Package 'addhaz'

Fit Binomial Additive Hazard Models

Description

This function fits binomial additive hazard models subject to linear inequality constraints using the function constrOptim in the stats package for binary outcomes. Additionally, it calculates the cause-specific contributions to the disability prevalence based on the attribution method, as proposed by Nusselder and Looman (2004).

Usage

BinAddHaz(formula, data, subset, weights, na.action, model = TRUE,
          contrasts = NULL, start, attrib = TRUE,
          attrib.var, collapse.background = FALSE, attrib.disease = FALSE,
          type.attrib = "abs", seed, bootstrap = FALSE, conf.level = 0.95,
          nbootstrap, parallel = FALSE, type.parallel = "snow", ncpus = 4,...)

Arguments

formula	a formula expression of the form response ~ predictors, similar to other regression models. In case of attrib = TRUE, the first predictor in the formula should be the attrib.var. See example.
data	an optional data frame or matrix containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which BinAddHaz is called.
subset	an optional vector specifying a subset of observations to be used in the fitting process. All observations are included by default.
weights	an optional vector of survey weights to be used in the fitting process.
na.action	a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The 'factory-fresh' default is na.omit.
model	logical. If TRUE, the model frame is included as a component of the returned object.
contrasts	an optional list to be used for some or all of the factors appearing as variables in the model formula.
start	an optional vector of starting values. If not provided by the user, it is automatically generated using glm, family = poisson.
attrib	logical. Should the attribution of disability to chronic diseases/conditions be estimated? Default is TRUE.
attrib.var	character indicating the name of the attribution variable to be used if attrib = TRUE. If missing, the attribution results will not be stratified by the levels of the attribution variable. The attribution variable must be the first variable included in the linear predictor in formula. See example.
collapse.background	logical. Should the background be collapsed across the levels of the attrib.var? If FALSE, the background will be estimated for each level of the attrib.var. If TRUE, only one background will be estimated. If TRUE, attrib.var must be specified. Default is FALSE.
attrib.disease	logical. Should the attribution of diseases be stratified by the levels of the attribution variable? If FALSE, the attribution of diseases will not be stratified by the levels of the attrib.var. If TRUE, the attribution of diseases will be estimated for each level of the attrib.var. If TRUE, interaction between diseases and the attribution variable must be provided in the formula. Default is FALSE.
type.attrib	type of attribution to be estimated. The options are "abs" for absolute contribution, "rel" for relative contribution, or "both" for both absolute and relative contributions. Default is "abs".
seed	an optional integer indicating the random seed.
bootstrap	logical. Should bootstrap percentile confidence intervals be estimated for the model parameters and attributions? Default is FALSE. See details.
conf.level	scalar containing the confidence level of the bootstrap percentile confidence intervals. Default is 0.95.
nbootstrap	integer. Number of bootstrap replicates.
parallel	logical. Should parallel calculations be used to obtain the bootstrap percentile confidence intervals? Only valid if bootstrap = TRUE. Default is FALSE.
type.parallel	type of parallel operation to be used (if parallel = TRUE), with options: "multicore" and "snow". Default is "snow". See details.
ncpus	integer. Number of processes to be used in the parallel operation: typically one would choose this to be the number of available CPUs. Default is 4.
...	other arguments passed to or from the other functions.

Details

The model is a generalized linear model with a non-canonical link function, which requires a restriction on the linear predictor ($\eta \ge 0$) to produce valid probabilities. This restriction is implemented in the optimization procedure, with an adaptive barrier algorithm, using the function constrOptim in the stats package.

The variance-covariance matrix is based on the observed information matrix.

This version of the package only allows the calculation of non-parametric bootstrap percentile confidence intervals (CI). Also, the function gives the user the option to do parallel calculation of the bootstrap CI. The snow parallel option is available for all operating systems (Windows, Linux, and Mac OS) while the multicore option is only available for Linux and Mac OS systems. These two calculations are done by calling the boot function in the boot package. For more details, see the documentation of the boot package.

More information about the binomial additive hazard model and the calculation of the contribution of chronic conditions to the disability prevalence can be found in the references.

