Proximal Causal Inference With Text Data
Authors: Jacob M. Chen
Rohit Bhattacharya
Katherine A. Keith
Venue: NeurIPS 2024 poster (2024)
Keywords: proximal causal inference
directed acyclic graphs
electronic health records
causal inference
Primary area: causal_inference
TL;DR: We propose a new causal inference method that infers valid proxies from unstructured text data for proximal causal inference.

Abstract: Recent text-based causal methods attempt to mitigate confounding bias by estimating proxies of confounding variables that are partially or imperfectly measured from unstructured text data. These approaches, however, assume analysts have supervised labels of the confounders given text for a subset of instances, a constraint that is sometimes infeasible due to data privacy or annotation costs. In this work, we address settings in which an important confounding variable is completely unobserved. We propose a new causal inference method that uses two instances of pre-treatment text data, infers two proxies using two zero-shot models on the separate instances, and applies these proxies in the proximal g-formula. We prove, under certain assumptions about the instances of text and accuracy of the zero-shot predictions, that our method of inferring text-based proxies satisfies identification conditions of the proximal g-formula while other seemingly reasonable proposals do not. To address untestable assumptions associated with our method and the proximal g-formula, we further propose an odds ratio falsification heuristic that flags when to proceed with downstream effect estimation using the inferred proxies. We evaluate our method in synthetic and semi-synthetic settings---the latter with real-world clinical notes from MIMIC-III and open large language models for zero-shot prediction---and find that our method produces estimates with low bias. We believe that this text-based design of proxies allows for the use of proximal causal inference in a wider range of scenarios, particularly those for which obtaining suitable proxies from structured data is difficult.

Proximal Causal Inference with Text Data
Jacob M. Chen Department of Computer Science
Rohit Bhattacharya Department Computer Science Williams College rb1 7@wi 1liams, edu
Johns Hopkins University jchen459ejhu.cm edu
Katherine Keith
Department of Computer Science
Williams College kak5@wi 1liams,,.. edu
Abstract
Recent text-based causal methods attempt to mitigate confounding bias by esti- mating proxies of confounding variables that are partially or imperfectly measured from unstructured text data. These approaches, however, assume analysts have pervised labels of the confounders given text for a subset of instances, a constraint that is sometimes infeasible due to data privacy annotation costs. In this work, we address settings in which an important confounding variable is completely unobserved. We propose of pre-treatment text data, infers two proxies using two zero-shot models on the separate instances, and applies these proxies in the proximal g-formula. We prove, under certain assumptions about the instances of text and accuracy of the zero-shot predictions, that method of inferring text-based proxies satisfies identification conditions of the proximal g-formula while other seemingly reasonable proposals do not. To address untestable assumptions associated with our method and the proximal g-formula, we further propose an odds ratio falsification heuristic that flags when proceed with downstream effect estimation using the inferred proxies. We evaluate our method in synthetic and semi-synthetic settings- -te latter with real-world clinical notes from MIMIC-III and open large language models for zero- shot prediction- and find that our method produces estimates with low bias. We believe that this text-based design of proxies allows for the use of proximal causal inference in wider range of scenarios, particularly those for which obtaining suitable proxies from structured data is difficult.
causal inference method that uses two instances
1 Introduction
Data-driven decision making relies on estimating the effect of interventions, i.e. causal effect estima- tion. For example, a doctor must decide which medicine she will give her patient, ideally the one with the greatest effect on positive outcomes. Many causal effects are estimated via randomized controlled trials considered the gold standard in causal inference; however, if an experiment is unfeasible or unethical, one must use observational data. In observational settings, a primary obstacle to unbiased causal effect estimation is confounding variables, variables that affect both the treatment (c.g., which medicine) and the outcome.
Recently, some studies have attempted to mitigate confounding by incorporating (pre-treatment) unstructured text data as proxies for confounding variables or by specifying confounding variables as linguistic properties, e.g., topic (Veitch et al. 20200 Roberts et al. 2020), tone (Sridhar and Getoor 2019), or use of specific word types (Olteanu et al. 2017). A wide range of fields have used text in
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Remove discharge
Clinical note categories
Passes
Extimate of
Nursing noies
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Figure I: Pipeline for proximal causal inference with text data. The top row of captions describe the general pipeline that uses text data from any setting, and the bottom italicized row describes an illustrative example based on our semi-synthetic experiments in Sec. 5 (1) We filter to only pre-treatment text; (2 and 3) for each individual in the analysis, we select two distinct instances of text (e.g., cchocardiogram and nursing notes) via metadata with the goal of satisfying T Ifl T U, C: (4 and 5) we T and T inputs into LLM-1 and LLM-2, respectively, to infer zero-shot proxies Z and W. (7) If the proxies fail our odds ratio heuristic, analysis stops. (8, 9, and 10) Else, use the proximal g- g-formula implied by the casual DAG to estimate the causal effect.
causal estimates, including medicine (Zeng et al., 2022). the behavioral social sciences (Kiciman cct al., 2018), and science-of-sciene (Zhang et al. 2023). See Keith et al. (2020); Feder et al. (2022)
Egami et al. 2022) for general overviews of text-based causal estimation.
If all confounders are directly observed, then causal estimation is relatively straightforward with backdoor adjustment (Pearl 2009). However, known confounders are often unobserved. In such scenarios, researchers typically use supervised classifiers to predict the confounding variables from text data, but these text classifiers rarely achieve perfect accuracy and meusurement error must be accounted for. To address this, another line of work has developed post-hoe corrections of causal estimates in the presence of noisy classifiers (Wood-Doughty et al., 2018:: Fong and Tyler 202T] Egami et al., 2023) Mozer et al., (023). These approaches, however, require ground-truth labels of the confounding variables for a subset of instances, constraint that is not always feasible due to
privacy restrictions, high annotation costs, or lack of expert labor for labeling.
Our work fills this gap. We address the causal estimation setting for which practitioner has specified a confounding variable that truly unmeasured (we have no observations of the variable). but unstructured text data could be used to infer proxies. For this setting, our method combines preximal causal inference with zero-shot classifiers.
Proximal causal inference (Miao et al. 2018 Tcchtgen Tchetgen et al., 2020 Liu et al. 2024 can identify the true causal effect given two proxies for the unmeasured confounder that satisfy certain causal identification conditions. A major criticism of this method is that it can be difficult to find two suitable proxies among the structured variables; however, we conjecture that unstructured text data (if available) could be a rich source of potential proxies.
In our proposed method, summarized in Figure I we estimate two proxies from text data via zero-shot classifiers, i.e. classifiers that perform an unseen task with no supervised examples. In subsequent sections, we expand upon this method and its assumptions and empirically validate it synthetic and semi-synthetic data with real-world clinical notes. Since large pre-trained language models (LLMs) have promising performance on zero-shot classification benchmarks (Yin et al., 2019 Brown et al.) 2020: Wei et al., 2021 [ann et al., 202T] inter alia), we use I.LMs to infer both of the proxies in our experimental pipeline. Our combination of proximal causal inference and shro-shot classifiers not only novel, but also expands the set of text-specific causal designs available to practitioners
In summary, contributions are
'Setting aside challenges of high-dimensional covariate selection for causal estimation (amarchenko) 2023 "Supporting code available at httpp:://iithhb http:/thww..c.ooooooooooooooonna text

