Package 'c212' reference manual

Title:	Methods for Detecting Safety Signals in Clinical Trials Using Body-Systems (System Organ Classes)
Description:	Provides a self-contained set of methods to aid clinical trial safety investigators, statisticians and researchers, in the early detection of adverse events using groupings by body-system or system organ class. This work was supported by the Engineering and Physical Sciences Research Council (UK) (EPSRC) [award reference 1521741] and Frontier Science (Scotland) Ltd. The package title c212 is in reference to the original Engineering and Physical Sciences Research Council (UK) funded project which was named CASE 2/12.
Authors:	Raymond Carragher [aut, cre]
Maintainer:	Raymond Carragher <[email protected]>
License:	GPL-3
Version:	1.0.1
Built:	2025-02-02 05:56:09 UTC
Source:	https://github.com/rcarragh/c212

Methods for the Detection of Safety Signals in Randomised Controlled Trials using Groupings.

Description

This package implements a number of methods for the detection of safety signals in Clinical Trials based on groupings of adverse events by body-system or system organ class. The methods include an implementation of the Three-Level Hierarchical model for Clinical Trial Adverse Event Incidence Data of Berry and Berry (2004) and an implementation of the same model without the Point Mass (Model 1a from Xia et al (2011)), extended Bayesian hierarchical methods based on system organ class or body-system groupings for interim analyses. The package also implements a number of methods for error control when testing multiple hypotheses, specifically control of the False Discovery Rate (FDR). The FDR control methods implemented are the Benjamini-Hochberg procedure, the Double False Discovery Rate, the Group Benjamini-Hochberg and subset Benjamini-Hochberg methods. Also included are the Bonferroni correction and the unadjusted testing procedure.

Details

The methods implemented use assumed groupings of adverse events by body-system or system organ class to detect differences in the occurrence of adverse events on trial arms. Methods based on Bayesian Hierarchical models and direct error controlling procedures are provided.

The basic (Bayesian) hierarchical models are described in Berry and Berry (2004), Xia et al (2011) (Model 1a) and Berry et al (2010). These methods are extended for interim analyses.

The direct error controlling methods are designed to control the number of Type-I errors at an acceptable level without compromising the power. If the Familywise Error Rate (FWER) is defined as the probability of making one or more Type-I errors when analysing multiple hypotheses (the “family”), then an alternative to controlling the FWER is to control the False Discovery Rate (FDR) - the expected proportion of false discoveries (Type-I errors) to the total number of discoveries. Essentially control of the FDR assumes that when many of the tested hypotheses are rejected it may be preferable to control the proportion of errors rather than the probability of making even one error. This is expected to lead to a gain in power. Further FDR controlling methods which use the information available in groupings of hypotheses have been developed (Double False Discovery Rate (Mehrotra and Adewale (2012)), Group Benjamini-Hochberg (Hu, Zhao and Zhou (2010))). For the methods contained in this package control of the False Discovery Rate has been established for independent test statistics and some forms of positive dependency (positive regression dependency), apart from the case of the Group Benjamini-Hochberg procedure where the control is asymptotic. Further details can be found in the references.

Author(s)

R. Carragher<[email protected]; [email protected]>

References

S. M. Berry and D. A. Berry (2004). Accounting for multiplicities in assessing drug safety: a three- level hierarchical mixture model. Biometrics, 60(2):418-26.

H. Amy Xia, Haijun Ma, and Bradley P. Carlin (2011). Bayesian hierarchical modelling for detecting safety signals in clinical trials. Journal of Biopharmaceutical Statistics, 21(5):1006– 1029.

Scott M. Berry, Bradley P. Carlin, J. Jack Lee, and Peter M¨ller (2010). Bayesian adaptive methods for clinical trials. CRC Press.

Benjamini, Yoav and Hochberg, Yosef, (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological), 57(1):289-300.

D. V. Mehrotra and J. F. Heyse (2004). Use of the false discovery rate for evaluating clinical safety data. Stat Methods Med Res, 13(3):227–38, 2004.

Mehrotra, D. V. and Adewale, A. J. (2012). Flagging clinical adverse experiences: reducing false discoveries without materially compromising power for detecting true signals. Stat Med, 31(18):1918-30.

Hu, J. X. and Zhao, H. and Zhou, H. H. (2010). False Discovery Rate Control With Groups. J Am Stat Assoc, 105(491):1215-1227.

Y. Benjamini, A. M. Krieger, and D. Yekutieli (2006). Adaptive linear step-up procedures that control the false discovery rate. Biometrika, 93(3):491–507.

