[R-meta] FW: Welcome to the "R-sig-meta-analysis" mailing list (Digest mode) _ question

[Tetyana Kendzerska]

Dear All,

I am wondering if you can help me understanding the underlaying
calculations/formula for the confidence intervals (both) using the
predic.rma function.

I will try to explain the situation using an example below.   

> test_TST = rma(yi=TST_Mean, sei=TST_E, method="DL",
mods=~Age_Mean+Sex__1+Night_coded, data=moderators[-c(5,69,117,168), ])
> test_TST

Mixed-Effects Model (k = 128; tau^2 estimator: DL)

tau^2 (estimated amount of residual heterogeneity):  439.3101 (SE =
263.3751) tau (square root of estimated tau^2 value):             20.9597
I^2 (residual heterogeneity / unaccounted variability): 91.95%
H^2 (unaccounted variability / sampling variability):   12.42
R^2 (amount of heterogeneity accounted for):            70.67%

Test for Residual Heterogeneity: 
QE(df = 124) = 1539.9995, p-val < .0001

Test of Moderators (coefficient(s) 2,3,4): 
QM(df = 3) = 183.5661, p-val < .0001

Model Results:

 		estimate       se     	zval    pval     ci.lb
ci.ub 
 intrcpt      	375.7589  10.4376  36.0005  <.0001  355.3016  396.2162  *** 
Age_Mean      	-1.0134     0.1345    -7.5366  <.0001   -1.2770   -0.7499
***
Sex__1           	0.0291       0.0667    0.4365  0.6624   -0.1017
0.1599 
Night_coded     38.3012     4.5223     8.4694  <.0001   29.4376   47.1647
***

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

I am trying to predict the estimates for the outcome, TST, based on certain
parameters using the predic.rma function:

> predict.rma (test_TST, newmods=cbind(c(65),c(100),c(1)))
     pred     se    		ci.lb    ci.ub    cr.lb    	cr.ub
351.1013 5.3417 340.6318 361.5708 308.7079 393.4947 


My question is how I can use estimates from the rm () model results above
(the formula) to get the ci.lb    ci.ub    cr.lb    cr.ub manually?  

To get pred value, we used the following formula which makes sense: 
Intercept_estimate + Age_coeff_estimate X Age (65) +Sex_coeff_estimate X 0
[if women] or 100 [if men] +  Sleep_Night_coeff_estimate X 0 [first night]
or 1 [second night].

Which formula we should use to get in the same way:  ci.lb    ci.ub    cr.lb
cr.ub?

Thank you in advance and sorry if it sounds somewhat confusing,
Tetyana