Skip to content

Commit

Permalink
again
Browse files Browse the repository at this point in the history
  • Loading branch information
sb452 committed Oct 29, 2015
1 parent 7371078 commit 6b6236d
Show file tree
Hide file tree
Showing 8 changed files with 87 additions and 60 deletions.
69 changes: 36 additions & 33 deletions ivrcode.aux
View file
Expand Up @@ -19,11 +19,13 @@
\citation{hernan2006}
\citation{glymour2012}
\citation{vanderweele2014}
\citation{burgess2015beyond}
\HyPL@Entry{2<</P(3)>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction and notation}{3}{section.1}}
\@writefile{brf}{\backcite{hernan2006}{{3}{1}{lstnumber.-1.14}}}
\@writefile{brf}{\backcite{glymour2012}{{3}{1}{lstnumber.-1.14}}}
\@writefile{brf}{\backcite{vanderweele2014}{{3}{1}{lstnumber.-1.14}}}
\@writefile{brf}{\backcite{burgess2015beyond}{{3}{1}{lstnumber.-1.14}}}
\citation{burgess2015review}
\citation{burgess2015book}
\HyPL@Entry{3<</P(4)>>}
Expand Down Expand Up @@ -143,40 +145,41 @@
\bibcite{bowden2011}{{4}{2011}{{Bowden and Vansteelandt}}{{}}}
\bibcite{buonaccorsi2005}{{5}{2005}{{Buonaccorsi}}{{}}}
\bibcite{burgess2013genepi}{{6}{2013}{{Burgess et~al.}}{{}}}
\bibcite{burgess2012noncollapse}{{7}{2013}{{Burgess and {CHD CRP Genetics Collaboration}}}{{}}}
\bibcite{burgess2014nonlin}{{8}{2014}{{Burgess et~al.}}{{}}}
\bibcite{burgess2015scoretj}{{9}{2015a}{{Burgess et~al.}}{{}}}
\bibcite{burgess2014pleioajeappendix}{{10}{2015b}{{Burgess et~al.}}{{}}}
\bibcite{burgess2014twosample}{{11}{2015c}{{Burgess et~al.}}{{}}}
\bibcite{burgess2015review}{{12}{2015d}{{Burgess et~al.}}{{}}}
\bibcite{burgess2015beyond}{{7}{2015a}{{Burgess et~al.}}{{}}}
\bibcite{burgess2012noncollapse}{{8}{2013}{{Burgess and {CHD CRP Genetics Collaboration}}}{{}}}
\bibcite{burgess2014nonlin}{{9}{2014}{{Burgess et~al.}}{{}}}
\bibcite{burgess2015scoretj}{{10}{2015b}{{Burgess et~al.}}{{}}}
\bibcite{burgess2014pleioajeappendix}{{11}{2015c}{{Burgess et~al.}}{{}}}
\bibcite{burgess2014twosample}{{12}{2015d}{{Burgess et~al.}}{{}}}
\HyPL@Entry{23<</P(24)>>}
\bibcite{burgess2012score}{{13}{2013}{{Burgess and Thompson}}{{}}}
\bibcite{burgess2014pleioaje}{{14}{2015a}{{Burgess and Thompson}}{{}}}
\bibcite{burgess2015book}{{15}{2015b}{{Burgess and Thompson}}{{}}}
\bibcite{cai2011}{{16}{2011}{{Cai et~al.}}{{}}}
\bibcite{clarke2011}{{17}{2011}{{Clarke et~al.}}{{}}}
\bibcite{clarke2012}{{18}{2012}{{Clarke and Windmeijer}}{{}}}
\bibcite{didelez2007}{{19}{2007}{{Didelez and Sheehan}}{{}}}
\bibcite{ehret2011bk}{{20}{2011}{{Ehret, G., Munroe, P., Rice, K., et al.\ (The International Consortium for Blood Pressure Genome-Wide Association Studies)}}{{}}}
\bibcite{fieller1954}{{21}{1954}{{Fieller}}{{}}}
\bibcite{glymour2012}{{22}{2012}{{Glymour et~al.}}{{}}}
\bibcite{greco2015}{{23}{2015}{{Greco et~al.}}{{}}}
\bibcite{greenland2000}{{24}{2000}{{Greenland}}{{}}}
