Replisims Juan and Felix.Rmd

---
title: Replication Report @Brookhart2006
author1: Juan Claramunt\textsuperscript{1}, 
author2: Felix Clouth\textsuperscript{2}
organization1: Leiden University
organization2: Tilburg University
date: \today
params:
  iblue: 008080
  igray: d4dbde
documentclass: article
fontsize: 10
papersize: a4paper
bibliography      : ["My Collection.bib"]
output: 
  RepliSimReport:::replisim_report:
    keep_tex: TRUE
    latex_engine: xelatex
    resetStyleFiles: FALSE
header-includes: 
  - \newcommand{\iblue}{`r params$iblue`}
  - \newcommand{\igray}{`r params$igray`}
include-before:
  - \renewcommand{\contentsname}{Table of Contents}
  - \renewcommand{\pagename}{Page}
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup, include = FALSE}
# packages
library(dplyr)
library(knitr)
library(xtable)

load("ResultsEnvironment.RData")
# settings
knitr::opts_chunk$set(echo = FALSE, message = FALSE, warning = FALSE)
```

\urlstyle{same}

<!--ensure urls have the same style as the rest of the text-->

\maketitle

Replication Report, Brookhart et al. (2006)

\subsection*{Abstract}

In this document, we describe a replication study of "Variable Selection
for Propensity Score Models" by Brookhart et al. (Brookhart et al.
2006). This report includes an analysis of the data-generating
mechanism, simulation study set-up and methods described in the original
paper, the feasibility of its implementation based on the information
available in the original document and the results we were able to
replicate. Furthermore, we analyze whether the presentation of the
methods and results on the original paper can be improved. We were able to replicate the results of the first experiment of the original paper by making a few small assumptions. However, we were not able to replicate the results of experiment two. This was probably caused by a lack of explanation of certain concepts used on the article, the lack of experience of the authors of this report and the extra difficulty that requires replicating a figure instead of a table.

\vskip 2em

\noindent\makebox[\textwidth]{\large Correspondence concerning this replication report should be addressed to:}

\par

\noindent\makebox[\textwidth]{\large f.j.clouth@tilburguniversity.edu}

\par

\clearpage

\section{Introduction}

This replication report documents the replication attempt of the
simulation study @Brookhart2006. Following the definition of
@rougier_sustainable_2017-1 we understand the replication of a published
study as writing and running new code based on the description provided
in the original publication with the aim of obtaining the same results.
This replication study was independently done by another pair of
researchers. In the discussion section we will include an overview of
the common findings an differences.

\section{Method}

\subsection{Information basis}

This replication was conducted mainly on information provided in
@Brookhart2006. Software code or additional information (such as
supplementary materials) were not available. The addition of the open
source code (according to the original paper, it exists but it is not
published) will make the replication of the study much easier.
Additionally, we used information provided in the splines2 and ROCR
R-package documentation. However, this information was not referred to
in the main article.

\subsection{Data Generating Mechanism}

Information provided in the above mentioned sources indicated that the
following simulation factors were systematically varied in generating
the artificial data.

\subsubsection{Experiment 11}

+-------------+---+----------------------------------------------------+
| Simulation  | N | Levels                                             |
| factor      | o |                                                    |
|             | . |                                                    |
|             | l |                                                    |
|             | e |                                                    |
|             | v |                                                    |
|             | e |                                                    |
|             | l |                                                    |
|             | s |                                                    |
+=============+===+====================================================+
| *Varied*    |   |                                                    |
+-------------+---+----------------------------------------------------+
| Sample size | 2 | 500, 2500                                          |
+-------------+---+----------------------------------------------------+
| *Fixed*     |   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0.5                                                |
| $\alpha_{0}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 4                                                  |
| $\alpha_{1}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 1                                                  |
| $\alpha_{2}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0                                                  |
| $\alpha_{3}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0.5                                                |
| $\alpha_{4}$|   |                                                    |
+-------------+---+----------------------------------------------------+
| $\beta_{0}$ |   | 0                                                  |
+-------------+---+----------------------------------------------------+
| $\beta_{1}$ |   | 0.5                                                |