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We propose a new causal inference method that uses distinct instances of pre treatment text data, infers two proxies from two different zero-shot models on the instances, and applies the proxies in the proximal g-formula (Tchetgen Tchetgen et al. 2020).
We provide theoretical proofs that our method satisfies the identification conditions of proximal causal inference and prove that other seemingly reasonable alternative methods do not.
We propose a falsification heuristic that uses the odds ratio the proxies conditional on observed covariates as an approximation of the (untestable) proximal causal inference conditions.
synthetic and semi-synthetic experiments using MIMIC-III's real-world clinical notes (Johnson let al., 2016), our odds ratio heuristic correctly flags when identification conditions are violated. When the heuristic passes, causal estimates from our method have low bias and confidence intervals that cover the true parameter, when the heuristic fails, causal estimates are often biased.
2 Problem Setup And Motivation
To motivate our approach, imagine we are an applied practitioner tasked with determining the effectiveness of thrombolytic (clot busting) medications relative to blood thinning medications to treat clots arising from an ischemic stroke. Such medications ally administered within three hours of the stroke to improve chances of patient recovery (Zaheer et al. 2011). Given the urgency and the short treatment window, running randomized experiment to com- pare these drugs difficult. Left with only obser- vational data, we examine electronic health records (EHRs) from a database like MIMIC-III (Johnson al. 2016).
usu-
Z
W
(a)
Figure 2: Causal DAGs (a) depicting unmea- sured confounding and (b) compatible with the canonical assumptions used for proximal causal inference (Tchetgen Tchetgen et al.
2020
We formalize our causal estimand as follows: let A denote a binary treatment variable corresponding to clot busting (A 1) or blood thinning (A = 0)
medication, and let Y denote measurements of the D-dimer protein in the patient's blood which directly measures how much of the clotting has dissolved. In do-calculus notation (Pearl 2009), the target causal estimand is the average causal effect, ACE B|y| do(A 1)] E do 0)].
Examining the EHRs, we find potential confounders (in structured tabular form), including biological factors, such as age, sex, and blood pressure, as well socio-economic factors, such as income. We denote the observed confounders as the set C. However, we are worried about biased causal effects because atrial fibrillation (irregular heart rhythms) is an important confounder corresponding to pre-existing heart condition that is not recorded in the structured data. We denote this unmeasured confounder as U, and assume for the rest of this paper that C and U form sufficient backdoor adjustment set with respect to A and Y (Pearl 1995). Figure 2(a) depicts this problem setup in the form of a causal directed acyclic graph (causal DAG) (Spirtes et al. 2000 Pearl 2009). With the presence of U. it is well known that adjusting for just the observed confounders via the backdoor formula Ee (E 1995). In response to this issue, we consider work that uses proxy variables of the unmeasured confounder. However, we subject the following restriction:
c] E 0, c)) x p(c) will give biased estimate of the ACE (Pearl
(R1) We do not have access to the value of U for any individuals in the dataset.
This kind of restriction is common in healthcare social science settings when data privacy issues, high costs, or lack of expert labor make analysts unable to hand-label unstructured text data. We elaborate in Appendix A
In such cases, we turn to using proxies for U. Pearl (2000) proposed method for obtaining unbiased effect estimates with a single proxy W under the assumption that p( p(W)U) is known or estimable, which are impossible for us under IR.). However, a more recent line of work, building from (eeliches)(997) and Kuroki and Pearl (2014), called proximal causal inference (Miao et al. 2018 T'chetgen Tchetgen et al.] 2020) is able to identify the true causal effect as long as the analyst proposes two proxies W and Z that satisfy the following independence conditions:
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(P1) Conditional independence of proxies: W TT Z U.C
(P2) One of the proxies, say W, does not depend on values of the treatment: W TT A U (P3) The other proxy, Z, does not depend values of the outcome: Z TT Y A,U,C
canonical example of proxies that satisfy these conditions is shown in Figure 2 In addition to these independence relations that impose the absence of certain edges in the causal DAG, e.g., no edge can be present between Z and W to satisfy (PI), there is an additional completeness condition that imposes the existence of U - Z and U - W. This condition is akin to the relevance condition in the instrumental variables literature Angrist et al. (1996) and ensures that the proxies W and Z exhibit sufficient variability relative to the variability of U.
(P4) Completeness: for any square integrable function v(-) and for all values w, a, C, we have Elo(U) w, a, c] = 0 + v(U) 0, and (l)( w, a, cj = - e(2) 0.
Intuitively, these completeness conditions do not hold unless Z and W truly hold some predictive value for the unmeasured confounder U. See Miao et al. (2018) for more details on completeness. Under (PI-P4), each piece of the ACE, [E[Y] do(A = a)}. is identified via the proximal g-formula,
E[y | do(a)]
= Σ h(a, w, c) x p(w, c)
(1)
w.c
where h(a, w, c) is the "outcome confounding bridge function" that is solution to the equation E[Y[a, 2, c] = Σn. h(,, w. c) x p( ((wla, 2, c) (Miao et al. 2018). Although the existence of a solution guaranteed under (P1-P4), solving it can still be difhcult. However, there exist simple two-stage regression estimators for the proximal g-formula (Tchetgen Tchetgen et al., 2020; Mastouri et al.) 202T) that we make use of in Section 5 oncc we have identified valid pair of proxies. This brings us to the primary criticism of proximal causal inference.
Primary criticism When using proximal causal inference in practice, how do we find two proxies W and among the structured variables such that they happen to satisfy all of (PI-P4)? We often cannot, at least not without a high degree of domain knowledge Fl Furthermore, empirically testing for any of (PI-P3) in general is, by definition of the problem, not possible because doing so requires complete access to the unobserved confounder U.
Our approach Instead, in this work, we propose relying on raw unstructured text data (e.g., clinical notes) in an attempt to infer proxies that satisfy (P1-P4) by design.
Returning our motivating problem, our approach applies classifiers zero-shot- since we have no training data with U given (R1) two distinct instances of pre-treatment clinical notes of each patient and obtains two predictions, W and Z, for atrial fibrillation (our U). In order make it more feasible to estimate the ACE from data, we make the following two relatively weak assumptions:
(S1) The unmeasured confounder U between A and Y can be specified as a binary variable. (S2) The text only causes W and Z (and no other variables).
Assuming (S1) simplifies estimation since text classification typically performs better empirically than text regression (Wang al.. 2022). Assumption (S2) asserts that the text data considered serves as record of events rather than actionable data 5
'One could also add the edges W + Y and Z + A to Figure b), but these relations will not show up in text-based setting. [Shpitser al. (2023) also propose a general proximal identification algorithm that compatible with other causal DAGs, but we focus on the canonical proximal learning assumptions stated in Tchetgen Tchetgen et al. (2020).
For instance, suppose we aim find proxies (in the structured variables) of atrial fibrillation (U) and have access to shortness of breath and heart palpitations. Although these proxies seem reasonable, we show how they may violate the proximal causal inference conditions. Patient complaints about shortness of breath may affect which medication climician prescribes (A); hence, using shortness of breath as the proxy W violates (P2). Furthermore, a lack of oxygen resulting from shortness of breath may affect the healing of blood clots. thus influencing measurements of the D D-dimer protein Y. In this case, using shortness of breath the proxy Z violates (P3). Shortness of breath can also sometimes a symptom of heart palpitations, violating (PI).
*We present an example of how to relax this assumption in Appendix B We leave to future work more complicated scenarios, e.g., if the reader's perception of text differs from the writer's intent (Pyyaant et al. 2021

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T
T
(b)
Causal DAGs depicting several different scenarios for inferring text-based proxies. Edges with different colors and patterns, e.g., T T Z and T W, indicate that different zero-shot models were used. Our final recommended method is based on (d).
Figure 3:
3 Designing Text-Based Proxies
In this section, describe our method for designing text-based proxies. In doing so, describe various "gotchas," pitfalls in attempting to use these text-based proxies in causal effect estimation. We deseribe each gotcha and explore how they lead to our final recommended design, given by Figure dd.. Our empirical results in result biased causal effect estimates.
demonstrate, as expected, that these pitfall approaches
Gotcha #1: Using predictions directly in backdoor adjustment. Suppose we try to avoid the complications of proximal causal inference by using the predictions from one of our zero-shot models, say W, as the confounding variable itself.
Proposition 1. Using proxy W in the backdoor adjustment formula results in biased estimates of the ACE in general.
Proof. If WWW * U for some subset of instances, there remains an open backdoor path through U, and the ACE remains biased as Ev.c (ElY A = 1,U, CJ -E = 0, U, x p(U, C) +f 1, CJ B A 0, W. CJ) p(W, C) in general (Pearl 1995).
(Bly
The most straightforward way to obtain unbiased results under Gotcha #1 is to have 100% accuracy between W and U, scenario that is extremely unlikely in the real world. Further, under (RI we cannot measure accuracy at inference time since we not have any observations of U. As expected, in our semi-synthetic experiments in Section [] we find using predictions of W directly in backdoor adjustment formula results in biased estimates; see Figure
Gotcha #2: Using post-treatment text. While it is well-known that adjusting for post- cost-treatment covariates in the backdoor formula often leads to bias (Pearl 2009). it is not obvious what might go wrong when using post-treatment text to infer proxies for the proximal g- g-formula.
Proposition 2. If both W and 7 are inferred from zero-shot models on text that contain post-treatment information, then the resulting proxies violate either (P2), (P3), or both.
Proof. Consider Figure Bja), where the proxies are produced using text that is post-outcome and thus also post-treatment. We show that this violates both (P2) and (P3). Clearly the DAG violates (P3): by a simple d-separation argument we see that 1 Y A, U, due to the open path T ..>> Z. Similarly, (P2) is violated from the open path A Y - T W.
Thus, before performing zero-shot inference, it is important that the text for each individual is filtered in such a way that it contains only the text preceding treatmen In our running clinical example, we avoid this gotcha by using the time stamps of the clinical notes and information about when the patient was treated and discharged.
'In the absence of (R.), direct readers work that adjusts via measurement error estimates assumptions that "missing at random" Wood -ouughyy et al. (2018).
IIn Appendix B we show how proxies could be inferred using mix of pre- and post-treatment text while satisfying (P1-P3). However, advocate for the the pre- treatmettnt rule due to its simplicity.
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Gotcha #3: Predicting both proxies from the same instance of text. After filtering to only pre-treatment text, THe for each individual, the intuitive next step to use T infer W and Z. Proposition 3. IfW and Z are inferred via zero-shot models on the same instance of pre-treatment text, the resulting proxies violate (PI).
Proof. Consider the causal DAG with proxies W and Z in Fig B(b). By d-separation we have W P Z U, C due to the path Z p.. T W.
In our synthetic experiments in Section we find inferring proxies from the same instance of text results in biased estimates; see Table I To avoid Gotcha #3, we select two distinct instances of pre-treatment text data for each unit of analysis, The and Tht such that T 11 The U, c For example, in the clinical setting we use metadata to select two separate categories of notes for each individual patient, e.g., nursing notes and echocardiogram notes. We hypothesize this satisfies Thee IL T U, C' since different providers will likely write reports that differ in content and style. Although the availability of distinct instances is domain-dependent, we hypothesize this type of data exists in other domains well; for example, one could select distinct social media posts written by the same individual or multiple speeches given by the same politician.
Using a single zero-shot model. After splitting text into T and The should we apply the same zero-shot model to these two instances of text to infer the proxies W and Z, as in Figure or should we apply two separate zero-shot models as in Figure dd)? We find different answers in theory and practice. Proposition 4 shows that, in theory, both are valid as long as T IL Tht U, C. However, we later describe how our semi-synthetic experiments demonstrate the need for two different models in practice in Section 5 both strategies.
Gotcha #4:
We first establish the theoretical validity of
Proposition 4. IfW and Z are inferred using zero-shot classification on two unique instances of pre-treatment text such that T 1I. Thee U, C, then these proxies satisfy (PI-P3). Additionally, if the proxies are predictive of U, i... Z X U C and W y. U C, then (P4) holds.
Proof. Suppose we apply zero-shot classification models two splits of pre-treatment text in way that results in causal DAGs shown in Figure Bie) or (d) depending on whether we use one or two models, respectively. Applying d separatiio confirms that the conditions (PI-P3) hold in both cases.
Let | denote the number of categorics of a variable V. Kuroki and Pcarl (014): Tehetgen Tch etgen et al. (2020) state that when W and Z are predictive of O (as stated in the proposition), sufficient condition for (P4) is min( |, [ 1) 2 | Since U is binary under (S1) and since
W and Z are discrete variables because they are inferred from classifiers, this condition is satisfied. Hence, (P4) is satisfied.
Our Final Design Procedure Figure I and the causal DAG in Figure dd) summarize our final design procedure-obtain two distinct instances of pre-treatment text for each individual and apply two distinct zero-shot models to obtain W and Z.
In Proposition 4 formalized how this procedure can be used to design proxies that satisfy the proximal conditions (P1-P4). However, this result relied on two important pre-conditions: (1) the conditional independence of the two instances of text, and (2) W and Z being (at least weakly) predictive of U. Yet, both of these conditions are untestable in general; this motivates the next section.
4 Falsification: Odds Ratio Heuristic
In practice, a major challenge for our procedure- and indeed all causal methods are its assumptions. Sometimes, causal models imply testable restrictions the observed data that can be used in falsification or confirmatinn tests of model assumptions, see Wang et al. (2017); Chen et al. (2023); ;
Bhattacharya and Nabi (202)) for tests of some popular models. In our case, the proximal model
"Note this independence condition does not imply the two pieces of text are completely uncorrelated. Since the text is written based on observations of the same individual, we certainly expect T _1l T we simply require that the two pieces correlated only due to C and U.

