[R-sig-ME] Print Bayes Factor and posterior odds

Kornbrot, Diana

2018-11-27 11:26:37 UTC

Print Bayes Factor and posterior odds
Have successfully performed bglmer and obtained asme F table as
glmer
bf<- glmer(cbind(freq, Nmax-freq) ~ b1*b2*w1*w2 +(w1|pno)+(w2|pno), data= s4,family=binomial(link=probit))
did not include prior statements, so assume it will do default Wishart

How does one obtain Bayes factors and posterior odds from the object bf created by this script?

bf<- glmer(cbind(freq, Nmax-freq) ~ b1*b2*w1*w2 +(w1|pno)+(w2|pno), data= s4,family=binomial(link=probit)
All help gratefully received
best
Diana

On 27 Nov 2018, at 04:31, r-sig-mixed-models-***@r-project.org<mailto:r-sig-mixed-models-***@r-project.org> wrote:

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Today's Topics:

1. Re: diverging results with and without random effects
(Leha, Andreas)

----------------------------------------------------------------------

Message: 1
Date: Tue, 27 Nov 2018 04:30:55 +0000
From: "Leha, Andreas" <***@med.uni-goettingen.de>
To: Thierry Onkelinx <***@inbo.be>
Cc: r-sig-mixed-models <r-sig-mixed-***@r-project.org>
Subject: Re: [R-sig-ME] diverging results with and without random
effects
Message-ID:
<d6c3e41b-3f92-2c06-15e4-***@med.uni-goettingen.de>
Content-Type: text/plain; charset="utf-8"

Dear Thierry and all,

Thanks for your continued help here. I am not versed with Bayesian
analyses.

Below is the code I currently use. The priors are basically due to
trial and error until I got expected/reasonable results.

Therefor I would be grateful for some comments on the
(in-)appropriateness of my (quite extreme) parameters.

As cov.prior I used
invwishart(df = 50, scale = diag(0.5, 1))

Thanks in advance!

Regards,
Andreas

PS: The code/results

library("blme")
dat %>%
bglmer(group ~ riskfactor + fu + riskfactor:fu + (1|patient),
family = "binomial",
data = .,
cov.prior = invwishart(df = 50, scale = diag(0.5, 1)),
fixef.prior = normal(cov = diag(9,4))) %>%
summary
## ,----
## | Cov prior : patient ~ invwishart(df = 50, scale = 0.5,
## | posterior.scale = cov, common.scale = TRUE)
## | Fixef prior: normal(sd = c(3, 3, ...), corr = c(0 ...),
## | common.scale = FALSE)
## | Prior dev : 6.2087
## |
## | Generalized linear mixed model fit by maximum likelihood (Laplace
## | Approximation) [bglmerMod]
## | Family: binomial ( logit )
## | Formula: group ~ riskfactor + fu + riskfactor:fu + (1 | patient)
## | Data: .
## |
## | AIC BIC logLik deviance df.resid
## | 540.0 560.8 -265.0 530.0 470
## |
## | Scaled residuals:
## | Min 1Q Median 3Q Max
## | -2.4984 -0.8512 0.3979 0.5038 1.6228
## |
## | Random effects:
## | Groups Name Variance Std.Dev.
## | patient (Intercept) 0.009725 0.09862
## | Number of obs: 475, groups: patient, 265
## |
## | Fixed effects:
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 1.3679 0.2355 5.810 6.26e-09 ***
## | riskfactornorisk -1.6776 0.2868 -5.850 4.91e-09 ***
## | fuFU 0.4718 0.3738 1.262 0.2069
## | riskfactornorisk:fuFU -1.1375 0.4539 -2.506 0.0122 *
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
## |
## | Correlation of Fixed Effects:
## | (Intr) rskfct fuFU
## | rskfctrnrsk -0.816
## | fuFU -0.617 0.502
## | rskfctrn:FU 0.503 -0.618 -0.817
## `----

On 26/11/18 17:05, Thierry Onkelinx wrote:
Dear Andreas,

You'll need a very informative prior for the random intercept variance
in order to keep the random intercepts reasonable small.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
***@inbo.be <mailto:***@inbo.be>
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be <http://www.inbo.be>

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data. ~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>

Op ma 26 nov. 2018 om 17:00 schreef Leha, Andreas
<***@med.uni-goettingen.de
<mailto:***@med.uni-goettingen.de>>:

Dear Thierry,

thanks for looking into this!

So, one solution would be a baysian analysis, right?

Would you have a recommendation for me?

