Package 'psc'

acc

Description

acc

Usage

acc(old, new)

Arguments

old	a numeric value
new	a numeric value

Details

A function for the evaluation of two likelihoods as part of the MCMC procedure

Value

returns the an evaluation of old/new > U where U is a draw from the uniform distribution

---

Example model for a survival outcome

Description

A model of class 'glm'

Usage

bin.mod

Format

A model of class 'flezsurvreg':

gamma

cumulative baseline hazard parameters

vi

vascular invasion

age60

patient age (centred at 60)

ecog

ECOG performance Status

logafp

AFP - log scale

alb

albumin

logcreat

Creatinine - log scale

allmets

metastesis

ageVasInv

centred age nested within vascular invasion

time

survival time

cen

censoring indicator

os

survival time

count

exapmple outcome for count data

trt

exapmple identifier for mulitple treatment comparisons

aet

Aetiology

Source

simulated

---

Returns the coefficeint estimate of a psc object.

Description

Returns the coefficeint estimate of a psc object.

Usage

## S3 method for class 'psc'
coef(object, ..., level = 0.05)

Arguments

object	a 'psc' object
...	not used
level	the level at which credibility intervals are assessed, defaults to 0.05

Value

The summary of the posterior distribution for the efficacy parameter in terms of the median and 95

---

cont.mod

Description

A model of class 'glm'

Usage

cont.mod

Format

A model of class 'flezsurvreg':

gamma

cumulative baseline hazard parameters

vi

vascular invasion

age60

patient age (centred at 60)

ecog

ECOG performance Status

logafp

AFP - log scale

alb

albumin

logcreat

Creatinine - log scale

allmets

metastesis

ageVasInv

centred age nested within vasculdevar invasion

time

survival time

cen

censoring indicator

os

survival time

count

exapmple outcome for count data

trt

exapmple identifier for mulitple treatment comparisons

aet

Aetiology

Source

simulated

---

Example model for a survival outcome

Description

A model of class 'glm'

Usage

count.mod

Format

A model of class 'flezsurvreg':

gamma

cumulative baseline hazard parameters

vi

vascular invasion

age60

patient age (centred at 60)

ecog

ECOG performance Status

logafp

AFP - log scale

alb

albumin

logcreat

Creatinine - log scale

allmets

metastesis

ageVasInv

centred age nested within vascular invasion

time

survival time

cen

censoring indicator

os

survival time

count

exapmple outcome for count data

trt

exapmple identifier for mulitple treatment comparisons

aet

Aetiology

Source

simulated

---

Example Dataset of patients with aHCC receiving Lenvetanib

Description

A dataset containing 100 simulated patients.

Usage

data

Format

A model of class 'flezsurvreg':

gamma

cumulative baseline hazard parameters

vi

vascular invasion

age60

patient age (centred at 60)

ecog

ECOG performance Status

logafp

AFP - log scale

alb

albumin

logcreat

Creatinine - log scale

allmets

metastesis

ageVasInv

centred age nested within vascular invasion

time

survival time

cen

censoring indicator

os

survival time

count

exapmple outcome for count data

trt

exapmple identifier for mulitple treatment comparisons

aet

Aetiology

Source

simulated

---

A generic function for cleaning data ready for analysis

Description

A generic function for cleaning data ready for analysis

Usage

dataComb(CFM, DC, id = NULL, trt = NULL)

Arguments

CFM	a model object supplied to pscfit
DC	a dataset including covariates to match the CFM
id	to specify which observations in the data cohort should be evaluated. Defualts to 'NULL' i.e all observations
trt	used to specify multiple treatment effects. Defaults to NULL

Value

datComb returns a list containing objects which detial the components of both the Counter Factual Model (CFM) and the Data Cohort (DC) the required exported components of the model and a cleaned data cohort.

