| Title: | Isotope Ratio Meta-Analysis |
|---|---|
| Description: | Calculation of consensus values for atomic weights, isotope amount ratios, and isotopic abundances with the associated uncertainties using multivariate meta-regression approach for consensus building. |
| Authors: | Juris Meija and Antonio Possolo |
| Maintainer: | Juris Meija <[email protected]> |
| License: | Unlimited |
| Version: | 1.3 |
| Built: | 2024-11-16 03:18:32 UTC |
| Source: | https://github.com/cran/CIAAWconsensus |
This function calculates the isotope ratios of a chemical element from the given isotopic abundances and their uncertainties. The uncertainty evaluation is done using the propagation of uncertainty and the missing correlations between the isotopic abundances are reconstructed using Monte Carlo methods.
abundances2ratios(x, ux, ref=1, iterations=1e4)abundances2ratios(x, ux, ref=1, iterations=1e4)
x |
A vector of isotopic abundances of an element |
ux |
Standard uncertainties of |
ref |
Index to specify the desired reference isotope for isotope amount ratios |
iterations |
Number of iterations for isotopic abundance correlation mapping |
Situations are often encountered where isotopic abundances are reported but not the isotope ratios. In such cases we reconstruct the isotope ratios that are consistent with the abundances and their uncertainties. Given only the abundances and their uncertainties, for elements with four or more isotopes one cannot unambiguously infer the uncertainties of the ratios due to the unknown correlations between isotopic abundances. This missing information can be reconstructed by mapping all possible correlations between isotopic abundances.
R |
Isotope ratio vector, excluding the trivial ratio |
R.u |
Standard uncertainties of the isotope ratios |
R.cov |
Isotope ratio covariance matrix |
N |
Number of sucessful Monte Carlo iterations |
Juris Meija <[email protected]> and Antonio Possolo
J. Meija and Z. Mester (2008) Atomic weight uncertainty calculation from isotopic composition of the elements. Metrologia, 45, 459
J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. Metrologia, 54, 229-238
JCGM 101:2008 Evaluation of measurement data - Supplement 1 to the "Guide to the expression of uncertainty in measurement" - Propagation of distributions using a Monte Carlo method
## Isotope ratios of zinc from the isotopic abundances x = c(0.48630, 0.27900, 0.04100, 0.18750, 0.00620) ux = c(0.00091, 0.00076, 0.00031, 0.00135, 0.00010) abundances2ratios(x,ux,ref=2) ## The corresponding atomic weight can be obtained using at.weight(z$R,z$R.cov,"zinc","66Zn")## Isotope ratios of zinc from the isotopic abundances x = c(0.48630, 0.27900, 0.04100, 0.18750, 0.00620) ux = c(0.00091, 0.00076, 0.00031, 0.00135, 0.00010) abundances2ratios(x,ux,ref=2) ## The corresponding atomic weight can be obtained using at.weight(z$R,z$R.cov,"zinc","66Zn")
This function calculates the isotopic abundances and the atomic weight of a chemical element from the given isotope amount ratios and their uncertainties. The uncertainty evaluation is done using the Monte Carlo method and the relevant masses of the isotopes are extracted from the www.ciaaw.org.
at.weight(ratio, ratio.cov, element, ref.isotope, data=NULL)at.weight(ratio, ratio.cov, element, ref.isotope, data=NULL)
ratio |
A vector of nontrivial isotope amount ratios of an element |
ratio.cov |
A covariance matrix of |
element |
A string consisting of the lowercase English name of the element. For example, "zinc" |
ref.isotope |
A string which specifies the reference isotope. For example, "64Zn" |
data |
Nuclide mass dataframe. Default dataframe is ciaaw.mass.2016 |
The isotopic composition of an element with N isotopes is characterized using a set of N-1 nontrivial isotope amount ratios.
