This is a function that incorporates ARSER, JTK_CYCLE and LombScargle to detect rhythmic signals from timeseries datasets.
1 2 3 4 5 6  meta2d(infile, outdir = "metaout", filestyle, timepoints, minper = 20,
maxper = 28, cycMethod = c("ARS", "JTK", "LS"),
analysisStrategy = "auto", outputFile = TRUE, outIntegration = "both",
adjustPhase = "predictedPer", combinePvalue = "fisher",
weightedPerPha = FALSE, ARSmle = "auto", ARSdefaultPer = 24,
outRawData = FALSE, releaseNote = TRUE, outSymbol = "")

infile 
a character string. The name of input file containing timeseries data. 
outdir 
a character string. The name of directory used to store output files. 
filestyle 
a character vector(length 1 or 3). The data format of
input file, must be 
timepoints 
a numeric vector corresponding to sampling time points of input timeseries data; if sampling time points are in the first line of input file, it could be set as a character sting"Line1" or "line1". 
minper 
a numeric value. The minimum period length of interested
rhythms. The default is 
maxper 
a numeric value. The maximum period length of interested
rhythms. The default is 
cycMethod 
a character vector(length 1 or 2 or 3). Userdefined
methods for detecting rhythmic signals, must be selected as any one, any
two or all three methods(default) from 
analysisStrategy 
a character string. The strategy used to select
proper methods from 
outputFile 
logical. If 
outIntegration 
a character string. This parameter controls what
kinds of analysis results will be outputted, must be one of 
adjustPhase 
a character string. The method used to adjust original
phase calculated by each method in integration file, must be one of

combinePvalue 
a character string. The method used to integrate
multiple pvalues, must be one of 
weightedPerPha 
logical. If 
ARSmle 
a character string. The strategy of using MLE method in