+-------------+---+----------------------------------------------------+
| $\beta_{2}$ |   | 0                                                  |
+-------------+---+----------------------------------------------------+
| $\beta_{3}$ |   | 0.75                                               |
+-------------+---+----------------------------------------------------+
| Dichotomous |   | sampled from rbern(N,                              |
| exposure A  |   | prob=pnorm($q=\beta_{0} + \beta_{1}*X_{1}+\beta_{2}*X_{2}+\beta_{3}*X_{3}$))|
|             |   |                                                    |
+-------------+---+----------------------------------------------------+
| Outcome Y   |   | sampled from rpois(N, lamda=$exp(\alpha_{0}+\alpha_{1}*(((1+exp(-3*X_{1}))^{-1})-0.5)+\alpha_{2}*X_{2}+\alpha_{3}*X_{3}+\alpha_{4}*A))$|
+-------------+---+----------------------------------------------------+
| Three       |   | independently sampled from rnorm(N, 0, 1)          |
| covariates  |   |                                                    |
+-------------+---+----------------------------------------------------+

\subsubsection{Experiment 1 (sensitivity analysis)}

+-------------+---+----------------------------------------------------+
| Simulation  | N | Levels                                             |
| factor      | o |                                                    |
|             | . |                                                    |
|             | l |                                                    |
|             | e |                                                    |
|             | v |                                                    |
|             | e |                                                    |
|             | l |                                                    |
|             | s |                                                    |
+=============+===+====================================================+
| *Varied*    |   |                                                    |
+-------------+---+----------------------------------------------------+
| Standard    | 2 | 0.5, 1.5                                           |
| deviation   |   |                                                    |
| of          |   |                                                    |
| covariates  |   |                                                    |
+-------------+---+----------------------------------------------------+
|             | 3 | 0.25, 0.5, 1                                       |
| $\alpha_{4}$|   |                                                    |
+-------------+---+----------------------------------------------------+
| $\beta_{0}$ | 2 | -1, 0                                              |
+-------------+---+----------------------------------------------------+
| *Fixed*     |   |                                                    |
+-------------+---+----------------------------------------------------+
| Sample size |   | 500                                                |
+-------------+---+----------------------------------------------------+
|             |   | 0.5                                                |
| $\alpha_{0}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 4                                                  |
| $\alpha_{1}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 1                                                  |
| $\alpha_{2}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0                                                  |
| $\alpha_{3}$|   |                                                    |
+-------------+---+----------------------------------------------------+
| $\beta_{1}$ |   | 0.5                                                |
+-------------+---+----------------------------------------------------+
| $\beta_{2}$ |   | 0                                                  |
+-------------+---+----------------------------------------------------+
| $\beta_{3}$ |   | 0.75                                               |
+-------------+---+----------------------------------------------------+
| Dichotomous |   | sampled from rbern(N,                              |
| exposure A  |   | prob=pnorm($q=\beta_{0} + \beta_{1}*X_{1}+\beta_{2}*X_{2}+\beta_{3}*X_{3}$)) |
+-------------+---+----------------------------------------------------+
| Outcome Y   |   | sampled from rpois(N, lamda=$exp(\alpha_{0}+*\alpha_{1}*(((1+exp(-3*X_{1}))^{-1})-0.5)+\alpha_{2}*X_{2}+\alpha_{3}*X_{3}+\alpha_{4}*A))$|
+-------------+---+----------------------------------------------------+

\subsubsection{Experiment 2}

+-------------+---+----------------------------------------------------+
| Simulation  | N | Levels                                             |
| factor      | o |                                                    |
|             | . |                                                    |
|             | l |                                                    |
|             | e |                                                    |
|             | v |                                                    |
|             | e |                                                    |
|             | l |                                                    |
|             | s |                                                    |
+=============+===+====================================================+
| *Varied*    |   |                                                    |
+-------------+---+----------------------------------------------------+