I followed [1] and used

library("blme")
dat %>%
bglmer(group ~ riskfactor + fu + riskfactor:fu + (1|patient),
family = "binomial",
data = .,
fixef.prior = normal(cov = diag(9,4))) %>%
summary

Which runs and gives the following fixed effect estimates:

Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 8.2598 0.7445 11.094 <2e-16 ***
riskfactornorisk -16.0942 1.3085 -12.300 <2e-16 ***
fuFU 1.0019 1.0047 0.997 0.319
riskfactornorisk:fuFU -1.8675 1.2365 -1.510 0.131

These still do not seem reasonable.

Thanks in advance!

Regards,
Andreas

[1]
https://stats.stackexchange.com/questions/132677/binomial-glmm-with-a-categorical-variable-with-full-successes/132678#132678

On 26/11/18 16:36, Thierry Onkelinx wrote:
Dear Andreas,

This is due to quasi complete separatation. This occurs when all
responses for a specific combination of levels are always TRUE or
FALSE.
In your case, you have only two observations per patient. Hence adding
the patient as random effect, guarantees quasi complete separation
issues.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
AND FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
***@inbo.be <mailto:***@inbo.be>
<mailto:***@inbo.be <mailto:***@inbo.be>>
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be <http://www.inbo.be> <http://www.inbo.be>

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no
more
than asking him to perform a post-mortem examination: he may be
able to
say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer
does not
ensure that a reasonable answer can be extracted from a given body of
data. ~ John Tukey

///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>

Op ma 26 nov. 2018 om 13:48 schreef Leha, Andreas
<***@med.uni-goettingen.de
<mailto:***@med.uni-goettingen.de>
<mailto:***@med.uni-goettingen.de
<mailto:***@med.uni-goettingen.de>>>:

Hi all,

sent the wrong code (w/o filtering for BL). If you want to
look at the
data, please use this code:

---------- cut here --------------------------------------------
library("dplyr")
library("lme4")
library("lmerTest")
## install_github("hrbrmstr/pastebin", upgrade_dependencies =
FALSE)
library("pastebin")

## ---------------------------------- ##
## load the data ##
## ---------------------------------- ##
dat <- pastebin::get_paste("Xgwgtb7j") %>% as.character %>%
gsub("\r\n",
"", .) %>% parse(text = .) %>% eval

## ---------------------------------- ##
## have a look ##
## ---------------------------------- ##
dat
## ,----
## | # A tibble: 475 x 4
## | patient group fu riskfactor
## | <fct> <fct> <fct> <fct>
## | 1 p001 wt BL norisk
## | 2 p002 wt BL norisk
## | 3 p003 wt BL norisk
## | 4 p004 wt BL norisk
## | 5 p005 wt BL norisk
## | 6 p006 wt BL norisk
## | 7 p007 wt BL norisk
## | 8 p008 wt BL norisk
## | 9 p009 wt BL risk
## | 10 p010 wt BL norisk
## | # ... with 465 more rows
## `----
dat %>% str
## ,----
## | Classes ‘tbl_df’, ‘tbl’ and 'data.frame': 475 obs. of 4
variables:
## | $ patient : Factor w/ 265 levels "p001","p002",..: 1 2
3 4 5 6 7
8 9 10 ...
## | $ group : Factor w/ 2 levels "wt","mut": 1 1 1 1 1 1
1 1 1
1 ...
## | $ fu : Factor w/ 2 levels "BL","FU": 1 1 1 1 1 1
1 1 1
1 ...
## | $ riskfactor: Factor w/ 2 levels "risk","norisk": 2 2 2
2 2 2 2 2
1 2 ...
## `----

## there are 265 patients
## in 2 groups: "wt" and "mut"
## with a dichotomous risk factor ("risk" and "norisk")
## measured at two time points ("BL" and "FU")

dat %>% summary
## ,----
## | patient group fu riskfactor
## | p001 : 2 wt :209 BL:258 risk :205
## | p002 : 2 mut:266 FU:217 norisk:270
## | p003 : 2
## | p004 : 2
## | p005 : 2
## | p006 : 2
## | (Other):463
## `----

## group sizes seem fine

## ---------------------------------------------- ##
## first, we look at the first time point, the BL ##
## ---------------------------------------------- ##

## we build a cross table
tab_bl <-
dat %>%
dplyr::filter(fu == "BL") %>%
dplyr::select(group, riskfactor) %>%
table
tab_bl
## ,----
## | riskfactor
## | group risk norisk
## | wt 22 86
## | mut 87 63
## `----

