Dear Users,
I am new to linear mixed model and really want to know your ideas on my analysis.
Here is the experiment design, we collected longitudinal data in four time points under two conditions, with  two replicates in each condition.
A scheme:subject  Time  (hours)       Condition   ValueA              2                            case           xx                A              8                            case           xxA              20                          case           xxA              44                          case           xxB              2                            case           xx                B              8                            case           xxB              20                          case           xxB              44                          case           xxC              2                            contr          xx                C              8                            contr          xxC              20                          contr          xxC              44                          contr          xxD              2                            contr          xx                D              8                            contr          xxD              20                          contr          xxD              44                          contr          xx
We collected the value with RNA-seq tech, counts on genes, log2 transformed.
My interest is:
1.  Find genes significantly changed in the time course in the "case" condition , comparing to the expression in "control".2.  For genes in 1., find the significant changes among time points in "case", comparing to "control". 
I used the Time (used as factor) and Condition as fixed effect, subject as random effect. 
I construct my hypothesis as :
test.hypo <- lmer(value ~ Time * Condition + (1| subject),data=test.da)
The null hypothesis, indicating no difference:
test.null <- lmer(value ~ 1 + (1| subject),data=test.da)
and pvalue from 
anova(test.hypo, test.null)

My questions:
1.  Does the pvalue answer my first interest, i.e., no difference in time course data for genes in case, comparing to control? If not, what is the proper way to design hypo and null ? 2.  How to do a post-hoc analysis with results got from linear mixed model to find the difference among time points? 3.  I got warnings like "In mer_finalize(ans) : false convergence (8)". How to handle this properly? How to identify in which analysis produce this warning since I have thousand genes?4.  I tried to treat the Time as continuous value, rather than factor. In that case I expect a linear change for gene expression. I used the same structure as before, i.e.,      lmer(value ~ Time * Condition + (1| subject),data=test.da) while Time is continuous now. Should I use lmer(value ~ Time + Condition + (1| subject),data=test.da) instead, like ANCOVA?      And what is the better way to treat Time, factor or continuous variable? 5.  The data is RNA-seq counts, I simply normalized them by dividing "size factor" calculated by DESeq, and log transformed data showed left-hand skew distribution.      Is it a big challenge for mixed model? How do you deal with RNA-seq data ?

I would like to know your suggestions on data analysis, experiment design  (import for future design), and recommend tutorial and  text books on this topic. 
Thanks very much for your patience and time!
Best regards,
--Shao Chunuxan













 		 	   		  
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