\bibcite{greenland1999}{{25}{1999}{{Greenland et~al.}}{{}}}
\bibcite{burgess2015review}{{13}{2015e}{{Burgess et~al.}}{{}}}
\bibcite{burgess2012score}{{14}{2013}{{Burgess and Thompson}}{{}}}
\bibcite{burgess2014pleioaje}{{15}{2015a}{{Burgess and Thompson}}{{}}}
\bibcite{burgess2015book}{{16}{2015b}{{Burgess and Thompson}}{{}}}
\bibcite{cai2011}{{17}{2011}{{Cai et~al.}}{{}}}
\bibcite{clarke2011}{{18}{2011}{{Clarke et~al.}}{{}}}
\bibcite{clarke2012}{{19}{2012}{{Clarke and Windmeijer}}{{}}}
\bibcite{didelez2007}{{20}{2007}{{Didelez and Sheehan}}{{}}}
\bibcite{ehret2011bk}{{21}{2011}{{Ehret, G., Munroe, P., Rice, K., et al.\ (The International Consortium for Blood Pressure Genome-Wide Association Studies)}}{{}}}
\bibcite{fieller1954}{{22}{1954}{{Fieller}}{{}}}
\bibcite{glymour2012}{{23}{2012}{{Glymour et~al.}}{{}}}
\bibcite{greco2015}{{24}{2015}{{Greco et~al.}}{{}}}
\HyPL@Entry{24<</P(25)>>}
\bibcite{han2008}{{26}{2008}{{Han}}{{}}}
\bibcite{hernan2006}{{27}{2006}{{Hern{\'a}n and Robins}}{{}}}
\bibcite{lawlor2007}{{28}{2008}{{Lawlor et~al.}}{{}}}
\bibcite{martens2006}{{29}{2006}{{Martens et~al.}}{{}}}
\bibcite{mikusheva2010}{{30}{2010}{{Mikusheva}}{{}}}
\bibcite{nagelkerke2000}{{31}{2000}{{Nagelkerke et~al.}}{{}}}
\bibcite{palmer2011b}{{32}{2011}{{Palmer et~al.}}{{}}}
\bibcite{palmer2008b}{{33}{2008}{{Palmer et~al.}}{{}}}
\bibcite{pierce2013}{{34}{2013}{{Pierce and Burgess}}{{}}}
\bibcite{terza2008}{{35}{2008}{{Terza et~al.}}{{}}}
\bibcite{vanderweele2014}{{36}{2014}{{VanderWeele et~al.}}{{}}}
\bibcite{vansteelandt2010}{{37}{2011}{{Vansteelandt et~al.}}{{}}}
\bibcite{vansteelandt2003}{{38}{2003}{{Vansteelandt and Goetghebeur}}{{}}}
\bibcite{greenland2000}{{25}{2000}{{Greenland}}{{}}}
\bibcite{greenland1999}{{26}{1999}{{Greenland et~al.}}{{}}}
\bibcite{han2008}{{27}{2008}{{Han}}{{}}}
\bibcite{hernan2006}{{28}{2006}{{Hern{\'a}n and Robins}}{{}}}
\bibcite{lawlor2007}{{29}{2008}{{Lawlor et~al.}}{{}}}
\bibcite{martens2006}{{30}{2006}{{Martens et~al.}}{{}}}
\bibcite{mikusheva2010}{{31}{2010}{{Mikusheva}}{{}}}
\bibcite{nagelkerke2000}{{32}{2000}{{Nagelkerke et~al.}}{{}}}
\bibcite{palmer2011b}{{33}{2011}{{Palmer et~al.}}{{}}}
\bibcite{palmer2008b}{{34}{2008}{{Palmer et~al.}}{{}}}
\bibcite{pierce2013}{{35}{2013}{{Pierce and Burgess}}{{}}}
\bibcite{terza2008}{{36}{2008}{{Terza et~al.}}{{}}}
\bibcite{vanderweele2014}{{37}{2014}{{VanderWeele et~al.}}{{}}}
\bibcite{vansteelandt2010}{{38}{2011}{{Vansteelandt et~al.}}{{}}}
\HyPL@Entry{25<</P(26)>>}
\bibcite{wald1940}{{39}{1940}{{Wald}}{{}}}
\bibcite{vansteelandt2003}{{39}{2003}{{Vansteelandt and Goetghebeur}}{{}}}
\bibcite{wald1940}{{40}{1940}{{Wald}}{{}}}
\HyPL@Entry{26<</P(27)>>}
22 changes: 14 additions & 8 deletions ivrcode.bbl
View file
Expand Up @@ -36,6 +36,12 @@ Burgess, S., Butterworth, A., and Thompson, S. 2013.
using summarized data}.
\newblock {\em Genetic Epidemiology}, 37(7):658--665.

