Package 'BASSLINE' reference manual

Title:	Bayesian Survival Analysis Using Shape Mixtures of Log-Normal Distributions
Description:	Mixtures of life distributions provide a convenient framework for survival analysis: particularly when standard models such as the Weibull are unable to capture some features from the data. These mixtures can also account for unobserved heterogeneity or outlying observations. BASSLINE uses shape mixtures of log-normal distributions and has particular applicability to data with fat tails.
Authors:	Catalina Vallejos [aut], Nathan Constantine-Cooke [cre, aut]
Maintainer:	Nathan Constantine-Cooke <[email protected]>
License:	GPL-3
Version:	0.0.0.9010
Built:	2024-11-12 04:12:00 UTC
Source:	https://github.com/nathansam/BASSLINE

Convert dataframe with mixed variables to a numeric matrix

Description

BASSLINE's functions require a numeric matrix be provided. This function converts a dataframe of mixed variable types (numeric and factors) to a matrix. A factor with $m$ levels is converted to $m$ columns with binary values used to denote which level the observation belongs to.

Usage

BASSLINE_convert(df)
BASSLINE_convert(df)

Arguments

`df`	A dataframe intended for conversion

Value

A numeric matrix suitable for BASSLINE functions

Examples

library(BASSLINE)
Time <- c(5,15,15)
Cens <- c(1,0,1)
experiment <- as.factor(c("chem1", "chem2", "chem3"))
age <- c(15,35,20)
df <- data.frame(Time, Cens, experiment, age)
converted <- BASSLINE_convert(df)

library(BASSLINE)
Time <- c(5,15,15)
Cens <- c(1,0,1)
experiment <- as.factor(c("chem1", "chem2", "chem3"))
age <- c(15,35,20)
df <- data.frame(Time, Cens, experiment, age)
converted <- BASSLINE_convert(df)

Outlier detection for observation for the log-Laplace model

Description

This returns a unique number corresponding to the Bayes Factor associated to the test $M_0: \Lambda_{obs} = \lambda_{ref}$ versus $M_1: \Lambda_{obs}\neq \lambda_{ref}$ (with all other $\Lambda_j,\neq obs$ free). The value of $\lambda_{ref}$ is required as input. The user should expect long running times for the log-Student’s t model, in which case a reduced chain given $\Lambda_{obs} = \lambda_{ref}$ needs to be generated

Usage

BF_lambda_obs_LLAP(obs, ref, X, chain)
BF_lambda_obs_LLAP(obs, ref, X, chain)

Arguments

`obs`	Indicates the number of the observation under analysis
`ref`	Reference value $\lambda_{ref}$ or $u_{ref}$
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function updates

Examples

#' library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.outlier <- BF_lambda_obs_LLAP(1,1, X = cancer[, 3:11], chain = LLAP)

#' library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.outlier <- BF_lambda_obs_LLAP(1,1, X = cancer[, 3:11], chain = LLAP)

Outlier detection for observation for the log-logistic model

Description

Usage

BF_lambda_obs_LLOG(ref, obs, X, chain)
BF_lambda_obs_LLOG(ref, obs, X, chain)

Arguments

`ref`	Reference value $\lambda_{ref}$ or $u_{ref}$
`obs`	Indicates the number of the observation under analysis
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.Outlier <- BF_lambda_obs_LLOG(1,1, X = cancer[, 3:11], chain = LLOG)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.Outlier <- BF_lambda_obs_LLOG(1,1, X = cancer[, 3:11], chain = LLOG)

Outlier detection for observation for the log-student's t model

Description

Usage

BF_lambda_obs_LST(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)
BF_lambda_obs_LST(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period
`ref`	Reference value $\lambda_{ref}$ or $u_{ref}$
`obs`	Indicates the number of the observation under analysis
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`Q`	Update period for the $\lambda_{i}$ ’s
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`ar`	Optimal acceptance rate for the adaptive Metropolis-Hastings updates

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

LST.Outlier <- BF_lambda_obs_LST(N = 100, thin = 20 , burn = 1, ref = 1,
                                 obs = 1, Time = cancer[, 1],
                                 Cens = cancer[, 2], X = cancer[, 3:11],
                                 chain = LST)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

LST.Outlier <- BF_lambda_obs_LST(N = 100, thin = 20 , burn = 1, ref = 1,
                                 obs = 1, Time = cancer[, 1],
                                 Cens = cancer[, 2], X = cancer[, 3:11],
                                 chain = LST)

