Time series with decreasing sample sizes what is the best way to analyze the data?

[aparach]

Hi all,

This is my first time here. Could you please help me on how to best analyze my data?

I started off with 30 animals and we took blood samples for hour 0 (pre-toxin exposure; baseline) and killed 6 of them for organ collection.

At hour 3 (post-toxin exposure), I had 24 animals for blood collection and another 6 killed for organ collection.

At hour 6 (post-toxin exposure), I had 18 animals for blood collection and another 6 killed for organ collection.

At hour 12 (post-toxin exposure), I had 12 animals for blood collection and another 6 killed for organ collection.

At hour 24 (post-toxin exposure), I had 6 animals left for blood and organ collection.

All animals had the same treatment. 

The goal was to see the effect of the toxin exposed in time series.

How could I analyze my data on blood collection? This is not a repeated measure because I lost 6 animals in each time period (if it is please give me a bit of advice). 

I could think of trend analysis as you can see from the code I have here.

For pairwise comparison, is it acceptable to do when each hour did not have the same animals (6 animals less)?

Thank you very much for your suggestions.

Proc glm data =A1;
class hour;
Model BW = hour;
Lsmeans hour / stderr CL Lines pdiff adjust=tukey ;
Contrast "Linear" hour -0.474342 -0.316228 -0.158114 0.1581139 0.7905694;
Contrast "Quadratic" hour 0.5459642 0.0352235 -0.334623 -0.651635 0.4050702;
Contrast "Cubic or LoF" hour -0.469987 0.4222581 0.5143463 -0.570498 0.10388;
run;
quit;

[sld]

I agree that the design does not involve repeated measurements for the organ collection data, because each animal was assigned to only one level of HOUR.

However, there are repeated measurements on animals for the blood sample data. You have 5 measurements over time for 6 animals, 4 measurements over time for 12 animals, 3 measurements over time for 18 animals, and 2 measurements over time for 24 animals.

I think that, theoretically, if animals were randomly selected for sacrifice HOUR, you could proceed with modeling while assuming that the missing data were missing at random. But this is a relatively small study, and I would not make this assumption without considering the possibility of bias in the "random selection" for sacrifice.

I would plot the values of a given blood variable over all HOURs for each animal. Based on this plot, I would visually assess whether animals are tracking through time in a similar fashion, or whether some animals are following their own path through time. This plot would also inform you about the shape of the relationship through time; you might be able to use a more parsimonious model that the curvilinear model you are currently using, for example, an exponential decay model.

Given that the analysis of blood variables requires a mixed model, you'll want to switch to GLIMMIX or MIXED for analysis. You could also consider different ways to incorporate the pre-toxin measurements in your statistical model, particularly if the pre-toxin values varied appreciably among animals. 

A regression on HOUR for each animal could be addressed with a random coefficients model (which essentially is a regression in a mixed model).

I hope this helps move your analysis forward.