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)
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type of analysis. For
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
visual fields sensitivity data
number of permutations. If the number of visits is 7 or less, then
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
plr return a list with the following
id patient ID
eye patient eye
type type of data analysis. . For
glr, it can be
vfi', or '
gh' for mean sensitivity,
standard deviation of sensitivities, mean deviation, standard
deviation of total deviation values, pattern mean deviation, pattern
standard deviation, VFI, and general height, respectively. For
poplr, it can be '
td', or '
sensitivities, total deviation values, or pattern deviation values,
testSlope slope for
glr or list of slopes for
to test as null hypotheses
nvisits number of visits
years years from baseline. Used for the pointwise linear
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)
int intercept estimated at each location for pointwise (simple)
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
poplr returns a list with the following additional fields
csl the modifed 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 ('
int'), standard errors ('
se'), and p-values ('
for the series at each location analyzed and for all
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
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
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