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Algorithm 1 for inferring two text-based proxies
1: Inputs: Observed confounders C; Text T; Zero-shot models Mi, M2: Specified Thigh
2: Select two distinct instances of pre-treatment text T and T from T
3: Infer 7 +- MM (TTr)) and W <- 22
low CT 4: Compute the confidence interval (CI) for wwz.c, (7W 2. wo..c:/..ee 7wz.C)
CT low and " w.w. Vhigh then return W and Z 5: if 1 < 7 2.C
high
6: else return "stop"
implies no testable restrictions (Tchetgen Tchetgen et al. 2020), so the best we can do is provide a falsification heuristic that allows analysts to detect serious violations of (P1-P4) when using the inferred proxies and stop analysis. Our heuristic is based on the odds ratio function described below.
Given arbitrary reference values wy and 20. the conditional odds ratio function for W and Z given covariates X defined as Chen (2007), OR(,, = x) p(w]z.x) p(wn Ro.2) This function is p(wa axx] p[u] [a.
important because W TT Z X if and only if OR (w, 2 x) = for all values w, x. We summarize this odds ratio as single free parameter, mw and, for the simplicity of our pipeline, we estimate it under a parametric model for p(W| [
Now, we describe our proximal conditions in terms of odds ratio parameters. If (P1-P3) are satisfied, then W 11 Z U, C and T Z.C. = 1. Further, if the zero-shot models are truly predictive of U, then (P4) is satisfied and W fl 7 C, which means that wZ * 1. Ideally, we would want to estimate both of these odds ratio parameters to confirm (P1-P4) empirically; however, 7WZ.C cannot be computed from observed data alone due (RI).
Using a parameter we can estimate from observed data, "W2 C. we propose an odds ratio falsification heuristic in lines 3-6 of Algorithm Now, explain why, if this heuristic holds, an analyst can be reasonably confident in using their inferred best- proxies for estimation.
First, we examine lower bound on 7. Based on our previous discussion, if z.Z.c is close to 1, then we should suspect that one or both of our zero-shot models failed to return informative predictions for U. Next, let us treat Z.C. z.C as an imperfect approximation of 7w Let W. Z, U be binary with reference values Wo- = 2g = ug = 0. VanderWeelc (2008) proposed the following three conditions under which an odds ratio Twz.c that fails to adjust for unmeasured confounder U is an overestimate of the true odds ratio zwZ. (i) { JUCCC C satisfies the backdoor criterion with respect to W and Z: (ii) U is univariate consists of independent components conditional on C; (iii) E[W] |u, z, c] is non-decreasing in for all æ and с and ZZ u, c] is non-decre in U for all c.
Condition (i) is satisfied from Graph 3 dd, and condition (ii) is satisfied by assumption (S1). Finally, condition (iii) satisfied when our zero-shot models are reasonable predictors of the unmeasured confounder U by the following argument. Notice that IR W u., 2, where the first equality follows from d-separation in Graph (d) and the second equality follows from the definition of expectation for binary variable W. Then we should expect, if the zero-shot models are reasonably accurate, that p(W = i|U = 1, c) > p(W = 1|0 = c). Therefore, the first part of condition (iii) is satisfied. Similar logic holds for E|Z|u, c].
E[ |u, c| p(W = 1/u, c).
Hence, we have shown that under ideal conditions that satisfy (P1-P4), we should expect Z.C.C > Z.Z. = 1, and we should reject proxies W and Z when we observe an odds ratio 222. S 1. Next, we examine the upper bound on Zwc.c. Consider the extreme case where 7w2.c = 0o. This corresponds to situation where W = 2, so (P1) is clearly not satisfied. In general, if 7wz.c is higher than some threshold "high. corresponding to the maximum association that one could reasonably explain by single open path through U, we should suspect that perhaps the proxies W and Z are associated with each other due to additional paths through other unmeasured variables that make it so that the two instances of text are not independent of each other, i.c., The 11 T C.
Following standard practice in sensitivity analysis, e.g., Liu et al. (2033); Leppälä (2023), we leave it to the analyst to specify the upper bound Thigh based on domain knowledge. In our experiments in Section 5 we found that, when the proximal conditions are not satisfied, Tw z. far exceeds
"More generally, the odds ratio can be treated as a finite p-dimensional parameter vector and estimated under marimerramttric restrictions on p( (1 X) and p( W. X) (Chen 2007 Tchetgen Tchetgen al. 2010
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Estimation Pipeline
Clow Twz.c
Est. ACE
Bias
Conf. Interval (CI)
CI Cov.
PIM
(1.35, 1442)*
1.304
0.004
(1.209,1.394]
Yes
PIM, same
(10"h 10th)
1.430
0.130
(1.405, 1.495)
No
P2M
(1.82, T
1.343
0.043
(1.273, 1.425)
Yes
P2M. same
(7.9, 8.41)
1.407
0.107
(1.376, 1.479)
No
Table 1: Fully synthetic results with the true ACE equal to 1.3. Here, v distinguishes settings that passed the odds ratio heuristic from those that failed it, with Thigh = 2. Corresponding Gotcha #3, "same" indicates we used the same instance of text to infer both W and Z.
ZwZ.
Twz.
U
The Cat.
T Cat.
PIM
P2M
PIM
P2M
A-Sis
Echo
Radiology
1.626
1.085
(2.381, 2.962)
(1.372, 1.995)
Hcart
Echo
Nursing
2.068
1.156
(2.298, 2.676)
(1.152, 1.376)
A-Sis
Radiology
Nursing
2.350
1.328
(4.337, 5.266)
(2.050, 2.663)
Table Semi-synthetic odds ratio heuristic (Ywz.c) as well as the oracle Tw Z.C. for different categories of notes (Cat.). We distinguish settings that passed the odds ratio heuristic (v) from those that failed, with Thigh 2.
1.7
17
17
ACE
1.6
1.6
1.6
ACE A-Sis Echoftadiologg
Est. ACE for Heart Echo/Nursing
Est. ACE for Sis
Rediology/Nursing
2.4
1.3
1.3
1.3
1.2
1.2
12-
Backdoor proxy
PIM
Backdoor proxy
P2M
Backdoor proxy
P2M
Figure 4: Semi-synthetic results for ACE point estimates (dots) and 95% CIs (bars). We distinguish settings that passed the odds ratio heuristic (V) from those that failed, with Thigh 2.
any reasonable setting of Thigh- Hence, our heuristic works quite well in practice even with generous suggestion for an upper bound. We describe our full design procedure with the diagnostic in Algorithm and calculate 95% confidence intervals for "w via the bootstrap percentile method Wasserman 2004). We now evaluate its effectiveness for downstream causal inference.
Empirical Experiments and Results
RQs In this section, we explore the following empirical research questions (RQs): How does Algorithm compiare other alternatives in terms of bias and confidence interval coverage of the estimated causal effects? Does our odds ratio heuristic effectively flag when to stop or proceed?
In causal inference, empirical evaluation is difficult because it requires ground-truth labels for counterfactual outcomes an individual under multiple versions of the treatment, data that is generally impossible to obtain (Holland, 1986). Thus, we turn to synthetic data and semi-synthetic data so we have access to the true ACE and U to evaluate methods. Semi-synthetic experiments which use real data for part of the DGP and then specify synthetic relationships for the remainder of the DGP-have been used extensively for other empirical evaluation causal estimation methods; see Shimoni al. (0018); Dorie et al. (2019); Veitch et al. (2020) We describe the experimental set-ups, the causal estimation procedure used by all experiments, and finally, the results to our RQs.
describe methods for evaluation that are more realistic than semi-synien synihsyythetic evaluation by downsampling RCT dataset to create an observational (confounded) dataset. However, for the proximal setting we investigated in this paper, could not find suitable existing RCT.
"Gentell et al. 2019) and Keith et al.
2023