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
dc <- dataComb(surv.mod,data)

---

Fucntion for cleaning the data of a model with class 'flexsurvreg'

Description

Fucntion for cleaning the data of a model with class 'flexsurvreg'

Usage

## S3 method for class 'flexsurvreg'
dataComb(CFM, DC, id = NULL, trt = NULL)

Arguments

CFM	a model object supplied to pscfit
DC	a dataset including covariates to match the CFM
id	a vector specifiying whether a subset of the dataset should be selected. Defaults to 'NULL' e.g. all data points included
trt	An optional additional vector denoting treatment allocations for multiple treatment comparisons. Defaults to 'NULL'

Value

a list containing objects which specifiy the required exported components of the model and a cleaned data cohort.

---

Fucntion for cleaning the data of a model with class 'flexsurvreg'

Description

Fucntion for cleaning the data of a model with class 'flexsurvreg'

Usage

## S3 method for class 'glm'
dataComb(CFM, DC, id = NULL, trt = NULL)

Arguments

CFM	a model object supplied to pscfit
DC	a dataset including covariates to match the CFM
id	to specify which observations in the data cohort should be evaluated. Defualts to 'NULL' i.e all observations
trt	used to specify multiple treatment effects. Defaults to NULL

Value

a list containing objects which specifiy the required exported components of the model and a cleaned data cohort.

---

Fucntion for estimating initial parameter values 'flexsurvreg'

Description

Fucntion for estimating initial parameter values 'flexsurvreg'

Usage

initParm(CFM, DC_clean, trt)

Arguments

CFM	A counter-factual model
DC_clean	a cleaned dataset obsect obtained using dataComb.flexsurvreg
trt	An optional additional vector denoting treatment allocations for multiple treatment comparisons. Defaults to 'NULL'

Details

This function takes the liklihood for a 'flexsurvreg' model and uses 'optim' to fit the likelihood.

Value

an 'optim' output giving the parameter values to be supplied as a starting value for the mcmc routine.

---

Fucntion for estimating initial parameter values 'flexsurvreg'

Description

Fucntion for estimating initial parameter values 'flexsurvreg'

Usage

## S3 method for class 'flexsurvreg'
initParm(CFM, DC_clean, trt = NULL)

Arguments

CFM	A counter-factual model
DC_clean	a cleaned dataset obsect obtained using dataComb.flexsurvreg
trt	An optional additional vector denoting treatment allocations for multiple treatment comparisons. Defaults to 'NULL'

Details

This function takes the liklihood for a 'flexsurvreg' model and uses 'optim' to fit the likelihood.

Value

an 'optim' output giving the parameter values to be supplied as a starting value for the mcmc routine.

---

Fucntion for estimating initial parameter values 'flexsurvreg'

Description

Fucntion for estimating initial parameter values 'flexsurvreg'

Usage

## S3 method for class 'glm'
initParm(CFM, DC_clean, trt = trt)

Arguments

CFM	A counter-factual model
DC_clean	a cleaned dataset obsect obtained using dataComb.flexsurvreg
trt	An optional additional vector denoting treatment allocations for multiple treatment comparisons. Defaults to 'NULL'

Details

This function takes the liklihood for a 'flexsurvreg' model and uses 'optim' to fit the likelihood.

Value

an 'optim' output giving the parameter values to be supplied as a starting value for the mcmc routine.

---

Likelihood functio for a a psc model of class 'flexsurvreg'

Description

Likelihood functio for a a psc model of class 'flexsurvreg'

Usage

lik.flexsurvreg(beta, DC_clean)

Arguments

beta	a parameter to be estimate
DC_clean	a cleaned dataset including covariates to match the CFM

Details

A likelihood function for use by pscfit for a model of class 'flexsurvreg'

---

Likelihood functio for a a psc model of class 'flexsurvreg'

Description

Likelihood functio for a a psc model of class 'flexsurvreg'

Usage

lik.flexsurvreg.mtc(beta, DC_clean)

Arguments

beta	a parameter to be estimate
DC_clean	a cleaned dataset including covariates to match the CFM

Details

A likelihood function for use by pscfit for a model of class 'flexsurvreg' where mulitple treatment comparisons are

---

Likelihood functio for a a psc model of class 'glm'

Description

Likelihood functio for a a psc model of class 'glm'

Usage

lik.glm(beta, DC_clean)