Outlier detection for observation for the log-exponential power model

Description

Usage

BF_u_obs_LEP(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)
BF_u_obs_LEP(
  N,
  thin,
  burn,
  ref,
  obs,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period
`ref`	Reference value $u_{ref}$ . Vallejos & Steel recommends this value be set to $1.6 +1_\alpha$ for the LEP model.
`obs`	Indicates the number of the observation under analysis
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`ar`	Optimal acceptance rate for the adaptive Metropolis-Hastings updates

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
alpha <- mean(LEP[, 11])
uref <- 1.6 + 1 / alpha
LEP.Outlier <- BF_u_obs_LEP(N = 100, thin = 20, burn =1 , ref = uref,
                            obs = 1, Time = cancer[, 1], Cens = cancer[, 2],
                            cancer[, 3:11], chain = LEP)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
alpha <- mean(LEP[, 11])
uref <- 1.6 + 1 / alpha
LEP.Outlier <- BF_u_obs_LEP(N = 100, thin = 20, burn =1 , ref = uref,
                            obs = 1, Time = cancer[, 1], Cens = cancer[, 2],
                            cancer[, 3:11], chain = LEP)

VA Lung Cancer Trial Dataset

Description

Data from a trial in which a therapy (standard or test chemotherapy) was randomly applied to 137 patients who were diagnosed with inoperable lung cancer. The survival times of the patients were measured in days since treatment.

Usage

cancer
cancer

Format

A matrix with 137 rows and 8 variables:

Time: Survival time (in days)
Cens: 0 or 1. If 0 the observation is right censored
Intercept: The intercept
Treat: The treatment applied to the patient (0: standard, 1: test)
Type.1: The histological type of the tumor (1: type 1, 0: otherwise)
Type.2: The histological type of the tumor (1: type 2, 0: otherwise)
Type.3: The histological type of the tumor (1: type 3, 0: otherwise)
Status: A continuous index representing the status of the patient: 10—30 completely hospitalized, 40—60 partial confinement, 70—90 able to care for self.
MFD: The time between the diagnosis and the treatment (in months)
Age: Age (in years)
Prior: Prior therapy, 0 or 10

Source

Appendix I of Kalbfleisch and Prentice (1980).

Case deletion analysis for the log-exponential power model

Description

Leave-one-out cross validation analysis. The function returns a matrix with n rows. The first column contains the logarithm of the CPO (Geisser and Eddy, 1979). Larger values of the CPO indicate better predictive accuracy of the model. The second and third columns contain the KL divergence between $\pi(\beta, \sigma^2, \theta | t_{-i})$ and $\pi(\beta, \sigma^2, \theta | t)$ and its calibration index $p_i$ , respectively.

Usage

CaseDeletion_LEP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
CaseDeletion_LEP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.CD <- CaseDeletion_LEP(Time = cancer[, 1], Cens = cancer[, 2],
                           X = cancer[, 3:11], chain = LEP)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.CD <- CaseDeletion_LEP(Time = cancer[, 1], Cens = cancer[, 2],
                           X = cancer[, 3:11], chain = LEP)

Case deletion analysis for the log-Laplace model

Description

Usage

CaseDeletion_LLAP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
CaseDeletion_LLAP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.CD <- CaseDeletion_LLAP(Time = cancer[, 1], Cens = cancer[, 2],
                             X = cancer[, 3:11], chain = LLAP)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.CD <- CaseDeletion_LLAP(Time = cancer[, 1], Cens = cancer[, 2],
                             X = cancer[, 3:11], chain = LLAP)

Case deletion analysis for the log-logistic model

Description

Usage

CaseDeletion_LLOG(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
CaseDeletion_LLOG(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.CD <- CaseDeletion_LLOG(Time = cancer[, 1], Cens = cancer[, 2],
                             X = cancer[, 3:11], chain = LLOG)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.CD <- CaseDeletion_LLOG(Time = cancer[, 1], Cens = cancer[, 2],
                             X = cancer[, 3:11], chain = LLOG)

Case deletion analysis for the log-normal model

Description

Usage

CaseDeletion_LN(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
CaseDeletion_LN(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.CD <- CaseDeletion_LN(Time = cancer[, 1], Cens = cancer[, 2],
                         X = cancer[, 3:11], chain = LN)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.CD <- CaseDeletion_LN(Time = cancer[, 1], Cens = cancer[, 2],
                         X = cancer[, 3:11], chain = LN)

