R help - Nov 2013 - Treatment effects on measurements through time: how to tell when (in time) treatment has a significant effect?

Hi, 

The data (attached) I am looking at consists of measurements of growth rate
at different ages, for individuals in two treatments (control and infected).
What I want to know is whether and when (what age) the growth rate of
infected individuals is higher than the growth rate for control individuals.

The simplest way to approach this question is to just do a t-test at each
age, but because the growth rates at a given age depend on the growth rates
at previous ages before, that seems statistically invalid. I have looked at
some of the time series literature, but most of that seems more complicated
than what I am trying to do. What I would like to be able to say is
something like, "The growth rate of infected individuals is higher than
control individuals for ages 18-30."

Any help or insight would be greatly appreciated.

Thanks!
Clay

P.S. The data is provided as two matrices: the first column are the ages at
which data was collected, and subsequent columns are the growth rate
trajectories for different individuals.  cntl.grates.rda
<http://r.789695.n4.nabble.com/file/n4679911/cntl.grates.rda>  
inf.grates.rda
<http://r.789695.n4.nabble.com/file/n4679911/inf.grates.rda>



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On 11/07/2013 07:46 AM, c_e_cressler wrote:
> Hi,
>
> The data (attached) I am looking at consists of measurements of growth rate
> at different ages, for individuals in two treatments (control and
infected).
> What I want to know is whether and when (what age) the growth rate of
> infected individuals is higher than the growth rate for control
individuals.
>
> The simplest way to approach this question is to just do a t-test at each
> age, but because the growth rates at a given age depend on the growth rates
> at previous ages before, that seems statistically invalid. I have looked at
> some of the time series literature, but most of that seems more complicated
> than what I am trying to do. What I would like to be able to say is
> something like, "The growth rate of infected individuals is higher
than
> control individuals for ages 18-30."
>
Hi Clay,
If you calculate the mean growth rates:

inf_mean<-apply(as.matrix(inf.grates),1,
  mean,na.rm=TRUE)
cntl_mean<-apply(as.matrix(cntl.grates),1,
  mean,na.rm=TRUE)

and plot them:

plot(cntl_mean,col=3)
points(inf_mean,col=2)

It looks like the growth rate in the infected group is consistently 
greater. Testing the linear models:

summary(lm(cntl_mean~I(1:length(cnf_mean))))
summary(lm(inf_mean~I(1:length(inf_mean))))

looks like there is a significant effect. The proper comparison would be 
a mixed model with the individual scores, I think.

Jim