[R-sig-ME] longitudinal with 2 time points

[Marc Schwartz]

Hi John,

If you read that article, you will see that your use of delta.y as the dependent variable does not make sense.

Thus, I would re-express your model 5 as:

  lm(wk4.glucose ~ baseline.glucose + treatment + gender + age)

and as noted, check for the interaction between baseline glucose and treatment:

  lm(wk4.glucose ~ baseline.glucose * treatment + gender + age)


You might also want to consider using a spline function on age, presuming that age is hopefully measured as a continuous variable (eg. not ordinal groups).

Since the ANCOVA based approach described in the paper is essentially an OLS linear regression, you can of course include the additional covariates for adjustment. If the interaction term p value is >0.1 (a common threshold), you can remove it and the beta coefficient and its CIs for the treatment factor is your estimated treatment effect relative to your control.

For the presentation of the results, besides the obvious tabular summaries and the scatter/regression lines plot, include a series of plots showing selected baseline values and the treatment versus control predicted follow up values and CIs for the same baseline value in each plot. This visually shows the common estimated treatment effect for each baseline value, which will also tend to reveal regression to the mean. This presentation is especially helpful if the interaction term is retained, which therefore shows how the treatment effect varies and will reverse, over the range of the baseline values. You can select a series of clinically relevant values over the range of the observed baseline values, and/or by default, select a five number plus mean series over the observed baseline values.

I don't see a role for a mixed effects model here, given that this is a pretty straightforward "change from baseline" type design, but there are many here with greater expertise than I. If this was a cross-over design, you have multiple measures of glucose for each patient at each time point, more than two time points, or a multi-center study, then a mixed effects model would make more sense to me.

HTH,

Marc



On Aug 12, 2010, at 12:39 AM, array chip wrote:

> Hi Marc,
> 
> Thanks for the reference. I will definitely read it. Please see my reponse to 
> John's reply. Your model is another model I should add to the 5 models I 
> proposed in that email. What's your overall thoughts on these different models?
> 
> Thank you for sharing.
> 
> John
> 
> 
> 
> ----- Original Message ----
> From: Marc Schwartz <marc_schwartz at me.com>
> To: Charles E. (Ted) Wright <cewright at uci.edu>; array chip 
> <arrayprofile at yahoo.com>
> Cc: John Maindonald <john.maindonald at anu.edu.au>; 
> r-sig-mixed-models at r-project.org
> Sent: Wed, August 11, 2010 6:20:13 AM
> Subject: Re: [R-sig-ME] longitudinal with 2 time points
> 
> Hi,
> 
> I'll throw in a reference that covers some of these issues:
> 
> Statistics Notes
> Analysing controlled trials with baseline and follow up measurements
> Vickers and Altman
> BMJ. 2001 November 10; 323(7321): 1123–1124.
> https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1121605/
> 
> 
> The basic model specification would of course be:
> 
>   lm(4Wks ~ Baseline + Group)
> 
> You will also want to test for an interaction between the baseline score and 
> your grouping factor, in case the observed group (eg. treatment) effect is 
> dependent upon the value of the baseline measurement. In this case, unlike in 
> the above paper, you of course end up with crossing fitted regression lines, 
> rather than parallel lines.
> 
> HTH,
> 
> Marc Schwartz
> 
> 
> On Aug 11, 2010, at 7:34 AM, Charles E. (Ted) Wright wrote:
> 
>> Keep in mind that running an ANOVA on the difference is not the same thing as 
>> using the baseline data as a covariate in an ANOVA on the Week 4 data. 
>> Essentially the ANOVA on the differences is like the ANCOVA with the slope 
>> constrained to be 1.
>> 
>> Ted Wright
>> 
>> On Wed, 11 Aug 2010, John Maindonald wrote:
>> 
>>> All these are possibilities, except maybe making baseline measurement
>>> a random factor.  This would make sense only if data divide into groups,
>>> and you want the baseline effect to vary randomly from group to group.
>>> That may limit your ability to estimate parameters that are of interest.
>>> In most circumstances that I am familiar with, it makes better sense to
>>> treat baseline effect as fixed.
>>> 
>>> John.
>>> 
>>> On 11/08/2010, at 8:11 AM, array chip wrote:
>>> 
>>>> Hi, I am wondering if it is still meaningful to run a mixed model if a
>>>> longitudinal dataset has only 2 time points (baseline and week 4)? Would it 
>> be
>>>> more appropriate to simply take the difference between the 2 time points and 
>>>> run
>>>> ANOVA (ANCOVA) on the difference? what about still running mixed model on 
> the
>>>> difference of the 2 time points, but adding baseline measurement as a random
>>>> factor?
>>>> 
>>>> Thanks for sharing your thoughts.
>>>> 
>>>> John
> 
> 
> 
>