## and we test using fisher:
tab_bl %>% fisher.test
## ,----
## | Fisher's Exact Test for Count Data
## |
## | data: .
## | p-value = 1.18e-09
## | alternative hypothesis: true odds ratio is not equal to 1
## | 95 percent confidence interval:
## | 0.09986548 0.33817966
## | sample estimates:
## | odds ratio
## | 0.1865377
## `----
log(0.187)
## ,----
## | [1] -1.676647
## `----

## so, we get a highly significant association of the riskfactor
## and the group with an log(odds ratio) of -1.7

## we get the same result using logistic regression:
dat %>%
filter(fu == "BL") %>%
glm(group ~ riskfactor, family = "binomial", data = .) %>%
summary
## ,----
## | Call:
## | glm(formula = group ~ riskfactor, family = "binomial",
data = .)
## |
## | Deviance Residuals:
## | Min 1Q Median 3Q Max
## | -1.7890 -1.0484 0.6715 0.6715 1.3121
## |
## | Coefficients:
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 1.3749 0.2386 5.761 8.35e-09 ***
## | riskfactornorisk -1.6861 0.2906 -5.802 6.55e-09 ***
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
## |
## | (Dispersion parameter for binomial family taken to be 1)
## |
## | Null deviance: 350.80 on 257 degrees of freedom
## | Residual deviance: 312.63 on 256 degrees of freedom
## | AIC: 316.63
## |
## | Number of Fisher Scoring iterations: 4
## `----

## ------------------------------------------------- ##
## Now, we analyse both time points with interaction ##
## ------------------------------------------------- ##

dat %>%
glmer(group ~ riskfactor + fu + riskfactor:fu + (1|patient),
family =
"binomial", data = .) %>%
summary
## ,----
## | Generalized linear mixed model fit by maximum likelihood
(Laplace
## | Approximation) [glmerMod]
## | Family: binomial ( logit )
## | Formula: group ~ riskfactor + fu + riskfactor:fu + (1 |
patient)
## | Data: .
## |
## | AIC BIC logLik deviance df.resid
## | 345.2 366.0 -167.6 335.2 470
## |
## | Scaled residuals:
## | Min 1Q Median 3Q Max
## | -0.095863 -0.058669 0.002278 0.002866 0.007324
## |
## | Random effects:
## | Groups Name Variance Std.Dev.
## | patient (Intercept) 1849 43
## | Number of obs: 475, groups: patient, 265
## |
## | Fixed effects:
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 11.6846 1.3736 8.507
<2e-16 ***
## | riskfactornorisk -1.5919 1.4166 -1.124 0.261
## | fuFU 0.4596 1.9165 0.240 0.810
## | riskfactornorisk:fuFU -0.8183 2.1651 -0.378 0.705
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
## |
## | Correlation of Fixed Effects:
## | (Intr) rskfct fuFU
## | rskfctrnrsk -0.746
## | fuFU -0.513 0.510
## | rskfctrn:FU 0.478 -0.576 -0.908
## `----

## I get huge variation in the random effects
##
## And the risk factor at BL gets an estimated log(odds ratio)
of -1.6
## but one which is not significant
---------- cut here --------------------------------------------

Hi all,
I am interested in assessing the association of a

(potential) risk

factor to a (binary) grouping.
I am having trouble with diverging results from modeling one

time
point

(without random effect) and modeling two time points (with

random
effect).

When analysing the first time point (base line, BL) only, I

get a
highly

significant association.
Now, I want to see, whether there is an interaction between

time and

risk factor (the risk factor is not constant). But when

analysing
both

time points, the estimated effect at BL is estimated to be not

significant.

(1) Is there an association at BL or not?
(2) How should I analyse both time points with this data?
The aim is to look for confounding with other factors. But I'd

like to

understand the simple models before moving on.
Below you find a reproducible example and the detailed results.
Any suggestions would be highly appreciated!
Regards,
Andreas
PS: The code / results
---------- cut here --------------------------------------------
library("dplyr")
library("lme4")
library("lmerTest")
## install_github("hrbrmstr/pastebin", upgrade_dependencies

