fix bibtex issues in ref; catch redundant labeling

tlverse · Jul 6, 2023 · f273201 · f273201
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diff --git a/04-roadmap.Rmd b/04-roadmap.Rmd
@@ -27,19 +27,18 @@ the choice of statistical model, selecting a statistical target parameter that
 represents an answer to the scientific question of interest, and developing
 efficient estimators of the statistical estimand.
 
-## The Roadmap {#roadmap}
+## The Roadmap {#roadmap-steps}
 
 The roadmap is a six-stage process:
 
 1. Define the data as a random variable with a probability distribution, $O \sim
    P_0$
 2. Specify the statistical model $\M$ realistically, such that $P_0 \in \M$
 3. Translate the scientific question of interest into a statistical target
-   parameter $\Psi$ and establish the target population 
+   parameter $\Psi$ and establish the target population
 4. Choose an estimator $\hat{\Psi}$ for $\Psi$ under realistic $\M$
 5. Construct a measure of uncertainty for the estimate $\hat{\Psi}(P_n)$
-6. Make substantive conclusion 
-
+6. Make substantive conclusion
 
 ### (1) Data: A random variable with a probability distribution, $O \sim P_0$ {-}
 
@@ -502,35 +501,37 @@ well known causal parameter that is most often called the "average treatment
 effect" (ATE) and is denoted
 
 \begin{equation}
-  ATE = \E_X(Y(1) - Y(0)),
+  ATE = \E_X[Y(1) - Y(0)],
   (\#eq:ate)
 \end{equation}
-where $\E_X$ is the mean under the theoretical (unobservable) full data 
-$X = (W, Y(1), Y(0))$. Note that the full data structure $X$ is, by its very
-definition, unobservable since one can never observe both of $Y(1)$ and $Y(0)$
-for the same observational unit.
-
-We can define much more complicated interventions on SCMs, such as
-interventions based upon dynamic rules (which assign particular interventions
-based on a function of the covariates $W$), stochastic rules (which can even 
-account for the natural value of $A$ observed in the absence of the 
-intervention), and much more. Each results in a different target causal 
-parameter and entails different identifiability assumptions discussed below.
+where $\E_X(\cdot)$ is the expectation taken over the theoretical (unobservable)
+full data (i.e., $X = (W, Y(1), Y(0))$) distribution $P_X$. Note that the full
+data structure $X$ is, by its very definition, unobservable since one can never
+observe both of $Y(1)$ and $Y(0)$ for the same observational unit.
+
+We can define much more complicated interventions on SCMs, such as interventions
+based upon dynamic rules (which assign particular interventions based on a
+function of the covariates $W$), stochastic rules (which can even account for
+the natural value of $A$ observed in the absence of the intervention), and much
+more. Each results in a different target causal parameter and entails different
+identifiability assumptions discussed below.
 
 ### Identifiability {-}
 
-Since we can never observe both $Y(0)$ (the counterfactual outcome when $A=0$)
-and $Y(1)$ (similarly, the counterfactual outcome when $A=1$), we cannot
-estimate the quantity in Equation \@ref(eq:ate) directly. This is called the
-_Fundamental Problem of Causal Inference_ [@holland1986statistics]. Thus, one of
-the primary activities in causal inference is to _identify_ the assumptions
-necessary to express causal quantities of interest as functions of the
-data-generating distribution of the observed data. To do this, we must make
-assumptions under which such quantities may be estimated from the observed data
-$O \sim P_0$ and its corresponding data-generating distribution $P_0$.
-Fortunately, given the causal model specified in the SCM above, we can, with a
-handful of untestable assumptions, estimate the ATE from observational data.
-These assumptions may be summarized as follows.
+Since we can never simultaneously observe $Y(0)$, the counterfactual outcome
+when $A=0$, and $Y(1)$, the counterfactual outcome when $A=1$, we cannot
+estimate their difference $Y(1) - Y(0)$ (the individual treatment effect), which
+appears in Equation \@ref(eq:ate) (inside the expectation $\E_X(\cdot)$ that
+defines ATE). This is called the _Fundamental Problem of Causal Inference_
+[@holland1986statistics]. Thus, one of the primary activities in causal
+inference is to _identify_ the assumptions necessary to express causal
+quantities of interest as functions of the data-generating distribution of the
+observed data. To do this, we must make assumptions under which such quantities
+may be estimated from the observed data $O \sim P_0$ and its corresponding
+data-generating distribution $P_0$. Fortunately, given the causal model
+specified in the SCM above, we can, with a handful of untestable assumptions,
+estimate the ATE from observational data. These assumptions may be summarized as
+follows.
 