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Fully Synthetic Experiments We create our fully synthetic DGP based on the DAG in Figure Bjd); see Appendix[[foo full details. To summarize, A and U are binary, and Y and C' are continuous. We generate (very simple) synthetic text data with four continuous variables, X1, X2, X3, X4. as functions of U and C. For training. we generate two realizations of these variables, which we call X and X and likewise two realizations for inference time, X and Xin
At inference time, we explore using one or two zero-shot models, which we refer to as Proximal 1- Model (PIM) and Proximal 2-Model (P2M), respectively. For one zero-shot model, we train a logistic
regression classifier to predict the true U from an aggregated variable Xurin = (X + 2/
as (U 1 train 11 For the other zero-shot model, we use the following heuristic: predict 1 X1 > 1.1 else O. PIM uses only the logistic regression model, and P2M uses both the logistic regression and heuristic models. Next, we vary whether Gotcha #3 holds at inference time for both PIM and P2M, i.e. whether the models infer Z and W from only inn or both X and X
Semi-Synthetic Experiments For our semi-synthetic experiments, we use MIMIC-III a de- identified dataset of patients admitted to critical care units at a large tertiary care hospital (Johnson jt al.] (016). See Appendices D and G for detailed pre-processe pre-proeessing steps, variables, and DGP. To summarize, we use the following real data from MIMIC-III in our DGP: ICD-9 code diagnoses, demographic information, and unstructured text notes. We choose the four diagnoses for oracle U that had the best Fl scores for a supervised aag-of-words logistic regression classifier (see Appendix [F] for full results): atrial fibrillation (Afib), congestive heart failure (Heart), coronary atherosclerosis of the native coronary artery (A-Sis), and hypertension (Hypertension). To avoid Gotcha #2, we explicitly exclude discharge summaries, which are post-treatment. In each experiment, we choose two out of the following four note categories Tee and Tho electrocardiogram (ECG), echocardiogram (Echo), Radiology. and Nursing notes. We hypothesize that notes written about different aspects of clinical care and by different providers will likely satisfy T 11 T U, C since each individual will write a conditionally independent realization of the patient's 's status. In Appendix [[ we find distinct unigram vocabularies between the note sets that pass our falsification heuristic, lending preliminary evidence to this assumption of conditional independence. Consistent with the DAG in Figure 3(d), we then synthetically generate binary A and continuous Y.
For our zero-shot models, we use FLAN-TS XXL (Flan) Chung et al. (022)) and OLMo-7B- Instruct (OLMo) Groeneveld et al. (2024), both "open" instruction- tuned large language models. In Appendix F we elaborate on our choice of these models. Following Ziems et al. (2024). we use the prompt template "Context: /T / (nts it likely the patient has (U) / Even if you are uncertain, you must pick either "Yes" or "No" without using any other words." We assign when the output from Flan or OLMo contains 'Yes' and O otherwise. PIM uses Flan for both proxies W and Z while P2M uses Flan for W and OLMo for Z. We compare PIM and P2M to a baseline that uses the inferred proxy W from Flan directly in a backdoor adjustment formula, corresponding to Gotcha #1.
Estimation of Proximal g-formula For all experiments, we estimate the ACE by using the inferred W and Z in two-stage linear regression estimator for the proximal g-formula provided by Tehetgen Tchetgen et al.) Although the linearity assumption is restrictive, it allows us to focus on evaluating the efficacy of our proposed method for inferring text-based proxies as opposed to complications with non-linear proximal estimation (Mastouri et al. 202T). Briefly, we first fit a linear regression E[W|A, |A, Z, C). Next, we infer W, continuous probabilistic predictions for W, using the fitted model. For the second stage, we linear model for | A, W, C). The coefficient for A in this second linear model is the estimated ACE. We calculate 95% confidence intervals for the ACE via the bootstrap percentile method (Wasserman) 2004). See Appendix [F for additional implementation details (e.g., addressing class imbalance and sample splitting).
Results Table I has synthetic results, and Tables and Figure have selected results for the semi-synthetic experiments. See Appendices E H and J for additional results. In short, our empirical
results corroborate preference for Algorithm over the baseline.
First, we discuss the "gotcha" methods we showed to be theoretically incorrect in Section 3 Regarding Gotcha #1, Figure shows that, across all settings of U, using the inferred W directly in the backdoor
Of course, having access to the true U may not qualify as "zero-shot" in the strict sense of the term, but we complement this idealized scenario with the difficult true zero- shot scenario in semi-synthetic experiments.

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adjustment formula results in estimates with large bias. Regarding Gotcha #3 in the fully synthetic experiments, using the same realization X results in high P2M, respectively, in [able and CIs that do not cover the true ACE. Regarding Gotcha #4, as in Proposition 4, using a single zero-shot model (PIM) results in low bias in the idealized setting the synthetic DGP (Table T first row). However, using real clinical notes and Flan, the second columns of Figure 4 show that PIM produces estimates with higher bias compared to P2M across all three settings. We hypothesize this could be due to Flan over-relying on its pre-training and thus making similar predictions regardless of the clinical note.
and 0.107 for PIM and
For all experiments we set Thigh = 2. With this setting, we find low bias and good CI coverage for the two settings that pass our heuristic (P2M for U = A-Sis with Echo and Radiology notes and P2M for U = Heart t with Echo and Nursing notes) and biased estimates in other cases. Although the confidence intervals sometimes cover the true ACE in settings that fail the heuristic, the interval is skewed and appears will asymptotically converge to biased value. This gives us confidence that Algorithm I approprriatlly flags when to stop or proceed.
Understanding why the odds ratio heuristic fails for a specific application requires oracle data. However, it may be helpful for analysts to reason about scenarios that influence this failure, such as when C and U are not sufficient backdoor adjustment set; T i To U, C; or Z and W are poorly predictive of U. Using oracle data, we examined these scenarios for a few settings of our semi semi-yynthetic experiments. For example, Figure 4 (rightt (right-most panel) shows that V-=A-Sis with nursing and radiology notes fails the odds ratio heuristic. We qualitatively examined samples of the clinical notes and found some had unmeasured confounding, e-g., a patient had lung cancer variable that was not in our C or Utahh influenced descriptions in both T and T Figure (bottom right-most panel) shows that for U==hypertension with echocardiogram (echo) and nursing notes also fails the odds ratio heuristic. However, we hypothesize this is due not to text dependence (see Tp but rather that the proxies W and Z have accuracies of 0.49 and 0.52 respectively (when evaluated against oracle U), which is lower accuracy than predicting the majority class (Table 21). We leave to future work disaggregating the odds ratio heuristic into tests for these specific scenarios.
6 Conclusion, Limitations, and Future Work
In this work we proposed novel causal inference method for estimating causal effects in observational studies when a confounding variable is completely unobserved but unstructured text data is available to infer potential proxies. Our method uses distinct instances of pre-treatment text data, infers two proxies using two zero-shot models on the instances, and applies these proxies in the proximal g- g-formula. We have shown why one should prefer our method to alternatives, both in theory and in the empirical results of synthetic and semi-synthetic experiments.
If the conditions we present hold, the estimates will be unbiased. Further, as the underlying predictive accuracy of Z and W improve, the confidence interval width will narrow. Thus, we see promise in work improving the zero-shot performance of LLMs. Future work could possibly combine proxies from a greater number of zero shot models, i.e. inspired by work in Yang et al. (2024).
Although we are careful to infer valid proxies by design, it is generally impossible to empirically test whether conditions for proximal causal inference are fulfilled. To address this, we proposed an odds ratio falsification heuristic test, but acceptable values of "Thggh depend on the domain. If these are set incorrectly, our method could result false positives (a setting for which the CI does not cover the true parameter and the estimated ACE is biased). In addition, our approach depends on the availability of pre-treatment text data and metadata to split text into independent pieces, which are not available across all applied settings.
Although we use clinical setting as our running example, our method is applicable to many other domains where it is infeasible to obtain ground-truth U labels due to privacy constraints or annotation costs, e.g., social media or education studies with private messaging data or sensitive student coursework. Other directions for future work include incorporating non-linear proximal estimators (including ones that use alternative assumptions to the completeness condition in (P4) (Kallus et al. 2021)), expanding beyond text to proxies learned from other modalities (see Knox et al. (2022)), providing more guidance for setting Thigh in our odds ratio heuristic, extending our method to incorporate categorical U, W, Z, and using soft probabilistic outputs from the zero-shot classifiers.
10