Benjamini Y, Hochberg Y. (2000). On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics. Journal of Educational and Behavioral Statistics, 25(1):60–83.

Yekutieli, Daniel (2008). False discovery rate control for non-positively regression dependent test statistics. Journal of Statistical Planning and Inference, 138(2):405-415.

Matthews, John N. S. (2006) Introduction to Randomized Controlled Clinical Trials, Second Edition. Chapman & Hall/CRC Texts in Statistical Science.

Implementation of the Berry and Berry Three-Level Hierarchical Model without Point-Mass.

Description

Implementaion of Berry and Berry model without the point-mass (Model 1a Xia et al (2011))

Usage

	c212.1a(trial.data, sim_type = "SLICE", burnin = 10000, iter = 40000,
	nchains = 3,
	global.sim.params = data.frame(type = c("MH", "SLICE"),
	param = c("sigma_MH", "w"),
	value = c(0.35,1), control = c(0,6), stringsAsFactors = FALSE),
	sim.params = NULL,
	initial_values = NULL,
	hyper_params = list(mu.gamma.0.0 = 0, tau2.gamma.0.0 = 10,
	mu.theta.0.0 = 0, tau2.theta.0.0 = 10, alpha.gamma.0.0 = 3,
	beta.gamma.0.0 = 1, alpha.theta.0.0 = 3, beta.theta.0.0 = 1,
	alpha.gamma = 3, beta.gamma = 1,
	alpha.theta = 3, beta.theta = 1))
c212.1a(trial.data, sim_type = "SLICE", burnin = 10000, iter = 40000,
	nchains = 3,
	global.sim.params = data.frame(type = c("MH", "SLICE"),
	param = c("sigma_MH", "w"),
	value = c(0.35,1), control = c(0,6), stringsAsFactors = FALSE),
	sim.params = NULL,
	initial_values = NULL,
	hyper_params = list(mu.gamma.0.0 = 0, tau2.gamma.0.0 = 10,
	mu.theta.0.0 = 0, tau2.theta.0.0 = 10, alpha.gamma.0.0 = 3,
	beta.gamma.0.0 = 1, alpha.theta.0.0 = 3, beta.theta.0.0 = 1,
	alpha.gamma = 3, beta.gamma = 1,
	alpha.theta = 3, beta.theta = 1))

Arguments

`trial.data`	A file or data frame containing the trial data. It must contain must contain the columns B (body-system), AE (adverse event), Group (1 - control, 2 treatment), Count (total number of events), Total (total number of participants in the trial arm).
`sim_type`	The type of MCMC method to use for simulating from non-standard distributions. Allowed values are "MH" and "SLICE" for Metropolis_Hastings and Slice sampling respectively.
`burnin`	The burnin period for the monte-carlo simulation. These are discarded from the returned samples.
`iter`	The total number of iterations for which the monte-carlo simulation is run. This includes the burnin period. The total number of samples returned is iter - burnin
`nchains`	The number of independent chains to run.
`global.sim.params`	A data frame containing the parameters for the simulation type sim_type. For "MH" the parameter is the variance of the normal distribution used to simulate the next candidate value centred on the current value. For "SLICE" the parameters are the estimated width of the slice and a value limiting the search for the next sample.
`sim.params`	A dataframe containing simulation parameters which override the global simulation parameters (global.sim.params) for particular model parameters. sim.params must contain the following columns: type: the simulation type ("MH" or "SLICE"); variable: the model parameter for which the simulation parameters are being overridden; B: the body-system (if applicable); AE: the adverse event (if applicable); param: the simulation parameter; value: the overridden value; control: the overridden control value. The function c212.sim.control.params generates a template for sim.params which can be edited by the user.
`initial_values`	The initial values for starting the chains. If NULL (the default) is passed the function generates the initial values for the chains. initial_values is a list with the following format: list(gamma, theta, mu.gamma, mu.theta, sigma2.gamma, sigma2.theta, mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0) where each element of the list is either a dataframe or array. The function c212.gen.initial.values can be used to generate a template for the list which can be updated by the user if required. The formats of the list elements are as follows: gamma, theta: dataframe with columns B, AE, chain, value mu.gamma, mu.theta, sigma2.gamma, sigma2.theta: dataframe with columns B, chain, value mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0: array of size chain.
`hyper_params`	The hyperparameters for the model. The default hyperparameters are those given in Berry and Berry 2004.

Details

The model is fitted by a Gibbs sampler. The details of the complete conditional densities are given in Berry and Berry (2004). The posterior distributions for gamma and theta are sampled with either a Metropolis-Hastings step or a slice sampler.

