
+@testset "meta_analytic.jl" begin
+    rng = StableRNG(123)
+
+    n_trials = 5
+    n_patients = 50
+    df = DataFrame(
+        y = rand(rng, Bernoulli(0.2), n_trials * n_patients),
+        time = rand(rng, Exponential(1), n_trials * n_patients),
+        trialindex = repeat(1:n_trials, n_patients)
+    )
+
+    chain = sample(
+        rng,
+        meta_analytic(df.y, df.time, df.trialindex, Beta(2, 8), Beta(9, 10)), 
+        HMC(0.05, 10), 
+        1000
+    )
+
+    check_numerical(chain, [:a], [0.223], rtol=0.001)
+    check_numerical(chain, [:b], [0.485], rtol=0.001)
+end