| Title: | Effects under Linear, Logistic and Poisson Regression Modelswith Transformed Variables |
| Version: | 0.2.0 |
| Description: | Computation of effects under linear, logistic and Poisson regression models with transformed variables. Logarithm and power transformations are allowed. Effects can be displayed both numerically and graphically in both the original and the transformed space of the variables. The methods are described in Barrera-Gomez and Basagana (2015) <doi:10.1097/EDE.0000000000000247>. |
| Depends: | R (≥ 4.1) |
| Encoding: | UTF-8 |
| LazyData: | true |
| Imports: | graphics, stats, utils, boot |
| Suggests: | knitr, rmarkdown, xtable |
| RoxygenNote: | 7.3.2 |
| VignetteBuilder: | knitr |
| License: | GPL (≥ 3) |
| NeedsCompilation: | no |
| Packaged: | 2025-01-07 10:20:59 UTC; jbarrera |
| Author: | Jose Barrera-Gomez [aut, cre], Xavier Basagana [aut] |
| Maintainer: | Jose Barrera-Gomez <jose.barrera@isglobal.org> |
| Repository: | CRAN |
| Date/Publication: | 2025-01-07 11:10:02 UTC |
tlm: Effects under Linear, Logistic and Poisson Regression Models with Transformed Variables
Description
Computation of effects under linear, logistic and Poisson regression models with transformed variables. Logarithm and power transformations are allowed. Effects can be displayed both numerically and graphically in both the original and the transformed space of the variables. The methods are described in Barrera-Gomez and Basagana (2015)doi:10.1097/EDE.0000000000000247.
Author(s)
Maintainer: Jose Barrera-Gomezjose.barrera@isglobal.org (ORCID)
Authors:
Xavier Basaganaxavier.basagana@isglobal.org (ORCID)
Expected Adjusted Median or Generalized Mean
Description
Computes expected measures of the response variable under a linear,logistic or Poisson regression fitted model with transformed variables. Measurescan be reported in both the original and the transformed space. The functionautomatically provides the name of the measure depending on the fitted model.
Usage
MY( object, x = NULL, npoints = 10, space = c("original", "transformed"), level = 0.95)## S3 method for class 'MY'print(x, ...)Arguments
object | object of class |
x | For |
npoints | numeric. If |
space | character. If " |
level | numeric. The confidence level for measures. Default is 0.95. |
... | additional arguments for |
Details
In order to compute adjusted measures, all explanatory variables inthe model different than the explanatory variable of interest are set at theirmeans.
Ifspace is "original", then the mean (for Poisson response) orthe probability (for binary response) is computed. For gaussian response, themean is computed if the response variable is not transformed; otherwise, thegeometric mean (for log transformation in the response) or the median (forpower transformation) is computed.
Ifspace is "transformed", then the mean (for Poisson responseor transformed gaussian response), or the logodds (for binary response) iscomputed.
Ifx argument inMY isNULL, the measure is computed innpoints values of the explanatory variable of interest. Those valuesare chosen to be in arithmetic progression in the givenspace, insidethe observed range of the explanatory variable.
Value
A list with class "MY" including the following items:
- M
adjusted measure of the response variable. See Details below.
- ymeasure
the type of measure for
M.- ypow
numeric power transformation assumed in the response variable.See
tlm.- xpow
numeric power transformation assumed in the explanatory variableof interest. See
tlm.
References
Barrera-Gomez J, Basagana X. Models with transformed variables:interpretation and software.Epidemiology. 2015;26(2):e16-17.
See Also
Examples
data(feld1)head(feld1)# Linear model with log-log transformation, adjusting for variable 'cat':modcat <- tlm(logroom ~ logmattress + cat, data = feld1, ypow = 0, xpow = 0)summary(modcat)# Geometric mean of the response as a function of the explanatory variable,# adjusted for 'cat': MY(modcat)MY(modcat, npoints = 3)# computed at 1st and 3rd quartiles of the explanatory variable:MY(modcat, x = quantile(feld1$mattress, probs = c(1, 3)/4))# Mean of the log(response) as a function of the log explanatory variable,# adjusted for 'cat': MY(modcat, space = "transformed")Birth Weight and Cord Serum Cotinine
Description
Simulated data for birth weight and cord serum cotinine levels in351 newborns.
