Functions that compute global and pointwise linear regression analyses:
glr performs global linear regression analysis
plr performs pointwise linear regression (PLR) analysis
poplr performs PoPLR analysis as in O'Leary et al (see reference)
glr(g, testSlope = 0)plr(vf, testSlope = 0)
poplr(vf, testSlope = 0, nperm = factorial(7), trunc = 1)
glr and plr return a list with the following
id patient ID
eye patient eye
testSlope slope for glr or list of slopes for plr
to test as null hypotheses
nvisits number of visits
years years from baseline. Used for the pointwise linear
regression analysis
data data analyzed. For glr, it is the values of the
global indes analyzed. For plr, each column is a location of the
visual field used for the analysis. Each row is a visit (as many as years)
pred predicted values. Each column is a location of the visual
field used for the analysis. Each row is a visit (as many as years)
sl slopes estimated at each location for pointwise (simple)
linear regression
int intercept estimated at each location for pointwise (simple)
linear regression
tval t-values obtained for the left-tailed-t-tests for the slopes
obtained in the pointwise (simple) linear regression at each location
pval p-values obtained for the left-tailed t-tests for the slopes
obtained
poplr returns a list with the following additional fields
csl the modified Fisher's S-statistic for the left-tailed permutation test
cslp the p-value for the left-tailed permutation test
csr the modifed Fisher's S-statistic for the right-tailed permutation test
csrp the p-value for the right-tailed permutation test
pstats a list with the poinwise slopes (`sl`), intercepts
(`int`), standard errors (`se`), and p-values (`pval`) obtained
for the series at each location analyzed and for all nperm permutations
(in `permutations`)
cstats a list with all combined stats:
csl, csr the combined Fisher S-statistics for the left- and right-tailed
permutation tests respectively
cslp, csrp the corresponding p-values for the permutation tests
cslall, csrall the combined Fisher S-statistics for all permutations
a data.frame with date on the first column and the value of the global index on the second column
slope, or slopes, to test as null hypothesis. Default is 0.
if a single value, then the same null hypothesis is used for all locations.
If a vector of values, then (for plr and poplr) each
location of the visual field will have a different null hypothesis. The length of
testSlope must be 1 or equal to the number of locations to be used in the PLR or
PoPLR analysis
visual fields sensitivity data
number of permutations. If the number of visits is 7 or less, then
nperm = factorial(nrow(vf)). For series greater than 8 visits, default is
factorial(7). For series up to 7 visits, it is the factorial of the number of visits
(with less than 7 visits, the number of possible permutations is small and results
can be unreliable. For instance, for 5 visits, the number of possible permutations is
only 120.)
truncation value for the Truncated Product Method (see reference)
poplr there is a small difference between this implementation of
PoPLR and that proposed by O'Leary et al. The combined S statistic in the
paper used a natural logarithm. Here we not only use a logarithm of base 10
but we also divide by the number of locations. This way the S statistic has
a more direct interpretation as the average number of leading zeros in the
p-values for pointwise (simple) linear regression. That is, if S = 2, then
the p-values have on average 2 leading zeros, if S = 3, then 3 leading zeros,
and so on
N. O'Leary, B. C. Chauhan, and P. H. Artes. Visual field progression in glaucoma: estimating the overall significance of deterioration with permutation analyses of pointwise linear regression (PoPLR). Investigative Ophthalmology and Visual Science, 53, 2012
vf <- vffilter(vfpwgRetest24d2, id == 1) # select one patient
res <- glr(getgl(vf)[,c("date", "tmd")]) # linear regression with mean deviation (MD)
res <- plr(gettd(vf)) # pointwise linear regression (PLR) with TD values
res <- poplr(gettd(vf)) # Permutation of PLR with TD values
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