‘mispitools’ is an open source package written in R statistical language. It consist in a set of decision making tools to conduct missing person searches. It allows computing several features, from preliminary investigation data based LRs to optimal LR threshold for declaring potential matches in DNA-based database search. mispitools imports forrel, https://doi.org/10.1016/j.fsigen.2020.102376, and pedtools packages, https://doi.org/10.1016/C2020-0-01956-0. More recently ‘mispitools’ incorporates preliminary investigation data based LRs. Statistical weight of different traces of evidence such as biological sex, age and hair color are presented. For citing mispitools please use the following references: Marsico and Caridi, 2023, http://dx.doi.org/10.2139/ssrn.4331033, and Marsico, Vigeland et al. 2021, https://doi.org/10.1016/j.fsigen.2021.102519.

The goal of mispitools is to bring a simulation framework for decision making in missing person identification cases. You can install it from CRAN typing on your R command line:

```
install.packages("mispitools")
library(mispitools)
```

You can install too the versions under development (unstable) of mispitools from Github with:

```
install.packages("devtools")
library(devtools)
install_github("MarsicoFL/mispitools")
library(mispitools)
```

Now you can analyze the mispitools documentation, it has a description for all functions and parameters.

` ?mispitools`

NOTE: These packages should be directly, if not previously, installed as dependencies with mispitools. Nevertheless, in some cases it is necesary to install them manually (specially if you are installing the under development version from github). This could be done with the following lines:

```
install.packages("ggplot2")
install.packages("forrel")
install.packages("pedtools")
install.packages("reshape2")
install.packages("tidyverse")
install.packages("patchwork")
```

NOTE: The methodology implemented in this section is explained in: http://dx.doi.org/10.2139/ssrn.4331033.

Now you are able to compute conditional probability phenotype tables considering Age, Sex and Hair color variables. Firstly you can analyze the different parameters from the documentation.

` ?CPT_POP`

For simplification, the population reference age distribution is treated as uniform (the function could be easily adapted to incorpore a dataset with the specified frequencies, this will be implemented soon).

```
CPT_POP(
propS = c(0.5, 0.5),
MPa = 40,
MPr = 6,
propC = c(0.3, 0.2, 0.25, 0.15, 0.1))
```

```
## [,1] [,2] [,3] [,4] [,5]
## F-T1 0.0225 0.015 0.01875 0.01125 0.0075
## F-T0 0.1275 0.085 0.10625 0.06375 0.0425
## M-T1 0.0225 0.015 0.01875 0.01125 0.0075
## M-T0 0.1275 0.085 0.10625 0.06375 0.0425
```

The obtained matrix represent the probabilities of the phenotypes in the reference population. F-T1 represent a female thats age matches with the age of the missing. F-T0 is a female with a mismatch in age with the missing. M correspond to males, and the number (columns) represent hair colors. Note that in the followin case, the parameters remains the same, but changin the MP range change the population probabilities.

```
CPT_POP(
propS = c(0.5, 0.5),
MPa = 40,
MPr = 15,
propC = c(0.3, 0.2, 0.25, 0.15, 0.1))
```

```
## [,1] [,2] [,3] [,4] [,5]
## F-T1 0.05625 0.0375 0.046875 0.028125 0.01875
## F-T0 0.09375 0.0625 0.078125 0.046875 0.03125
## M-T1 0.05625 0.0375 0.046875 0.028125 0.01875
## M-T0 0.09375 0.0625 0.078125 0.046875 0.03125
```

This could be counterintuitive, because there are population frequencies, and the population parameters remains the same in both cases. But T1 and T0 values depends on MP age and error rate. In the same way, MP conditioned probabilities could be computed. Again, we first see the documentation:

` ?CPT_MP`

Then, we can select a specified MP. One of the parameters is epc, that comes from the function Cmodel(). Lets see that function:

`Cmodel() ?`

It has two options, uniform, that adds the same ep for all combinations of colors, and custom, that allows specifying a specific value for each pair. Here we select the custom:

```
Cmodel(
errorModel = "custom",
ep = 0.01,ep12 = 0.01,ep13 = 0.005,
ep14 = 0.01,ep15 = 0.003,ep23 = 0.01,
ep24 = 0.003,ep25 = 0.01,ep34 = 0.003,
ep35 = 0.003,ep45 = 0.01)
```

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.972762646 0.009727626 0.004863813 0.009727626 0.002918288
## [2,] 0.009680542 0.968054211 0.004840271 0.009680542 0.002904163
## [3,] 0.004897160 0.009794319 0.979431929 0.002938296 0.002938296
## [4,] 0.009746589 0.002923977 0.002923977 0.974658869 0.009746589
## [5,] 0.002923977 0.009746589 0.002923977 0.009746589 0.974658869
```

Now we can specify the phenotype probabilities conditioned on MP characteristics.