 ::: {#consist-ass .definition name="Consistency"}
 The outcome for unit $i$ is $Y_i(a)$ whenever $A_i = a$, which may be thought of
@@ -551,27 +552,27 @@ experiments, ensuring that the effect of $A$ on $Y$ can be disentangled from
 that of $W$ on $Y$, even though $W$ affects both.
 :::
 
-::: {#posit-ass .definition name="Positivity (or Overlap)"}
+::: {#posit-ass .definition name="Positivity/Overlap"}
 All observed units, across strata defined by $W$, must have a bounded
-(non-deterministic) probability of receiving treatment -- that is,
-$\epsilon < \P(A = a \mid W) < 1 - \epsilon$ for all $a$ and $W$ and for some
-$\epsilon > 0$) \ .
+probability of receiving treatment -- that is, $\epsilon < \P(A = a \mid W) < 1
+- \epsilon$ for all $a$ and $W$ and for some $\epsilon > 0$) \ .
 :::
 
 Technically speaking, only the latter two of these assumptions are necessary
 when working within the SCM framework, as the first two are implied properties
 of an SCM for i.i.d. data (if you're really curious, see this commentary of
-@pearl2010brief for an extended philosophical discussion). We introduce all four
+@pearl2010brief for an extended discussion). We introduce all four
 identification assumptions because they are most often considered together, and
-all four are necessary when working within the potential outcomes framework.
+all four are necessary when working within the potential outcomes framework
+[@rubin2005causal; @imbens2015causal].
 
-Given these assumptions, the ATE may be re-written as a function of $P_0$ --
-specifically
+Under these assumptions, the ATE may be re-written as a function of $P_0$, the
+distribution of the observed data:
 
 \begin{align}
-  \psi_{\text{ATE}} &= \E_0(Y(1) - Y(0)) \\ \nonumber
-                    &= \E_0 \left(\E_0[Y \mid A = 1, W] -
-                       \E_0[Y \mid A = 0, W]\right) \ .
+  \psi_{\text{ATE}} &= \E_0[Y(1) - Y(0)] \\ \nonumber
+                    &= \E_0 [\E_0[Y \mid A = 1, W] -
+                       \E_0[Y \mid A = 0, W]] \ .
   (\#eq:estimand)
 \end{align}
 In words, the ATE is the mean difference in the predicted outcome values for

diff --git a/book.bib b/book.bib
@@ -19,7 +19,7 @@ @article{holland1986statistics
 @book{fisher1946statistical,
   title={Statistical Methods for Research Workers},
   author={Fisher, Ronald Aylmer},
-  number={10\textsuperscript{th} ed.},
+  edition={10\textsuperscript{th}},
   year={1946},
   publisher={Oliver and Boyd}
 }
@@ -139,17 +139,6 @@ @book{pearl2009causality
   publisher={Cambridge University Press}
 }
 
-@article{holland1986statistics,
-  title={Statistics and causal inference},
-  author={Holland, Paul W},
-  journal={Journal of the American statistical Association},
-  volume={81},
-  number={396},
-  pages={945--960},
-  year={1986},
-  publisher={Taylor \& Francis}
-}
-
 @article{rosenbaum1983central,
   title={The central role of the propensity score in observational studies for
     causal effects},
@@ -765,14 +754,13 @@ @article{hejazi2021nonparametric
   author = {Hejazi, Nima S and Rudolph, Kara E and {van der Laan}, Mark J and
     D{\'\i}az, Iv{\'a}n},
   year = {2022},
-  doi = {10.1093/biostatistics/kxac002},
-  url = {https://arxiv.org/abs/2009.06203},
-  year = {2022},
-  publisher = {Oxford University Press},
   journal = {Biostatistics},
   volume = {(in press)},
   number = {},
-  pages = {}
+  pages = {},
+  publisher = {Oxford University Press},
+  url = {https://arxiv.org/abs/2009.06203},
+  doi = {10.1093/biostatistics/kxac002}
 }
 
