MultAddHaz {addhaz} | R Documentation |

## 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 |

`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 randomly generated. |

`attrib` |
logical. Should the attribution of chronic diseases/conditions for each disability level 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 for each disability level? If |

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

`seed` |
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? Default is |

`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). 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 |

`resDeviance` |
residual deviance. |

`df` |
degrees of freedom. |

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

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

`vcov` |
variance-covariance matrix (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? |

`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

### 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)
```

*addhaz*version 0.5 Index]