Usage
cotinineFormat
Adata.frame with 351 observations on the following 4 variables:
- cotinine
cord serum cotinine level in the mother (ng/ml).
- logcotinine
logarithm of
cotinine.- weight
birth weight (g).
- underweight
a factor with levels
noandyes, indicatingunderweight (weight< 2500 g).
Details
Data were simulated to emulate true data pattern observed in a realstudy (see References).
Source
See References.
References
Pichini Set al. Cord serum cotinine as a biomarker of fetalexposure to cigarette smoke at the end of pregnancy.Environmental HealthPerspectives. 2000;108(11):1079-1083.
Examples
data(cotinine)par(las = 1, mfrow = c(2, 2))with(cotinine, plot(cotinine, weight))with(cotinine, plot(logcotinine, weight))with(cotinine, boxplot(cotinine ~ underweight))with(cotinine, boxplot(logcotinine ~ underweight))Effects Estimate in Linear, Logistic and Poisson Regression Modelswith Transformed Variables
Description
Estimates the effect of a explanatory variable of interest on aresponse variable, under a fitted linear, logistic or Poisson regression modelwith transformed variables. The effect is reported in the original scale of thevariables.
Usage
effect( object, x1 = NULL, x2 = NULL, c = NULL, q = NULL, r = NULL, npoints = NULL, level = 0.95, nboot = 999, seed = 4321, verbose = TRUE)## S3 method for class 'effect'print(x, ...)Arguments
object | object of class " |
x1 | numeric. The values of the explanatory variable where the effectshould be computed. See Details below. |
x2 | numeric. The alternative values of the explanatory variable(changing from |
c | numeric. The additive change in the explanatory variable. See Detailsbelow. |
q | numeric. The multiplicative change in the explanatory variable. SeeDetails below. |
r | numeric. The percent change in the explanatory variable. See Detailsbelow. |
npoints | numeric. The number of points where the effect should becomputed. See Details below. |
level | numeric. Confidence level for the effect estimate. Default is 0.95. |
nboot | numeric. The number of non parametric bootstrap samples to computeconfidence intervals. Default is 999. See Details below. |
seed | numeric. A single value, the seed for bootstrapping. Default is4321. |
verbose | logical. Whether to print detailed progress on R prompt.Default is |
x | for |
... | additional arguments for |
Details
In order to compute the effect, both the initial and the final valuesof the explanatory should be provided. It can be done in several ways. Forinstance, providing,x1 andx2;x1 and one ofc,q orr;x1,npoints and one ofc,q orr. Only one of the argumentsc,q orr is used, prevailingc and thenq. If no enougharguments are passed, the interquartile range will be considered and asummary effect is computed, if it exists.
Confidence intervals are computed by transforming the endpoints of theintervals in the transformed scale when it is possible, while non-parametricbootstrap is used otherwise.
Value
A list with class "effect" including the following items:
- effect
point estimate and confidence interval for the effect size.
- info
information on how to interpret the effect. Used by the function
effectInfo.
References
Barrera-Gomez J, Basagana X. Models with transformed variables:interpretation and software.Epidemiology. 2015;26(2):e16-17.
See Also
Examples
### Linear model with log transformation in the response variable:data(imt)head(imt)# model fitting:modimt <- tlm(logimt ~ age, data = imt, ypow = 0)modimt# information on interpreting the effect:effectInfo(modimt)# the function effect provides as default the expected change in IMT# for an additive change in age equal to the interquartile range:effect(modimt)# other effects:(minage <- min(imt$age))(maxage <- max(imt$age))effect(modimt, c = maxage - minage)## Not run: effect(modimt, x1 = minage, r = 50, npoints = 3)## End(Not run)Interpretation of Effects in Linear, Logistic and Poisson Models withTransformed Variables
Description
Provides information on interpreting effects in linear, logisticand Poisson models with transformed variables. Specifically, if a summarymeasure for the effect exists, the function details how to obtain and interpret it.
Usage
effectInfo(object)## S3 method for class 'effectInfo'print(x, ...)Arguments
object | object of class " |
x | for |
... | additional arguments for |
Value
A list with class "effectInfo" including the following items:
- beta
regression coefficient estimate in the fitted model which isassociated to the effect of the explanatory variable of interest on theresponse variable.
