Re: st: glm for binomial regression with

["Airey, David C" <david.airey@vanderbilt.edu>]

.

The fundamental observation was paralysis of locomotory/swimming movement (1 or 0) in a small nematode (worm), called C. elegans. C. elegans is a popular genetic model organism, that surprisingly has appreciable conservation in genetic makeup with other organisms that think about statistics.

Part of the procedure involves transfer of worms (n about 10) to a small dish (concave well) with a fixed volume of liquid containing a known concentration of drug. The worms are not touching each other in the well. At a fixed time point, the number of paralyzed worms and the total worms in the dish are recorded. This constitutes a "well" observation. Eight wells were observed in this way for each concentration level per worm strain, and several worms strains are measured, with the goal of discerning dose-response curve shape differences between strains.

So we have worm and well replicates and a binary endpoint at the level of the worm replicate. The well constitutes a cluster of worm replicates. With the data arranged with one worm per row, the Stata command below seems reasonable:

xtset well
xtgee paralyzed i.strain##c.log_dose, family(binomial) link(logit)

There are a number of experimental details that could contribute to wells with the same concentration and same worms giving differing results. To the extent these are experimentally minimized, the within well correlation is minimized.

With a single worm per well (experimentally inefficient not practical), or lack of within well correlation, we might choose:

logit paralyzed i.strain##c.log_dose

or if the data are organized as a well per row with the data having variables for number of worms paralyzed and total worms in a well, we can use

glm paralyzed i.strain##c.log_dose, family(binomial) link(logit)
glm paralyzed i.strain##c.log_dose, family(binomial) link(cloglog)

WRT to your comments, are you talking about error in the X variables that are assumed to be measured without error? I think experimental control of X variables is rarely without some error, but the magnitude of that error relative to X variables in observational studies is probably different.


> I guess this was a puzzling question because as David clearly
> indicates it depends on how the experiment was conducted and we don't
> know what he doesn't tell us.
> 
> My take is simple. If replicates mean that you should reach for -xt-
> analyses then the same argument goes for any ties observed on
> predictors. That is, if the argument is that values that are similar
> on predictors should be grouped then it applies also to those that
> arise by chance and not just by design. In experimental practice the
> intention is clearly to give the same dose, or whatever, but in
> practice the received dose will not be identical even if what is
> recorded is the same number, so experimental set-ups don't differ so
> much from observational set-ups as is sometimes implied.
> 
> Otherwise, the key point with -xt- is that there is other information,
> typically in categorical variable form, indicating that observations
> should be grouped. A simple example would be if data came from
> different laboratories, so that even if everyone was trying to follow
> the same protocol, there could still be all sorts of differences.
> 
> An even simpler argument is that is this is how the analysis should be
> done, should not be most applications of -anova- be revisited?
> 
> Nick

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