\bibitem[Burgess et~al., 2015a]{burgess2015beyond}
Burgess, S., Butterworth, A.~S., and Thompson, J.~R. 2015a.
\newblock {Beyond Mendelian randomization: how to interpret evidence of shared
genetic predictors}.
\newblock {\em Journal of Clinical Epidemiology}.

\bibitem[Burgess and {CHD CRP Genetics Collaboration},
2013]{burgess2012noncollapse}
Burgess, S. and {CHD CRP Genetics Collaboration} 2013.
Expand All @@ -49,28 +55,28 @@ Burgess, S., Davies, N., Thompson, S., and {EPIC-InterAct Consortium} 2014.
relationship}.
\newblock {\em Epidemiology}, 25(6):877--885.

\bibitem[Burgess et~al., 2015a]{burgess2015scoretj}
Burgess, S., Dudbridge, F., and Thompson, S. 2015a.
\bibitem[Burgess et~al., 2015b]{burgess2015scoretj}
Burgess, S., Dudbridge, F., and Thompson, S. 2015b.
\newblock {Combining information on multiple instrumental variables in
Mendelian randomization: comparison of allele score and summarized data
methods}.
\newblock Available at https://www.academia.edu/15479109/Combining.

\bibitem[Burgess et~al., 2015b]{burgess2014pleioajeappendix}
Burgess, S., Dudbridge, F., and Thompson, S.~G. 2015b.
\bibitem[Burgess et~al., 2015c]{burgess2014pleioajeappendix}
Burgess, S., Dudbridge, F., and Thompson, S.~G. 2015c.
\newblock {Re: ``Multivariable Mendelian randomization: the use of pleiotropic
genetic variants to estimate causal effects''}.
\newblock {\em American Journal of Epidemiology}, 181(4):290--291.

\bibitem[Burgess et~al., 2015c]{burgess2014twosample}
\bibitem[Burgess et~al., 2015d]{burgess2014twosample}
Burgess, S., Scott, R., Timpson, N., Davey~Smith, G., Thompson, S., and
{EPIC-InterAct Consortium} 2015c.
{EPIC-InterAct Consortium} 2015d.
\newblock {Using published data in Mendelian randomization: a blueprint for
efficient identification of causal risk factors}.
\newblock {\em European Journal of Epidemiology}, 30(7):543--552.