| Sample size | 2 | 500, 2500                                          |
+-------------+---+----------------------------------------------------+
|             | 2 | [0, .01, ..., .2]                                  |
| $\alpha_{1}$| 1 |                                                    |
+-------------+---+----------------------------------------------------+
| $\beta_{1}$ | 2 | [0, .05, ..., 1.25]                                |
|             | 6 |                                                    |
+-------------+---+----------------------------------------------------+
| *Fixed*     |   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0.5                                                |
| $\alpha_{0}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 1                                                  |
| $\alpha_{2}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0                                                  |
| $\alpha_{3}$|   |                                                    |
+-------------+---+----------------------------------------------------+
|             |   | 0.5                                                |
| $\alpha_{4}$|   |                                                    |
+-------------+---+----------------------------------------------------+
| $\beta_{0}$ |   | 0                                                  |
+-------------+---+----------------------------------------------------+
| $\beta_{2}$ |   | 0                                                  |
+-------------+---+----------------------------------------------------+
| $\beta_{3}$ |   | 0.75                                               |
+-------------+---+----------------------------------------------------+
| Three       |   | independently sampled from rnorm(N, 0, 1)          |
| covariates  |   |                                                    |
+-------------+---+----------------------------------------------------+
| Outcome Y   |   | sampled from                                       |
|             |   | rpois(exp($\alpha_{0}+\alpha_{1}*X_{1 }+\alpha_{2}*X_{2}+\alpha_{3}*X_{3}+\alpha_{4}*A$))            |
|             |   |                                                    |
+-------------+---+----------------------------------------------------+
| Dichotomous |   | sampled from rbern(N,                              |
| exposure A  |   | prob=pnorm($q=\beta_{0} + \beta_{1}*X_{1}+\beta_{2}*X_{2}+\beta_{3}*X_{3}$))                         |
+-------------+---+----------------------------------------------------+

The design was full-factorial in the main analyses of Experiment 1 and
Experiment 2. For the sensitivity analyses of Experiment 1, all
parameters were held at their default values while a single parameter
was altered.

\subsection{Research Comparison}

The study compares different specifications of a propensity scores (PS)
model using a Monte-Carlo simulation. The model examines the effects of
the inclusion of three types of covariates: X1 (a true confounder), X2
(a predictor of the outcome) or X3 (a variable related to the exposure
but not the outcome).

The exposure effects are estimated using two methods: (1) by adjusting
for the PS in a multivariate outcome model in which the effect of the
estimated PS was modeled through a regression spline. In this case, the
propensity score model fit is given by the following formula:

$$
E[Y|\hat{PS},A] = exp \{ \lambda + \sum_k \psi_k B_k(\hat{PS}) + \gamma A \}
$$

where $\lambda$ is the baseline rate, $B_k$ are B-spline basis
functions and $\gamma$ is the treatment effect. (2) Using
subclassification in which strata are defined by quintiles of the
estimated propensity scores and taking the average treatment effect
across strata.

\subsection{Performance measures}

To measure the performance of the different specifications of the PS
models of the original simulation study, the authors measured the bias,
the variance and the mean square error of the estimates of the parameter
$\alpha_{4}$ and the average C-stat.

\subsection{Technical implementation}

While the original simulation study was carried out in R version 1.9.1
running on a Windows XP platform, our replication was implemented using
the R programming environment version 4.0.3 on a Windows 10 environment
(details regarding software versions can be obtained from the section
Reproducibility Information). The corresponding R code can be obtained
from <https://github.com/replisims/your_repo>. 
<!-- Add zenodo doi once obtained MISSING-->

The following table provides an overview of replicator degrees of
freedom, i.e. decisions that had to be made by the replicators because
of insufficient or contradicting information. Issues were resolved by
discussion among the replicators. Decisions were based on what the
replicators perceived to be the most likely implementation with
likeliness estimated by common practice and/or guideline
recommendations. Wherever feasible multiple interpretations where
implemented.



+-------------------------+-------------------------+------------------+
| Issue                   | Replicator decision     | Justification    |
+=========================+=========================+==================+
| It was not clear        | Estimate the PS         | It should result |
| whether to estimate the |                         | in a better fit  |
| PS or to calculate them |                         | for each         |
| from the population     |                         | simulated        |
| model                   |                         | dataset.         |
+-------------------------+-------------------------+------------------+