Value

The output from the simulation including all the sampled values is as follows:

list(id, sim_type, chains, nBodySys, maxAEs, nAE, AE, B, burnin,
	iter, mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0,
	mu.gamma, mu.theta, sigma2.gamma, sigma2.theta, gamma,
	theta, gamma_acc, theta_acc)

where

id - a string identifying the version of the function

sim_type - an string identifying the sampling method used for non-standard distributions, either "MH" or "SLICE"

chains - the number of chains for which the simulation was run

nBodySys - the number of body-systems

maxAEs - the maximum number of AEs in a body-system

nAE - an array. The number of AEs in each body-system.

AE - an array of dimension nBodySys, maxAEs. The Adverse Events.

B - an array. The body-systems.

burnin - the burnin period for the simulation.

iter - the total number of iterations in the simulation.

mu.gamma.0 - array of samples of dimension chains, iter - burnin

mu.theta.0 - array of samples of dimension chains, iter - burnin

tau2.gamma.0 - array of samples of dimension chains, iter - burnin

tau2.theta.0 - array of samples of dimension chains, iter - burnin

mu.gamma - array of samples of dimension chains, nBodySys iter - burnin

mu.theta - array of samples of dimension chains, nBodySys iter - burnin

sigma2.gamma - array of samples of dimension chains, nBodySys iter - burnin

sigma2.theta - array of samples of dimension chains, nBodySys iter - burnin

gamma - array of samples of dimension chains, nBodySys, maxAEs, iter - burnin

theta - array of samples of dimension chains, nBodySys, maxAEs, iter - burnin

gamma_acc - the acceptance rate for the gamma samples if a Metropolis-Hastings method is used. An array of dimension chains, nBodySys, maxAEs

theta_acc - the acceptance rate for the theta samples if a Metropolis-Hastings method is used. An array of dimension chains, nBodySys, maxAEs

Note

The function performs the simulation and returns the raw output. No checks for convergence are performed.

Author(s)

R. Carragher

References

S. M. Berry and D. A. Berry (2004). Accounting for multiplicities in assessing drug safety: a three- level hierarchical mixture model. Biometrics, 60(2):418-26.

H. Amy Xia, Haijun Ma, and Bradley P. Carlin (2011). Bayesian hierarchical modelling for detecting safety signals in clinical trials. Journal of Biopharmaceutical Statistics, 21(5):1006– 1029.

Scott M. Berry, Bradley P. Carlin, J. Jack Lee, and Peter M¨ller (2010). Bayesian adaptive methods for clinical trials. CRC Press.

Examples

data(c212.trial.data)
raw = c212.1a(c212.trial.data, burnin = 100, iter = 200)
## Not run: 
data(c212.trial.data)
raw = c212.1a(c212.trial.data)

raw$B
[1] "Bdy-sys_1" "Bdy-sys_2" "Bdy-sys_3" "Bdy-sys_4" "Bdy-sys_5" "Bdy-sys_6"
[7] "Bdy-sys_7" "Bdy-sys_8"

mean(rm$theta[2, 3,1,])
[1] 1.306362


## End(Not run)
data(c212.trial.data)
raw = c212.1a(c212.trial.data, burnin = 100, iter = 200)
## Not run: 
data(c212.trial.data)
raw = c212.1a(c212.trial.data)

raw$B
[1] "Bdy-sys_1" "Bdy-sys_2" "Bdy-sys_3" "Bdy-sys_4" "Bdy-sys_5" "Bdy-sys_6"
[7] "Bdy-sys_7" "Bdy-sys_8"

mean(rm$theta[2, 3,1,])
[1] 1.306362


## End(Not run)

A Two or Three-Level Hierarchical Body-system based Model for interim analysis without Point-Mass.

Description

Implementation of a Two or Three-Level Hierarchical Body-system based Model for interim analysis without Point-Mass.