\bibitem[Burgess et~al., 2015d]{burgess2015review}
Burgess, S., Small, D.~S., and Thompson, S.~G. 2015d.
\bibitem[Burgess et~al., 2015e]{burgess2015review}
Burgess, S., Small, D.~S., and Thompson, S.~G. 2015e.
\newblock {A review of instrumental variable estimators for Mendelian
randomization}.
\newblock {\em Statistical Methods in Medical Research}.
Expand Down
1 change: 1 addition & 0 deletions ivrcode.brf
View file
@@ -1,6 +1,7 @@
\backcite {hernan2006}{{3}{1}{lstnumber.-1.14}}
\backcite {glymour2012}{{3}{1}{lstnumber.-1.14}}
\backcite {vanderweele2014}{{3}{1}{lstnumber.-1.14}}
\backcite {burgess2015beyond}{{3}{1}{lstnumber.-1.14}}
\backcite {burgess2015review}{{4}{2}{section.2}}
\backcite {burgess2015book}{{4}{2}{section.2}}
\backcite {wald1940}{{5}{2.1}{subsection.2.1}}
Expand Down
Binary file modified ivrcode.dvi
View file
Binary file not shown.
20 changes: 10 additions & 10 deletions ivrcode.log
View file
@@ -1,4 +1,4 @@
This is pdfTeX, Version 3.1415926-2.3-1.40.12 (MiKTeX 2.9 64-bit) (preloaded format=latex 2014.9.19) 29 OCT 2015 17:04
This is pdfTeX, Version 3.1415926-2.3-1.40.12 (MiKTeX 2.9 64-bit) (preloaded format=latex 2014.9.19) 29 OCT 2015 17:17
entering extended mode
**ivrcode.tex
(U:\github\mr-code\ivrcode.tex
Expand Down Expand Up @@ -464,19 +464,19 @@ Overfull \hbox (37.01689pt too wide) in paragraph at lines 511--512
(U:\github\mr-code\ivrcode.brf)
\tf@brf=\write5

Underfull \hbox (badness 4156) in paragraph at lines 58--58
[]\OT1/cmr/m/n/12 Burgess, S., Dud-bridge, F., and Thomp-son, S. 2015a. Com-bi
Underfull \hbox (badness 4060) in paragraph at lines 64--64
[]\OT1/cmr/m/n/12 Burgess, S., Dud-bridge, F., and Thomp-son, S. 2015b. Com-bi
n-ing in-
[]


Underfull \hbox (badness 2894) in paragraph at lines 58--58
Underfull \hbox (badness 2894) in paragraph at lines 64--64
\OT1/cmr/m/n/12 for-ma-tion on mul-ti-ple in-stru-men-tal vari-ables in Mendeli
an ran-dom-iza-tion:
[]


Underfull \hbox (badness 2158) in paragraph at lines 58--58
Underfull \hbox (badness 2158) in paragraph at lines 64--64
\OT1/cmr/m/n/12 com-par-i-son of al-lele score and sum-ma-rized data meth-ods.
Avail-able at
[]
Expand All @@ -493,15 +493,15 @@ Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 639.
Package rerunfilecheck Info: File `ivrcode.out' has not changed.
(rerunfilecheck) Checksum: A3BC1229B69DA48BA0FF084536123FA7;1101.
Package rerunfilecheck Info: File `ivrcode.brf' has not changed.
(rerunfilecheck) Checksum: C1E76061DC456F29D99C2A7692B420C2;2233.
(rerunfilecheck) Checksum: 062B6993DFD228776E8195113065D8D6;2289.
)
Here is how much of TeX's memory you used:
9180 strings out of 494046
131070 string characters out of 3148410
9188 strings out of 494046
131251 string characters out of 3148410
292384 words of memory out of 3000000
12363 multiletter control sequences out of 15000+200000
12371 multiletter control sequences out of 15000+200000
13555 words of font info for 53 fonts, out of 3000000 for 9000
715 hyphenation exceptions out of 8191
32i,6n,40p,758b,1689s stack positions out of 5000i,500n,10000p,200000b,50000s

Output written on ivrcode.dvi (27 pages, 192748 bytes).
Output written on ivrcode.dvi (27 pages, 193844 bytes).
Binary file modified ivrcode.pdf
View file
Binary file not shown.
25 changes: 16 additions & 9 deletions ivrcode.tex
View file
Expand Up @@ -87,7 +87,7 @@ \section{Introduction and notation}
byse # standard errors of genetic associations with outcome
\end{lstlisting}

This document describes methods for causal estimation using Mendelian randomization. Little attention is paid as to the assumptions for Mendelian randomization, or the interpretation of estimates from these methods. See \cite{hernan2006}, \cite{glymour2012} and \cite{vanderweele2014} for some critical comments.
This document describes methods for causal estimation using Mendelian randomization. Little attention is paid as to the assumptions for Mendelian randomization, or the interpretation of estimates from these methods. See \cite{hernan2006}, \cite{glymour2012}, \cite{vanderweele2014} and \cite{burgess2015beyond} for some critical comments.

