BinAddHaz {addhaz} | R Documentation |

## 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 |

`data` |
an optional data frame or matrix containing the variables in the model. If not found in |

`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 |

`model` |
logical. If |

`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 |

`attrib` |
logical. Should the attribution of disability to chronic diseases/conditions be estimated? Default is |

`attrib.var` |
character indicating the name of the attribution variable to be used if |

`collapse.background` |
logical. Should the background be collapsed across the levels of the |

`attrib.disease` |
logical. Should the attribution of diseases be stratified by the levels of the attribution variable? If |

`type.attrib` |
type of attribution to be estimated. The options are |

`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 |

`conf.level` |
scalar containing the confidence level of the bootstrap percentile confidence intervals. Default is |

`nbootstrap` |
integer. Number of bootstrap replicates. |

`parallel` |
logical. Should parallel calculations be used to obtain the bootstrap percentile confidence intervals? Only valid if |

`type.parallel` |
type of parallel operation to be used (if |

`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 |

`resDeviance` |
residual deviance. |

`df` |
degrees of freedom. |

`pvalue` |
numerical vector of p-values based on the Wald test. Only provided if |

`stdError` |
numerical vector with the standard errors for the parameter estimates based on the inverse of the observed information matrix. Only provided if |

`vcov` |
variance-covariance (inverse of the observed information matrix). Only provided if |

`contribution` |
for |

`bootsRep` |
matrix with the bootstrap replicates of the regression coefficients and contributions (if |

`conf.level` |
confidence level of the bootstrap CI. Only provided if |

`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 (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>.

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

### 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)
```

*addhaz*version 0.5 Index]