Arguments

beta	a parameter to be estimate
DC_clean	a cleaned dataset including covariates to match the CFM

Details

A likelihood function for use by pscfit for a model of class 'flexsurvreg'

---

Likelihood functio for a a psc model of class 'flexsurvreg'

Description

Likelihood functio for a a psc model of class 'flexsurvreg'

Usage

lik.glm.mtc(beta, DC_clean)

Arguments

beta	a parameter to be estimate
DC_clean	a cleaned dataset including covariates to match the CFM

Details

A likelihood function for use by pscfit for a model of class 'flexsurvreg' where mulitple treatment comparisons are

---

Estimates the linear predictor of a psc object

Description

Estimates the linear predictor of a psc object

Usage

linPred(DC_clean, resp = FALSE)

Arguments

DC_clean	a cleaned data obhject created using dataComb()
resp	detailing whether the linear predictor shoudl be returned on the natural or response level. Defaults to the natural scale (resp=F)

Details

A function which combines the data from the data cohort against the model parameters of the PSC

Value

Extracts the linear predictor from a object containing both a counter factual model and a data cohort which is created using the dataComb() fucntion.

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
dc <- dataComb(surv.mod,data)
lp <- linPred(dc)

---

A generic function for extracting model information

Description

A generic function for extracting model information

Usage

modelExtract(CFM)

Arguments

CFM	a model of class either 'glm' or 'flexsurvreg'

Details

A function for extracting the model information required for using pscfit

Value

a list of extracted model components

---

A generic function for extracting model information

Description

A generic function for extracting model information

Usage

## S3 method for class 'flexsurvreg'
modelExtract(CFM)

Arguments

CFM	a model of class 'flexsurvreg'

Details

A function for extracting the model information required for using pscfit

Value

a list of extracted model components

---

A generic function for extracting model information

Description

A generic function for extracting model information

Usage

## S3 method for class 'glm'
modelExtract(CFM)

Arguments

CFM	a model of class 'glm'

Details

A function for extracting the model information required for using pscfit

Value

a list of extracted model components

---

modp

Description

modp

Usage

modp(x)

Arguments

x	a numberic vector

Details

A fucntion which returns a version of x with negative values replacd with 0

Value

a numeric vector with negative values replaced with 0

---

Fucntion for Plotting PSC objects

Description

Fucntion for Plotting PSC objects

Usage

## S3 method for class 'psc'
plot(x, ...)

Arguments

x	an object of class 'psc'
...	not used

Details

making use of the generic 'plot' functions this will provide some graphical output of the fitted psc object. The form of the output will depend on the class of the initial model

Value

a plot corresponding to the psc fit

---

Personalised Synthetic Controls - print

Description

Personalised Synthetic Controls - print

Usage

## S3 method for class 'psc'
print(x, ...)

Arguments

x	an object of class 'psc'
...	not used

Value

printing psc results

---

Wrapper function for individual treatment effects

Description

Wrapper function for individual treatment effects

Usage

psc_ite(model, data)

Arguments

model	a CFM
data	a data cohort

Details

A wrapper function that estimates individual treatment effects usinf pscfit

---

Fitted psc object

Description

An object returned by the pscfit function, inheriting from class psc and representing a fitted personlised synthetic control model.

Usage

psc.object

Format

An object of class NULL of length 0.

Author(s)

Richard Jasckson ([email protected])

---

Function for performing estimation procedures in 'pscfit'

Description

Function for performing estimation procedures in 'pscfit'

Usage

pscEst(CFM, DC_clean, nsim, start, trt)

Arguments

CFM	a model object supplied to pscfit
DC_clean	a cleaned dataset ontained using dataComb().
nsim	the number of MCMC simulations to run
start	the stating value for
trt	an optional vector denoting treatment allocations where mulitple treatment comparisons are bieng made

Details

Define the set of model parameters $B$ to contain $\Gamma$ which summarize the parameters of the CFM. Prior distributions are defined for B using a multivariate normal distribution $\pi (B) \sim MVN(\mu ,\Sigma)$ where $\mu|$ is the vector of coefficient estimates from the validated model and $\Sigma$ is the variance-covariance matrix. This information is taken directly from the outputs of the parametric model and no further elicitation is required. The prior distirbution for the efficacy parameter ($\pi{(\beta)}$) is set as an uniformative $N(0,1000)$.