NAcorresponds to those models for which asummary effect does not exist.- Xincrease
type of change in the exploratory variable of interest(additive or realtive) for which a summary effect exists.
NAcorresponds to those models for which a summary effect does not exist.- effecttype
type of effect on the response variable for which asummary effect exists.
NAcorresponds to those models for which asummary effect is not available.- effectsize
formula for the summary effect size, if any.
NAcorresponds to those models for which a summary effect is not available.- furtherinfo
further information about how to interpret effects.
References
Barrera-Gomez J, Basagana X. Models with transformed variables:interpretation and software.Epidemiology. 2015;26(2):e16-17.
See Also
Examples
### Linear model with log transformation in the explanatory variable:data(cotinine)head(cotinine)# model fitting:modcot <- tlm(weight ~ logcotinine, data = cotinine, xpow = 0)modcot# information on interpreting the effect:effectInfo(modcot)### Linear model with no summary measure of effect:data(glucose)head(glucose)# transformations Y^(-2) and X^(-1/2): modgluco <- tlm(inv2glu ~ inv12tri, data = glucose, ypow = -2, xpow = -1/2)modglucoeffectInfo(modgluco)Cat Allergen Concentrations
Description
Simulated data for cat allergen concentrations (Fel d 1) in 471homes, measured in both the living room and the bed mattress.
Usage
feld1Format
Adata.frame with 471 observations on the following 5 variables:
- mattress
Feld d 1 concentration in the bed mattress (
\mug/g).- room
Feld d 1 concentration in the living room (
\mug/g).- logmattress
logarithm of
mattress.- logroom
logarithm of
room.- cat
a factor with levels
noandyes, indicating cat ownership.
Details
Data were simulated to emulate true data pattern observed in a realstudy (see References).
Source
See References.
References
Basagana Xet al. Domestic aeroallergen levels in Barcelonaand Menorca (Spain).Pediatric Allergy and Immunology. 2002;13(6):412-417.
Examples
data(feld1)par(las = 1, mfrow = c(1, 2))with(feld1, plot(mattress, room, col = as.numeric(cat)))with(feld1, plot(logmattress, logroom, col = as.numeric(cat)))Glucose and Triglycerides Levels in Blood
Description
Simulated data for glucose and triglycerides levels in blood in400 adults.
Usage
glucoseFormat
Adata.frame with 400 observations on the following 4 variables:
- trigly
triglycerides levels in blood (mg/dl).
- gluco
glucose levels in blood (mg/dl).
- inv12tri
numeric. Reciprocal of the square root of
trigly(i.e., -1/2 power transformation).- inv2glu
numeric. Reciprocal of the
glucosquare (i.e., -2 power transformation).
Details
Data were simulated to emulate true data pattern observed in a realstudy (see References).
Source
See References.
References
Rivera Met al. Association between long-term exposure totraffic-related air pollution and subclinical atherosclerosis: the REGICORStudy.Environmental Health Perspectives. 2013;121(2):223-230.
Examples
data(glucose)par(las = 1, mfrow = c(1, 2))with(glucose, plot(trigly, gluco))with(glucose, plot(inv12tri, inv2glu))Intima Media Thickness of the Carotid Artery
Description
Simulated data for intima media thickness of the carotid arteryand age in 2784 adults.
Usage
imtFormat
Adata.frame with 2784 observations on the following 3 variables:
- age
age of the individual (years).
- imt
intima media thickness of the carotid artery (mm).
- logimt
logarithm of
imt.
Details
Data were simulated to emulate true data pattern observed in a realstudy (see References).
Source
See References.
References
Rivera Met al. Association between long-term exposure totraffic-related air pollution and subclinical atherosclerosis: the REGICORStudy.Environmental Health Perspectives. 2013;121(2):223-230.
Examples
data(imt)par(las = 1, mfrow = c(1, 2))with(imt, plot(age, imt))with(imt, plot(age, logimt))Summarizing the Model Fitting
Description
Asummary method for an object created by the functiontlm.
