[R-meta] Reproducing results using regtest in metafor
Sutton, Alex (Prof.)
@j@22 @end|ng |rom |e|ce@ter@@c@uk
Mon Aug 12 14:34:26 CEST 2019
Dear James
Thank you for taking the time to think about this and write. I think your approach of writing the model out is a good one for discussing exactly what is going on "under the hood".
Your justification of the degrees of freedom seems sound - much appreciated.
I am still a little uncertain about the model specification because an additive random effect is specified in the initial meta-regression using the rma command. But then a multiplicative error is specified in the regtest command. These probably dont have any bearing on the degrees of freedom, but I would greatly appreciate it if someone could explain how these are jointly implemented.
With very best wishes
Alex
________________________________
From: James Pustejovsky <jepusto using gmail.com>
Sent: 09 August 2019 19:04
To: Sutton, Alex (Prof.) <ajs22 using leicester.ac.uk>
Cc: Michael Dewey <lists using dewey.myzen.co.uk>; r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>; DOLEMAN, Brett (UNIVERSITY HOSPITALS OF DERBY AND BURTON NHS FOUNDATION TRUST) <brett.doleman using nhs.net>; Freeman, Suzanne C. (Dr.) <suzanne.freeman using leicester.ac.uk>
Subject: Re: [R-meta] Reproducing results using regtest in metafor
Option 1 amounts to fitting the model
Y_i = b0 + b1 m.c_i + b2 se_i + e_i
with the assumption that Var(e_i) = sigma^2 v_i for unknown sigma^2. It can be fit using the nlme package using the following syntax (building off of the previous code):
library(nlme)
gls_fit <- gls(yi ~ m.c + sqrt(vi), data = ma.dataset, weights = varFixed(~ vi))
summary(gls_fit)
I think the correct df would be 27 in this case.
With option 2, the residuals from the first stage have lost 2 degrees of freedom (down to 28), and then they lose two more with the second stage fit (because the intercept is re-estimated when it should be constrained to zero).
James
On Fri, Aug 9, 2019 at 8:24 AM Sutton, Alex (Prof.) <ajs22 using leicester.ac.uk<mailto:ajs22 using leicester.ac.uk>> wrote:
Dear Michael
Many thanks for taking the time to write. (And let me thank you for all your hard work on the R meta-analysis web page - this is a fantastic resource I use all the time)
I think your suggestion is very plausible and I was thinking along related lines. Then I convinced myself that the df used in first regression was reflected in the se of the residuals (in a very "hand wavy" sort of way!) .
As you say, the issue then focuses on which is "better" - my concern with option 1 is that I don't know how to reproduce it outside of the package - but as you say it may well be theoretically superior.
I am also hoping Wolfgang can supply some definitive insight!
Thanks again
Alex
Alex Sutton
Professor of Medical Statistics
Department of Health Sciences
College of Life Sciences
University of Leicester
George Davies Centre
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-----Original Message-----
From: Michael Dewey [mailto:lists using dewey.myzen.co.uk<mailto:lists using dewey.myzen.co.uk>]
Sent: 09 August 2019 13:19
To: Sutton, Alex (Prof.) <ajs22 using leicester.ac.uk<mailto:ajs22 using leicester.ac.uk>>; r-sig-meta-analysis using r-project.org<mailto:r-sig-meta-analysis using r-project.org>
Cc: DOLEMAN, Brett (UNIVERSITY HOSPITALS OF DERBY AND BURTON NHS FOUNDATION TRUST) <brett.doleman using nhs.net<mailto:brett.doleman using nhs.net>>; Freeman, Suzanne C. (Dr.) <suzanne.freeman using leicester.ac.uk<mailto:suzanne.freeman using leicester.ac.uk>>
Subject: Re: [R-meta] Reproducing results using regtest in metafor
Dear Alex
I suspect the answer is that regtest.rma refits the model and so "knows"
you have a moderator and hence loses you a degree of freedom whereas regtest.default does not "know" that and so proceeds as though you had just the single predictor (sei). That probably explains the change in t too although we may need to wait for Wolfgang to give us the definitive answer.
Of course that leaves open the question which is better. I think your option 1 is what I would prefer but that is just based on instainct rather than any higher mathematics.
Michael
On 08/08/2019 17:42, Sutton, Alex (Prof.) wrote:
> Hi All list members
>
> I wish to adjust a meta-analytic dataset by the control arm event rate
> using meta-regression (ignoring any regression to the mean issues) and
> then run Egger's funnel asymmetry test after the adjustment.
>
> (I paste complete data, R code and output below my query.)
>
> The regtest command in metafor can do this and an example is given in
> the manual (option 1 in the code).
>
> But a colleague tried to do the same analysis in another package -
> STATA
> - but did not get the same result.