Value

A list with arguments:

coefficients	numerical vector with the regression coefficients.
ci	confidence intervals calculated via bootstraping (if bootstrap = TRUE) or as the inverse of the observed information matrix.
resDeviance	residual deviance.
df	degrees of freedom.
pvalue	numerical vector of p-values based on the Wald test. Only provided if bootstrap = FALSE.
stdError	numerical vector with the standard errors for the parameter estimates based on the inverse of the observed information matrix. Only provided if bootstrap = FALSE.
vcov	variance-covariance (inverse of the observed information matrix). Only provided if bootstrap = FALSE.
contribution	for type.attrib = "abs" or "rel", a matrix is provided. For type.attrib = "both", a list with two matrices ( "abs" and "rel") is provided. This represents the contribution of each predictor in the model (usually diseases) to the disability prevalence. Percentile bootstrap confidence intervals are provided if bootstrap = TRUE.
bootsRep	matrix with the bootstrap replicates of the regression coefficients and contributions (if attrib = TRUE). If attrib = FALSE, it returns a logical, FALSE.
conf.level	confidence level of the bootstrap CI. Only provided if bootstrap = TRUE.
bootstrap	logical. Was bootstrap CI requested?
fitted.values	the fitted mean values, obtained by transforming the linear predictor by the inverse of the link function.
residuals	difference between the observed response and the fitted values.
call	the matched call.

Author(s)

Renata T C Yokota. This function is based on the R code developed by Caspar W N Looman and Wilma J Nusselder for non R-users, with modifications. Original R code is available upon request to Wilma J Nusselder ([email protected]).

References

Nusselder, W.J., Looman, C.W.N. (2004). Decomposition of differences in health expectancy by cause. Demography, 41(2), 315-334.

Nusselder, W.J., Looman, C.W.N. (2010). WP7: Decomposition tools: technical report on attribution tool. European Health Expectancy Monitoring Unit (EHEMU). Available at <http://www.eurohex.eu/pdf/Reports_2010/2010TR7.2_TR%20on%20attribution%20tool.pdf>.

Yokota, R.T.C., Van Oyen, H., Looman, C.W.N., Nusselder, W.J., Otava, M., Kifle, Y.W., Molenberghs, G. (2017). Multinomial additive hazard model to assess the disability burden using cross-sectional data. Biometrical Journal, 59(5), 901-917.

See Also

MultAddHaz

Examples

data(disabData)

  ## Model without bootstrap CI and no attribution

  fit1 <- BinAddHaz(dis.bin ~ diab + arth + stro , data = disabData, weights = wgt,
                    attrib = FALSE)
  summary(fit1)

  ## Model with bootstrap CI and attribution without stratification, no parallel calculation
  # Warning message due to the low number of bootstrap replicates
## Not run: 
  fit2 <- BinAddHaz(dis.bin ~ diab + arth + stro , data = disabData, weights = wgt,
                    attrib = TRUE, collapse.background = FALSE, attrib.disease = FALSE,
                    type.attrib = "both", seed = 111, bootstrap = TRUE, conf.level = 0.95,
                    nbootstrap = 5)
  summary(fit2)

  ## Model with bootstrap CI and attribution of diseases and background stratified by
  ## age, with parallel calculation of bootstrap CI
  # Warning message due to the low number of bootstrap replicates

  diseases <- as.matrix(disabData[,c("diab", "arth", "stro")])
  fit3 <- BinAddHaz(dis.bin ~ factor(age) -1 + diseases:factor(age), data = disabData,
                    weights = wgt, attrib = TRUE, attrib.var = age,
                    collapse.background = FALSE, attrib.disease = TRUE, type.attrib = "both",
                    seed = 111,  bootstrap = TRUE, conf.level = 0.95, nbootstrap = 10,
                    parallel = TRUE, type.parallel = "snow", ncpus = 4)
  summary(fit3)
## End(Not run)

---

Example of disability data

Description

The disabData is a subset of the data from the 2013 National Health Survey in Brazil ("Pesquisa Nacional de Saude, 2013"). The data are restricted to women aged 60 years or older, resulting in 6294 individuals.

Usage

data(disabData)

Format

This dataset has information about disability and chronic conditions. The disability outcomes were defined as limitations on instrumental activities of daily living (IADL). Individuals with missing data were excluded. The data frame contains 7 variables:

• dis.bin: disability as a binary variable, with 2 categories: 0 (no disability), 1 (disability).

• dis.mult: disability as a multinomial variable, with 3 categories: 0 (no disability), 1 (mild disability), and 2 (severe disability).

• wgt: survey weights.

• age: binary variable for age: 0 (60-79 years) or 1 (80+ years).

• diab: binary variable for diabetes: 0 (no) or 1 (yes).

• arth: binary variable for arthritis: 0 (no) or 1 (yes).

• stro: binary variable for stroke: 0 (no) or 1 (yes).

Source

The data were obtained from the National Health Survey 2013, Brazil. For more information about the survey, see references.

References

Szwarcwald, C.L., Malta, D.C., Pereira, C.A., Vieira, M.L., Conde, W.L., Souza Junior, P.R., et al. (2013). National Health Survey in Brazil: design and methodology of application. Cien Saude Colet., 19(2): 333:42 [Article in Portuguese].