 @article{tchetgen2013inverse,
@@ -1009,47 +997,52 @@ @Article{bembom2007realistic
 }
 
 @article{montoya2021optimal,
-  title={The Optimal Dynamic Treatment Rule {SuperLearner}: Considerations,
-    Performance, and Application},
-  author={Montoya, Lina and {van der Laan}, Mark J and Luedtke, Alexander and
-    Skeem, Jennifer and Coyle, Jeremy and Petersen, Maya},
-  year={2021},
-  eprint={2101.12326},
-  archivePrefix={arXiv},
-  primaryClass={stat.AP}
+  title={The optimal dynamic treatment rule superlearner: considerations,
+    performance, and application to criminal justice interventions},
+  author={Montoya, Lina M and {van der Laan}, Mark J and Luedtke, Alexander R
+    and Skeem, Jennifer L and Coyle, Jeremy R and Petersen, Maya L},
+  journal={The International Journal of Biostatistics},
+  volume={19},
+  number={1},
+  pages={217--238},
+  year={2023},
+  publisher={De Gruyter},
+  doi={10.1515/ijb-2020-0127}
 }
 
 @article{montoya2021performance,
-  title={Performance and Application of Estimators for the Value of an
-    Optimal Dynamic Treatment Rule},
-  author={Montoya, Lina and Skeem, Jennifer and {van der Laan}, Mark and
-    Petersen, Maya},
-  year={2021},
-  eprint={2101.12333},
-  archivePrefix={arXiv},
-  primaryClass={stat.ME}
+  title={Estimators for the value of the optimal dynamic treatment rule with
+    application to criminal justice interventions},
+  author={Montoya, Lina M and {van der Laan}, Mark J and Skeem, Jennifer L and
+    Petersen, Maya L},
+  journal={The International Journal of Biostatistics},
+  volume={19},
+  number={1},
+  pages={239--259},
+  year={2023},
+  publisher={De Gruyter},
+  doi={10.1515/ijb-2020-0128}
 }
 
 @Article{luedtke2016resource,
-   Author={Luedtke, Alexander R  and {van der Laan}, Mark J},
-   Title={Optimal individualized treatments in resource-limited settings},
-   Journal={International Journal of Biostatisics},
-   Year={2016},
-   Volume={12},
-   Number={1},
-   Pages={283--303},
-   Month={05}
+  Title={Optimal individualized treatments in resource-limited settings},
+  Author={Luedtke, Alexander R  and {van der Laan}, Mark J},
+  Journal={The International Journal of Biostatisics},
+  Volume={12},
+  Number={1},
+  Pages={283--303},
+  Year={2016},
+  publisher={De Gruyter},
+  doi={10.1515/ijb-2015-0007}
 }
 
 @phdthesis{hejazi2021semiparametric,
   title = {Semiparametric statistical methods for causal inference with
     stochastic treatment regimes},
   school = {University of California, Berkeley},
   author = {Hejazi, Nima S},
-  author+an = {1=highlight},
   year = {2021},
   url = {https://www.stat.berkeley.edu/~nhejazi/publications/thesis-phd-biostat.pdf},
-  keywords = {theses}
 }
 
 @article{stock1989nonparametric,
@@ -1265,66 +1258,75 @@ @article{naimi2018stacked
 }
 
 @article{rvp2022super,
-  doi = {10.48550/ARXIV.2204.06139},
-  url = {https://arxiv.org/abs/2204.06139},
-  author = {Phillips, Rachael V and {van der Laan}, Mark J and Lee, Hana and
+  title={Practical considerations for specifying a super learner},
+  author={Phillips, Rachael V and van der Laan, Mark J and Lee, Hana and
     Gruber, Susan},
-  title = {Practical considerations for specifying a super learner},
-  publisher = {arXiv},
-  year = {2022}
+  journal={International Journal of Epidemiology},
+  volume={},
+  pages={},
+  year={2023},
+  publisher={Oxford University Press},
+  doi={10.1093/ije/dyad023}
 }
 
