RJaCGH {RJaCGH} | R Documentation |
This function fits a non-homogeneous hidden Markov model to CGH data through bayesian methods and Reversible Jump Markov chain Montecarlo.
RJaCGH(y, Chrom = NULL, Start=NULL, End=NULL, Pos = NULL, Dist=NULL, probe.names=NULL, maxVar=NULL, model = "genome", var.equal=TRUE, max.dist=NULL, normal.reference=0, normal.ref.percentile=0.95, burnin = 10000, TOT =10000, k.max = 6, stat = NULL, mu.alfa = NULL, mu.beta = NULL, prob.k = NULL, jump.parameters=list(), start.k = NULL, RJ=TRUE, auto.label=NULL)
y |
Vector with Log Ratio observations. |
Chrom |
Vector with Chromosome indicator. |
Start |
Vector with start positions of the probes. |
End |
Vector with end positions of the probes. |
Pos |
Vector with Positions of every gene. They can be absolute
to the genome or relative to the chromosome. They should be ordered
within every chromosome. This is, the arrays must be ordered by their
positions in the genome. They must be integers. Positions can be
specified with Start , End or Pos , but only in
one of the two ways. |
Dist |
Optional vector of distances between genes. It should be a vector
of length length(y)-1 . Note that when Chrom is not NULL,
every last value of every Chromosome is not used. |
probe.names |
Character vector with the number of the probes. |
maxVar |
Maximum value for the variance of the states. If
NULL , the range of the data is chosen. |
model |
if model ="genome", the same model is fitted for
the whole genome. If model ="Chrom", a different model is
fitted for each chromosome. |
var.equal |
Logical. If TRUE the variances of the hidden
states are restricted to be the same. |
max.dist |
maximal distance between spots. When two spots have
a distance between them as far or further than max.dist , they
are considered independent. That is, the state of that spot
does not affect the state of the other. If NULL (the default) the
maximum Dist or maximum difference in Pos is taken. |
normal.reference |
The value considered as the mean of the normal
state. See details. By default is 0 . |
normal.ref.percentile |
Percentage for the relabelling of states. See details. by default is 0.95. |
burnin |
Number of burn-in iterations in the Markov Chain |
TOT |
Number of iterations after the burn-in |
k.max |
Maximum number of hidden states to fit. |
stat |
Initial Distribution for the hidden states. Must be a
vector of size 1 + 2 + ... +k.max . If NULL , it is assumed a
uniform distribution for every model. |
mu.alfa |
Hyperparameter. See details |
mu.beta |
Hyperparameter. See details |
prob.k |
Hyperparameter. See details |
jump.parameters |
List with the parameters for the MCMC jumps. See details. |
start.k |
Initial number of states. if NULL , a random draw from
prob.k is chosen. |
RJ |
Logical. If TRUE , Reversible Jump is performed.
If not, MCMC
over a fixed number of hidden states. Note that if NULL , most
of the methods for extracting information won't work. |
auto.label |
If not NULL , should be the minimum proportion of
observations labeled as 'Normal'. See details. |
RJaCGH fits the following bayesian model: There is a priori
distribution for the number of hidden states (different copy numbers)
as stated by prob.k
. If NULL
, a uniform distribution between 1
and k.max
is used.
The hidden states follow a normal distribution which mean (mu
)
follows
itself a normal distribution with mean
mu.alfa
and stdev mu.beta
. If NULL
, these are the
median of the data and the range. The square
root of the variance (sigma.2
)of the hidden states
follows a uniform distribution between $0$ and maxVar
.
The model for the transition matrix is based on a random matrix
beta
whose diagonal is zero. The transition matrix, Q
,
has the form:
Q[i,j] = exp(-beta[i,j] + beta[i,j]*x) / sum(i,.) {exp(-beta[i,.] +
beta[i,.]*x}
The prior distribution for beta
is gamma with parameters 1, 1.
The x
are the distances between positions, normalized to lay
between zero and 1 (x=diff(Pos) / max(diff(Pos))
)
RJaCGH performs Markov Chain MonteCarlo with Reversible Jump to sample for the posterior distribution. Every sweep has 3 steps:
1.- A Metropolis-Hastings move is used to update, for a fixed number
of hidden states, mu
, sigma.2
and beta
. A
symmetric proposal with a normal distribution and standard deviation
sigma.tau.mu
, sigma.tau.sigma.2
and
sigma.tau.beta
is sampled.
2.- A transdimensional move is chosen, between birth (a new hidden state is sampled from the prior) or death (an existing hidden state is erased).
