I have a dataset where I want to see effect of a drug on my patients who responded and not responded towards treatment. I collected their blood at three different time point or visit. For each patient I have their age and sex information with me. Now to perform differential expression analysis I used DESeq2 to perform time series analysis as I have collected blood at three different visit. I want to control age and gender effect on my data and I am interested to find out genes that changed expression with time in responder group.

Please let me know which design I should follow to control age and gender effect and to find out diff. expressed genes with time. This is my datasets (few samples are given here)

sample  Phenotype     visit  Age  Gender
1       NonResponder  1      42   female
2       NonResponder  2      42   female
3       NonResponder  3      42   female
4       NonResponder  1      49   female
5       NonResponder  2      49   female
6       NonResponder  3      49   female
7       NonResponder  1      27   male
8       NonResponder  2      27   male
9       NonResponder  3      27   male
10      Responder     1      77   female
11      Responder     2      77   female
12      Responder     3      77   female
13      Responder     1      51   male
14      Responder     2      51   male
15      Responder     3      51   male
16      Responder     1      47   male
17      Responder     2      47   male
18      Responder     3      47   male

and these are the designs

# design (a)

dds=(design=~age+gender+visit+phenotype+visit:phenotype)
dds=DESeq(dds,test="LRT", reduced=~age+gender)

# design (b)

dds=(design= ~age+gender+visit+phenotype+visit:phenotype+age:phenotype+gender:phenotype)
dds=DESeq(dds,test="LRT", reduced=~age+gender)

# design (c)

dds=(design= ~age+gender+visit+phenotype+visit:phenotype+age:phenotype+gender:phenotype)
dds=DESeq(dds,test="LRT", reduced=~age+gender+visit+phenotype)