Case deletion analysis for the log-student's t model

Description

Usage

CaseDeletion_LST(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
CaseDeletion_LST(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LST.CD <- CaseDeletion_LST(Time = cancer[, 1], Cens = cancer[, 2],
                           cancer[, 3:11], chain = LST)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LST.CD <- CaseDeletion_LST(Time = cancer[, 1], Cens = cancer[, 2],
                           cancer[, 3:11], chain = LST)

Deviance information criterion for the log-exponential power model

Description

Deviance information criterion is based on the deviance function $D(\theta, y) = -2 log(f(y|\theta))$ but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LEP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
DIC_LEP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.DIC <- DIC_LEP(Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.DIC <- DIC_LEP(Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)

Deviance information criterion for the log-Laplace model

Description

Deviance information criterion is based on the deviance function $D(\theta, y) = -2 log(f(y|\theta))$ but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LLAP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
DIC_LLAP(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.DIC <- DIC_LLAP(Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLAP)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLAP.DIC <- DIC_LLAP(Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLAP)

Deviance information criterion for the log-logistic model

Description

Deviance information criterion is based on the deviance function $D(\theta, y) = -2 log(f(y|\theta))$ but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LLOG(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
DIC_LLOG(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.DIC <- DIC_LLOG(Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLOG)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.DIC <- DIC_LLOG(Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLOG)

Deviance information criterion for the log-normal model

Description

Deviance information criterion is based on the deviance function $D(\theta, y) = -2 log(f(y|\theta))$ but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LN(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
DIC_LN(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.DIC <- DIC_LN(Time = cancer[, 1], Cens = cancer[, 2], X = cancer[, 3:11],
                 chain = LN)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.DIC <- DIC_LN(Time = cancer[, 1], Cens = cancer[, 2], X = cancer[, 3:11],
                 chain = LN)

Deviance information criterion for the log-student's t model

Description

Deviance information criterion is based on the deviance function $D(\theta, y) = -2 log(f(y|\theta))$ but also incorporates a penalization factor of the complexity of the model

Usage

DIC_LST(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)
DIC_LST(Time, Cens, X, chain, set = TRUE, eps_l = 0.5, eps_r = 0.5)

Arguments

`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LST.DIC <- DIC_LST(Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LST)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LST.DIC <- DIC_LST(Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LST)

Log-marginal likelihood estimator for the log-exponential power model

Description

Log-marginal likelihood estimator for the log-exponential power model

Usage

LML_LEP(
  thin,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
LML_LEP(
  thin,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`thin`	Thinning period.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=100 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 100, thin = 2, burn = 20, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.LML <- LML_LEP(thin = 2, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)

library(BASSLINE)

# Please note: N=100 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 100, thin = 2, burn = 20, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])
LEP.LML <- LML_LEP(thin = 2, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LEP)

Log-marginal likelihood estimator for the log-Laplace model

Description

Log-marginal likelihood estimator for the log-Laplace model

Usage

LML_LLAP(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
LML_LLAP(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`thin`	Thinning period.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`Q`	Update period for the $\lambda_{i}$ ’s
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

Log-marginal likelihood estimator for the log-logistic model

Description

Log-marginal likelihood estimator for the log-logistic model

Usage

LML_LLOG(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 10,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  N.AKS = 3
)
LML_LLOG(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 10,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  N.AKS = 3
)

Arguments

`thin`	Thinning period.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`Q`	Update period for the $\lambda_{i}$ ’s
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`N.AKS`	Maximum number of terms of the Kolmogorov-Smirnov density used for the rejection sampling when updating mixing parameters (default value: 3)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.LML <- LML_LLOG(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLOG)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])
LLOG.LML <- LML_LLOG(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                     X = cancer[, 3:11], chain = LLOG)

Log-marginal Likelihood estimator for the log-normal model

Description

Log-marginal Likelihood estimator for the log-normal model

Usage

LML_LN(
  thin,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
LML_LN(
  thin,
  Time,
  Cens,
  X,
  chain,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`thin`	Thinning period.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.LML <- LML_LN(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                         X = cancer[, 3:11], chain = LN)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.LM

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
LN.LML <- LML_LN(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                         X = cancer[, 3:11], chain = LN)

Log-marginal Likelihood estimator for the log-student's t model

Description

Log-marginal Likelihood estimator for the log-student's t model

Usage

LML_LST(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
LML_LST(
  thin,
  Time,
  Cens,
  X,
  chain,
  Q = 1,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`thin`	Thinning period.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`chain`	MCMC chains generated by a BASSLINE MCMC function
`Q`	Update period for the $\lambda_{i}$ ’s
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