| The implementation of   | We used the function    | Only available   |
| the cubic spline        | bs() in splines         | function in R.   |
| estimation was not      |                         | We used the      |
| clearly explained.      | package, with           | default options. |
| Moreover, the reference | specifying three        |                  |
| included does not       |                         |                  |
| provide enough insight  | knots splines::bs(PS,   |                  |
|                         | knots =                 |                  |
|                         |                         |                  |
|                         | quantile(PS, probs =    |                  |
|                         | c(0.25, 0.5,            |                  |
|                         |                         |                  |
|                         | 0.75)))                 |                  |
+-------------------------+-------------------------+------------------+
| Subclassification       | We used the mean as     | It is the most   |
| approach not fully      | estimator               | reasonable       |
| defined. Not clear how  |                         | choice.          |
| to obatin the estimates |                         |                  |
| of the exposure rate    |                         |                  |
| within strata.          |                         |                  |
+-------------------------+-------------------------+------------------+
| No description of       | Hmisc::somers2(PS,      | Most likely      |
| c-statistic             |                         | meaning of the   |
|                         | data[,"exposure"])["C"] | c-statistic.     |
|                         |                         | Most common R    |
|                         |                         | package to       |
|                         |                         | compute the area |
|                         |                         | under the ROC    |
|                         |                         | curve.           |
+-------------------------+-------------------------+------------------+
| Some values required    | Used the same values we | If the values    |
| for experiment 2 were   | used in experiment 1    | are omitted, the |
| missing                 |                         | most likely      |
|                         |                         | reason is that   |
|                         |                         | the values are   |
|                         |                         | the same for     |
|                         |                         | both             |
|                         |                         | experiments.     |
+-------------------------+-------------------------+------------------+
| Definition and scales   | No solution             |                  |
| of the variables        |                         |                  |
| measured in the axes of |                         |                  |
| the figures of          |                         |                  |
| experiment 2 were not   |                         |                  |
| clearly described.      |                         |                  |
+-------------------------+-------------------------+------------------+
| Estimators of           | Use the estimators of   | It is the most   |
| experiment 2 were not   | experiment 1 that       | reasonable       |
| clearly explained.      | fitted better the brief | choice.          |
|                         | explanation             |                  |
+-------------------------+-------------------------+------------------+
| According to the        | No solution             |                  |
| Methods section, the PS |                         |                  |
| was adjusted using the  |                         |                  |
| spline function in      |                         |                  |
| experiment 2. However,  |                         |                  |
| in the results section  |                         |                  |
| we can find the         |                         |                  |
| quintile approach as    |                         |                  |
| well.                   |                         |                  |
+-------------------------+-------------------------+------------------+

\subsection{C-statistic issue}

In a first version of the original paper we were trying to replicate, it
was not specified what the *c* statistic mean. Therefore, it was not
clear what measure we were replicating nor how we were supposed to do
so. In latter versions, it is stated that the *c*-statistics they use in
this research is the area under the receiver operating characteristic
(ROC) curve.

\subsection{Experiment 2 issue}

Whilw trying to replicate the results of the second experiment we found
multiple issues. First, they use multiple transformation of the results
that are not defined in the paper. Second, it is far more difficult to compare the results obtained in a graph than in a table. While we could easily check that the results we obtained for experiment 1 were exactly the same as the results obtained in the original paper, it was incredibly difficult to do the same with experiment 2. Furthermore, there is no open code available to replicate these figures. These difficulties did not allow us to replicate the figures of experiment 2.

\section{Results} 

\subsection{Experiment 1}
In this section we show the tables we obtain during the replication of experiment 1.

