Fit Binomial Additive Hazards Models

Description

This function fits binomial additive hazards 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

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BinAddHaz(formula, data, subset, weights, na.action, model = TRUE,
          contrasts = NULL, start = FALSE, start.val, attrib = FALSE,
          attrib.var, type.attrib = "abs", set.seed = FALSE, seed,
          bootstrap = FALSE, 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

logical. Will the user provide starting values? Default is FALSE, in which case the starting values will be the absolute values of the coefficients for a Poisson glm.

start.val

vector of the starting values. They should be provided if start = TRUE and lie inside the parameter space.

attrib

logical. Should the attribution of disability to chronic diseases/conditions be calculated? Default is FALSE.

attrib.var

character indicating the name of the attribution variable to be used if attrib = TRUE. If missing, the attribution variable is the intercept (no stratification of the attribution results). The attribution variable must be the first variable included in the linear predictor in formula. See example.

type.attrib

type of attribution to be calculated. The options are "abs" for absolute contribution, "rel" for relative contribution, or "both" for both absolute and relative contributions. Default is "abs".

set.seed

logical. Should a random seed be set? Default is FALSE.

seed

integer indicating the random seed. Only valid if set.seed = TRUE.

bootstrap

logical. Should bootstrap percentile confidence intervals be calculated for the parameters and attributions? Default is FALSE. See details.

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 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 (η ≥ 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 the package only allows the calculation of non-parametric bootstrap percentile confidence intervals (CI), which are based on the 2.5 and 97.5 percentiles. 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 hazards 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

numeric 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 or conditions) to the disability prevalence. Percentile bootstrap confidence intervals are provided if bootstrap = TRUE.

bootsRep

matrix with the bootstrap replicates.

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 response variable 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 (w.nusselder@erasmusmc.nl).

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>.

See Also

MultAddHaz

Examples

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  data(disabData)

  ## Model without bootstrap percentile confidence intervals and no attribution

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

  ## Model with bootstrap percentile confidence intervals 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, type.attrib = "both", set.seed = TRUE, seed = 111,
                    bootstrap = TRUE, nbootstrap = 5)
  summary(fit2)

  ## Model with bootstrap percentile confidence intervals with attribution based on
  ## the age variable and 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.var = age, attrib = TRUE, type.attrib = "both",
                    set.seed = TRUE, seed = 111, bootstrap = TRUE, nbootstrap = 10,
                    parallel = TRUE, type.parallel = "snow", ncpus = 4)
  summary(fit3)
## End(Not run)

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