As an example, silicon has three stable isotopes (silicon-28, silicon-29, and silicon-30) and its isotope ratios can be reported against
either of its stable isotopes in three distinct ways: (1) 29Si/28Si and 29Si/28Si or (2) 28Si/29Si and 30Si/29Si, or (3) 28Si/30Si and 29Si/30Si.
aw |
Atomic weight |
aw.u |
Standard uncertainty of the atomic weight |
aw.U95 |
Expanded uncertainty of the atomic weight corresponding to 95% confidence |
abundances |
Isotopic abundances |
abundances.u |
Standard uncertainty of the isotopic abundances |
abundances.U95 |
Expanded uncertainty of the isotopic abundances corresponding to 95% confidence |
abundances.cov |
Covariance matrix of the isotopic abundances |
Juris Meija <[email protected]> and Antonio Possolo
J.Meija and Z. Mester (2008) Uncertainty propagation of atomic weight measurement results. Metrologia, 45, 53-62
J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. Metrologia, 54, 229-238
JCGM 101:2008 Evaluation of measurement data - Supplement 1 to the "Guide to the expression of uncertainty in measurement" - Propagation of distributions using a Monte Carlo method
## Atomic weight and isotopic abundances of iridium which correspond ## to the isotope ratio 191Ir/193Ir = 0.59471(13) at.weight(0.59471, matrix(0.00013^2), "iridium", "193Ir") ## Atomic weight and isotopic abundances of silicon which correspond ## to isotope ratios 28Si/29Si = 1.074(69) and 30Si/29Si = 260(11) ## with a correlation of 0.80 between the two isotope ratios ratios = c(1.074,260) r.cov = matrix(c(0.069^2,0.80*0.069*11,0.80*0.069*11,11^2),ncol=2,byrow=TRUE) at.weight(ratios, r.cov, "silicon", "29Si")## Atomic weight and isotopic abundances of iridium which correspond ## to the isotope ratio 191Ir/193Ir = 0.59471(13) at.weight(0.59471, matrix(0.00013^2), "iridium", "193Ir") ## Atomic weight and isotopic abundances of silicon which correspond ## to isotope ratios 28Si/29Si = 1.074(69) and 30Si/29Si = 260(11) ## with a correlation of 0.80 between the two isotope ratios ratios = c(1.074,260) r.cov = matrix(c(0.069^2,0.80*0.069*11,0.80*0.069*11,11^2),ncol=2,byrow=TRUE) at.weight(ratios, r.cov, "silicon", "29Si")
This data set gives the atomic masses and uncertainties of all polyisotopic nuclides as they are used by the IUPAC/CIAAW.
ciaaw.mass.2003ciaaw.mass.2003
A data frame with 268 rows and 4 variables:
isotope: Symbol of the isotope
element: Name of the element (lowercase english)
mass: Atomic mass of the isotope in daltons
uncertainty: Uncertainty of the atomic mass of the isotope as used by the IUPAC-CIAAW
AME2003, http://www.ciaaw.org/
This data set gives the atomic masses and uncertainties of all polyisotopic nuclides as they are used by the IUPAC/CIAAW.
ciaaw.mass.2012ciaaw.mass.2012
A data frame with 268 rows and 4 variables:
isotope: Symbol of the isotope
element: Name of the element (lowercase english)
mass: Atomic mass of the isotope in daltons
uncertainty: Uncertainty of the atomic mass of the isotope as used by the IUPAC-CIAAW
AME2012 https://doi.org/10.1088/1674-1137/41/3/030003, http://www.ciaaw.org/
This data set gives the atomic masses and uncertainties of all polyisotopic nuclides as they are used by the IUPAC/CIAAW.
ciaaw.mass.2016ciaaw.mass.2016
A data frame with 268 rows and 4 variables:
isotope: Symbol of the isotope
element: Name of the element (lowercase english)
mass: Atomic mass of the isotope in daltons
uncertainty: Uncertainty of the atomic mass of the isotope as used by the IUPAC-CIAAW
AME2016 https://doi.org/10.1088/1674-1137/41/3/030003, http://www.ciaaw.org/
This data set gives the iridium isotope ratios as reported by various studies. These data are used by the IUPAC/CIAAW to determine the standard atomic weight of iridium.
iridium.datairidium.data
A data frame.
