[R-meta] standard error in predictive nonlinear meta-regression model

[Viechtbauer Wolfgang (SP)]

The usual approach to compute SEs for predicted values in a non-linear model is by means of the delta method. For this model, this would be:

p1 <- 5.5447
p2 <- 0.3856
A  <- 9
d <- cbind(exp(-p2*A), -p1 * A * exp(-p2 * A))
V <- matrix(c(4.2592^2, 0.5*4.2592*0.0835, 0.5*4.2592*0.0835, 0.0835^2), nrow=2)
SE <- c(sqrt(d %*% V %*% t(d)))

pred <- p1 * exp(-p2 * A)
pred
CI <- pred + c(-1,1) * qnorm(.975) * SE
CI

make_pct <- function(x) (exp(x) - 1) * 100

make_pct(pred)
make_pct(CI)

V is the var-cov matrix of the parameter estimates (i.e., p1 and p2). I can recreate the diagonal values (by squaring the se values), but I do not know the covariance -- I just assumed that the correlation is 0.5, but you should use the actual covariance.

And I just saw that Philipp answered with the same suggestion.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Cesar Terrer Moreno
Sent: Thursday, 18 January, 2018 18:07
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] standard error in predictive nonlinear meta-regression model

I am using a nonlinear meta-regression of the form y ~ p1 * exp(-p2*A), with the following coefficients: 

     estimate     se  zval    pval
p1     5.5447 4.2592 1.302 0.19298
p2     0.3856 0.0835 4.616 0.00000
tau2   0.0000     NA    NA      NA

I want to use this model to predict the effect size (in %) of a treatment, influenced by the variable A. Let's assume, for example, this is the effectiveness of a cancer treatment at a certain age A. For example, when A= 9, effect size is ~19%:

make_pct <- function(x) (exp(x) - 1) * 100
> make_pct(5.5447 * exp (-0.3856 * 9))
[1] 18.82309

The problem is that now I don't know how to calculate the standard error at e.g. A=9 using this model. I am sure this is very basic but I don't have any experience in this particular matter. Thanks