LST.LML <- LML_LST(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LST)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

LST.LML <- LML_LST(thin = 20, Time = cancer[, 1], Cens = cancer[, 2],
                   X = cancer[, 3:11], chain = LST)

MCMC algorithm for the log-exponential power model

Description

Adaptive Metropolis-within-Gibbs algorithm with univariate Gaussian random walk proposals for the log-exponential model

Usage

MCMC_LEP(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  beta0 = NULL,
  sigma20 = NULL,
  alpha0 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)
MCMC_LEP(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  beta0 = NULL,
  sigma20 = NULL,
  alpha0 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period. Must be a multiple of thin.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`beta0`	Starting values for $\beta$ . If not provided, they will be randomly generated from a normal distribution.
`sigma20`	Starting value for $\sigma^2$ . If not provided, it will be randomly generated from a gamma distribution.
`alpha0`	Starting value for $\alpha$ . If not provided, then it will be randomly generated from a uniform distribution.
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`ar`	Optimal acceptance rate for the adaptive Metropolis-Hastings updates

Value

A matrix with $N / thin + 1$ rows. The columns are the MCMC chains for $\beta$ ( $k$ columns), $\sigma^2$ (1 column), $\theta$ (1 column, if appropriate), $u$ ( $n$ columns, not provided for log-normal model), $\log(t)$ ( $n$ columns, simulated via data augmentation) and the logarithm of the adaptive variances (the number varies among models). The latter allows the user to evaluate if the adaptive variances have been stabilized.

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations (especially for the log-exponential power model).

LEP <- MCMC_LEP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

MCMC algorithm for the log-Laplace model

Description

Adaptive Metropolis-within-Gibbs algorithm with univariate Gaussian random walk proposals for the log-Laplace model

Usage

MCMC_LLAP(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 1,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
MCMC_LLAP(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 1,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period. Must be a multiple of thin.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`Q`	Update period for the $\lambda_{i}$ ’s
`beta0`	Starting values for $\beta$ . If not provided, they will be randomly generated from a normal distribution.
`sigma20`	Starting value for $\sigma^2$ . If not provided, it will be randomly generated from a gamma distribution.
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Value

A matrix with $N / thin + 1$ rows. The columns are the MCMC chains for $\beta$ ( $k$ columns), $\sigma^2$ (1 column), $\theta$ (1 column, if appropriate), $\lambda$ ( $n$ columns, not provided for log-normal model), $\log(t)$ ( $n$ columns, simulated via data augmentation) and the logarithm of the adaptive variances (the number varies among models). The latter allows the user to evaluate if the adaptive variances have been stabilized.

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLAP <- MCMC_LLAP(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

MCMC algorithm for the log-logistic model

Description

Adaptive Metropolis-within-Gibbs algorithm with univariate Gaussian random walk proposals for the log-logistic model

Usage

MCMC_LLOG(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 10,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  N.AKS = 3
)
MCMC_LLOG(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 10,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  N.AKS = 3
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period. Must be a multiple of thin.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`Q`	Update period for the $\lambda_{i}$ ’s
`beta0`	Starting values for $\beta$ . If not provided, they will be randomly generated from a normal distribution.
`sigma20`	Starting value for $\sigma^2$ . If not provided, it will be randomly generated from a gamma distribution.
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`N.AKS`	Maximum number of terms of the Kolmogorov-Smirnov density used for the rejection sampling when updating mixing parameters (default value: 3)

Value

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LLOG <- MCMC_LLOG(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                  Cens = cancer[, 2], X = cancer[, 3:11])

MCMC algorithm for the log-normal model

Description

Adaptive Metropolis-within-Gibbs algorithm with univariate Gaussian random walk proposals for the log-normal model (no mixture)

Usage

MCMC_LN(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)
MCMC_LN(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  beta0 = NULL,
  sigma20 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period. Must be a multiple of thin.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`beta0`	Starting values for $\beta$ . If not provided, they will be randomly generated from a normal distribution.
`sigma20`	Starting value for $\sigma^2$ . If not provided, it will be randomly generated from a gamma distribution.
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)

Value

A matrix with $(N - burn) / thin + 1$ rows. The columns are the MCMC chains for $\beta$ ( $k$ columns), $\sigma^2$ (1 column), $\theta$ (1 column, if appropriate), $\log(t)$ ( $n$ columns, simulated via data augmentation) and the logarithm of the adaptive variances (the number varies among models). The latter allows the user to evaluate if the adaptive variances have been stabilized.

