Graph Recommendations

[AC Del Re]

Wow, the new version of ggplot2 is great, Hadley! Thanks for making the legend parameters more flexible. I have altered the graph (discussed in a previous post) where I wanted one of the 2 legends removed. 

I have a question for the group (and my apologies in advance if this is an inappropriate question for this group): Attached is the graph I have been working on and I am very interested in any feedback on it. I am really interested in expert opinion about how well the graph conveys important information and any aesthetic recommendations. Thank you, AC.

Description of graph:

Background.  Previous meta-analyses have concluded that grief counseling is effective only for patients experiencing complicated grief—i.e., extreme or chronic grief reactions that do not abate as normally expected over time.  In this analysis we demonstrate that the larger effect sizes for chronic grievers as compared with normal grievers are an artifact of differences in the length of treatment (number of sessions).  Poor outcomes for a third group, so-called at-risk grievers, do appear to be significantly lower than those for normal and chronic grievers.

Findings of univariate moderator analyses.  As was the case in previous reviews, we found a significant difference in effect size (D₊) by treatment population, where superior outcomes were seen in studies involving chronic grievers.  In Figure 1 (below), the inset boxplot on the right illustrates this pattern of means, with the mean effect size (represented by a ‘+’ symbol) for the chronic group hovering at around 1.0, that for the normal group closer to 0.5, and even lower mean effects for the at-risk group.  (It also shows that the mean for the chronic group is quite a bit higher than the median, indicating that the large effect size for this group is strongly influenced by three studies reporting abnormally large effect sizes.)

Confounds among moderators.  However, the inset boxplot on the left in Figure 1 shows that client type (normal, at-risk, or chronic) was confounded with another significant moderator variable:  number of sessions, or treatment dosage.  In fact, the pattern of means for number of sessions mimics quite closely the pattern of means for effect size in the other inset boxplot, suggesting that the superior effect sizes for the chronic group might simply reflect the greater treatment dosage received by this group. 

The main graph in Figure 1 illustrates how this confounding operates.  Effect size is plotted on the y axis as a function of number of sessions on the x axis.  Type of grief is represented by the shape of the point, with circles, triangles, and squares representing normal, at-risk, and chronic grievers, respectively.  The size of the point reflects the weight of the study in the meta-analysis (mostly a function of sample size, with larger points corresponding to studies with larger Ns, which therefore provide a more precise estimate of the population effect size).

Note the upward trend on this graph, reflecting the importance of number of sessions as a predictor of effect size.  As expected, studies with longer treatment durations tend to show greater effectiveness.  Note too that interventions tended to be longer in studies involving chronic grievers, with no study involving an intervention with fewer than 12 sessions, whereas many of the effect sizes for normal and at-risk grievers were derived from studies of interventions involving 10 or fewer sessions. 

This figure shows that the straightforward interpretation of the differences in risk group means (inset boxplot on the right) may be misleading.  The superior effect size for chronic grievers may reflect the longer treatments in studies involving this population, rather than a greater responsiveness to treatment in this group.  To draw clear conclusions about this, it is necessary to study dosage and risk group simultaneously as predictors of effect size.  As we demonstrate subseauently in our multivariate moderator analyses, the apparent difference in effectiveness between normal and chronic grievers disappears completely when treatment duration is controlled, leading to very different conclusions about the importance of risk group, and very different implications about who can and cannot benefit from grief counseling.

[Peter Flom]

Hi

It looks to me like, among other things, you've got an interaction.  So, why not plot lines for normal, atrisk and chronic separately on the main graph?

It also looks like you have outliers for both normal and chronic.  So, rather than regression lines, why not some sort of smoothed lines (loess or spline or whatever, take your pick) for each of these?

Just some ideas

Peter

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Peter L. Flom, PhD
Statistical Consultant
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[Nicholas Lewin-Koh]

It looks like more than interaction, looks like Simpsons paradox.

If you do as Peter says, it looks like the trend fro the at-risk  group goes down with # of sessions.

I would  either add lines (smooths)  for each group or do three seperate panels.

 

Nicholas

[Peter Flom]

Indeed it does look like Simpson's Paradox, but isn't that a specific type of interaction?
Can you have simpsons without an interaction?

Peter

[Nicholas Lewin-Koh]

 Suppose not, I just meant BIG interaction ;-)

[jc]

A Simpson's paradox can occur with non significant interaction in the
model but with an interaction term included. In fact, it most
problematically occurs when there is no interaction but by adding the
interaction term to the model you allow the individual condition lines
to vary freely and the slope reverses. I'm not sure that this is
strictly a Simpsons paradox based on a quick look at the graph. Of
course, if I had read the description I might see that that's an
erroneous conclusion in the context... or maybe not.

On Dec 17, 3:42 pm, "Nicholas Lewin-Koh" <ni...@hailmail.net> wrote:
>  Suppose not, I just meant BIG interaction ;-)
>
> On Thu, 17 Dec 2009 12:53 -0500, "Peter Flom"
>

> size (D[+]) by treatment population, where superior outcomes were

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> Peter L. Flom, PhD
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> Peter L. Flom, PhD
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