```
CPT_MP(MPs = "F", MPc = 1,
eps = 0.05, epa = 0.05,
epc = Cmodel())
```

```
## 1 2 3 4 5
## F-T1 0.877918288 8.779183e-03 4.389591e-03 8.779183e-03 2.633755e-03
## F-T0 0.046206226 4.620623e-04 2.310311e-04 4.620623e-04 1.386187e-04
## M-T1 0.046206226 4.620623e-04 2.310311e-04 4.620623e-04 1.386187e-04
## M-T0 0.002431907 2.431907e-05 1.215953e-05 2.431907e-05 7.295720e-06
```

Moreover, LR can be computed as follows:

```
<- CPT_MP(MPs = "F", MPc = 1,
MP eps = 0.05, epa = 0.05,
epc = Cmodel())
<- CPT_POP(
POP propS = c(0.5, 0.5),
MPa = 40,
MPr = 6,
propC = c(0.3, 0.2, 0.25, 0.15, 0.1))
/POP MP
```

```
## 1 2 3 4 5
## F-T1 39.01859058 0.5852788586 0.2341115435 0.7803718115 0.351167315
## F-T0 0.36240177 0.0054360266 0.0021744106 0.0072480354 0.003261616
## M-T1 2.05361003 0.0308041505 0.0123216602 0.0410722006 0.018482490
## M-T0 0.01907378 0.0002861067 0.0001144427 0.0003814755 0.000171664
```

We can see that the sex-age-color: F-T1-1 and M-T1-1 are the only two LR values over 1, being the former (perfect match) the largest. All these information could be summarized in the following plot:

```
library(ggplot2)
CondPlot(POP,MP)
```

Furthermore, a ShinyApp could be executed using the following command:

`mispiApp()`

It will open an interactive panel where parameters could be selected in order to comput conditioned probability tables and LR for each phenotype. PropF refer to the female proportion in the population (the male proportion is 1-PropF). PropC indicate the proportion of the specific hair colour. After defining five hair color proportion mispitools normalize it all to sum 1.

Note: mispiApp is under development. Particularly age variable assumes a uniform population frequency distribution from 0 to 80 years old. Introducing incoherent parameters, i.e MPa= 40 with a range error (MPr) of 100 (error being more than two times the age allowing negative results), will lead to incoherent probabilities. Please select realiable values.

NOTE: The methodology used in this section is explained in: https://doi.org/10.1016/j.fsigen.2021.102519

\[{\color{red}WARNING}\] At the moment mispitools works with under development forrel version (soon on CRAN). In order to perform genetic simulations some steps should be done previously:

```
remove.packages(forrel) #This will remove the version 1.5.0 installed by default with mispitools
install.packages("devtools")
library(devtools)
::install_github("magnusdv/forrel") devtools
```

After this, please restart r session, and everything will work in the right way. If there is any doubt about the process do not hesitate in contact me: francol.marsico@gmail.com. If this step isnt done, some inconsistent results and error will appear. Please verify that version 1.4.1 is installed.

In this example, forrel and pedtools packages provides the scafold for pedigree definition and genetic profile simulations.The allele frequency database from Argentina is used, provided by mispitools.

```
library(mispitools)
library(pedtools)
library(forrel)
= mispitools::getfreqs(Argentina)[1:5]
freq = pedtools::linearPed(2)
x = pedtools::setMarkers(x, locusAttributes = freq)
x = forrel::profileSim(x, N = 1, ids = 2)
x plot(x, hatched = typedMembers(x))
```

Mispitools allows LR distributions simulations considering both, H1: UP is MP and H2: UP is not MP, as true, as follows:

`= simLRgen(x, missing = 5, 1000, 123) datasim `

Once obtained, false postive (FPR) and false negative rates (FNR) could be computed. This allows to calculate Matthews correlation coefficient (MCC) for a specific LR threshold (T):

`Trates(datasim, 10)`

`## [1] "FNR = 0.757 ; FPR = 0.005 ; MCC = 0.361063897416207"`

Likelihoold ratio distributions under both hypothesis, relatedness and unrelatedness could be plotted.

`LRdist(datasim, type = 2)`

Or other plotting option:

`LRdist(datasim, type = 1)`

Decision plot brings the posibility of analyzing FPR and FNR for each LR threshold. It could be obtained doing:

`deplot(datasim)`

This last plot show how different thresholds have different FNR and FPR values. The optimal (named decision threshold, DT) could be computed with the following command:

`DeT(datasim, 10)`

where 10 is the weight_1 (please see mispitools related papers on the top for further information)

NOTE: The methodology implemented in this section is explained in: http://dx.doi.org/10.2139/ssrn.4331033.

In this section we introduce a simple code for computing posterior odds of the genetic step. Prior Odds could be based on two models: (i) Preliminary investigation data based prior odds, or (ii) uniform prior odds. The first option assign a specific prior odds for each MP-UP pair, the second assigns the same. To see the documentation please run the following code:

` ?postSim`

As you can see, several parameters correspond to non-genetic LRs simulations, and datasim (output of simLRgen) is taken as the genetic LR simulations. With the following code we can calculate the posteriors of the example analyzed above.

```
<- postSim(
Postdata Prior = 0.01, PriorModel = "prelim",
datasim, eps = 0.05, erRs = 0.01, epc = Cmodel(),
erRc = Cmodel(), MPc = 1, epa = 0.05,
erRa = 0.01, MPa = 10, MPr = 2
)
LRdist(Postdata, type = 2)
```

You can compare it with the previous violing plot, elucidating the increasement in distribution separation. This would impact on performance metrics, that could be analyzed with the same function (Trates). Also, decision threshold could be setted for posterior odds.