= FALSE)

library("pastebin")
## ---------------------------------- ##
## load the data ##
## ---------------------------------- ##
dat <- pastebin::get_paste("Xgwgtb7j") %>%
as.character %>%
gsub("\r\n", "", .) %>%
parse(text = .) %>%
eval
## ---------------------------------- ##
## have a look ##
## ---------------------------------- ##
dat
## ,----
## | # A tibble: 475 x 4
## | patient group fu riskfactor
## | <fct> <fct> <fct> <fct>
## | 1 p001 wt BL norisk
## | 2 p002 wt BL norisk
## | 3 p003 wt BL norisk
## | 4 p004 wt BL norisk
## | 5 p005 wt BL norisk
## | 6 p006 wt BL norisk
## | 7 p007 wt BL norisk
## | 8 p008 wt BL norisk
## | 9 p009 wt BL risk
## | 10 p010 wt BL norisk
## | # ... with 465 more rows
## `----
dat %>% str
## ,----
## | Classes ‘tbl_df’, ‘tbl’ and 'data.frame': 475

obs. of

## | $ patient : Factor w/ 265 levels "p001","p002",..: 1

2 3 4
5 6 7

8 9 10 ...
## | $ group : Factor w/ 2 levels "wt","mut": 1 1 1 1 1

1 1 1
1 1 ...

## | $ fu : Factor w/ 2 levels "BL","FU": 1 1 1 1 1

1 1 1
1 1 ...

## | $ riskfactor: Factor w/ 2 levels "risk","norisk": 2 2

2 2 2
2 2 2

1 2 ...
## `----
## there are 265 patients
## in 2 groups: "wt" and "mut"
## with a dichotomous risk factor ("risk" and "norisk")
## measured at two time points ("BL" and "FU")
dat %>% summary
## ,----
## | patient group fu riskfactor
## | p001 : 2 wt :209 BL:258 risk :205
## | p002 : 2 mut:266 FU:217 norisk:270
## | p003 : 2
## | p004 : 2
## | p005 : 2
## | p006 : 2
## | (Other):463
## `----
## group sizes seem fine
## ---------------------------------------------- ##
## first, we look at the first time point, the BL ##
## ---------------------------------------------- ##
## we build a cross table
tab_bl <-
dat %>%
dplyr::select(group, riskfactor) %>%
table
tab_bl
## ,----
## | riskfactor
## | group risk norisk
## | wt 35 174
## | mut 170 96
## `----
tab_bl %>% fisher.test
## ,----
## | Fisher's Exact Test for Count Data
## |
## | data: .
## | p-value < 2.2e-16
## | alternative hypothesis: true odds ratio is not equal to 1
## | 0.07099792 0.18002325
## | odds ratio
## | 0.1141677
## `----
log(0.114)
## ,----
## | [1] -2.171557
## `----
## so, we get a highly significant association of the riskfactor
## and the group with an log(odds ratio) of -2.2
dat %>%
glm(group ~ riskfactor, family = "binomial", data = .) %>%
summary
## ,----
## |
## | glm(formula = group ~ riskfactor, family = "binomial",

data = .)

## |
## | Min 1Q Median 3Q Max
## | -1.8802 -0.9374 0.6119 0.6119 1.4381
## |
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 1.5805 0.1856 8.515 <2e-16 ***
## | riskfactornorisk -2.1752 0.2250 -9.668 <2e-16 ***
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

0.1 ‘ ’ 1

## |
## | (Dispersion parameter for binomial family taken to be 1)
## |
## | Null deviance: 651.63 on 474 degrees of freedom
## | Residual deviance: 538.83 on 473 degrees of freedom
## | AIC: 542.83
## |
## | Number of Fisher Scoring iterations: 4
## `----
## ------------------------------------------------- ##
## Now, we analyse both time points with interaction ##
## ------------------------------------------------- ##
dat %>%
glmer(group ~ riskfactor + fu + riskfactor:fu + (1|patient),

family =

"binomial", data = .) %>%
summary
## ,----
## | Generalized linear mixed model fit by maximum

likelihood (Laplace

## | Approximation) [glmerMod]
## | Family: binomial ( logit )
## | Formula: group ~ riskfactor + fu + riskfactor:fu + (1 |

patient)

## | Data: .
## |
## | AIC BIC logLik deviance df.resid
## | 345.2 366.0 -167.6 335.2 470
## |
## | Min 1Q Median 3Q Max
## | -0.095863 -0.058669 0.002278 0.002866 0.007324
## |
## | Groups Name Variance Std.Dev.
## | patient (Intercept) 1849 43
## | Number of obs: 475, groups: patient, 265
## |
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 11.6846 1.3736 8.507

<2e-16 ***

## | riskfactornorisk -1.5919 1.4166 -1.124 0.261
## | fuFU 0.4596 1.9165 0.240 0.810
## | riskfactornorisk:fuFU -0.8183 2.1651 -0.378 0.705
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