\clearpage

Expand Down Expand Up @@ -206,8 +206,8 @@ \subsection{Two-stage methods}
The same point estimate (although not the standard error) can be obtained using sequential regression:

\begin{lstlisting}
beta_seqreg_tsls = lm(y~lm(x~g)$fitted)
\end{lstlisting}.
beta_seqreg_tsls = lm(y~lm(x~g)$fitted)$coef[2]
\end{lstlisting}

\begin{lstlisting}
## B. Binary outcome, logistic-linear model (assuming case--control data)
Expand Down Expand Up @@ -236,7 +236,11 @@ \subsection{Two-stage methods}
\clearpage

\subsection{Likelihood-based methods}
Not aware of a generic implementation of likelihood-based methods (such as limited information maximum likelihood, LIML) in R. The LIML approach can be implemented in Stata: \texttt{ivreg2 y (x = g1), liml} for one variant; \texttt{ivreg2 y (x = g1 g2 g3), liml} for multiple variants.
Not aware of a generic implementation of likelihood-based methods (such as limited information maximum likelihood, LIML) in R. The LIML approach can be implemented in Stata:
\begin{lstlisting}
ivreg2 y (x = g1), liml * for one variant
ivreg2 y (x = g1 g2 g3), liml * for multiple variants.
\end{lstlisting}

\clearpage

Expand Down Expand Up @@ -377,14 +381,14 @@ \subsection{Semi-parametric methods}
\section{Mendelian randomization analysis with summarized data}
This section on Mendelian randomization methods with summarized data covers the inverse-variance weighted method that is equivalent asymptotically to the two-stage least squares method, as well as robust methods such as Egger regression, median-based estimation (including simple median and weighted median methods), a test for heterogeneity of the causal estimates from different genetic variants, and some code for the presentation of summarized data.

We assume that data are available on genetic associations with the risk factor and with the outcome in the form of beta-coefficients and standard errors.
We assume that data are available on genetic associations with the risk factor and with the outcome in the form of beta-coefficients (\textt{bx} and \textt{by}) and standard errors (\textt{bxse} and \textt{byse}).

A one-sample Mendelian randomization setting is one in which data on genetic associations with the risk factor and with the outcome are estimated in the same individuals. A two-sample Mendelian randomization setting is one in which data on genetic associations with the risk factor and with the outcome are estimated in different samples \citep{pierce2013}. Although two-sample investigations are not limited to those using summarized data, the use of summarized (particularly published) data means that genetic associations are often taken from separate sources, which may be non-overlapping \citep{burgess2014twosample}.

\clearpage

\subsection{Inverse-variance weighted method}
The inverse-variance weighted method can be motivated in several ways \citep{burgess2013genepi}. 1) It is a weighted mean of the causal estimates from multiple genetic variants, where the weights are the inverse-variance weights also used in meta-analysis. 2) It is asymptotically equivalent to a two-stage least squares analysis (and so can be motivated using an allele score). 3) It is the coefficient from a weighted linear regression of the gene--outcome coefficients on the gene-risk factor coefficients (intercept is constrained to equal zero).
The inverse-variance weighted method can be motivated in several ways \citep{burgess2013genepi}. 1) It is a weighted mean of the ratio causal estimates from multiple genetic variants, where the weights are the inverse-variance weights also used in meta-analysis. 2) It is asymptotically equivalent to a two-stage least squares analysis (and so can be motivated using an allele score). 3) It is the coefficient from a weighted linear regression of the gene--outcome coefficients on the gene-risk factor coefficients (intercept is constrained to equal zero).

We initially present the inverse-variance weighted estimate and standard error as it was initially proposed (using a fixed-effect assumption -- that all the genetic variants identify the same causal effect, and using a simple formulation of the variances used as weights) \citepalias{ehret2011bk}. We then give random-effects estimates, as well as a correction to the variances that should be used in a one-sample setting, particularly when the instruments are weak. We initially assume that genetic variants are uncorrelated (not in linkage disequilibrium).

