Sparse Concordance-assisted Learning for Optimal Treatment Decision
Authors: Shuhan Liang, Wenbin Lu, Rui Song, Lan Wang
JMLR 2017 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Simulation results of various settings and application to STAR*D both illustrate that the proposed method can still estimate optimal treatment regime successfully when the number of covariates is large. In Section 4, we demonstrate the performance of sparse concordance-assisted learning at different settings. We present results of the proposed method for the STAR*D clinical trial in Section 5. |
| Researcher Affiliation | Academia | Shuhan Liang EMAIL Department of Statistics North Carolina State University Raleigh, NC 27695, USA; Wenbin Lu EMAIL Department of Statistics North Carolina State University Raleigh, NC 27695, USA; Rui Song EMAIL Department of Statistics North Carolina State University Raleigh, NC 27695, USA; Lan Wang EMAIL School of Statistics University of Minnesota Minneapolis, MN 55455, USA |
| Pseudocode | Yes | We add ancillary variables θ and reformulate (1) as: minf1(β) + f2(θ) subject to θ = Dβ where f1(β) = λ||β||1,f2(θ) = P(n 2) i=1 δwi(1 Diβ)+. The iterative algorithm is as follows: 1. V + 1 = proxtf1(β), proxtf2(θ) , where [proxtf1(β)]j = S(βj, tλ), S is soft thresholding operator: S(x, λ) = sgn(x)(|x| λ)+. [proxtf2(β)]i = 1 θ [1 tδwi, 1], θi θ > 1, θi + tδwi θ < 1 tδwi. 2. V + 2 = I D R T R 1h P1(2V + 1 V3) + DT P2(2V + 1 V3) i , P1(β, θ) = β, P2(β, θ) = θ, RRT = I + DT D is Cholesky decomposition. 3. V + 3 = V3 + V + 2 V + 1 . until convergence. Output: β |
| Open Source Code | No | We use three methods: CVX, a package for specifying and solving convex programs (Michael and Stephen 2014, Grant and Boyd 2008), GLPK (GNU Linear Programming Kit, glp 2016) and the method proposed by Spingarn (1985) to find the minimizer. |
| Open Datasets | Yes | We apply the proposed method to STAR*D Study, the largest and longest study ever conducted to assess effectiveness of depression treatments. ... We would like to acknowledge support for this project from National Institute of Mental Health for providing the STAR*D data. |
| Dataset Splits | Yes | λopt is tuned using 5-fold cross validation. ... For comparison, we also evaluate the performance of POWL using 5-fold cross validation. |
| Hardware Specification | No | In summary, CVX is the least computational efficient way to estimate prescriptive index and Spingarn s Method is the only approach that can handle STAR*D trial in terms of its scale. |
| Software Dependencies | No | We use three methods: CVX, a package for specifying and solving convex programs (Michael and Stephen 2014, Grant and Boyd 2008), GLPK (GNU Linear Programming Kit, glp 2016) and the method proposed by Spingarn (1985) to find the minimizer. ... POWL is implemented using convex toolbox in MATLAB. |
| Experiment Setup | Yes | Xi1, Xi2, ..., Xi50 are generated independently from a uniform distribution on [ 1, 1], i = 1, , n. The treatment indicator A is generated from Bernoulli distribution with p = 0.5. The conditional density of the response Y given X and A is normal, with mean Q0(Xi) = 1 + 2Xi1 + Xi2 + 0.5Xi3 + 0.442(1 Xi1 Xi2)(2Ai 1) and variance 1. ... Covariates Xi = (Xi1, Xi2, ..., Xip)T are generated from a multivariate normal distribution: each entry is standard normal and the correlation between covariates is Corr(Xij, Xik) = ρ|j k| for 1 j = k p. ρ is chosen to be 0 and 0.2 respectively. The error term ϵ is generated from standard normal distribution. We ran 100 simulations for each scenario with n=100 and p=500, 1000 respectively. ... λopt is tuned using 5-fold cross validation. A pre-defined range (0, 4) is searched and λ is chosen based on the IPW estimator. ... The response is shifted with the smallest value to be 0.01. |