```{=tex}
\begin{table}
\caption{Table 1. Simulation experiment 1, with results based on an analysis in which the propensity score is entered into an outcome model as a parametric spline term.}
\begin{tabular}{l r r r r r r r r}
\hline
\multicolumn{8}{c}{Variable(s) in propensity score model}\\
\hline
  & $X_{1}$ & $X_{2}$ & $X_{3}$ & $X_{1}$, $X_{2}$ & $X_{1}$, $X_{3}$ & $X_{2}$, $X_{3}$ & $X_{1}$, $X_{2}$, $X_{3}$ & None\\
\hline
n = 500\\

Bias & 0.008 & 0.601 & 0.744 & 0.006 & 0.007 & 0.744 & 0.006 & 0.599\\

Variance & 0.030 & 0.025 & 0.047 & 0.020 & 0.040 & 0.038 & 0.030 & 0.040\\

MSE & 0.030 & 0.386 & 0.600 & 0.020 & 0.040 & 0.591 & 0.030 & 0.398\\

avg c-stat & 0.67 & 0.52 & 0.76 & 0.67 & 0.82 & 0.76 & 0.82 & \\

n = 2500\\

Bias & 0.008 & 0.601 & 0.744 & 0.006 & 0.007 & 0.744 & 0.006 & 0.592\\

Variance & 0.030 & 0.025 & 0.047 & 0.020 & 0.040 & 0.038 & 0.030 & 0.009\\

MSE & 0.030 & 0.386 & 0.600 & 0.020 & 0.040 & 0.591 & 0.030 & 0.359\\

avg c-stat & 0.67 & 0.51 & 0.76 & 0.67 & 0.81 & 0.76 & 0.81 & \\
\hline
\end{tabular}
\end{table}
```


```{=tex}
\begin{table}
\caption{Table 2. Simulation experiment 1, with results based on an analysis using
subclassification in which strata are defined by quintiles of the estimated propensity
score.}
\begin{tabular}{l r r r r r r r r}
\hline
\multicolumn{8}{c}{Variable(s) in propensity score model}\\
\hline
  & $X_{1}$ & $X_{2}$ & $X_{3}$ & $X_{1}$, $X_{2}$ & $X_{1}$, $X_{3}$ & $X_{2}$, $X_{3}$ & $X_{1}$, $X_{2}$, $X_{3}$ & None\\
\hline
n = 500\\

Bias & 0.027 & 0.607 & 0.802 & 0.030 & 0.037 & 0.801 & 0.033 & 0.599\\

Variance & 0.022 & 0.018 & 0.050 & 0.016 & 0.048 & 0.039 & 0.038 & 0.040\\

MSE & 0.023 & 0.386 & 0.693 & 0.016 & 0.050 & 0.680 & 0.039 & 0.398\\

n = 2500\\

Bias & 0.029 & 0.597 & 0.763 & 0.029 & 0.063 & 0.762 & 0.061 & 0.592\\

Variance & 0.004 & 0.003 & 0.011 & 0.003 & 0.012 & 0.009 & 0.010 & 0.009\\

MSE & 0.005 & 0.360 & 0.594 & 0.004 & 0.016 & 0.589 & 0.014 & 0.359\\
\hline
\end{tabular}
\end{table}
```

```{=tex}
\begin{table}
\caption{Table 3. Sensitivity analysis of simulation study 1. We consider nine different perturbations of the simulation parameters. Results are from 1,000 simulations of
data (n = 500), using a parametric spline to adjust for the estimated propensity score.}
\begin{tabular}{l r r r r r r r r}
\hline
\multicolumn{8}{c}{Variable(s) in propensity score model}\\
\hline
  & $X_{1}$ & $X_{2}$ & $X_{3}$ & $X_{1}$, $X_{2}$ & $X_{1}$, $X_{3}$ & $X_{2}$, $X_{3}$ & $X_{1}$, $X_{2}$, $X_{3}$ & None\\
\hline
std1 = 0.5\\
Bias & -0.003 & 0.281 & 0.364 & -0.006 & -0.001 & 0.360 & -0.005 & 0.278\\