Usage
## S3 method for class 'tlm'summary(object, ...)## S3 method for class 'summary.tlm'print(x, ...)Arguments
object | an object of class " |
... | additional arguments. |
x | an object of class " |
Details
Essentially, the output ofsummary.lm orsummary.glmis displayed. In addition, further information on the fitted model is alsodisplayed.
Value
A list with class "summary.tlm" including the following items:
- model
the fitted model in the transformed space.
- ypow
the value of
ypow.- xpow
the value of
xpow.- summary
the summary of the fitted model provide by
summary.lm(for gaussian response) orsummary.glm(otherwise).
References
Barrera-Gomez J, Basagana X. Models with transformed variables:interpretation and software. Epidemiology. 2015;26(2):e16-17.
See Also
Examples
### linear model with log-log transformation:data(feld1)modcat <- tlm(logroom ~ logmattress + cat, data = feld1, ypow = 0, xpow = 0)modcatsummary(modcat)Fitting, Reporting and Visualizing Linear, Logistic and PoissonRegression Models with Transformed Variables
Description
tlm is the main function of the package. It fits a linear,logistic or Poisson regression model with transformed variables and createsan object which can be subsequently used to compute adjusted measures of theresponse variable (withMY) and compute and interpret adjustedeffects of the explanatory variable of interest on the response variable (witheffect andeffectInfo, respectively), in the naturalscale of the variables. In addition, the fitted model can be visualized withtheplot.tlm method.
Usage
tlm( formula, family = gaussian, data, ypow = 1, xpow = 1, ..., y, x, z = "none")## S3 method for class 'tlm'print(x, ...)## S3 method for class 'tlm'plot(x, type = c("original", "transformed", "diagnosis"), observed = FALSE, xname = "x", yname = "y", level = 0.95, ...)Arguments
formula | model |
family | the response variable |
data | a |
ypow | numeric. Power transformation already done in the response variable.See Details below. |
xpow | numeric. Power transformation already done in the explanatoryvariable of interest. See Details below. |
... | for |
y,z | old arguments for back compatibility only. To be removed, seeDetails below. |
x | for |
type | For |
observed | For |
xname,yname | For |
level | For |
Details
The transformations already done in the response variable and in theexplanatory variable of interest are passed byypow andxpow,respectively, and must be numbers. Default is 1, meaning no transformation.The value 0 corresponds to the logarithmic transformation. Iffamilyis notgaussian, the response variable is assumed non transformed. Ifthe explanatory variable of interest is categorical or takes only two differentvalues, the value ofxpow is assumed to be 1. If the explanatoryvariable of interest takes only two different values, it is handled as abinary variable.
Plots obtained fortype = "transformed" are intended to visually explorethe model goodness of fit and should not be reported because values of thetransformed variables are meaningless (e.g. log(cotinine) has no sense).
Old argumentsy,x andz, are deprecated and bugs areno longer fixed. They will be removed in the first version posterior to 0.2.0.Use argumentformula instead.
Value
A list with class "tlm" including the following items:
- model
the fitted model in the transformed space.
- ypow
the value of
ypow.- xpow
the value of
xpow.
References
Barrera-Gomez J, Basagana X. Models with transformed variables:interpretation and software.Epidemiology. 2015;26(2):e16-17.
See Also
Examples
### Linear model with log-log transformation:### effect of mattress levels on room levels, adjusting for cat:# model fitting in the transformed space:data(feld1)head(feld1)modcat <- tlm(logroom ~ logmattress + cat, data = feld1, ypow = 0, xpow = 0)modcatsummary(modcat)# plot of the geometric mean of the response (original space), adjusting for 'cat':plot(modcat, xname = "Mattress levels", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting for 'cat' and# adding the observations:plot(modcat, type = "transformed", xname = "mattress levels", yname = "room levels", observed = TRUE)# diagnosis plot:plot(modcat, type = "diagnosis")### effect of cat in house on room levels, adjusting for matress levels:modcat2 <- tlm(logroom ~ cat + logmattress, data = feld1, ypow = 0)summary(modcat2)# plot of the geometric mean of the response (original space), adjusting# for mattress levels:plot(modcat2, xname = "Cat", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting# for mattress levels:plot(modcat2, type = "transformed", xname = "Cat", yname = "room levels")