0.1 ‘ ’ 1

ratio) of -1.6

## but one which is not significant
---------- cut here --------------------------------------------
_______________________________________________
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

--
Dr. Andreas Leha
Head of the 'Core Facility
Medical Biometry and Statistical Bioinformatics'

UNIVERSITY MEDICAL CENTER GÖTTINGEN
GEORG-AUGUST-UNIVERSITÄT
Department of Medical Statistics
Humboldtallee 32
37073 Göttingen
Mailing Address: 37099 Göttingen, Germany
Fax: +49 (0) 551 39-4995
Tel: +49 (0) 551 39-4987
http://www.ams.med.uni-goettingen.de/service-de.shtml
_______________________________________________
R-sig-mixed-***@r-project.org
<mailto:R-sig-mixed-***@r-project.org>
<mailto:R-sig-mixed-***@r-project.org
<mailto:R-sig-mixed-***@r-project.org>> mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

--
Dr. Andreas Leha
Head of the 'Core Facility
Medical Biometry and Statistical Bioinformatics'

UNIVERSITY MEDICAL CENTER GÖTTINGEN
GEORG-AUGUST-UNIVERSITÄT
Department of Medical Statistics
Humboldtallee 32
37073 Göttingen
Mailing Address: 37099 Göttingen, Germany
Fax: +49 (0) 551 39-4995
Tel: +49 (0) 551 39-4987
http://www.ams.med.uni-goettingen.de/service-de.shtml
--
Dr. Andreas Leha
Head of the 'Core Facility
Medical Biometry and Statistical Bioinformatics'

UNIVERSITY MEDICAL CENTER GÖTTINGEN
GEORG-AUGUST-UNIVERSITÄT
Department of Medical Statistics
Humboldtallee 32
37073 Göttingen
Mailing Address: 37099 Göttingen, Germany
Fax: +49 (0) 551 39-4995
Tel: +49 (0) 551 39-4987
http://www.ams.med.uni-goettingen.de/service-de.shtml

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Kornbrot, Diana

2018-12-03 13:52:26 UTC

Permalink

Post by Kornbrot, Diana
Hi all,
I am interested in assessing the association of a

(potential) risk

Post by Kornbrot, Diana
factor to a (binary) grouping.
I am having trouble with diverging results from modeling one

time
point

Post by Kornbrot, Diana
(without random effect) and modeling two time points (with

random
effect).

Post by Kornbrot, Diana
When analysing the first time point (base line, BL) only, I

get a
highly

Post by Kornbrot, Diana
significant association.
Now, I want to see, whether there is an interaction between

time and

Post by Kornbrot, Diana
risk factor (the risk factor is not constant). But when

analysing
both

Post by Kornbrot, Diana
time points, the estimated effect at BL is estimated to be not

significant.

Post by Kornbrot, Diana
(1) Is there an association at BL or not?
(2) How should I analyse both time points with this data?
The aim is to look for confounding with other factors. But I'd

like to

Post by Kornbrot, Diana
understand the simple models before moving on.
Below you find a reproducible example and the detailed results.
Any suggestions would be highly appreciated!
Regards,
Andreas
PS: The code / results
---------- cut here --------------------------------------------
library("dplyr")
library("lme4")
library("lmerTest")
## install_github("hrbrmstr/pastebin", upgrade_dependencies

= FALSE)

Post by Kornbrot, Diana
library("pastebin")
## ---------------------------------- ##
## load the data ##
## ---------------------------------- ##
dat <- pastebin::get_paste("Xgwgtb7j") %>%
as.character %>%
gsub("\r\n", "", .) %>%
parse(text = .) %>%
eval
## ---------------------------------- ##
## have a look ##
## ---------------------------------- ##
dat
## ,----
## | # A tibble: 475 x 4
## | patient group fu riskfactor
## | <fct> <fct> <fct> <fct>
## | 1 p001 wt BL norisk
## | 2 p002 wt BL norisk
## | 3 p003 wt BL norisk
## | 4 p004 wt BL norisk
## | 5 p005 wt BL norisk
## | 6 p006 wt BL norisk
## | 7 p007 wt BL norisk
## | 8 p008 wt BL norisk
## | 9 p009 wt BL risk
## | 10 p010 wt BL norisk
## | # ... with 465 more rows
## `----
dat %>% str
## ,----
## | Classes ‘tbl_df’, ‘tbl’ and 'data.frame': 475

obs. of

Post by Kornbrot, Diana
## | $ patient : Factor w/ 265 levels "p001","p002",..: 1

2 3 4
5 6 7

Post by Kornbrot, Diana
8 9 10 ...
## | $ group : Factor w/ 2 levels "wt","mut": 1 1 1 1 1

1 1 1
1 1 ...