>
> I have tried to reconcile the 2, and have succeeded getting the STATA
> result in R using the code in option 2. But I don't understand why
> option 1 and option 2 code below give different results - I thought
> they should be equivalent? (The degrees of freedom are different as
> well as the test p-values)
>
> The key lines extracted from the below are:
>
> model2 <- rma(yi, vi, data = ma.dataset, mods = cbind(m.c),
> control=list(maxiter=200, stepadj=0.5))
>
> print(summary(model2))
>
> # Option 1: Put model 2 directly into regtest
>
> option1 <- regtest(model2, model = "lm", predictor="sei")
>
> print(option1)
>
> # Option 2: Extract residuals and SE from model 2 and then put these
> into regtest manually
>
> a <- rstandard.rma.uni(model2)
>
> option2 <- regtest(x=a$resid, sei=a$se, model = "lm", predictor="sei")
>
> print(option2)
>
> Hoping someone can offer me some insight.
>
> Many thanks in advance.
>
> Alex
>
> DATA BELOW:
>
> n.c
>
>
>
> n.t
>
>
>
> m.c
>
>
>
> m.t
>
>
>
> sd.c
>
>
>
> sd.t
>
> 15
>
>
>
> 15
>
>
>
> 43.34736
>
>
>
> 22.6778
>
>
>
> 20.14634
>
>
>
> 13.2187
>
> 15
>
>
>
> 15
>
>
>
> 36.66456
>
>
>
> 26.95877
>
>
>
> 14.24828
>
>
>
> 14.89395
>
> 15
>
>
>
> 15
>
>
>
> 51.74782
>
>
>
> 28.44658
>
>
>
> 23.83604
>
>
>
> 26.70313
>
> 15
>
>
>
> 15
>
>
>
> 49.80753
>
>
>
> 19.04398
>
>
>
> 24.16307
>
>
>
> 11.40324
>
> 15
>
>
>
> 15
>
>
>
> 60.67109
>
>
>
> 44.62121
>
>
>
> 29.01649
>
>
>
> 23.60531
>
> 15
>
>
>
> 15
>
>
>
> 31.34018
>
>
>
> 14.65917
>
>
>
> 18.27904
>
>
>
> 13.30416
>
> 25
>
>
>
> 25
>
>
>
> 44.48585
>
>
>
> 22.18729
>
>
>
> 24.98121
>
>
>
> 11.94804
>
> 25
>
>
>
> 25
>
>
>
> 42.19917
>
>
>
> 27.97304
>
>
>
> 27.69334
>
>
>
> 19.4292
>
> 25
>
>
>
> 25
>
>
>
> 44.99957
>
>
>
> 26.77364
>
>
>
> 33.80657
>
>
>
> 18.46828
>
> 25
>
>
>
> 25
>
>
>
> 62.6953
>
>
>
> 36.15569
>
>
>
> 32.1401
>
>
>
> 28.75357
>
> 25
>
>
>
> 25
>
>
>
> 35.38889
>
>
>
> 19.77613
>
>
>
> 16.96604
>
>
>
> 15.69643
>
> 25
>
>
>
> 25
>
>
>
> 36.46263
>
>
>
> 27.69418
>
>
>
> 22.18271
>
>
>
> 22.04955
>
> 25
>
>
>
> 25
>
>
>
> 42.63761
>
>
>
> 26.83291
>
>
>
> 22.60301
>
>
>
> 23.47935
>
> 50
>
>
>
> 50
>
>
>
> 57.92533
>
>
>
> 30.96353
>
>
>
> 28.90083
>
>
>
> 17.40233
>
> 50
>
>
>
> 50
>
>
>
> 26.15427
>
>
>
> 21.06599
>
>
>
> 17.39962
>
>
>
> 14.29371
>
> 50
>
>
>
> 50
>
>
>
> 39.98736
>
>
>
> 29.13268
>
>
>
> 19.99763
>
>
>
> 18.44498
>
> 50
>
>
>
> 50
>
>
>
> 46.11657
>
>
>
> 27.34703
>
>
>
> 24.23706
>
>
>
> 15.55458
>
> 50
>
>
>
> 50
>
>
>
> 48.0687
>
>
>
> 34.85292
>
>
>
> 25.19593
>
>
>
> 21.33037
>
> 50
>
>
>
> 50
>
>
>
> 53.43902
>
>
>
> 31.4177
>
>
>
> 31.33719
>
>
>
> 19.16536
>
> 50
>
>
>
> 50
>
>
>
> 56.2192
>
>
>
> 39.338
>
>
>
> 28.10021
>
>
>
> 24.66106
>
> 50
>
>
>
> 50
>
>
>
> 29.25929
>
>
>
> 15.60332
>
>
>
> 17.00783
>
>
>
> 12.57914
>
> 50
>
>
>
> 50
>
>
>
> 30.72385
>
>
>
> 20.22988
>
>
>
> 18.93253
>
>
>
> 15.11565
>
> 15
>
>
>
> 15
>
>
>
> 55.86973
>
>
>
> 27.38925
>
>
>
> 33.32485
>
>
>
> 22.29828
>
> 15
>
>
>
> 15
>
>
>
> 47.10929
>
>
>
> 28.39797
>
>
>
> 21.93013
>
>
>
> 25.12405
>
> 15
>
>
>
> 15
>
>
>
> 31.87787
>
>
>
> 15.31057
>
>
>
> 17.05947
>
>
>
> 10.99065
>
> 15
>
>
>
> 15
>
>
>
> 36.91457
>
>
>
> 26.14574
>
>
>
> 18.46971
>
>
>
> 18.57387
>
> 15
>
>
>
> 15
>
>
>
> 49.84609
>
>
>
> 34.04816
>
>
>
> 24.64221
>
>
>
> 21.22332
>
> 25
>
>
>
> 25
>
