# [R-meta] metafor: Interaction between a factor and a continous variable

Kraus, Ute, Dr. ute@kr@u@ @end|ng |rom he|mho|tz-muenchen@de
Tue Jan 5 10:55:51 CET 2021

```Dear everybody!

This is my very first post and I would appreciate it very much if somebody
has time enough and could help me.

I am currently working on a meta-analysis on sex differences in the
association between air pollutants and cardiovascular mortality. I
calculated a mixed effects model including an interaction of a factor
(sex) and a continuous variable (publication year). However, I find it
difficult to interpret the estimates, and I get stuck when I want to graph
the results.

Here are the code and the results. The continuous variable “publication
year” is called “moderator” in my program.

Question 1: Are my following interpretations correct?

The Test of moderators shows that main effects and interaction term has no
significant effect (p-value 0.3482), explaining no heterogeneity between
studies (R2=0%).

The interaction between sex and publication year is not significant
(pval=0.3176).

Meaning of model results:

Intercept à estimate for men, when moderator (=publication year) = 0

Moderator à estimate for moderator (=publication year); with each 1 year
that an article is published later, the average estimate for the
association between air pollution and cardiovascular mortality increases
by 0.0001 (not significant)

Factor(sex)women à estimate indicates the effect of women compared to men;
women have a 0.2127 lower average mortality risk related to air pollutants
than men (not significant)

Moderator:factor(sex)women à estimate indicate by how much the risk in
women increases with each increase of one year of publication compared to
men (0.0001 greater increase than men; not significant).

Question 2: How can I present the results graphically?

I would need an intercept and a slope for each sex group showing the
change in the average mortality risk by a 1-year increase in publication
year. I would calculate it from the model results:

Intercept men: -0.1013 (estimate intrcpt)

Slope men: 0.0001 (estimate moderator)

Intercept women: -0.1013 – 0.2127 (estimate intrcpt + estimate
factor(sex)women)

Slope women: 0.0001+0.0001 (estimate moderator + estimate
moderator:factor(sex)women)

However, I am not really convinced that this is correct. And I think there
is a more elegant and easier way, isn’t there? I think it does not make
sense to calculate a model without intercept
(mods=~moderator:factor(sex)-1), which would give me the slopes, I guess,
but then I have just a slope but no intercept.

Best,

Ute

Helmholtz Zentrum MÃ¼nchen

Helmholtz Zentrum Muenchen

Deutsches Forschungszentrum fuer Gesundheit und Umwelt (GmbH)

Ingolstaedter Landstr. 1

85764 Neuherberg

www.helmholtz-muenchen.de

Aufsichtsratsvorsitzende: MinDir.in Prof. Dr. Veronika von Messling

Geschaeftsfuehrung: Prof. Dr. med. Dr. h.c. Matthias Tschoep, Kerstin Guenther

Registergericht: Amtsgericht Muenchen HRB 6466

USt-IdNr: DE 129521671

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