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Acknowledgements
We are very grateful for feedback from Naoki Egami and Zach Wood-Dought as well as helpful comments from anonymous reviewers from NeurIPS 2024. KK acknowledges support from the Allen Institute for Artificial Intelligence's 's Young Investigator Grant. RB acknowledges support from the NSF CRII grant 2348287. The content of the information does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred.
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A Elaboration on Problem Restriction
Restriction (RI) is clearly present in settings for which we need to adjust for a confouding variable that is impossible or difficult to measure-forr example, atrial fibrillation can go undiagnosed for years. A logical first attempt to mitigate this constraint is to train a supervised classifier on a subset of the data create proxies for the rest of the dataset, explored in Wood- This, however, requires humans to hand-label large amounts of text data. If labeling takes place crowd-soureing platform, e.g., Amazon's Mechanical Turk, crowd-sourcing costs quickly sky-moket and often exceed tens of thousands of dollars, even for small datasets. Furthermone, many datasets- partsculaarrclllll those in clinical featinns-requiin domain expertise (e.g.. trained medical doctors) which will likely increase costs significantly and limit the availability of labelers.
al. (2018).
Cost and expertise of labelers aside, the possibility of supervised learning is further restricted by patient privacy legislation. We typically cannot transport sensitive data regarding patients' personal data to platforms such as Amazon's Mechanical Turk for labeling due to the Health Insurance Portability and Accountability Act (HIPAA) 12 in the United States. In addition, legal acts such as the General Data Protection Regulation (GDPR in the European Union and the California Consumer Privacy Act (CCPA [Td] restrict the movement and repurposing of user data across platforms. Our proposed method overcomes restriction (R1) 1) by using zero-shot learners that do not require previously labeled examples.
B
Using Post-Treatment or Actionable Text Data
Here, first describe scenario for which may infer valid proxies using both post-treatment and pre-treatment text. In Figure T is post- post-treatment text whereas The is pre-treatment text. Through simple d-separation arguments, we
that each of (P1-P3) are fulfilled. Hence, it is still possible to use post-treatment text to generate valid proxies as long as we use pre-treatment text to generate one proxy and nost-treatment text generate the other. However, requiring both instances of text data to be pre-treatment is simpler to implement and validate, so we recommend this rule in our final method.
Tost
W
U
Figure Using both pre-treatment and post-treatment text to generate valid proxies.
actionable text to generate valid proxies. Suppose T is an instance text data that influences a health practitioner's decision to assign different treatments to a patient, and Tpe is instance of pre-treatment text that is not actionable. Then, Test has a direct edge to the treatment A. Despite the addition of this edge, we can apply d-separation again to verify that (P1-P3) valid in a more relaxed setting where clinicians use one instance of the text data to make treatment decisions long the other instance of text data both pre-treatment and not actionable.
Figure 6 further illustrates example where
still fulfilled. Therefore, our proposed method is still
ca. https://oag.cc.goo/rrrvaaaccc/
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THE
Tact
w
U
A
Figure 6: Using one instance of actionable text data and another instance of non-actionable text data generate valid proxies.
C Fully Synthetic Data-Generating Process
The DAG representing the fully synthetic data-generating process is shown in Figure 7 U, binary variable, as follows
We simulate
U ~ Bernoulli(0.48)
Next, we simulate baseline confounders and synthetic "text" X1, 12,X2, X3, X4 as follows:
C ~ 1),
X1 ~ (O 1) +
X2 ~ 1) +
X3 ~ +12.1))+
X4 ~ ()) + +x* +
+U+3+0
Finally, the treatment and outcome variables are generated via
p(A 1) expit(0.8 + +C 0.3)
A ~ Bemoulli(p(A = 1))
Y 1) A U
X4
X3
XI
X2
A
Figure 7: DAG showing the fully synthetic data Kata-generating process.
the fully synthetic Sata-generating process, increasing the coefficient the variable C decreases the odds ratio conditional on observed confounders "w Z.C while decreasing the coefficient for the variable C' increases 2.W..C.
D MIMIC-III Pre-Processing Steps
In the MIMIC-II dataset (Johnson et al. 2016). data is organized into multiple tables. Patients are anonymized and each have unique identifier. addition, each unique hospital admission assigned hospital admission identification number (HAID). Each patient can have multiple HAIDs, and each HAID can have multiple notes (e.g., an ECG note and nursing note). Our pre-processing steps are outlined in the following steps:
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1. We start with the table in MIMIC-III containing the clinicians' notes for all patients and drop rows of data where the HAID has a missing value. We refer to this main table we are working with as our reference table.
2. Next, for each unique patient in the reference table, we select one HAID by choosing the HAID with the earliest "chart date," the day on which the clinician's 's note was recorded. We limit each patient to only one hospital admission to better fit the assumption of i.i.d. data (which would be violated if there were multiple hospital admissions for a single patient since these multiple admissions would be dependent).
3. We drop all clinicians' notes that have the category label "Discharge summary" because such notes would be considered post-treatment text that violate (P2) as we have shown in Section 3 For each HAID, we combine separate notes of the same category into one string.
4. We now move on to the table in MIMIC-III that contains information on which patients were given which medical diagnoses for each HAID. For each HAID in the reference table, we select all the diagnoses (ICD-9 codes) assigned to the patient in that hospital visit.
5. The 10 most common diagnoses for the patients in our reference table are, in order, hyper- tension, coronary atherosclerosis of the native coronary artery, atrial fibrillation, congestive heart failure, diabetes mellitus, hyperlipidemia, acute kidney failure, need for vaccination against viral hepatitis. suspected newborn infection, and acute respiratory failure. In our reference table, we add column for each of these 10 diagnoses and record 0 or 1 that indicates whether each patient was assigned diagnosis for each condition on particular hospital admission.
6. From the table containing bascline information for each patient, we append onto the refer- ence table the gender and age of each patient. We infer each patient's 's age by subtracting the "chart date" of the patient's clinician's note by the patient's date of birth. We drop from the reference table all patients with an age less than 18 or greater than 100. We drop the diagnosis suspected newborn infection from the reference table because we have eliminated all patients younger than 18. At this stage in the preprocessing pipeline, the total number of HAIDs, or rows of data, in the reference table 990,172.
7. In the final step, we evaluate which pairs of note categories are the most often simultancously recorded for patients on the same hospital admission in the reference table. The top 5 simultaneously recorded note category pairs are Electrocardiogram (ECG) and Radiology with 27, 7,,963 HAIDs, Nursing and ECG with 18,505 HAIDs, Nursing and Radiology with 18,302 HAIDs, ECG and Echocardiogram (Echo) with 17,291 HAIDs, and Echo and Radiology with 15,558 HAIDs. We consider these 5 pairs of note categories for downstream proximal causal inference.
E
Diagnosing Signal With Oracle Text Classifiers
To ensure that the text contains predictive signal for the diagnoses (a precondition necessary to use our zero-shot classifiers later on in our analysis), we train supervised classifiers to predict the diagnoses, Y. separately using text data from each note category, X, with bag-of-words representation.
Our procedure as follows. We first truncate all the clinicians' notes data 470 tokens (due the context window of Plan-T5 which we use later in our pipeline). We ignore oracles and note categories combinations where positivity rates are 0 or after subsetting on the note category in question. We then use the scikit-learn library's CountVector izer to convert the text data to bag of words features with vocabulary size 5, 000 and train a linear logistic regression with the hyperparameter penal ty set to "None". We further calculate the FI score, accuracy, precision, and recall with the scikit-learn library Pedregosa et al. (20TT). The results are summarized in Table
We choose oracles with at least two note categories that achieve Fl scores greater than 0.7 for downstream inference with zero-shot classifiers. Such oracles and note categories are:
1. Atrial fibrillation (A-fib) with ECG, Echo, and Nursing notes.
2. Congestive heart failure (Heart) with Fcho and Nursing notes.
3. Coronary atherosclerosis of the native coronary artery (A-sis) with Echo, Nursing, and Radiology notes.
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4. Hypertension with Echo and Nursing notes.
Diagnosis (Possible U)
Note Category
p(U =
F1 Score
Accuracy
Precision
Recall
Hyperlipidemia
Nursing
0.087
1.000
1,000
1.000
1.000
Acute respiratory failure
Nursing
0.132
1.000
1.000
1.000
1.000
Coronary atherosclerosis (A-sis)
Nursing
0.279
0.993
0,996
0.995
0.991
Acule kidney failure
Nursing
0.135
0.958
0,989
0.981
0.937
Atrial fibrillatinn (A-fib)
Nursing
0.231
0.879
0.946
0.909
0.851
Coronary atherosclerosis (A (A-sis)
Echo
0.375
0.844
0.888
0.885
0.807
Coronary atherosclerosis (A-sis)
Radiology
0.249
0.843
0.926
0.901
0.792
Congestive heart failure (Heart)
Nursing
0.2255
0.789
0.910
0.840
0.744
Hypertension
Nursing
0.417
0.762
0.806
0.779
0.747
Congestive heart failure (Heart
Echo
0.326
0.759
0.853
0.813
0.713
Atrial fibrillation (A-fib)
Echo
0.328
0.750
0.850
0.827
0.686
Diabetes
Nursing
0.168
0.744
0.922
0.828
0.675
Atrial fibrillation (A-iib)
ECG
0.263
0.742
0.883
0.886
0.638
Hypertension
Fccho
0.445
0.712
0.744
0.733
0.693
Hyperiension
Radiology
0,420
0.679
0.741
0.707
0.633
Acute respiratory failure
Radiology
0.675
0.917
0.594
Hyperlipidemia
Echo
0,226
0.662
0.866
0.768
Congestive heart failure
Radiology
0.207
0.661
0.877
0.771
Atrial fibrillation
Radiology
0,233
0.655
0.858
0.761
0.574
Acute respiratory failure
Rcho
0.179
0.622
018887
0.777
0.519
Acute kidney failure
Radiology
0.154
0.607
0.898
0.748
0.511
Coronary atherosclerosis
ECG
0.297
0.590
0.806
0.791
0.471
Hyperlipidemia
Radiology
0.163
0,578
0.885
0.723
0.481
Acute kidney failure
Echo
0.194
0,571
0.863
0.732
0.468
Congestive heart failure
ECG
0.238
0.555
0.835
0.772
0.433
Hypertension
ECG
0.445
0.541
0.658
0.672
0.453
Diabetes
Echo
0.201
0.524
0.851
0.729
0.409
Diabetes
Radiology
0.172
0,453
0.860
0.688
0.338
Acute respiratory failure
ECG
0.148
0.391
0.879
0.769
0.262
Hyperlipidemia
ECG
0.182
0.381
0.849
0.746
0.256
Acute kidney failure Diabetes
ECG
0.167
0.365
0.861
0.774
0.239
ECG
0.187
0.307
0.839
0.785
0.191
Table 3: Descending order of F1 scores (as well as accuracy, precision and recall) from bag of words linear logistic regressions predicting various medical diagnoses from the MIMIC-III dataset using different medical note categories as input. We set 0.7 our Fl score cutoff for choosing the diagnoses to use downstream analysis with zero-shot classifiers (dashed horizontal line). We bold the diagnoses that passed this threshold and also have at least two note categories. We used these (bolded) diagnoses in the final oracle U in downstream analyses.
F LLM and Estimation Details
Choosing LLMs: FLAN and OLMo We used the large language models FLAN-T5 XXL and OLMo-7B-Instruul for inferring the oracle diagnoses from text data Chung al. (024)) Groeneveld et al. 2024). These are both fully "open" models in that we have full knowledge of their pre-training data, training objectives, and training details, and can be downloaded and updated on a local machine,
all of which are important for reproducible science (Palmer et al. 2024). We chose these two models because they have been fine-tuned for zero-shot classification and because they have been trained on different text corpora. Furthermore, we hypothesize that Flan will perform well on clinical notes because, according to Dodge et al. (202T)'s 'ss analysis, C4 (the pre-training data in Flan-T5) has among its top 25 domains patents. googlee com, journals, plw..ppllsooooooo.ooo.oo org, link. springer. com, wcw.ncbi. nlm. nih. gov, all of which likely contain medical text.
We use the following string as the prompt for both models: 'Context: [T AII it likely the patient has [U]?),nConstriinn you musl pick either "Yex" "No" without using any other words. We consider only the first five tokens of output for both models and assign value of for the proxy if the output string converted to all lowercase characters contains the word 'yes' and 0 otherwise.
Creating inferences from FLAN and OLMo
Even if you are uncertain.
18

