fmrs.mle-methods: fmrs.mle method

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Provides MLE for Finite Mixture of Accelerated Failure Time Regression Models or Finite Mixture of Regression Models. It also provides Ridge Regression.

Usage

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fmrs.mle(y, delta, x, nComp, ...)

## S4 method for signature 'ANY'
fmrs.mle(y, delta, x, nComp = 2, disFamily = "lnorm",
  initCoeff, initDispersion, initmixProp, lambRidge = 0, nIterEM = 400,
  nIterNR = 2, conveps = 1e-08, convepsEM = 1e-08, convepsNR = 1e-08,
  porNR = 2, activeset)

Arguments

y

Responses (observations)

delta

Censoring indicator vector

x

Design matrix (covariates)

nComp

Order (Number of components) of mixture model

...

Other possible options

disFamily

A sub-distribution family. The options are "norm" for FMR models, "lnorm" for mixture of AFT regression models with Log-Normal sub-distributions,"weibull" for mixture of AFT regression models with Weibull sub-distributions

initCoeff

Vector of initial values for regression coefficients including intercepts

initDispersion

Vector of initial values for standard deviations

initmixProp

Vector of initial values for proportion of components

lambRidge

A positive value for tuning parameter in Ridge Regression or Elastic Net

nIterEM

Maximum number of iterations for EM algorithm

nIterNR

Maximum number of iterations for Newton-Raphson algorithm

conveps

A positive value for avoiding NaN in computing divisions

convepsEM

A positive value for threshold of convergence in EM algorithm

convepsNR

A positive value for threshold of convergence in Newton-Raphson algorithm

porNR

A positive integer for maximum number of searches in NR algorithm

activeset

A matrix of zero-one that shows which intercepts and covariates are active in the fitted fmrs model

Details

Finite mixture of AFT regression models are represented as follows. Let X be the survival time with non-negative values, and \boldsymbol{z} =(z_{1}, …, z_{d})^{\top} be a d-dimensional vector of covariates that may have an effect on X. If the survival time is subject to right censoring, then the observed response time is T=\min \{Y, C\}, where Y=\log X, C is logarithm of the censoring time and δ=I_{\{y<c\}} is the censoring indicator. We say that V=(T,δ,\boldsymbol z) follows a finite mixture of AFT regression models of order K if the conditional density of (T,δ) given \boldsymbol z has the form

f(t,δ;\boldsymbol{z},\boldsymbolΨ) =∑\limits_{k=1}^{K}π_{k}[f_Y(t;θ_{k}(\boldsymbol z), σ_{k})]^{δ}[S_Y(t;θ_{k}(\boldsymbol z) ,σ_{k})]^{1-δ}[f_{C}(t)]^{1-δ}[S_{C}(t)]^{δ}

where f_Y(.) and S_Y(.) are respectively the density and survival functions of Y, f_C(.) and S_C(.) are respectively the density and survival functions of C; and {θ}_{k}(\boldsymbol{z})=h(β_{0k}+\boldsymbol{z}^{\top} \boldsymbolβ_{k}) for a known link function h(.), \boldsymbolΨ=(π_{1},…,π_{K},β_{01},…, β_{0K},\boldsymbolβ_{1}, …,\boldsymbolβ_{K},σ_{1}, …,σ_{K})^{\top} with \boldsymbolβ_{k}= (β_{k1},β_{k2},…,β_{kd})^{\top} and 0<π_{k}<1 with ∑_{k=1}^{K}π_{k}=1. The log-likelihood of a sample of size $n$ is formed as

\ell_{n}(\boldsymbolΨ) = ∑\limits_{i=1}^{n}\log∑\limits_{k=1}^{K}π_{k}≤ft[f_Y(t_{i}, θ_{k}({\boldsymbol z}_{i}),σ_{k}) \right]^{δ_{i}} ≤ft[S_Y(t_{i},θ_{k}({\boldsymbol z}_{i}), σ_{k})\right]^{1-δ_{i}}.

Note that we assume the censoring distribution is non-informative and hence won't play any role in the estimation process. We use EM and Newton-Raphson algorithms in our method to find the maximizer of above Log-Likelihood.

Value

An fmrsfit-class that includes parameter estimates of the specified FMRs model

Author(s)

Farhad Shokoohi <shokoohi@icloud.com>

References

Shokoohi, F., Khalili, A., Asgharian, M. and Lin, S. (2016 submitted) Variable Selection in Mixture of Survival Models for Biomedical Genomic Studies

See Also

Other lnorm..norm..weibull: fmrs.gendata, fmrs.tunsel, fmrs.varsel

Examples

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set.seed(1980)
nComp = 2
nCov = 10
nObs = 500
dispersion = c(1, 1)
mixProp = c(0.4, 0.6)
rho = 0.5
coeff1 = c( 2,  2, -1, -2, 1, 2, 0, 0,  0, 0,  0)
coeff2 = c(-1, -1,  1,  2, 0, 0, 0, 0, -1, 2, -2)
umax = 40

dat <- fmrs.gendata(nObs = nObs, nComp = nComp, nCov = nCov,
                     coeff = c(coeff1, coeff2), dispersion = dispersion,
                     mixProp = mixProp, rho = rho, umax = umax,
                     disFamily = "lnorm")

res.mle <- fmrs.mle(y = dat$y, x = dat$x, delta = dat$delta,
                    nComp = nComp, disFamily = "lnorm",
                    initCoeff = rnorm(nComp*nCov+nComp),
                    initDispersion = rep(1, nComp),
                    initmixProp = rep(1/nComp, nComp))
summary(res.mle)

Example output

fmrs package, Version 1.0.9, Released 2016-07-01
Provides parameter estimation as well as variable selection in
    Finite Mixture of Accelerated Failure Time Regression and Finite
    Mixture of Regression Models.
    Furthermore, this package provides Ridge Regression and Elastic Net.
BugReports: https://github.com/shokoohi/fmrs/issues
-------------------------------------------
Fitted Model: 
-------------------------------------------
  Finite Mixture of Accelerated Failure Time Regression
    Models 
  Log-Normal Sub-Distributions 
  2 Components; 10 Covariates; 500 samples.

Coefficients:
               Comp.1      Comp.2
Intercept -1.00349450  2.17843339
X.1       -1.00004354  1.99106085
X.2        0.83655769 -0.93351656
X.3        2.18914131 -2.04967951
X.4       -0.07449988  1.05050552
X.5        0.09586936  2.09544856
X.6       -0.07588099  0.03695586
X.7       -0.06296324  0.04254180
X.8       -0.86426301 -0.09600356
X.9        1.90112797  0.07228263
X.10      -1.98054474 -0.11106189


Active Set:
          Comp.1 Comp.2
Intercept      1      1
X.1            1      1
X.2            1      1
X.3            1      1
X.4            1      1
X.5            1      1
X.6            1      1
X.7            1      1
X.8            1      1
X.9            1      1
X.10           1      1

Dispersions:
        Comp.1   Comp.2
[1,] 0.8813775 1.043012

Mixing Proportions:
        Comp.1    Comp.2
[1,] 0.5929567 0.4070433

LogLik: -768.8555; BIC: -831.0016

fmrs documentation built on May 2, 2019, 4:18 a.m.