3.- Another transdimensional move is performed; an split move (divide
an existing state in two) or a combine move (join two adjacent
states). The length of the split is sampled from a normal distribution
with standard deviation tau.split.mu
for the mu
and
tau.split.beta
for beta
.
jump.parameters
must be a list with the parameters for the
moves. It must have components sigma.tau.mu
,
sigma.tau.sigma.2
, sigma.tau.beta
These are vectors of
length k.max
. tau.split.mu
, tau.split.beta
are vectors of
length 1. If any of them is NULL, a call to the internal function
get.jump()
is made to find 'good' values.
A relabelling of hidden states is performed to match biological
states. The states that have the normal.reference
value
inside a normal.ref.percentile
% probability interval
based on a normal distribution with means the median of mu
and sd the square root of the median of sigma.2
are labelled as
'Normal'. If no state is close enough to normal.reference
then
there will not be a normal state. Bear this in mind for
normalization issues.
If auto.label
is not null, closest states to 'Normal' are also
labelled as 'Normal' until a proportion of auto.label
is
reached. Please note that the default value is 0.60, so at least the
60% of the observations will be labelled as 'Normal'.
If this laeblling is not satisfactory, you can relabel with
relabelStates
.
The object returned follows a hierarchy:
If y is a matrix or data.frame (i.e., several arrays), an object of
class RJaCGH.array
is returned, with components:
[[]] |
A list with an object of corresponding class (see below) for every array. |
array.names |
Vector with the names of the arrays. |
[[]] |
a list with as many objects as k.max, with the fits. |
k |
sequence of number of hidden states sampled. |
prob.b |
Number of birth moves performed (Includes burn-in. |
prob.d |
Number of death moves performed (Includes burn-in. |
prob.s |
Number of split moves performed (Includes burn-in. |
prob.c |
Number of combine moves performed (Includes burn-in. |
y |
y vector. |
Pos |
Pos vector. |
model |
model. |
Chrom |
Chromosome vector. |
x |
x vector of distances between genes. |
[[]] |
a list with as many components as chromosomes, of class
RJaCGH (See below). |
Pos |
Pos vector. |
Start |
Start positions. |
End |
End positions. |
probe.names |
Names of the probes. |
model |
model. |
Chrom |
Chromosome vector. |
mu |
a matrix with the means sampled |
sigma.2 |
a matrix with the variances sampled |
beta |
an array of dimension 3 with beta values sampled |
stat |
vector of initial distribution |
loglik |
log likelihoods of every MCMC iteration |
prob.mu |
probability of aceptance of mu in the
Metropolis-Hastings step. |
prob.sigma.2 |
probability of aceptance of sigma.2 in the
Metropolis-Hastings step. |
prob.beta |
probability of aceptance of beta in the
Metropolis-Hastings step. |
state.labels |
Labels of the biological states. |
prob.states |
Marginal posterior probabilities of belonging to every hidden state. |
The number of rows of components mu
, sigma.2
and
beta
is random, because it depends on the number of times
a particular model is visited and on the number of moves between
models, because when we visit a new model we also explore the space
of its means, variances and parameters of its transition functions.
The data must be ordered by chromosome and within chromosome by position.
Oscar M. Rueda and Ramon Diaz Uriarte
Rueda OM, Diaz-Uriarte R. Flexible and Accurate Detection of Genomic Copy-Number Changes from aCGH. PLoS Comput Biol. 2007;3(6):e122
Cappe, Moulines and Ryden, 2005. Inference in Hidden Markov Models. Springer.
Green, P.J. (1995) Reversible Jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711-732.
summary.RJaCGH
,
states
, model.averaging
,
plot.RJaCGH
, trace.plot
,
gelman.brooks.plot
, collapseChain
,
relabelStates
, pREC_A
,
pREC_S
y <- c(rnorm(100, 0, 1), rnorm(10, -3, 1), rnorm(20, 3, 1), rnorm(100,0, 1)) Pos <- sample(x=1:500, size=230, replace=TRUE) Pos <- cumsum(Pos) Chrom <- rep(1:23, rep(10, 23)) jp <- list(sigma.tau.mu=rep(0.05, 4), sigma.tau.sigma.2=rep(0.03, 4), sigma.tau.beta=rep(0.07, 4), tau.split.mu=0.1, tau.split.beta=0.1) fit.chrom <- RJaCGH(y=y, Pos=Pos, Chrom=Chrom, model="Chrom", burnin=10, TOT=1000, k.max = 4, jump.parameters=jp) ##RJ results for chromosome 5 table(fit.chrom[[5]]$k) fit.genome <- RJaCGH(y=y, Pos=Pos, Chrom=Chrom, model="genome", burnin=100, TOT=1000, jump.parameters=jp, k.max = 4) ## Results for the model with 3 states: apply(fit.genome[[3]]$mu, 2, summary) apply(fit.genome[[3]]$sigma.2, 2, summary) apply(fit.genome[[3]]$beta, c(1,2), summary)