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Odds ratio confidence interval estimation We calculate point estimate for the odds ratio Yw using the scikit-learn library (Pedregosa et al. 201T) by first training a linear logistic regression with W as the target outcome and { U C as the features. Whenever the positivity rate of W is less than 0.2 or greater than 0.8, i.e. there a class imbalance, we set the hyperparameter to "balanced". This uses the values of W to automatically adjust weights inversely proportional to class frequencies in the dataset. Regardless of whether we adjust for class imbalance, we set the hyperparameter penal ty to None to turn off regularization. Finally, we calculate the natural exponent of the coefficient of Z as the point estimate for the odds ratio TWZ.C.
Lass_weigh
We calculate the confidence interval for the odds ratio by drawing 200 bootstrap samples and repeating the steps above for each bootstrap sample to create bootstrap distribution. We then take the 0.025th CC low and CI low W Z.C. respectively.
and 0.975th percentiles of the bootstrap distribution as 7W2.C 2.C
Two-stage linear proximal causal inference estimator for the ACE Following sample splitting from the causal inference literature Hansen (2000), we start by splitting the semi-synthetic dataset into two splits-spil and split 2 where both splits are 50% the original dataset. We then train a linear logistic regression using split 1 with W as the target outcome and (A, 2 as the features. Like in the estimation procedure for the odds ratio. we set the hyperparameter plass_weight to "balanced" whenever there is class imbalance in the target outcome W and always set the hyperparameter penalty to None. Next, make probabilistic predictions W for W with the previously trained linear logistic regression model using split 2. Finally, we train a linear regression using split 2 of the data with Y as the target outcome and (A, W) U C as the features. The coefficient of A in the trained linear regression model is the estimate for the ACE.
We calculate the confidence interval for the ACE by drawing 200 bootstrap samples and repeating the steps above for each bootstrap sample create a bootstrap distribution. We then take the 0. 0.025th and 0.975th percentiles of the bootstrap distribution as the lower and upper bound of the confidence interval for the ACE, respectively.
G Semi-Synthetic Data Generating Process
The DAG representing the semi-synthetic data luta-gennrating process is shown in Figure 8 The variable U represents atrial fibrillation, congestive heart failure, coronary atherosclerosi of the native coronary artery, or hypertension depending on the setting. We use the reference table created in the pre-processing steps described in Section of the Appendix and start by normalizing the variable Age with the formula
Age:
-XAge
Age;
aAge
We then simulate draws of the binary variable via
p(A 1) expit(U + Gender
+ 0.9 Age)
A Bernoulliptt (p(A 1))
Next, we simulate draws of the continuous variable Y from:
Y N/00 1) + 1.3 A
+ 0.9 * Gender + 0.9 * Age
When estimating the ACE using the two-stage linear regression described in Section we condition on the baseline covariates Age and Gender as well the other diagnoses not being used as U.
H Additional P2M Experiments
In Figure g we report additional experimental results from PIM using Flan to infer proxies from both note categories and P2M using Flan and OLMo to infer proxies from one note category each. As expected, using one inferred proxy from L.LM directly in backdoor adjustment produces biased estimates for the ACE, When using PIM and P2M, the odds ratio falsification heuristic successfully
19

---

Age
U
Gender
A
Figure 8: Causal DAG showing the semi-synthetic data-generating process.
flags invalid estimates of the ACE. In the two cases where the inferred proxies pass the odds ratio falsification heuristic, we observe valid estimates for the ACE.
notable example of when the odds ratio heuristic correctly failed is for Echo and Nursing notes on the diagnosis hypertension. As shown in Figure | the estimates for the ACE for both PIM and P2M are far from the true ACE of 1.3. This explained by Table 21 where the oracle odds ratios between both proxies W and Z and the oracle U are nearly 1, suggesting that the zero-shot classifiers were not able to accurately predict the oracle. As expected such a scenario, the estimates for the ACE are biased, and our odds ratio heuristic successfully detects the violation of Assumption (P4) for proximal causal inference.
I Examining Text Conditional Independence
Recall, our procedure requires split text such that T 11 The U.C. This condition must hold at inference time when practioners are using our procedure and it must hold in the "real" part of semi-synthetic experiments in Section real-world clinical notes, we aim to investigate when this condition does or does not hold. To the best of our knowledge, is open problem on how to perform (conditional) independence tests on high-dimensional, compositional language data. Instead, we turn to an approximation that can lend us some preliminary evidence and examine the probabilities of top unigram features for each pairing of text categories. We show the results in Tables below.
Thus, for our semi-synthetic experiments with
After tokenization into unigrams, select the top five features via tf-idf scores. The tf-idf scores created under two settings: (1) fitting tf-idf on both note categories combined, or (2) fitting tf-idf separately each note category. Unique features (unigrams) must oceur in minimum of 10% of the documents and maximum 90% of the documents to be considered. Note, when we look at combinations of note pairings subset patients that have both notes, so subsets of documents are overlapping but not the exact same, resulting in different top features for the same category in different note pairs.
Key Metrics from Semi-Synthetic Simulations
We report key metrics, mostly requiring access to the oracle U, for the semi-synthetie simulations in the tables below. Although these metries will typically not be available to practitioners inference time, they are helpful in understanding the relationship between the inferred proxies W and Z under various conditions. The odds ratio values between the proxies and the oracle, 7WUC and 7zuC. show how correlated the proxies are with the oracle, an important indicator for (P4). The difference between and the positivity rate of the oracle describes the minimum accuracy threshold for which the inferred proxy must perform to be more accurate than simply predicting the majority class.
20

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1.7
1.7
True ACE
1.6
1.6
Est. ACE for A-Fib
Est. ACE for A-Fib ECG/Nursing
ECG/Echo
1.5
1.4
1.4
1.
1.3
12
1.2
1.1
1.1
1.7
1.7
1.6
1.6
Est. ACE for A-Fib
Est. ACE for Heart
Echo/Nursing
1.
Echo/Nursine
1.4
1.4
1.3
1.3
12
1.2
1.1
1.1
1.7
1.7
1.6
1.6
Est. ACE for A-Sis
Est. ACE for A-Sis Echo/Radiology
Echo/Nursing
1.
1.5
1.4
1.4
1.3
1.3
12
1.2
1.1
1.1
1.7
Est. ACE for Hypertension
1.6
1.6
Est. ACE for A-Sis
Radiology/Nur Badiology/Nursing
1.5
Echo/Nursing
1.5
I
1
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
Backdoor w/ proxy
P1M
Backdoor w/ proxy
P1M
P2M
Figure 9: Semi-synthetic results for ACE point estimates (dots) and confidence intervals (bars) for all oracles and note categories that detected sufficient signal in. Here, v distinguishes settings that passed the odds ratio heuristic from those that failed it, with Thigh 2.
21