>
>
> 57.06665
>
>
>
> 32.91816
>
>
>
> 27.6288
>
>
>
> 19.84755
>
> 25
>
>
>
> 25
>
>
>
> 50.57364
>
>
>
> 36.87816
>
>
>
> 33.87053
>
>
>
> 21.38415
>
> 25
>
>
>
> 25
>
>
>
> 28.80046
>
>
>
> 21.97428
>
>
>
> 16.45233
>
>
>
> 15.75454
>
> CODE BELOW:
>
> library(metafor)
>
> rm(list=ls())
>
> ##simdat <- read.csv("s4_data.csv")
>
> ma.dataset <- escalc(n1i = n.t, n2i = n.c, m1i = m.t, m2i = m.c,
>
> sd1i = sd.t, sd2i = sd.c, data = simdat, measure
> = "MD",
>
> append = TRUE)
>
> model2 <- rma(yi, vi, data = ma.dataset, mods = cbind(m.c),
> control=list(maxiter=200, stepadj=0.5))
>
> print(summary(model2))
>
> # Option 1: Put model 2 directly into regtest
>
> option1 <- regtest(model2, model = "lm", predictor="sei")
>
> print(option1)
>
> # Option 2: Extract residuals and SE from model 2 and then put these
> directly into regtest
>
> a <- rstandard.rma.uni(model2)
>
> option2 <- regtest(x=a$resid, sei=a$se, model = "lm", predictor="sei")
>
> print(option2)
>
> OUTPUT BELOW:
>
> Mixed-Effects Model (k = 30; tau^2 estimator: REML)
>
> logLik deviance AIC BIC AICc
>
> -84.1061 168.2122 174.2122 178.2088 175.2122
>
> tau^2 (estimated amount of residual heterogeneity): 0 (SE =
> 6.3793)
>
> tau (square root of estimated tau^2 value): 0
>
> I^2 (residual heterogeneity / unaccounted variability): 0.00%
>
> H^2 (unaccounted variability / sampling variability): 1.00
>
> R^2 (amount of heterogeneity accounted for): 100.00%
>
> Test for Residual Heterogeneity:
>
> QE(df = 28) = 17.1497, p-val = 0.9456
>
> Test of Moderators (coefficient(s) 2):
>
> QM(df = 1) = 24.9726, p-val < .0001
>
> Model Results:
>
> estimate se zval pval ci.lb<https://eur03.safelinks.protection.outlook.com/?url=http%3A%2F%2Fci.lb&data=02%7C01%7Cajs22%40leicester.ac.uk%7C20c831bfa58542425a5108d71cf419a3%7Caebecd6a31d44b0195ce8274afe853d9%7C0%7C0%7C637009707043643604&sdata=rPy8TD2UakuaBYZIcxoeb137ohT%2FoN8MayfplxEc3pI%3D&reserved=0> ci.ub
>
> intrcpt 3.5641 3.8211 0.9327 0.3510 -3.9251 11.0534
>
> m.c -0.4633 0.0927 -4.9973 <.0001 -0.6450 -0.2816 ***
>
> ---
>
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
>>
>
>>
>
>> # Option 1: Put model 2 directly into regtest
>
>> option1 <- regtest(model2, model = "lm", predictor="sei")
>
>> print(option1)
>
> Regression Test for Funnel Plot Asymmetry
>
> model: weighted regression with multiplicative dispersion
>
> predictor: standard error
>
> test for funnel plot asymmetry: t = -0.2787, df = 27, p = 0.7826
>
>> # Option 2: Extract residuals and SE from model 2 and then put these
>> directly into regtest
>
>> a <- rstandard.rma.uni(model2)
>
>> residuals <- a$resid
>
>> SEresiduals <- a$se
>
>>
>
>> option2 <- regtest(x=residuals, sei=SEresiduals, model = "lm",
>> predictor="sei")
>
>> print(option2)
>
> Regression Test for Funnel Plot Asymmetry
>
> model: weighted regression with multiplicative dispersion
>
> predictor: standard error
>
> test for funnel plot asymmetry: t = -0.2170, df = 28, p = 0.8297
>
> *Alex Sutton
> Professor of Medical Statistics
>
> ***
>
> Department of Health Sciences
>
> College of Life Sciences
>
> University of Leicester
>
> George Davies Centre
>
> University Road
>
> LEICESTER LE1 7RH UK
>
> *Please use Lancaster Road, Leicester, LE1 7HA for SatNav*
>
> Member of the Complex Reviews Support Unit
>
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