Instituto Brasileiro de Geografia e Estatistica (IBGE). Pesquisa Nacional de Saude 2013. Available at <http://www.ibge.gov.br/home/estatistica/populacao/pns/2013/>.

Examples

data(disabData)
  str(disabData)

---

Perform likelihood ratio test

Description

This function performs the likelihood ratio test to compare two nested binomial or multinomial additive hazard models. It can be used for model selection.

Usage

LRTest(model1, model2)

Arguments

model1, model2

objects of class "binaddhazmod" or "multaddhazmod" to be compared. See example.

Details

The likelihood ratio test is defined as -2*log(likelihood model 1/likelihood model 2).The resulting test statistic is assumed to follow a chi-squared distribution, with degrees of freedom (df) equal to the difference of the df between the models. If the test is statistically significant, the model with more variables fits the data significantly better than the model with less variables.

Value

A data frame with columns:

Res.df	degrees of freedom for each model.
Res.dev	2*log-likelihood of each model.
df	difference in the degrees of freedom between models 1 and 2.
Deviance	difference between the 2*log-likelihood of models 1 and 2, representing the value of the likelihood ratio test statistic.
Pr(>Chi)	p-value, based on the chi-squared distribution.

Examples

data(disabData)

  ## Comparing two binomial models

  fit1 <- BinAddHaz(dis.bin ~ diab + arth + stro , data = disabData, weights = wgt,
                    attrib = FALSE)

  diseases <- as.matrix(disabData[,c("diab", "arth", "stro")])
  fit2 <- BinAddHaz(dis.bin ~ factor(age) -1 + diseases:factor(age), data = disabData,
                    weights = wgt, attrib = FALSE)

  LRTest(fit2, fit1)

  ## Comparing two multinomial models
## Not run: 
  fit3 <- MultAddHaz(dis.mult ~ diab + arth + stro , data = disabData, weights = wgt,
                     attrib = FALSE)
  fit4 <- MultAddHaz(dis.mult ~ factor(age) -1 + diseases: factor(age), data = disabData,
                     weights = wgt, attrib = FALSE)
  LRTest(fit4, fit3)
## End(Not run)

---

Fit Multinomial Additive Hazard Models

Description

This function fits multinomial additive hazard models subject to linear inequality constraints using the function constrOptim in the stats package for multinomial (multi-category) outcomes. It also calculates the cause-specific contributions to the disability prevalence for each category of the response variable based on the extension of the attribution method, as proposed by Yokota et al (2017).

Usage

MultAddHaz(formula, data, subset, weights, na.action, model = TRUE,
           contrasts = NULL, start, attrib = TRUE, attrib.var,
           collapse.background = FALSE, attrib.disease = FALSE,
           type.attrib = "abs", seed, bootstrap = FALSE, conf.level = 0.95,
           nbootstrap, parallel = FALSE, type.parallel = "snow", ncpus = 4,...)

Arguments

formula	a formula expression of the form response ~ predictors, similar to other regression models. In case of attrib = TRUE, the first predictor in the formula should be the attrib.var. See example.
data	an optional data frame or matrix containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which MultAddHaz is called.
subset	an optional vector specifying a subset of observations to be used in the fitting process. All observations are included by default.
weights	an optional vector of survey weights to be used in the fitting process.
na.action	a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The 'factory-fresh' default is na.omit.
model	logical. If TRUE, the model frame is included as a component of the returned object.
contrasts	an optional list to be used for some or all of the factors appearing as variables in the model formula.
start	an optional vector of starting values. If not provided by the user, it is randomly generated.
attrib	logical. Should the attribution of chronic diseases/conditions for each disability level be estimated? Default is TRUE.
attrib.var	character indicating the name of the attribution variable to be used if attrib = TRUE. If missing, the attribution results will not be stratified by the levels of the attribution variable. The attribution variable must be the first variable included in the linear predictor in formula. See example.
collapse.background	logical. Should the background be collapsed across the levels of the attrib.var for each disability level? If FALSE, the background will be estimated for each level of the attrib.var. If TRUE, only one background will be estimated. If TRUE, attrib.var must be specified. Default is FALSE.
attrib.disease	logical. Should the attribution of diseases be stratified by the levels of the attribution variable for each disability level? If FALSE, the attribution of diseases will not be stratified by the levels of the attrib.var. If TRUE, the attribution of diseases will be estimated for each level of the attrib.var. If TRUE, interaction between diseases and the attribution variable must be provided in the formula. Default is FALSE.
type.attrib	type of attribution to be estimated. The options are "abs" for absolute contribution, "rel" for relative contribution, or "both" for both absolute and relative contributions. Default is "abs".
seed	integer indicating the random seed.
bootstrap	logical. Should bootstrap percentile confidence intervals be estimated for the model parameters and attributions? Default is FALSE. See details.
conf.level	scalar containing the confidence level of the bootstrap percentile confidence intervals. Default is 0.95.
nbootstrap	integer. Number of bootstrap replicates.
parallel	logical. Should parallel calculations be used to obtain the bootstrap percentile confidence intervals? Default is FALSE.
type.parallel	type of parallel operation to be used (if parallel = TRUE), with options: "multicore" and "snow". Default is "snow". See details.
ncpus	integer. Number of processes to be used in the parallel operation: typically one would choose this to be the number of available CPUs. Default is 4.
...	other arguments passed to or from the other functions.