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mild
mildly
rhythm
thickened
ECG
0,000
0.026
0.003
0.851
0.000
Echo
0.897
0.847
0.845
0.150
0.743
name
rhythm
the
ECG
0.000
0.004
0.824
0.581
0.638
Nursing
0.872
0.816
0.113
0.266
0.647
chest
contrast
left
pm
right
ECG
0,004
0.000
0.385
0.000
0.175
Radiology
0.845
0.517
0.824
0.876
0.858
mild
mildly
name
thickened
was
Echo
0.830
0.845
0.137
0.734
0.388
Nursing
0.094
0.018
0.810
0.004
0,596
chest
dilated
mild
mildly
thickened
Echo
0.072
0.695
0.839
0.838
0.732
Radiology
0.883
0.071
0.420
0.102
0.018
chest
left
right
Nursing
0.306
0.521
0.389
0,339
0.600
Radiology 0.834
0.556
0.827
0.856
0.417
Table Combined ff-idf. For each pair of note categories (subsequent rows), we selected the top five unigram features (columns) via tf-idf scores on the combined note pairs. We report the proportion of notes in each category that contain that feature.
ECG
sis, of, rhythm, the, wave]
Echo
[aorta, mild, mildly, of, thickened]
ECG
[of, rhythm, st, the, wave] [hr. is, name, this, was]
Nursing
ECG
[is, of, rhythm, the, wavel [chest, contrast, left, right, to]
Radiology
Echo
[dilated, mild, mildly. thickened, with] [hr, is, name, this, was]
Nursing
Echo
[aorta, mild, mildly, of, thickened] [chest, contrast, left, pm, right]
Radiology
Nursing
[hr, is, name, neuro, this] [chest, contrast, left, right, to]
Radiology
Table 5: Separate tf-idf. For each pair of note categories (subsequent rows), report the top five unigram features via tf-idf scores that were fit on each note category separately.
Oracle?
Proxies
Metric
U-A-Fiib
Yes
p(U = 1)
0.665
WUCC
21.255
Accuracy
0.802
Yes
from Flan T (ECG)
p(W
0.186
Precision
0.870
Recall
0.481
Yzuc Accuracy
17.815
0.716
Yes
Z from Flan The (Echo)
pl Z =
0.064
Precision
0.899
Recall
0.172
No
Z, Z.W
Raw Agreement Rate; p(W = 2)
0.841
Table 6: Key metrics for the diagnosis atrial fibrillation when inferring proxies from ECG and Echo clinicians' notes with one zero-shot classifier.
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Oracle?
Proxies
Metric
U/=A-Fib
Yes
1 1-p --UUU =
0.665
CWCC
21,255
Accuracy
0.802
Yes
W from Flan on T (ECG)
p( = !)
0.186
Precision
0.870
Recall
0.481
2.666
Accuracy
0.677
Yes
Z from OLMo on T (Fcho)
plZ =
0.170
Precision
0.537
Recall
0.272
No
Z,
Raw Agreement Rate; p(W %)
0.766
Table 7: Key metries for the diagnosis atrial fibrillation when inferring proxies from ECG and Echo
clinicians' notes with two zero-shot classifiers.
Oracle?
Proxies
Metric
U=A-Fib
Yes
p(U 1)
0.738
wwcc
23,825
Accuracy
0.839
Yes
W from Flan on T (ECG)
p(W 1)
0.143
Precision
0.853
Recall
0.466
6.751
Accuracy
0.794
Yes
Z from Flan T (Nursing)
p(Z 1)
0.240
Precision
0.615
Recall
0.563
No
Z,
Raw Agreement Rate; p(W 2)
0.812
Table 8: Key metrics for the diagnosis atrial fibrillation when inferring proxies from ECG and Nursing clinicians' notes with one zero-shot classifier.
Oracle?
Proxies
Metric
U=A-Ft A-bb
Yes
p(U 1)
0.738
Twu.
23,825
Accuracy
0.839
Yes
W from Flan on T (ECG)
p p(W = 1)
0.143
Precision
0.853
Recall
0.466
"zu.c
2,400
Accuracy
0.689
Yes
Z from OLMo T (Nursing)
p(Z
0.288
Precision
0.415
Recall
0.456
No
Z.
Raw Agreement Rate; p(W 2)
0.716
Table 9: Key metrics for the diagnosis atrial fibrillation when inferring proxies from ECG and Nursing clinicians' notes with two zero-shot classifiers.
23

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Oracle?
Proxies
Metric
U=A-Fib
Yes
1-p(U = 1)
0.685
wwcc
15.959
Accuracy
0.731
Yes
W from Flan The (Echo)
p(W 1)
0.060
Precision
0.885
Recall
0.169
7ZUC
6.044
Accuracy
0.760
Yes
Z from Flan T (Nursing)
p(Z
0.283
Precision
0.632
Recall
0.569
No
Z,
Raw Agreement Rate; p(W = 2)
0.746
Table 10:
Key metrics for the diagnosis atrial fibrillation when inferring proxies from Echo and Nursing clinicians' notes with one zero-shot classifier.
Oracle?
Proxics
Metric
U=A-Fib
Yes
1-U =)
0.685
Twu.c
15,959
Accuracy
0.731
Yes
W from Flan on TT (Echo)
P( 1)
0.060
Precision
0,885
Recall
0.169
TZU.C
2.237
Accuracy
0.655
Yes
Z from OLMo T (Nursing)
p(Z=
0.318
Precision
0.454
Recall
0.458
No
Z.W
Raw Agreement Rate; p(W 2)
0.683
Table 11:
Key metrics for the diagnosis atrial fibrillation when inferring proxies from Echo and Nursing clinicians' notes with two zero-shot classifiers.
Oracle?
Proxics
Metric
U=Heart
Yes
1 p(U 1)
0.651
TwF. Accuracy
3.863
0.704
Yes
W from Flan on The (Echo)
p(W 1)
0.297
Precision
0.591
Recall
0.502
7zu.
2.450
Accuracy
0.643
Yes
2 from Flan on T (Nursing)
p(Z =
0.407
Precision
0.490
Recall
0.572
No
2, W
Raw Agreement Rate; p(W 2)
0.648
Table 12: This setting was included the main text of the paper. Key metrics for the diagnosis congestive heart failure when inferring proxies from Echo and Nursing clinicians' notes with one zero-shot classifier.
24

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Oracle?
Proxies
Metric
U=Heart
Yes
1-p(U =1)
0.651
WWU.
3.863
Accuracy
0.704
Yes
W from Flan on Th (Echo)
p(W = 1)
0.297
Precision
0.591
Recall
0.502
'2UC
1.416
Accuracy
0.588
from OLMo on T (Nursing)
p(Z = 1)
0.357
Precision
0,412
Recall
0.421
No
Z, W
Raw Agreement Rate; p(W = 2)
0.590
Table 13: This setting was included in the main text of the paper. Key metrics for the diagnosis congestive heart failure when inferring proxies from Echo and Nursing clinicians' notes with two zero-shot classifiers.
Oracle?
Proxies
Metric
U=A-Sis
Yes
--UUU 1)
0.627
WwCc Accuracy
6.232
0.704
Yes
W from Flan on TiT (Echo)
p(W = 1)
0.156
Precision
0.746
Recall
0.313
10.546
Accuracy
0.785
Yes
Z from Flan T (Nursing)
p(Z =
0.331
Precision
0.739
Recall
0.656
No
Z,
Raw Agreement Rate; p(W = Z)
0.721
Table 14: Key metries for the diagnosis coronary atherosclerosis when inferring proxies from Echo and Nursing clinicians' notes with one zero-shot classifier.
Oracle?
Proxies
Metric
U=A Sis
Yes
p(U 1)
0.627
"ww.. Accuracy
6.232
0.704
Yes
W from Flan on The (Echo)
p(W = 1)
0.156
Precision
0.746
Recall
0.313
T
4.134
Accuracy
0.680
Z from OLMo on T (Nursing)
p(Z = 1)
0.135
Precision
0.693
Recall
0.251
No
W
Raw Agreement Rate; p(W = Z)
0.787
Table 15: Key metrics for the diagnosis coronary atherosclerosis when inferring proxies from Echo and Nursing clinicians' notes with two zero-shot classifiers.
25

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Oraclc?
Proxies
Metric
U-s
Yes
1 1-p(U = 1)
0.643
"ww.
6.240
Accuracy
0.708
Yes
W from Flan TT (Echo)
p(W = 1)
0.133
Precision
0.745
Recall
0.277
T2EC Accuracy
6.344
0.727
Yes
Z from Flan on T (Radiology)
p =
0,180
Precision
0.733
Recall
0.370
No
Z, W
Raw Agreement Rate; p(W Z)
0.784
Table 16: This setting was included the main text of the paper. Key metries for the diagnosis coronary atherosclerosis when inferring proxies from Echo and Radiology clinicians' notes with one zero-shot classifier.
Oracle? Proxies
Metric
U==-Siis
Yes
1 1-p(U=11 =)
0.643
wwtc Accuracy
6.240
0.708
Yes
W from Flan on T (Echo)
p(W = 1)
0.133
Precision
0.745
Recall
0.277
1ZEC
5.046
Accuracy
0,678
Yes
Z from OLMo T (Radiology)
p(Z =1)
0.069
Precision
0.753
Recall
0.146
No
2, W
Raw Agreement Rate; p(W Z)
0.830
Table This setting was included the main of the paper. Key metries for the diagnosis coronary atherosclerosis when inferring proxies from Echo and Radiology clinicians' notes with two zero-shot classifiers.
Oracle? Proxies
Metric
U U=A-Sis
Yes
1-p(U =
0.735
WwC
7.265
Accuracy
0.784
Yes
W from Flan T (Radiology)
p(W
0.129
Precision
0.690
Recall
0.335
ZZU.
12,800
Accuracy
0.833
Yes
Z from Flan on Thee (Nursing)
p(Z = 1)
0,224
Precision
0.719
Recall
0.606
No
Z, W
Raw Agreement Rate; p(W = 2)
0.793
Table 18: This setting was included in the main text of the paper. Key metrics for the diagnosis coronary atherosclerosis when inferring proxies from Radiology and Nursing clinicians' notes with zero-shot classifier.
26