Ultimately the aim is to estimate the posterior distribution for $\beta$ conditional on the distribution of B and the observed data. A full form for the posterior distribution is then given as

$P(\beta \vert B,D) \propto L(D \vert B,\beta) \pi(B) \pi(\beta)$

Please see 'pscfit' for more details on liklihood formation.

For each iteration of the MCMC procedure, the following algorithm is performed

1. Set and indicator s=1, and define an initial state based on prior hyperparameters for $\pi(B)$ and $\pi(\beta)$ such that $b_s = \mu and \tau_s=0$

2. Update $s = s+1$ and draw model parameters $b_s$ from $\pi(B)$ and an draw a proposal estimate of $\beta$ from some target distribution

3. Estimate $\Gamma_(i,S)=\nu^T x_i$ where $\nu$ is the subset of parameters from $b_s$ which relate to the model covariates and define 2 new likelihood functions $\Theta_(s,1)=L(D \vert B=b_s,\beta=\tau_(s-1) )$ & $\Theta_(s,2)= L(D \vert B=b_s,\beta=\tau_s)$

4. Draw a single value $\psi$ from a Uniform (0,1) distribution and estimate the condition $\omega= \Theta_(s,1)/\Theta_(s,2)$. If $\omega > \psi$ then accept $\tau_s$ as belonging to the posterior distribution $P(\beta \vert B,D)$ otherwise retain $\tau_(s-1)$

5. Repeat steps 2 – 4 for the required number of iterations

The result of the algorithm is a posterior distribution for the log hazard ratio, $\beta$, captures the variability in B through the defined priors $\pi{(\beta)}$.

Value

A matrix containing the draws form the posterior distribution

---

Fucntion for estimating initial parameter values 'flexsurvreg'

Description

Fucntion for estimating initial parameter values 'flexsurvreg'

Usage

## S3 method for class 'flexsurvreg'
pscEst(CFM, DC_clean, nsim, start, trt = trt)

Arguments

CFM	a model object supplied to pscfit
DC_clean	a cleaned dataset ontained using dataComb().
nsim	the number of MCMC simulations to run
start	the stating value for
trt	an optional vector denoting treatment allocations where multiple treatment comparisons are being made

Details

An MCMC routine for fitting a psc model

Value

A matrix containing the draws form the posterior distribution

---

Fucntion for estimating initial parameter values 'glm'

Description

Fucntion for estimating initial parameter values 'glm'

Usage

## S3 method for class 'glm'
pscEst(CFM, DC_clean, nsim, start, trt = trt)

Arguments

CFM	a model object supplied to pscfit
DC_clean	a cleaned dataset ontained using dataComb().
nsim	the number of MCMC simulations to run
start	the stating value for
trt	an optional vector denoting treatment allocations where multiple treatment comparisons are being made

Details

An MCMC routine for fitting a psc model

Value

a matrix containing the draws form the posterior distribution

---

Personalised Synthetic Controls model fit

Description

Personalised Synthetic Controls model fit

Usage

pscfit(CFM, DC, nsim = 5000, id = NULL, trt = NULL)

Arguments

CFM	A model of type 'glm' or 'flexsurvspline'
DC	A dataset including columns to match to covariates in the model
nsim	The number of simulations for the MCMC routine
id	Numeric vector stating which patient(s) from the dataset should be included in the analysis. Defaults to all patients
trt	An optional vector denoting treatment allocations for multiple treatment comparisons. Defaults to NULL.

Details

the pscfit function compares a dataset ('DC') against a parametric model. This is done by selecting a likelihood which is identified by the type of CFM that is supplied. At present, two types of model are supported, a flexible parmaeteric survival model of type 'flexsurvreg' and a geleneralised linear model of type 'glm'.