Details

The model is a generalized linear model with a non-canonical link function, which requires a restriction on the linear predictor ($\eta \ge 0$) to produce valid probabilities. This restriction is implemented in the optimization procedure, with an adaptive barrier algorithm, using the function constrOptim in the stats package.

The variance-covariance matrix is based on the observed information matrix.

This version of the package only allows the calculation of non-parametric bootstrap percentile confidence intervals (CI). Stratified bootstrap is applied to each category of the outcome. Also, the function gives the user the option to do parallel calculation of the bootstrap CI. The snow parallel option is available for all operating systems (Windows, Linux, and Mac OS) while the multicore option is only available for Linux and Mac OS systems. These two calculations are done by calling the boot function in the boot package. For more details see the documentation of the boot package.

More information about the multinomial additive hazard model and the estimation of the contribution of chronic conditions to the disability prevalence can be found in the references.

Value

A list with arguments:

coefficients	column matrix with the regression coefficients.
ci	matrix with confidence intervals calculated via bootstraping (if bootstrap = TRUE) or as the inverse of the observed information matrix.
resDeviance	residual deviance.
df	degrees of freedom.
pvalue	column matrix of p-values based on the Wald test. Only provided if bootstrap = FALSE.
stdError	column matrix with the standard errors for the parameter estimates based on the inverse of the observed information matrix. Only provided if bootstrap = FALSE.
vcov	variance-covariance matrix (inverse of the observed information matrix). Only provided if bootstrap = FALSE.
contribution	for type.attrib = "abs" or "rel", a matrix is provided. For type.attrib = "both", a list with two matrices ("abs" and "rel") is provided. This represents the contribution of each predictor in the model (usually diseases) to the disability prevalence. Percentile bootstrap confidence intervals are provided if bootstrap = TRUE. If attrib = FALSE, it returns a logical, FALSE.
bootsRep	matrix with the bootstrap replicates of the regression coefficients and contributions (if attrib = TRUE).
conf.level	confidence level of the bootstrap CI. Only provided if bootstrap = TRUE.
bootstrap	logical. Was bootstrap CI requested?
call	the matched call.

Author(s)

Renata T. C. Yokota. This function is based on the R code developed by Caspar W. N. Looman and Wilma J. Nusselder for the binomial additive hazard model with modifications and adaptations for the multinomial case.

References

Yokota, R.T.C., Van Oyen, H., Looman, C.W.N., Nusselder, W.J., Otava, M., Kifle, Y.W., Molenberghs, G. (2017). Multinomial additive hazard model to assess the disability burden using cross-sectional data. Biometrical Journal, 59(5), 901-917.

See Also

BinAddHaz

Examples

data(disabData)

  ## Model without bootstrap CI and no attribution
## Not run: 
  fit1 <- MultAddHaz(dis.mult ~ diab + arth + stro , data = disabData, weights = wgt,
                     attrib = FALSE)
  summary(fit1)

  ## Model with bootstrap CI and attribution without stratification, no parallel calculation
  # Warning message due to the low number of bootstrap replicates

  fit2 <- MultAddHaz(dis.mult ~ diab + arth + stro , data = disabData, weights = wgt,
                     attrib = TRUE, collapse.background = FALSE, attrib.disease = FALSE,
                     type.attrib = "both", seed = 111, bootstrap = TRUE, conf.level = 0.95,
                     nbootstrap = 5)
  summary(fit2)

  ## Model with bootstrap CI and attribution of diseases and background stratified by
  ## age, with parallel calculation of bootstrap CI
  # Warning message due to the low number of bootstrap replicates

  diseases <- as.matrix(disabData[,c("diab", "arth", "stro")])
  fit3 <- MultAddHaz(dis.mult ~ factor(age) -1 + diseases: factor(age), data = disabData,
                     weights = wgt, attrib = TRUE, attrib.var = age,
                     collapse.background = FALSE, attrib.disease = TRUE, type.attrib = "both",
                     seed = 111, bootstrap = TRUE, conf.level = 0.95, nbootstrap = 5,
                     parallel = TRUE, type.parallel = "snow", ncpus = 4)

  summary(fit3)
## End(Not run)

---