Usage

	c212.1a.interim(trial.data, sim_type = "SLICE", burnin = 10000,
		iter = 40000, nchains = 3,
		global.sim.params = NULL,
		sim.params = NULL,
		monitor = NULL,
		initial_values = NULL,
		hier = 3,
		level = 1,
		hyper_params = NULL,
		memory_model = "HIGH")
c212.1a.interim(trial.data, sim_type = "SLICE", burnin = 10000,
		iter = 40000, nchains = 3,
		global.sim.params = NULL,
		sim.params = NULL,
		monitor = NULL,
		initial_values = NULL,
		hier = 3,
		level = 1,
		hyper_params = NULL,
		memory_model = "HIGH")

Arguments

`trial.data`	A file or data frame containing the trial data. It must contain must contain the columns I_index (interval index), B (body-system), AE (adverse event), Group (1 - control, 2 treatment), Count (total number of events), Total (total number of participants in the trial arm).
`sim_type`	The type of MCMC method to use for simulating from non-standard distributions. Allowed values are "MH" and "SLICE" for Metropolis_Hastings and Slice sampling respectively.
`burnin`	The burnin period for the monte-carlo simulation. These are discarded from the returned samples.
`iter`	The total number of iterations for which the monte-carlo simulation is run. This includes the burnin period. The total number of samples returned is iter - burnin
`nchains`	The number of independent chains to run.
`global.sim.params`	A data frame containing the parameters for the simulation type sim_type. For "MH" the parameter is the variance of the normal distribution used to simulate the next candidate value centred on the current value. For "SLICE" the parameters are the estimated width of the slice and a value limiting the search for the next sample. Passing NULL uses the model defaults.
`sim.params`	A dataframe containing simulation parameters which override the global simulation parameters (global.sim.params) for particular model parameters. sim.params must contain the following columns: type: the simulation type ("MH" or "SLICE"); variable: the model parameter for which the simulation parameters are being overridden; B: the body-system (if applicable); AE: the adverse event (if applicable); param: the simulation parameter; value: the overridden value; control: the overridden control value. Passing NULL uses the model defaults. The function c212.sim.control.params generates a template for sim.params which can be edited by the user.
`monitor`	A dataframe indicating which sets of If NULL is passed default parameters are variables to monitor. Passing NULL uses the model defaults.
`initial_values`	The initial values for starting the chains. If NULL (the default) is passed the function generates the initial values for the chains. initial_values is a list with the following format: list(gamma, theta, mu.gamma, mu.theta, sigma2.gamma, sigma2.theta, mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0) where each element of the list is either a dataframe or array. The function c212.gen.initial.values can be used to generate a template for the list which can be updated by the user if required. The formats of the list elements are as follows: gamma, theta: dataframe with columns B, AE, chain, value mu.gamma, mu.theta, sigma2.gamma, sigma2.theta: dataframe with columns B, chain, value mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0: array of size chain.
`hier`	Model using a two or three level hierarchy. 2 - two-level hierarchy, 3 - three level hierarchy.
`level`	The level of longitudinal dependency between the intervals. Allowed values are 0, 1, 2 for a three-level hierarchy and 0, 1 for a two-level hierarchy. 0 - independent intervals, 1 - common interval body-system means, 2 - weak dependency.
`hyper_params`	The hyperparameters for the model. The default hyperparameters are based on those given in Berry and Berry 2004. Passing NULL uses the model defaults.
`memory_model`	Allowed values are "HIGH" and "LOW". "HIGH" means use as much memory as possible. "LOW" means use the minimum amount of memory.

Details

The models are fitted by Gibbs samplers. The posterior distributions for gamma and theta are sampled with either a Metropolis-Hastings step or a slice sampler.

Value

The output from the simulation including all the sampled values for the three-level hierarchy is as follows:

list(id, sim_type, chains, nIntervals, Intervals, nBodySys, maxBs,
	maxAEs, nAE, AE, B, burnin, iter, monitor,
	mu.gamma.0, mu.theta.0, tau2.gamma.0, tau2.theta.0,
	mu.gamma, mu.theta, sigma2.gamma, sigma2.theta, gamma,
	theta, gamma_acc, theta_acc)

The output from the simulation including all the sampled values for the two-level hierarchy is as follows:

list(id, sim_type, chains, nIntervals, Intervals, nBodySys, maxBs,
	maxAEs, nAE, AE, B, burnin, iter, monitor,
	mu.gamma, mu.theta, sigma2.gamma, sigma2.theta, gamma,
	theta, gamma_acc, theta_acc)

where

id - a string identifying the version of the function

sim_type - an string identifying the sampling method used for non-standard distributions, either "MH" or "SLICE"

chains - the number of chains for which the simulation was run.

nIntervals - the number of intervals in the simulation

Intervals - an array. The intervals.

nBodySys - the number of body-systems

maxBs - the maximum number of body-systems in an interval

maxAEs - the maximum number of AEs in a body-system

nAE - an array. The number of AEs in each body-system.

AE - an array of dimension nBodySys, maxAEs. The Adverse Events.

B - an array. The body-systems.

burnin - burnin used for the simulation.

iter - the total number of iterations in the simulation.

monitor - the variables being monitored. A dataframe.