# DALY sensitivity analysis

### Description

This function performs a probabilistic global sensitivity analysis of the
overall DALY estimate, based on standardized regression coefficients
(method `src`

) or partial correlation coefficients (method `pcc`

).
Actual or ranked values may be used, and for method `src`

, coefficients
or mapped values may be reported. See below for more details.

### Usage

1 2 3 4 5 6 7 8 | ```
sensitivity(x, method = c("src", "pcc"), rank = FALSE, mapped = TRUE)
## S3 method for class 'DALY_sensitivity'
print(x, digits = 3, signif_stars = getOption("show.signif.stars"), ...)
## S3 method for class 'DALY_sensitivity'
plot(x, alpha = 0.05, main = "Sensitivity analysis",
show_values = FALSE, value_digits = 3, value_cex = 0.6, ...)
``` |

### Arguments

`x` |
Object of class |

`method` |
Sensitivity analysis method: |

`rank` |
Should ranked values be used? Defaults to |

`mapped` |
Should mapped regression coefficients be presented?
Defaults to |

`digits ` |
Number of decimals to be printed; defaults to |

`signif_stars ` |
Should significance stars be printed? |

`alpha ` |
Significance level for selecting significant variables; defaults to 0.05 |

`main ` |
Main title of tornado plot; defaults to "Sensitivity analysis" |

`show_values ` |
Should values be plotted next to bars?; defaults to FALSE |

`value_digits ` |
Number of significant digits for plotted values; defaults to 3 |

`value_cex ` |
Size of plotted values; defaults to 0.6 |

`... ` |
Additional arguments to be passed to methods |

### Details

Sensitivity analysis studies how the uncertainty in the overall DALY estimate can be apportioned to the different sources of uncertainty in the input parameters. These results can therefore help to identify those input parameters that cause significant uncertainty in the overall DALY estimate and that therefore may be the focus of further research if one wishes to reduce the uncertainty in the overall estimate.

The `sensitivity`

function implements a *probabilistic global*
sensitivity analysis, in which the analysis is conducted over the full range
of plausible input values (hence *global*), determined by the specified
uncertainty distributions (hence *probabilistic*).

Specifying `method = "src"`

will perform a linear regression-based
sensitivity analysis. Here, the simulated overall DALY estimates will be
regressed against the simulated values for the stochastic input parameters
(using `lm`

). To facilitate comparison, the independent terms
are standardized such that they are normally distributed with mean zero and
standard deviation one (using `scale`

). The resulting regression
coefficients are therefore referred to as *standardized* regression
coefficients.

Argument `rank`

specifies whether the regression should be performed on
the actual values (`rank = FALSE`

; default) or on the ranked values
(`rank = TRUE`

). Rank-based regression may be preferred when the
relation between output and inputs is non-linear. R^2 values smaller than
0.60 may be indicative of a poor fit of the default linear regression model.

If `mapped = TRUE`

, the dependent term is not standardized, such that
the resulting *mapped* regression coefficients correspond to the change
in overall DALY given one standard deviation change in the corresponding
input parameter. If `mapped = FALSE`

, the dependent term is
standardized, such that the resulting *standardized* regression
coefficients correspond to the number of standard deviations change in
overall DALY given one standard deviation change in the corresponding input
parameter.

Specifying `method = "pcc"`

will calculate partial correlation
coefficients for each of the input variables. Partial correlation
coefficients represent the correlation between two variables when adjusting
for other variables. In the presence of important interactions between input
variables, partial correlation coefficients may be preferred over
standardized regression coefficients.

Argument `rank`

specifies whether the correlation should be calculated
between the actual values (`rank = FALSE`

; default) or between the
ranked values (`rank = TRUE`

).

Method `plot`

can be used to generate a tornado plot of the significant
input variables.

### Value

An object of S3 class `DALY_sensitivity`

, containing the following two
elements:

`method` |
List containing the specified values for |

`out` |
Either the output of |

### Author(s)

Brecht.Devleesschauwer@UGent.be

### References

Vose D (2000).

*Risk analysis: a quantitative guide*. John Wiley & Sons.Saltelli A, Chan K, Scott EM (2000).

*Sensitivity analysis*. John Wiley & Sons.

### See Also

Package sensitivity, for more advanced sensitivity
analysis methods.

`getDALY`

`lm`

`cor.test`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ```
## Not run:
##= load NCC example ======================================
setDALYexample(1)
##= perform DALY calculation, store results in 'x' ========
x <- getDALY()
##= perform DALY sensitivity analysis =====================
## default sensitivity analysis
sa <- sensitivity(x)
print(sa)
## tornado plot of default sensitivity analysis
plot(sa, show_values = TRUE)
## standardized regression coefficients -------------------
sensitivity(x, method = "src", rank = FALSE, mapped = TRUE)
sensitivity(x, method = "src", rank = FALSE, mapped = FALSE)
## standardized rank regression coefficients --------------
sensitivity(x, method = "src", rank = TRUE, mapped = TRUE)
sensitivity(x, method = "src", rank = TRUE, mapped = FALSE)
## partial correlation coefficients -----------------------
sensitivity(x, method = "pcc", rank = FALSE)
## partial rank correlation coefficients ------------------
sensitivity(x, method = "pcc", rank = FALSE)
## End(Not run)
``` |