Variance & 0.031 & 0.021 & 0.047 & 0.021 & 0.041 & 0.037 & 0.029 & 0.037\\

MSE & 0.031 & 0.101 & 0.180 & 0.021 & 0.041 & 0.166 & 0.029 & 0.115\\

std1 = 1.5\\
Bias & 0.008 & 0.855 & 1.009 & 0.007 & 0.004 & 1.013 & 0.008 & 0.847\\

Variance & 0.033 & 0.028 & 0.048 & 0.024 & 0.046 & 0.040 & 0.035 & 0.041\\

MSE & 0.033 & 0.759 & 1.066 & 0.024 & 0.046 & 1.066 & 0.035 & 0.759\\

std2 = 0.5\\
Bias & 0.003 & 0.595 & 0.738 & -0.001 & 0.001 & 0.734 & -0.004 & 0.599\\

Variance & 0.007 & 0.015 & 0.020 & 0.005 & 0.011 & 0.018 & 0.009 & 0.017\\

MSE & 0.007 & 0.369 & 0.564 & 0.005 & 0.011 & 0.557 & 0.009 & 0.376\\

std2 = 1.5\\
Bias & 0.015 & 0.602 & 0.751 & 0.014 & 0.019 & 0.748 & 0.014 & 0.586\\

Variance & 0.106 & 0.055 & 0.146 & 0.090 & 0.147 & 0.122 & 0.121 & 0.137\\

MSE & 0.106 & 0.418 & 0.710 & 0.090 & 0.147 & 0.680 & 0.121 & 0.480\\

std3 = 0.5\\
Bias & -0.003 & 0.698 & 0.732 & -0.004 & -0.002 & 0.732 & -0.003 & 0.691\\

Variance & 0.032 & 0.025 & 0.045 & 0.022 & 0.038 & 0.035 & 0.027 & 0.041\\

MSE & 0.032 & 0.512 & 0.581 & 0.022 & 0.038 & 0.571 & 0.027 & 0.518\\

std3 = 1.5\\
Bias & -0.001 & 0.495 & 0.734 & -0.004 & -0.006 & 0.734 & -0.008 & 5.07\\

Variance & 0.027 & 0.022 & 0.055 & 0.021 & 0.049 & 0.044 & 0.037 & 0.041\\

MSE & 0.028 & 0.267 & 0.593 & 0.021 & 0.049 & 0.582 & 0.038 & 0.518\\

a4 = 0.25\\
Bias & -0.004 & 0.593 & 0.731 & 0.000 & -0.007 & 0.737 & 0.000 & 0.600\\

Variance & 0.032 & 0.025 & 0.049 & 0.023 & 0.044 & 0.039 & 0.033 & 0.040\\

MSE & 0.032 & 0.377 & 0.583 & 0.023 & 0.044 & 0.582 & 0.033 & 0.399\\

a4 = 1\\
Bias & 0.004 & 0.601 & 0.735 & 0.005 & 0.004 & 0.735 & 0.005 & 0.597\\

Variance & 0.033 & 0.027 & 0.052 & 0.023 & 0.047 & 0.042 & 0.035 & 0.040\\

MSE & 0.033 & 0.387 & 0.592 & 0.023 & 0.047 & 0.582 & 0.035 & 0.397\\

b0 = 1\\
Bias & -0.012 & 0.562 & 0.687 & -0.010 & -0.015 & 0.690 & -0.012 & 0.575\\

