### A Pluto.jl notebook ###
# v0.19.9

using Markdown
using InteractiveUtils

# ╔═╡ 34fbdb77-8899-4ded-b7c3-d8ce5bf389e4
begin 
	using LsqFit
	using MortalityTables
	using Plots
	using Distributions
	using Optim
	using DataFrames
	using PlutoUI; TableOfContents()
end

# ╔═╡ 2487083e-d93f-4b71-b137-9611edde71df
using Survival

# ╔═╡ f79bd079-777a-4e76-9f83-63ae34330ff5
md"# Fitting survival data with MortaltityTables.jl

via [PharmCat on Github](https://gist.github.com/PharmCat/fe1e64a2241aa35d3a3fa925989c3784) (this link has similar code with comments in Russian and English).

"

# ╔═╡ 3a565024-a060-49ff-ae3b-9636fc5abb84
md"## Fitting a Weibull survival curve"

# ╔═╡ eabce1d8-a7e6-40fc-8ce1-d545c5a987ff
md" Sample data:"

# ╔═╡ 942d11f7-98e5-4e2b-b8ed-ccdac7c7739a
data = let
	survival = [0.99,0.98,0.95,0.9,0.8,0.65,0.5,0.38,0.25,0.2,0.1,0.05,0.02,0.01]
	times = 1:length(survival)
	DataFrame(;times,survival)
end

# ╔═╡ a2da7554-86fc-438e-8b2f-0529237c178a
plt = plot(data.times,data.survival,label="observed survival proportion",xlabel="time")

# ╔═╡ 6f386750-3f06-4933-ba8a-bb27e1c199a8
md"""
Define the two-parameter Weibull model:

- `x`: array of independent variables
- `p`: array of model parameters

model(x, p) will accept the full data set as the first argument `x`.
This means that we need to write our model function so it applies the model to the full dataset. We use `@.` to apply ("broadcast") the calculations across all rows.

"""

# ╔═╡ e268f308-0ded-40fd-9fc7-a8af811b3d05
@. model1(x, p) = survival(MortalityTables.Weibull(;m = p[1],σ = p[2]), x)

# ╔═╡ d67dabc3-0a99-4c52-b9f9-54b7eb943ed3
md" 
#### Fitting the Model
And fit the model with [LsqFit.jl](https://github.com/JuliaNLSolvers/LsqFit.jl):"

# ╔═╡ 2969a021-5bae-4608-bd7c-b6a133816dc1
fit1 = curve_fit(model1, data.times, data.survival, [1.0, 1.0])

# ╔═╡ db56dad3-1220-4476-a364-efd7473262fc
plot!(plt,data.times, model1(data.times, fit1.param),label="fitted model")

# ╔═╡ a34e7551-83f6-487c-8227-61fa3ea5d729
md" ### Maximum Likelihood estimation

Generate 100 sample datapoints:"

# ╔═╡ f64f0d83-d95d-4f90-bfde-6c040381c281
t = rand(Weibull(fit1.param[2], fit1.param[1]), 100)

# ╔═╡ 04096c4d-a4e4-486e-ae35-20bdff6af1ac
md"### Without Censored Data"

# ╔═╡ 1cc70ce0-8779-439b-bc88-eae4e40c07aa
#No censored data
fit_mle(Weibull, t)

# ╔═╡ 14f8309c-de59-49a3-aee6-504fbda29de9
md"
### With Censored Data
"

# ╔═╡ a0540aa8-046b-4ee0-8637-5d0bda68b7b8
c = collect(trues(100))

# ╔═╡ 89f90fec-31bb-4b5d-aed4-7e04e83856f4
c[[1,3,7,9]] .= false

# ╔═╡ 5e6c184a-467a-4350-8d16-dbc54d1ea2f7
#ML function
survmle(x) = begin
    ml = 0.0
    for i = 1:length(t)
        if c[i]
            ml += logpdf(Weibull(x[2], x[1]), t[i]) #if not censored log(f(x))
        else
            ml += logccdf(Weibull(x[2], x[1]), t[i]) #if censored log(1-F)
        end
    end
    -ml
end

# ╔═╡ d9fd961a-ac4e-497e-9f46-6a5014731851

opt = Optim.optimize(
	survmle,          	# function to optimize
	[1.0,1.0], 			# lower bound
	[15.,15.],            # upper bound
	[3.,3.]          	# initial guess
)

# ╔═╡ 3fb53bc8-3eb0-4e10-9a2a-d0f1c07beb49
md" The solution converges to similar values as the function generating the synthetic data:"

# ╔═╡ 11820bd2-8c11-4c1a-a2d4-0f5efdaf8f4c
Optim.minimizer(opt)

# ╔═╡ 979e6a2b-a367-4d23-8d60-2f63573ccf2f
md" ## Fitting Kaplan Meier

KaplanMeier comes from [Survival.jl](https://github.com/JuliaStats/Survival.jl)"

# ╔═╡ e6bc4703-89c6-4abd-823e-6559c27566eb
#4
#Подгонка модели по эмпирической функции KM
#Fitting for survival function from Kaplan Meier


# ╔═╡ 075d13cd-1972-4d4c-9eaa-637e5cb770a3
#t- time vector;c - censored events vector
km = fit(Survival.KaplanMeier, t, c)

# ╔═╡ 35219013-d1ba-4ca9-95d9-12700e24338b
plt2 = plot(km.times, km.survival; labels="Empirical")

# ╔═╡ a4a026f4-ba70-4d44-a3c4-8a4ffb69d118
@. model(x, p) = survival(MortalityTables.Weibull(;m = p[1],σ = p[2]), x)

# ╔═╡ aba4714d-6736-41a7-b34d-f1c80473a4de
mfit = LsqFit.curve_fit(model, km.times, km.survival, [2.0, 2.0])

# ╔═╡ 46238ca0-3010-4235-97f6-98cebfe47442
plot!(plt2,km.times, model(km.times, mfit.param), labels="Theoretical")

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version = "5.1.1+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.47.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

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