-@Manual{SuperLearner,
- title = {SuperLearner: Super Learner Prediction},
- author = {Eric Polley and Erin LeDell and Chris Kennedy and Mark
-   {van der Laan}},
+@manual{SuperLearner,
+ title = {{\texttt{SuperLearner}}: Super Learner Prediction},
+ author = {Polley, Eric and LeDell, Erin and Kennedy, Chris and {van der Laan},
+   Mark},
  year = {2021},
- note = {R package version 2.0-28},
+ note = {\texttt{R} package version 2.0-28},
  url = {https://CRAN.R-project.org/package=SuperLearner},
 }
 
-@software{coyle-cran-origami,
-  doi = {10.5281/zenodo.835602},
-  url = {https://CRAN.R-project.org/package=origami},
-  note = {{\texttt{R}} package with \input{./metrics/downloads_origami.txt}},
-  version = {1.0.5},
+@manual{coyle-cran-origami,
+  title = {{\texttt{origami}}: Generalized framework for cross-validation}
   author = {Coyle, Jeremy R and Hejazi, Nima S and Malenica, Ivana and
     Phillips, Rachael V},
-  author+an = {2=highlight},
-  title = {{\texttt{origami}}: Generalized framework for cross-validation},
-  keywords = {software-pkg}
+  note = {\texttt{R} package version 1.0.5},
+  doi = {10.5281/zenodo.835602},
+  url = {https://CRAN.R-project.org/package=origami}
 }
 
 @incollection{kennedy2016semiparametric,
   title={Semiparametric theory and empirical processes in causal inference},
   author={Kennedy, Edward H},
-  booktitle={Statistical causal inferences and their applications in public health research},
+  booktitle={Statistical Causal Inferences and Their Applications in Public
+    Health Research},
   pages={141--167},
   year={2016},
   publisher={Springer}
 }
 
 @article{diaz2013sensitivity,
-  title={Sensitivity analysis for causal inference under unmeasured confounding and measurement error problems},
-  author={D{\'\i}az, Iv{\'a}n and van der Laan, Mark J},
-  journal={The international journal of biostatistics},
+  title={Sensitivity analysis for causal inference under unmeasured confounding
+    and measurement error problems},
+  author={D{\'\i}az, Iv{\'a}n and {van der Laan}, Mark J},
+  journal={The International Journal of Biostatistics},
   volume={9},
   number={2},
   pages={149--160},
   year={2013},
-  publisher={De Gruyter}
+  publisher={De Gruyter},
+  doi={10.1515/ijb-2013-0004}
 }
 
 @article{gruber2022targeted,
-  title={Targeted learning: Towards a future informed by real-world evidence},
-  author={Gruber, Susan and Phillips, Rachael V and Lee, Hana and Ho, Martin and Concato, John and van der Laan, Mark J},
-  journal={arXiv preprint arXiv:2205.08643},
-  year={2022}
+  title={{Targeted Learning}: Toward a Future Informed by Real-World Evidence},
+  author={Gruber, Susan and Phillips, Rachael V and Lee, Hana and Ho, Martin
+    and Concato, John and {van der Laan}, Mark J},
+  journal={Statistics in Biopharmaceutical Research},
+  volume={},
+  number={},
+  pages={},
+  year={2023},
+  publisher={Taylor \& Francis},
+  doi={10.1080/19466315.2023.2182356}
 }
 
 @article{gruber2022evaluating,
   title={Evaluating and improving real-world evidence with Targeted Learning},
-  author={Gruber, Susan and Phillips, Rachael V and Lee, Hana and Concato, John and van der Laan, Mark},
+  author={Gruber, Susan and Phillips, Rachael V and Lee, Hana and Concato, John
+    and {van der Laan}, Mark},
   journal={arXiv preprint arXiv:2208.07283},
   year={2022}
-}
+}