Variance & 0.034 & 0.021 & 0.052 & 0.022 & 0.047 & 0.039 & 0.032 & 0.041\\

MSE & 0.035 & 0.337 & 0.525 & 0.022 & 0.047 & 0.515 & 0.032 & 0.372\\
\hline
\end{tabular}
\end{table}
```

\subsection{Experiment 2}

We were not able to replicate the figures of experiment 2.

\FloatBarrier

\section{Discussion}

\subsection{Replicability}

In general, the data-generating mechanism is easy to replicate. It is clearly described in the original paper and it can be easily coded. Also, experiment 1 can be replicated with only a few replication degrees of freedom. However, availability of open source code will improve its replicability. The initial lack of explanation for the c-statistic or the issue with the model with splines could have been solved easily if the code was available.
Experiment two is more difficult to replicate, or, at least, the figures on the paper. The model estimation and the computation of the measures are similar to experiment one. However, once these results are obtained, it is necessary to use some transformations that are not explained at all in the paper. Also, as stated previously, replicating a complex figure is not an easy task.In fact, we were not able to do so. The fact that we were not able to replicate experiment 2 does not mean that it is not possible. It is likely that more experienced researchers in the field would be able to replicate experiment 2.

\subsection{Replicator degrees of freedom} 

In experiment 1, we needed to guess some concepts due to the lack of information on the article. However, the choices were straightforward and it we were able to replicate the experiment.
In experiment 2, the lack of information about some concepts and scales did not allow us to replicate the experiment. Probably, when writing the paper the authors addressed an audience with a higher experience in the field than the authors of this report. However, it is always a good practice to write a paper as self-explanatory as possible. This will help reaching a wider audience and reduce the replicator degrees of freedom. At the same time, these technical details are not relevant for understanding the main concept or the message the authors want to present. They are mainly necessary for the purpose of replication.


\subsection{Equivalence of results} 

The equivalence of results in experiment 1 is extremely good. Despite using a different R version and code, we were able to obtain very similar same tables.
We cannot judge the results of experiment 2 because we were not able to obtain the same figures. 

\section{Comparison with other pair performing the same replication study} 

The other pair was able to perform an even more successful replication. Both groups were able to replicate experiment 1 with similar issues that we solved similarly yet independently. On the other hand, the other pair was able to replicate figure 2 and figure 3 from the original paper and almost able to replicate figure 4.

A discussion between both groups leaded to the following conclusions:

The order in which the method, measures and results are presented in the paper can be improved in order to facilitate the understanding and replicability of the research.

The original paper omit some basic information assuming it is common knowledge. However, we do not consider it common knowledge. This fact could explain why one of the groups was able to replicate more than the other. Actually, in latter versions of the paper they included explanations of some concepts (e.g. meaning of c-statistic).

The first experiment is explained with more detail, which makes it easier to replicate. On the other hand, both groups consider that experiment two contains some concepts that are not fully explained, which hurts its replicability.

Both groups consider that the original code of the research could be available publicly since it is coded in an open source programming laguage (R), and it does not require new functions that could be under copyrigth. Publishing the code will improve the replicability and transparency of the research.  

\section{Contributions}

Authors made the following contributions according to the CRediT
framework <https://casrai.org/credit/>

Primary Replicator:

-   Data Curation\
-   Formal Analysis (supporting)\
-   Investigation\
-   Software\
-   Visualization (lead)\
-   Writing - Original Draft Preparation\
-   Writing - Review & Editing

Co-Pilot:

-   Formal Analysis (lead)\
-   Investigation\
-   Software (supporting)\
-   Visualization (supporting)\
-   Validation\
-   Writing - Review & Editing

\newpage

```{=tex}
\section*{References}
\begingroup
\hphantom{x}
\setlength{\parindent}{-0.5in}
\setlength{\leftskip}{0.5in}
```
::: {#refs custom-style="Bibliography"}
:::

```{=tex}
\FloatBarrier
\endgroup
\newpage
```
\section\*{Appendix}

\subsection{Code organization}

The code and the files associated are organized in the form of a
research compendium which can be found in the following git repository
`https://github.com/replisims/Brookhart-2006-FJ`

```{r code_structure, cache = FALSE}
# which R packages and versions?
if ("fs" %in% installed.packages()) fs::dir_tree(path = ".", recurse = TRUE)
```


\subsubsection\*{Reproducibility Information}

This report was last updated on `r Sys.time()`. The simulation
replication was conducted using the following computational environment
and dependencies:

\FloatBarrier

```{r colophon, cache = FALSE}
# which R packages and versions?
if ("devtools" %in% installed.packages()) devtools::session_info()
```

The current Git commit details are:

```{r git}
# what commit is this file at? 
if ("git2r" %in% installed.packages() & git2r::in_repository(path = ".")) git2r::repository(here::here())  
```