Post by Kornbrot, Diana
## | $ fu : Factor w/ 2 levels "BL","FU": 1 1 1 1 1

1 1 1
1 1 ...

Post by Kornbrot, Diana
## | $ riskfactor: Factor w/ 2 levels "risk","norisk": 2 2

2 2 2
2 2 2

Post by Kornbrot, Diana
1 2 ...
## `----
## there are 265 patients
## in 2 groups: "wt" and "mut"
## with a dichotomous risk factor ("risk" and "norisk")
## measured at two time points ("BL" and "FU")
dat %>% summary
## ,----
## | patient group fu riskfactor
## | p001 : 2 wt :209 BL:258 risk :205
## | p002 : 2 mut:266 FU:217 norisk:270
## | p003 : 2
## | p004 : 2
## | p005 : 2
## | p006 : 2
## | (Other):463
## `----
## group sizes seem fine
## ---------------------------------------------- ##
## first, we look at the first time point, the BL ##
## ---------------------------------------------- ##
## we build a cross table
tab_bl <-
dat %>%
dplyr::select(group, riskfactor) %>%
table
tab_bl
## ,----
## | riskfactor
## | group risk norisk
## | wt 35 174
## | mut 170 96
## `----
tab_bl %>% fisher.test
## ,----
## | Fisher's Exact Test for Count Data
## |
## | data: .
## | p-value < 2.2e-16
## | alternative hypothesis: true odds ratio is not equal to 1
## | 0.07099792 0.18002325
## | odds ratio
## | 0.1141677
## `----
log(0.114)
## ,----
## | [1] -2.171557
## `----
## so, we get a highly significant association of the riskfactor
## and the group with an log(odds ratio) of -2.2
dat %>%
glm(group ~ riskfactor, family = "binomial", data = .) %>%
summary
## ,----
## |
## | glm(formula = group ~ riskfactor, family = "binomial",

data = .)

Post by Kornbrot, Diana
## |
## | Min 1Q Median 3Q Max
## | -1.8802 -0.9374 0.6119 0.6119 1.4381
## |
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 1.5805 0.1856 8.515 <2e-16 ***
## | riskfactornorisk -2.1752 0.2250 -9.668 <2e-16 ***
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

0.1 ‘ ’ 1

Post by Kornbrot, Diana
## |
## | (Dispersion parameter for binomial family taken to be 1)
## |
## | Null deviance: 651.63 on 474 degrees of freedom
## | Residual deviance: 538.83 on 473 degrees of freedom
## | AIC: 542.83
## |
## | Number of Fisher Scoring iterations: 4
## `----
## ------------------------------------------------- ##
## Now, we analyse both time points with interaction ##
## ------------------------------------------------- ##
dat %>%
glmer(group ~ riskfactor + fu + riskfactor:fu + (1|patient),

family =

Post by Kornbrot, Diana
"binomial", data = .) %>%
summary
## ,----
## | Generalized linear mixed model fit by maximum

likelihood (Laplace

Post by Kornbrot, Diana
## | Approximation) [glmerMod]
## | Family: binomial ( logit )
## | Formula: group ~ riskfactor + fu + riskfactor:fu + (1 |

patient)

Post by Kornbrot, Diana
## | Data: .
## |
## | AIC BIC logLik deviance df.resid
## | 345.2 366.0 -167.6 335.2 470
## |
## | Min 1Q Median 3Q Max
## | -0.095863 -0.058669 0.002278 0.002866 0.007324
## |
## | Groups Name Variance Std.Dev.
## | patient (Intercept) 1849 43
## | Number of obs: 475, groups: patient, 265
## |
## | Estimate Std. Error z value Pr(>|z|)
## | (Intercept) 11.6846 1.3736 8.507

<2e-16 ***

Post by Kornbrot, Diana
## | riskfactornorisk -1.5919 1.4166 -1.124 0.261
## | fuFU 0.4596 1.9165 0.240 0.810
## | riskfactornorisk:fuFU -0.8183 2.1651 -0.378 0.705
## | ---
## | Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’

0.1 ‘ ’ 1

ratio) of -1.6

Post by Kornbrot, Diana
## but one which is not significant
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