ARSdefaultPer 
a numeric value. The expected period length of
interested rhythm, which is a necessary parameter for 
outRawData 
logical. If 
releaseNote 
logical. If 
outSymbol 
a character string. A common prefix exists in the names of output files. 
ARSER(Yang, 2010),
JTK_CYCLE(
Hughes, 2010), and
LombScargle(Glynn, 2006) are three popular methods of detecting
rhythmic signals. ARS
can not analyze unevenly sampled datasets,
or evenly sampled datasets but with missing values, or with replicate
samples, or with noninteger sampling interval. JTK
is not
suitable to analyze unevenly sampled datasets or evenly sampled datasets
but with noninteger sampling interval. If set analysisStrategy
as "auto"
(default), meta2d
will automatically select
proper method from cycMethod
for each input dataset. If the user
clearly know that the dataset could be analyzed by each method defined
by cycMethod
and do not hope to output integrated values,
analysisStrategy
can be set as "selfUSE"
.
ARS
used here is translated from its python version which always
uses "yulewalker"
, "burg"
, and "mle"
methods(see
ar
) to fit autoregressive models to timeseries
data. Fitting by "mle"
will be very slow for datasets
with many time points. If ARSmle = "auto"
is used,
meta2d
will only include "mle"
when number of time points
is smaller than 24. In addition, one evaluation work(Wu, 2014) indicates
that ARS
shows relative high false positive rate in analyzing
highresolution datasets (1h/2days and 2h/2days). JTK
(version 3)
used here is the latest version, which improves its pvalue calculation
in analyzing datasets with missing values.
The power of detecting rhythmic signals for an algorithm is associated
with the nature of data and interested periodic pattern(Deckard, 2013),
which indicates that integrating analysis results from multiple methods
may be helpful to rhythmic detection. For integrating pvalues,
Bonferroni correction("bonferroni"
) and Fisher's method(
"fisher"
) (Fisher, 1925; implementation code from MADAM)
could be selected, and "bonferroni"
is usually more conservative
than "fisher"
. The integrated period is arithmetic mean of
multiple periods. For integrating phase, meta2d
takes use of
mean of circular quantities. Integrated period and phase is further
used to calculate the baseline value and amplitude through fitting a
constructed periodic model.
Phases given by JTK
and LS
need to be adjusted with their
predicted period (adjustedPhase = "predictedPer"
) before
integration. If adjustedPhas = "notAdjusted"
is selected, no
integrated phase will be calculated. If set weightedPerPha
as
TRUE
, weighted scores will be used in averaging periods and
phases. Weighted scores for one method are based on all its reported
pvalues, which means a weighted score assigned to any one profile will
be affected by all other profiles. It is always a problem of averaging
phases with quite different period lengths(eg. averaging two phases
with 16hours' and 30hours' period length). Currently, setting
minper
, maxper
and ARSdefaultPer
to a same value
may be the only way of completely eliminating such problem.
This function is originally aimed to analyze large scale periodic data(
eg. circadian transcriptome data) without individual information.
Please pay attention to data format of input file(see Examples
part). Except the first column and first row, others are timeseries
experimental values(setting missing values as NA
).
meta2d
will write analysis results in different files under
outdir
if set outputFile = TRUE
. Files named with
"ARSresult", "JTKresult" and "LSreult" store analysis results from
ARS
, JTK
and LS
respectively. The file named with
"meta2d" is the integration file, and it stores integrated values in
columns with a common name tag"meta2d". The integration file also
contains pvalue, FDR value, period, phase(adjusted phase if
adjustedPhase = "predictedPer"
) and amplitude values calculated
by each method.
If outputFile = FALSE
is selected, meta2d
will return a
list containing the following components:
ARS  analysis results from ARS method 
JTK  analysis results from JTK method 
LS  analysis results from LS method 
meta  the integrated analysis results as mentioned above 
Yang R. and Su Z. (2010). Analyzing circadian expression data by harmonic regression based on autoregressive spectral estimation. Bioinformatics, 26(12), i168–i174.
Hughes M. E., Hogenesch J. B. and Kornacker K. (2010). JTK_CYCLE: an efficient nonparametric algorithm for detecting rhythmic components in genomescale data sets. Journal of Biological Rhythms, 25(5), 372–380.
Glynn E. F., Chen J. and Mushegian A. R. (2006). Detecting periodic patterns in unevenly spaced gene expression time series using LombScargle periodograms. Bioinformatics, 22(3), 310–316.
Wu G., Zhu J., Yu J., Zhou L., Huang J. Z. and Zhang Z. (2014). Evaluation of five methods for genomewide circadian gene identification. Journal of Biological Rhythms, 29(4), 231–242.
Deckard A., Anafi R. C., Hogenesch J. B., Haase S.B. and Harer J. (2013). Design and analysis of largescale biological rhythm studies: a comparison of algorithms for detecting periodic signals in biological data. Bioinformatics, 29(24), 3174–3180.
Fisher, R.A. (1925). Statistical methods for research workers. Oliver and Boyd (Edinburgh).
Kugler K. G., Mueller L.A. and Graber A. (2010). MADAM  an open source toolbox for metaanalysis. Source Code for Biology and Medicine, 5, 3.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  # write 'cycMouseLiverProtein' into a 'txt' file
write.table(cycMouseLiverProtein, file="cycMouseLiverProtein.txt",
sep="\t", quote=FALSE, row.names=FALSE)
# write 'cycSimu4h2d' and 'cycYeastCycle' into two 'csv' files
write.csv(cycSimu4h2d, file="cycSimu4h2d.csv", row.names=FALSE)
write.csv(cycYeastCycle, file="cycYeastCycle.csv", row.names=FALSE)
# analyze 'cycMouseLiverProtein.txt' with JTK_CYCLE and LombScargle
meta2d(infile="cycMouseLiverProtein.txt", filestyle="txt",
outdir="example", timepoints=rep(seq(0, 45, by=3), each=3),
cycMethod=c("JTK","LS"), outIntegration="noIntegration")
# analyze 'cycSimu4h2d.csv' with ARSER, JTK_CYCLE and LombScargle and
# output integration file with analysis results from each method
meta2d(infile="cycSimu4h2d.csv", filestyle="csv", outdir="example",
timepoints="Line1")
# analyze 'cycYeastCycle.csv' with ARSER, JTK_CYCLE and LombScargle to
# detect transcripts associated with cell cycle, and return analysis
# results instead of output them into files
cyc < meta2d(infile="cycYeastCycle.csv",filestyle="csv",
minper=80, maxper=96, timepoints=seq(2, 162, by=16),
outputFile=FALSE, ARSdefaultPer=85, outRawData=TRUE)
head(cyc$ARS)
head(cyc$JTK)
head(cyc$LS)
head(cyc$meta)

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
All documentation is copyright its authors; we didn't write any of that.