# linreg: Global and pointwise linear regression analyses In visualFields: Statistical Methods for Visual Fields

## 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

 ```1 2 3 4 5``` ```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

 ```1 2 3 4``` ```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 ```

visualFields documentation built on Aug. 17, 2021, 1:06 a.m.