IUPAC/CIAAW 2018
This function provides meta-analysis of multivariate correlated data using the marginal method of moments with working independence assumption as described by Chen et al (2016). As such, the meta-analysis does not require correlations between the outcomes within each dataset.
mmm(y, uy, knha = TRUE, verbose = TRUE)mmm(y, uy, knha = TRUE, verbose = TRUE)
y |
A matrix of results from each of the |
uy |
A matrix with uncertainties of the results given in |
knha |
(Logical) Allows for the adjustment of consensus uncertainties using the Birge ratio (Knapp-Hartung adjustment) |
verbose |
(Logical) Requests annotated summary output of the results |
The marginal method of moments delivers the inference for correlated effect sizes using multiple univariate meta-analyses.
studies |
The number of independent studies |
beta |
The consensus estimates for all outcomes |
beta.u |
Standard uncertainties of the consensus estimates |
beta.U95 |
Expanded uncertainties of the consensus estimates corresponding to 95% confidence |
beta.cov |
Covariance matrix of the consensus estimates |
beta.cor |
Correlation matrix of the consensus estimates |
H |
Birge ratios (Knapp-Hartung adjustment) which were applied to adjust the standard uncertainties of each consensus outcome |
I2 |
Relative total variability due to heterogeneity (in percent) for each outcome |
Juris Meija <[email protected]> and Antonio Possolo
Y. Chen, Y. Cai, C. Hong, and D. Jackson (2016) Inference for correlated effect sizes using multiple univariate meta-analyses. Statistics in Medicine, 35, 1405-1422
J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. Metrologia, 54, 229-238
## Consensus isotope amount ratios for platinum df=normalize.ratios(platinum.data, "platinum", "195Pt") mmm(df$R, df$u.R)## Consensus isotope amount ratios for platinum df=normalize.ratios(platinum.data, "platinum", "195Pt") mmm(df$R, df$u.R)
This function converts the isotope amount ratios of an element from various studies to a single common reference isotope so that all isotope ratios can be directly compared to one another. The conversion involves a direct application of the law of propagation of uncertainty and this function discards the possible covariances between the isotope ratios.
normalize.ratios(dat, element, ref.isotope, expand = FALSE)normalize.ratios(dat, element, ref.isotope, expand = FALSE)
dat |
A data frame of results from each study where each study reports one or more isotope ratios (outcomes). The data frame must include the following named columns: Study, Year, Author, Outcome, Value, Unc, k_extra (see Details). |
element |
Lowercase english name of the element, e.g., "antimony" |
ref.isotope |
Desired reference isotope, e.g., "121Sb" |
expand |
(Logical) Specification of whether or not to expand the isotope ratio uncertainties using the values of |
The isotope ratio vector is transformed to the reference isotope by dividing each element of the set to the chosen reference isotope.
The covariances of the transformed isotope ratios are obtained using the Law of Propagation of Uncertainty. This function assumes all isotope ratios reported by a given study as uncorrelated.
While this is not strictly true in practice, such assumption is made largely because of the lack of reported correlations in the literature.
The format of dat data frame for a simple dataset is as follows:
| Study | Year | Author | Outcome | Value | Unc | k_extra |
| 1 | 1954 | Howard | 191Ir/193Ir | 0.5949 | 0.0025 | 9 |
| 2 | 1991 | Creaser | 191Ir/193Ir | 0.5948 | 0.0001 | 9 |
| 3 | 1992 | Chang | 191Ir/193Ir | 0.59399 | 0.00103 | 6 |
| 4 | 1993 | Walczyk | 191Ir/193Ir | 0.59418 | 0.00037 | 9 |
| 5 | 2017 | Zhu | 191Ir/193Ir | 0.59290 | 0.00021 | 6 |
R |
A list of the normalized isotope amount ratios |
u.R |
A list of standard uncertainties for |
cov.R |
A list of covariance matrices for |
Juris Meija <[email protected]> and Antonio Possolo
J. Meija and Z. Mester (2008) Uncertainty propagation of atomic weight measurement results. Metrologia, 45, 53-62
J. Meija and A. Possolo (2017) Data reduction framework for standard atomic weights and isotopic compositions of the elements. Metrologia, 54, 229-238
## Normalize all platinum isotope data to platinum-195 normalize.ratios(platinum.data, "platinum", "195Pt")## Normalize all platinum isotope data to platinum-195 normalize.ratios(platinum.data, "platinum", "195Pt")
This data set gives the platinum isotope ratios as reported by various studies. These data are used by the IUPAC/CIAAW to determine the standard atomic weight of platinum.
platinum.dataplatinum.data
A data frame.
IUPAC/CIAAW 2016