How to analyze the data for measuring three time point for mouse in different treatment group?

[Dennisky]

We are doing a study to evaluate the effect of different drugs on bone mineral density in mouse

（each mouse is tested for bone mineral density only once in the study）.

The purpose was to explore whether the BMD value is different between 5 drug types at different age groups (3 months, 5 months，7 months).

There are 5 different drug types in the study (control group, drug A, drug B, drug C and drug D).

And we also have three mature adult group (3, 5, 7 months).

Generally, we could conduct the Repeated Measures Analysis for the dataset. However, the analysis might not fit in our study.

Although we should examine the BMD in the three time points, each mouse is tested for bone density only once. Because we must dissect the mice for getting the precise data of BMD.

Thus, we need 60 mice and divided into 15 groups (4/group, see Table 1).

How to analyze the data in the study?

Table1

Moreover, could we consider this data as randomized block design (ANOVA for blocked designs)?

In other words，three mature adult group (3, 5, 7 months of age) was considered as blocking factors (see table2).

Table2

[PaigeMiller · Accepted solution]

For a randomized block design, you need to have created blocks, and I don't see where you have done that, or even where this is possible given your description of the experiment.

So you have 3 time periods times 5 drugs experiment, with four replicates (not repeated values as in a time experiment where each subject is measured at multiple times).

Thus, in PROC GLM, for example:

proc glm data=have;
     class drug time;
     model bone_density = drug | time;
run;

[Dennisky]

Dear Prof. PaigeMiller,

Thank you very much for your help and great solution!

We try to conduct the analysis using your code.

Is this the method of Two-way ANOVA analysis?

It seems that we could explore the interaction for two factors (such as, drug*time).

Notably, we found our data not follow a normal distribution (although we log transform this data or using the Box-Cox Transformation, it was non-normal distributions).

Could we still conduct the analysis using the previous code? If the data was non-normal distributions, how to conduct the analysis?

Best regards