glr {visualFields}

Global and pointwise linear regression analyses

Description

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)

Usage

glr(g, type = "md", testSlope = 0)

plr(vf, type = "td", testSlope = 0)

poplr(vf, type = "td", testSlope = 0, nperm = factorial(7), trunc = 1)

Arguments

g

global indices

type

type of analysis. For glr, it can be 'ms', 'ss', 'md', 'sd', 'pmd', 'psd', '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 plr and poplr, it can be 's', 'td', or 'pd' for sensitivities, total deviation values, or pattern deviation values, respectively

testSlope

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

vf

visual fields sensitivity data

nperm

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.)

trunc

truncation value for the Truncated Product Method (see reference)

Details

• 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

Value

• glr and plr return a list with the following

  • id patient ID

  • eye patient eye

  • type type of data analysis. . For glr, it can be 'ms', 'ss', 'md', 'sd', 'pmd', 'psd', '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 plr and poplr, it can be 's', 'td', or 'pd' for sensitivities, total deviation values, or pattern deviation values, respectively

  • 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 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 ('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

References

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

Examples

vf <- vffilter(vfpwgRetest24d2, id == 1) # select one patient
res <- glr(getgl(vf)) # linear regression with global indices
res <- plr(vf)   # pointwise linear regression (PLR) with TD values
res <- poplr(vf) # Permutation of PLR with TD values