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])

MCMC algorithm for the log-student's t model

Description

Adaptive Metropolis-within-Gibbs algorithm with univariate Gaussian random walk proposals for the log-student's T model (no mixture)

Usage

MCMC_LST(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 1,
  beta0 = NULL,
  sigma20 = NULL,
  nu0 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)
MCMC_LST(
  N,
  thin,
  burn,
  Time,
  Cens,
  X,
  Q = 1,
  beta0 = NULL,
  sigma20 = NULL,
  nu0 = NULL,
  prior = 2,
  set = TRUE,
  eps_l = 0.5,
  eps_r = 0.5,
  ar = 0.44
)

Arguments

`N`	Total number of iterations. Must be a multiple of thin.
`thin`	Thinning period.
`burn`	Burn-in period. Must be a multiple of thin.
`Time`	Vector containing the survival times.
`Cens`	Censoring indication (1: observed, 0: right-censored).
`X`	Design matrix with dimensions $n$ x $k$ where $n$ is the number of observations and $k$ is the number of covariates (including the intercept).
`Q`	Update period for the $\lambda_{i}$ ’s
`beta0`	Starting values for $\beta$ . If not provided, they will be randomly generated from a normal distribution.
`sigma20`	Starting value for $\sigma^2$ . If not provided, it will be randomly generated from a gamma distribution.
`nu0`	Starting value for $v$ . If not provided, then it will be randomly generated from a gamma distribution.
`prior`	Indicator of prior (1: Jeffreys, 2: Type I Ind. Jeffreys, 3: Ind. Jeffreys).
`set`	Indicator for the use of set observations (1: set observations, 0: point observations). The former is strongly recommended over the latter as point observations cause problems in the context of Bayesian inference (due to continuous sampling models assigning zero probability to a point).
`eps_l`	Lower imprecision $(\epsilon_l)$ for set observations (default value: 0.5).
`eps_r`	Upper imprecision $(\epsilon_r)$ for set observations (default value: 0.5)
`ar`	Optimal acceptance rate for the adaptive Metropolis-Hastings updates

Value

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LST <- MCMC_LST(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
                Cens = cancer[, 2], X = cancer[, 3:11])

Produce a trace plot of a variable's MCMC chain

Description

Plots the chain across (non-discarded) iterations for a specified observation

Usage

Trace_plot(variable = NULL, chain = NULL)
Trace_plot(variable = NULL, chain = NULL)

Arguments

`variable`	Indicates the index of the variable
`chain`	MCMC chains generated by a BASSLINE MCMC function

Value

A ggplot2 object

Examples

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
Trace_plot(1, LN)

library(BASSLINE)

# Please note: N=1000 is not enough to reach convergence.
# This is only an illustration. Run longer chains for more accurate
# estimations.

LN <- MCMC_LN(N = 1000, thin = 20, burn = 40, Time = cancer[, 1],
              Cens = cancer[, 2], X = cancer[, 3:11])
Trace_plot(1, LN)

Package 'BASSLINE'

Help Index

Convert dataframe with mixed variables to a numeric matrix

Description

Usage

Arguments

Value

Examples

Outlier detection for observation for the log-Laplace model

Description

Usage

Arguments

Examples

Outlier detection for observation for the log-logistic model

Description

Usage

Arguments

Examples

Outlier detection for observation for the log-student's t model

Description

Usage

Arguments

Examples

Outlier detection for observation for the log-exponential power model

Description

Usage

Arguments

Examples

VA Lung Cancer Trial Dataset

Description

Usage

Format

Source

Case deletion analysis for the log-exponential power model

Description

Usage

Arguments

Examples

Case deletion analysis for the log-Laplace model

Description

Usage

Arguments

Examples

Case deletion analysis for the log-logistic model

Description

Usage

Arguments

Examples

Case deletion analysis for the log-normal model

Description

Usage

Arguments

Examples

Case deletion analysis for the log-student's t model

Description

Usage

Arguments

Examples

Deviance information criterion for the log-exponential power model

Description

Usage

Arguments

Examples

Deviance information criterion for the log-Laplace model

Description

Usage

Arguments

Examples

Deviance information criterion for the log-logistic model

Description

Usage

Arguments

Examples

Deviance information criterion for the log-normal model

Description

Usage

Arguments

Examples

Deviance information criterion for the log-student's t model

Description