Expand All @@ -407,6 +411,9 @@ \subsection{Inverse-variance weighted method}

\begin{lstlisting}
## B. Genetic variants uncorrelated, heterogeneity -- random-effects model
# (the use of a random-effects model is preferred,
# particularly if there is any chance of heterogeneity
# in the estimates obtained using different genetic variants)

# 1. Additive random-effects model
betafirst.addran = metagen(by/bx, abs(byse/bx))$TE.random
Expand Down Expand Up @@ -454,7 +461,7 @@ \subsection{Inverse-variance weighted method}
sesecond.theta.mulran = reg.second.theta$coef[1,2]/min(reg.second.theta$sigma,1)
\end{lstlisting}

When the genetic associations with the risk factor and with the outcome are estimated in non-overlapping datasets (a two-sample setting), the estimates in section B give reasonable coverage rates and those in section C give overcoverage (confidence intervals are too wide) [unpublished]. However, when the datasets overlap (as is often the case in practice for major genetic consortia), the coverage of estimates in section B is below nominal levels and Type 1 error rates are too frequent. This is particularly true when the genetic variants are weak. Estimates in section C give much better coverage properties.
When the genetic associations with the risk factor and with the outcome are estimated in non-overlapping datasets (a two-sample setting), the estimates in section B give reasonable coverage rates and those in section C give overcoverage (confidence intervals are too wide) [unpublished]. However, when the datasets overlap (as is often the case in practice for major genetic consortia), the coverage of estimates in section B is below nominal levels and Type 1 error rates are too frequent. This is particularly true when the genetic variants are weak. In the one-sample or overlapping sample setting, estimates in section C have much better coverage properties.

The correlation term $\theta$ is the correlation between the genetic associations with the risk factor and the genetic associations with the outcome. This is zero in a two-sample setting, and approximately the same as the correlation between the risk factor and the outcome in a one-sample setting.

Expand All @@ -466,7 +473,7 @@ \subsection{Inverse-variance weighted method}
sefirst.fixed.correl = sqrt(solve(t(bx)%*%solve(Omega)%*%bx))
\end{lstlisting}

When genetic variants are correlated, the causal effect can be estimated using generalized weighted linear regression \citep{burgess2015scoretj}. The matrix \texttt{rho} is the matrix of correlations between the genetic variants. This method can give odd results, particularly if the genetic variants are highly correlated.
When genetic variants are correlated, the causal effect can be estimated using generalized weighted linear regression \citep{burgess2015scoretj}. The matrix \texttt{rho} is the matrix of correlations between the genetic variants. This method can give odd results, particularly if the genetic variants are highly correlated, or the correlations are misspecified.

\clearpage

Expand Down Expand Up @@ -594,7 +601,7 @@ \subsection{Multivariable Mendelian randomization}
summary(ivmodel)
\end{lstlisting}

With summarized data, the inverse-variance weighted method can be used, except that instead of a univariate weighted linear regression model, a multivariate weighted linear regression model can be employed \cite{burgess2014pleioajeappendix}.
With summarized data, the inverse-variance weighted method can be used, except that instead of a univariate weighted linear regression model, a multivariate weighted linear regression model can be employed \citep{burgess2014pleioajeappendix}.

\begin{lstlisting}
## B. Summarized data
Expand Down
10 changes: 10 additions & 0 deletions masterrefcode.bib
View file
Expand Up @@ -466,6 +466,16 @@ @ARTICLE{terza2008
publisher = {Elsevier}
}

@ARTICLE{burgess2015beyond,
author = {Burgess, Stephen and Butterworth, Adam S and Thompson, John R},
title = {{Beyond Mendelian randomization: how to interpret evidence of shared
genetic predictors}},
journal = {Journal of Clinical Epidemiology},
year = {2015},
doi = {10.1016/j.jclinepi.2015.08.001},
publisher = {Elsevier}
}

@ARTICLE{nagelkerke2000,
author = {Nagelkerke, N. and Fidler, V. and Bernsen, R. and Borgdorff, M.},
title = {{Estimating treatment effects in randomized clinical trials in the
Expand Down

0 comments on commit 6b6236d

Please sign in to comment.