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marivascruz authored Feb 9, 2021
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# Multi-snpnet-Cox (mrcox) Efficient Group-Sparse Lasso solver for multi-response Cox model
This package provide functions that solve the following multi-response, group-sparse regularized Cox regression:

![equation](https://latex.codecogs.com/svg.latex?%5Cmin_%7B%5Cbeta_1%2C%5Ccdots%2C%26space%3B%5Cbeta_K%7D%26space%3B%5Csum_%7Bk%3D1%7D%5EK%26space%3B%5Cfrac%7B1%7D%7Bn_k%7D%26space%3B%5Cleft%5B%5Csum_%7Bi%3AO_i%5Ek%26space%3B%3D%26space%3B1%7D%26space%3B-%5Cbeta_k%5ET%26space%3BX_i%26space%3B%26plus%3B%26space%3B%5Clog%26space%3B%5Cleft%28%5Csum_%7Bj%3AT%5Ek_j%26space%3B%5Cge%26space%3BT%5Ek_i%7D%26space%3B%5Cexp%28%5Cbeta_k%5ET%26space%3BX_j%29%5Cright%29%5Cright%5D%26space%3B%26plus%3B%26space%3B%5Clambda%26space%3B%5Cleft%28%26space%3B%5Csum_%7Bj%3D1%7D%5Ed%26space%3B%5C%7C%5Cbeta%5Ej%5C%7C_1%26space%3B%26plus%3B%26space%3B%5Calpha%26space%3B%5C%7C%5Cbeta%5Ej%5C%7C_2%26space%3B%5Cright%29.)
![equation](https://latex.codecogs.com/svg.latex?%5Cmin_%7B%5Cbeta_1%2C%5Ccdots%2C%26space%3B%5Cbeta_K%7D%26space%3B%5Csum_%7Bk%3D1%7D%5EK%26space%3B%5Cfrac%7B1%7D%7Bn_k%7D%26space%3B%5Cleft%5B%5Csum_%7Bi%3AO_i%5Ek%26space%3B%3D%26space%3B1%7D%26space%3B-%5Cbeta_k%5ET%26space%3BX_i%26space%3B%26plus%3B%26space%3B%5Clog%26space%3B%5Cleft%28%5Csum_%7Bj%3AT%5Ek_j%26space%3B%5Cge%26space%3BT%5Ek_i%7D%26space%3B%5Cexp%28%5Cbeta_k%5ET%26space%3BX_j%29%5Cright%29%5Cright%5D%26space%3B%26plus%3B%26space%3B%5Clambda%26space%3B%5Cleft%28%26space%3B%5Csum_%7Bj%3D1%7D%5Ed%26space%3B%5C%7C%5Cbeta%5Ej%5C%7C_1%26space%3B%26plus%3B%26space%3B%5Calpha%26space%3B%5C%7C%5Cbeta%5Ej%5C%7C_2%26space%3B%5Cright%29)

Where <img src="https://latex.codecogs.com/gif.latex?\inline&space;\beta_k" title="\beta_k" /> is the coefficient vector of the kth (out of K) responses, and <img src="https://latex.codecogs.com/gif.latex?\inline&space;\beta^j" title="\beta^j" /> are the coefficients of the jth variable on the K responses.

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