Where the CFM is of type 'flexsurvreg' the likeihood supplied is of the form:

$L(D \vert \Lambda, \Gamma_i) = \prod^{n}_{i=1} f(t_i \vert \Lambda, \Gamma_i)^{c_i} S(t_i|\Lambda, \Gamma_i)^{(1-c_i)}$

Where $\Lambda$ defines the cumulative baseline hazard function, $\Gamma$ is the linear predictor and $t$ and $c$ are the event time and indicator variables.

Where the CFM is of the type 'glm' the likelihood supplied is of the form:

$L(x \vert \Gamma_i) = \prod^{n}_{i=1} b(x \vert \Gamma_i) \exp{\{\Gamma_i^T t(x) - c(\Gamma_i)\} }$

Where $b(.)$, $t(.)$ and $c(.)$ represent the functions of the exponential family. In both cases, $\Gamma$ is defined as:

$\Gamma = \gamma x + \beta$

Where $\gamma$ are the model coefficients supplied by the CFM and $\beta$ is the parameter set to measure the difference between the CFM and the DC.

Estimation is performed using a Bayesian MCMC procedure. Prior distributions for $\Gamma$ (& $\Lambda$) are derived directly from the model coefficients (mean and variance covariance matrix) or the CFM. A bespoke MCMC routine is performed to estimate $\beta$. Please see '?mcmc' for more detials.

For the standard example where the DC contains information from only a single treatment, trt need not be specified. Where comparisons between the CFM and multiple treatments are require, a covariate of treamtne allocations must be specified sperately (using the 'trt' option).

Value

a object of class 'psc' with attributes model.type, the cleaned Dataset and the posterior distribution of the fitted model

Attributes include

• A 'cleaned' dataset including extracted components of the CFM and the cleaned DC included in the procedure

• An object defining the class of model (and therefore the procedure applied - see above)

• A matrix containing the draws of the posterior distributions

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
surv.psc <- pscfit(surv.mod,data)

---

Personalised Synthetic Controls - summary

Description

Personalised Synthetic Controls - summary

Usage

pscSumm(DC_clean)

Arguments

DC_clean

a cleaned dataset ontained using dataComb().

Value

psc summary results including an estimate of the linear predictor combing the data and the model, an estimate of patient level response and summary statistics of the average responses for the sythenthic and observed populations

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
dc <- dataComb(surv.mod,data)
summ <- pscSumm(dc)

---

Personalised Synthetic Controls - summary

Description

Personalised Synthetic Controls - summary

Usage

## S3 method for class 'psc'
summary(object, ...)

Arguments

object	an object of class 'psc'
...	not used

Value

A summary of a psc object obtained using pscSumm and a copy of the pscfit object

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
psc.ob <- pscfit(surv.mod,data)
summary(psc.ob)

---

modp

Description

modp

Usage

surv_fpm(DC_clean, beta = 0, s = NULL)

Arguments

DC_clean	a cleaned dataset ontained using dataComb().
beta	a parameter to determine if the survival probabilities should be adjusted by some (log) hazard ratio. Defaults to beta=0, i.e. no adjustment.
s	if specified will return the time at which some threshold is passed (e.g. s=0.5 for median survival time)

Details

A fucntion which extracts survival probabilities from a flexsurvreg object

Value

a list of times and assoicated survival probabilities

Examples

library(psc)
library(survival)
data("surv.mod")
data("data")
dc <- dataComb(surv.mod,data)
s_est <- surv_fpm(dc)

---

Example model for a survival outcome

Description

A model of class 'flezsurvreg'

Usage

surv.mod

Format

A model of class 'flezsurvreg':

gamma

cumulative baseline hazard parameters

vi

vascular invasion

age60

patient age (centred at 60)

ecog

ECOG performance Status

logafp

AFP - log scale

alb

albumin

logcreat

Creatinine - log scale

allmets

metastesis

ageVasInv

centred age nested within vascular invasion

time

survival time

cen

censoring indicator

os

survival time

count

exapmple outcome for count data

trt

exapmple identifier for mulitple treatment comparisons

aet

Aetiology

Source

simulated

---