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Oracle?
Proxies
Metric
U=A-Sis
Yes
1-p(U =1)
0.735
7wCC
7.265
Accuracy
0.784
Yes
W from Flan T (Radiology)
p(W =
0.129
Precision
0.690
Recall
0.335
4.081
Accuracy
0.754
Z from OLMo on T (Nursing)
p pZ= =711
0. 0.104
Precision
0.590
Recall
0.231
No
Z, W
Raw Agreement Rate; p(W = Z)
0.821
Table 19: This setting was included in the main text of the paper. Key metrics for the diagnosis coronary atherosclerosis when inferring proxies from Radiology and Nursing clinicians' notes with two zero-shot classifiers.
Oracle? Proxies
Metric
Hypertenniinn
Yes
p(U =)
0.569
1.057
Accuracy
0.488
Yes
W from Flan T (Echo)
p(W 1)
0.648
Precision
0.438
Recall
0.657
1.414
Accuracy
0.532
Yes
Z from Flan on T (Nursing)
p(Z 1)
0.619
Precision
0,470
Recall
0.675
No
Z.
Raw Agreement Rate; p(W Z)
0.546
Table 20: Key metrics for the diagnosis hypertension when inferring proxies from Echo and Nursing clinicians' notes with zero-shot classifier.
Orucle?
Proxies
Metric
U U'=Hypertension
Yes
p(U 1)
0.569
Twvc
1.057
Accuracy
0.488
Yes
W from Flan on T (Echo)
p(W = 1)
0. 0.648
Precision
0.438
Recall
0.657
Czucc
1.053
Accuracy
0.524
Yes
Z from OLMo T (Nursing)
p(Z = 1)
0.432
Precision
0,448
Recall
0.449
No
Raw Agreement Rute; p(W Z)
0.494
Table 21: Key metrics for the diagnosis hypertension when inferring proxies from Echo and Nursing clinicians' notes with two zero-shot classifiers.
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K
Compute Resources
To run the experiments in this paper, we used a local server with 64 cores of CPUs and 4 NVIDIA RTX A6000 48GB GPUs. Our semi-synthetic pipeline ran for approximately 36 hours where Flan took roughly 12 hours and OLMo took roughly 24 hours to compute inferences from the text data.
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NeurIPS Paper Checklist
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Reviews:
[{"review_id": "EqfYU4zCLS", "reviewer": "Reviewer_dab7", "summary": "The paper considers the causal effect estimation setting where a confounder is latent but with unstructured text data that could serve as proxies. Specifically, the paper proposes to incorporate zero-shot classifiers (to operate on text-based proxies), together with a falsification heuristic, into the proximal causal inference framework. The goal of the text-based proxy design is to craft W and Z that satisfy the identification condition in proximal causal inference framework. Empirical evaluations are presented in synthetic and semi-synthetic experiments.\n\n---\n\n**Post rebuttal**\n\nI have increased my score, under the assumption that the revised manuscript could sufficiently address the original concerns on material organizations.", "questions": "(1) regarding a series of different constraints, conditions, gotcha's, assumptions\n\nIn Section 2, there are P1 -- P4, a set of conditions should be satisfied in order for the proximal g-formula to work. In order to respond to the criticism of potential unavailability of W and Z in structured data, further assumptions S1 -- S2 are proposed. Then in Section 3 and Section 4, a set of gotcha's, two additional pre-conditions (lines 216 -- 218), and another set of conditions related to odds-ratio based heuristics (lines 245 -- 247) are presented. How do these conditions fit together to respond to the criticism of proximal causal inference on structured data? Are they all identification conditions for the text-based proxy proximal causal inference (other than the fact that they are conditions specified by previous works for different components put together)?\n\n(2) the fully and semi- synthetic experiments consider structured data, it is not exactly clear how these text proxies look like and if they correspond to all or part of the aforementioned constraints/conditions\n\nFor fully and semi- synthetic experiments, the setting is largely structured data instead of text-based proxies. Examples of text proxies that the proposed design procedure yields would be much more intuitive than just claiming \"satisfy by design\" (line 136).", "limitations": "The organization of material could be improved to better present how the proposed approach responds to criticism of proximal causal inference (with structured data). Examples beyond fully and semi- synthetic experiments will make it clearer w.r.t. how the designed text-based proxies help to address the aforementioned criticism on previous work.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The strength of the paper comes from the attempt to conduct proximal causal inference on unstructured text data. The paper carefully considers identification conditions specified in the proximal causal inference framework, and proposes a design procedure together with a falsification heuristic to find two text-based proxies (so that the proximal inference can be conducted).", "weaknesses": "The weakness of the paper comes from the organization of the material (especially the constraints/conditions involved), and relatively simple settings considered in (fully-/semi-) synthetic experiments. In particular, further clarifications and/or discussions on following points would be very helpful (detailed in \"Questions\" section):\n\n(1) regarding a series of different constraints, conditions, gotcha's, assumptions\n\n(2) the fully and semi- synthetic experiments consider structured data, it is not exactly clear how these text proxies look like and if they correspond to all or part of the aforementioned constraints/conditions. Examples of text proxies would be much more intuitive than claiming \"satisfy by design\" (line 136)", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the reviewer’s comments on questions. We address each below.\n\n>[F]urther assumptions S1 -- S2 are proposed. Then in Section 3 and Section 4, a set of gotcha's, two additional pre-conditions (lines 216 -- 218), and another set of conditions related to odds-ratio based heuristics (lines 245 -- 247) are presented [...] How do these conditions fit together to respond to the criticism of proximal causal inference on structured data? Are they all identification conditions for the text-based proxy proximal causal inference (other than the fact that they are conditions specified by previous works for different components put together)?\n\n(P1) – (P4) are conditions for proximal causal inference as previously defined by Tchetgen Tchetgen (2020). The primary criticism of this work, as stated in lines 130-131, is that it is often difficult in practice to find structured proxies that fulfill (P1) – (P4). \n\n(S1) and (S2) are assumptions that limit the scope of our method. In lines 216-218, we further state two additional assumptions for our method: (1) the conditional independence of the two pieces of text and (2) W and Z being predictive of U. In Section 3, we show that (1) maps to (P1) – (P3), and (2) maps to (P4). These assumptions are not strictly necessary, and there may be other ways to satisfy the conditions for proximal causal inference, but we find these to be the most intuitive and easy for an analyst to verify/understand.\n\nIn lines 245-247, we describe an odds ratio falsification heuristic: This is not an identification condition; rather,  it is an empirical check for violations of (P1) – (P4). As we show in our synthetic and semi-synthetic experiments, the falsification heuristic correctly flags potentially problematic proxies and prevents the practitioner from making incorrect downstream estimates.\n\n> For fully and semi- synthetic experiments, the setting is largely structured data instead of text-based proxies. Examples of text proxies that the proposed design procedure yields would be much more intuitive than just claiming \"satisfy by design\" (line 136).\n\nWe kindly refer the reviewer to lines 292-313 as well as Appendices D, E, and F for descriptions of our semi-synthetic experiments. We use real-world clinical notes from the MIMIC-III dataset.\n\nWe expand upon what we wrote in Section 5, and describe an example of how text proxies are obtained  with an example clinical note. Let us say that we are interested in obtaining text proxies for the latent variable atrial fibrillation. A clinical note may contain the following text:\n\n\n“The patient was suffering from breathing difficulties and irregular heart rate.”\n\nWe then append a prompt to the clinical note and use it as input to a  zero-shot classifier (Flan-T5, for example):\n\n“Context: The patient was suffering from breathing difficulties and irregular heart rate.\n\nIs it likely the patient has atrial fibrillation?\n\nConstraint: Even if you are uncertain, you must pick either “Yes” or “No” without using any\nother words.”\n\nIf Flan-T5 outputs “Yes”, the text proxy has a value of 1. If Flan-T5 outputs “No” or any other text, the text proxy has a value of 0.\n\nWith more space in a camera-ready version, we are happy to include this example and the figure in the attached PDF file to our rebuttal in the paper to make this procedure more explicit. \n\n> The organization of material could be improved to better present how the proposed approach responds to criticism of proximal causal inference (with structured data). Examples beyond fully and semi- synthetic experiments will make it clearer w.r.t. how the designed text-based proxies help to address the aforementioned criticism on previous work.\n\nWe thank the reviewer for this comment. Below is an example describing why proximal causal inference with structured data can be challenging. We had this example in  a previous draft but had to cut due to space constraints. With an extra page in the camera ready version, we plan to put this example back in to more clearly express our criticism of proximal causal inference with structured data: \n\nSuppose we aim to find proxies (in the structured variables) of atrial fibrillation (U) and have access to shortness of breath and heart palpitations. Although these proxies seem reasonable, we show how they violate the proximal causal inference conditions. Patient complaints about shortness of breath may affect which medication a clinician prescribes (A); hence, using shortness of breath as the proxy W violates (P2). Furthermore, a lack of oxygen resulting from shortness of breath may affect the healing of blood clots, thus influencing measurements of the D-dimer protein Y. In this case, using shortness of breath as the proxy Z violates (P3). Shortness of breath can also sometimes be a symptom of heart palpitations, violating (P1).", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Uo3CTynFPf", "reviewer": "Reviewer_iLUt", "summary": "Causal inference techniques often rely on the assumption that all confounders can be observed or inferred from available data. This paper proposes a method to address the setting where a confounder is entirely unobserved; instead there is available pre-treatment text that can be used to infer proxies, which in turn have predictive value for the unobserved confounder. The authors adapt proximal causal inference ideas to text-data settings, discuss \"gotchas\" in naive implementations of such a method, and explore various relevant choices before presenting best performing method. Specifically, they use multiple instances of pre-treatment text to infer two proxies for each datapoint using two different zero-shot language models. This is then used for average causal effect estimation via the proximal g-formula. The paper provides empirical evaluation on synthetic and semi-synthetic datasets as well as a falsifcation heuristic for untestable assumptions.", "questions": "As mentioned above:\n\n- Do the authors expect the performance of their method to improve as they use larger language models to infer proxies? \n\n- Can the authors provide any intuition for what they expect to be the impact of using a language model that has been trained on post-treatment text data to infer proxies and plug them into the causal effect estimation?", "limitations": "The paper sufficiently addresses limitations of the setting and method proposed.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Originality: While proximal causal inference has been proposed and studied, this paper adapts existing methods to text data and explores practical considerations in their implementation.\n\nClarity: The paper is well-written, with clear statements of the requirements of the method and the assumptions it relies on. \n\nQuality: The paper proves various propositions that guide the design of the proposed method in a principled manner. It also explores a falsification heuristic for untestable assumptions and empirically verifies that the heuristic is aligned with final performance in synthetic and semi-synthetic settings. \n\nSignificance: Unobserved confounding is a significant challenge in causal inference. The paper is well-motivated by the availability of large amounts of text data and the recent progress in language modeling.", "weaknesses": "- The significance of the empirical evaluation is limited due to synthetic and semi-synthetic experiments. The impact of the proposed method in realistic settings is hard to assess. While the evaluation of real settings is hampered by the lack of ground-truth, it may still be possible to synthesize data that is as realistic as possible so that the more realistic challenges of deploying such a method may be uncovered.\n\n- The experiment design of the paper carefully avoids post-treatment text to avoid biased effect estimation. However, the proxy inference from language models indirectly depends on the pretraining dataset used to train the language model. The data in that pretraining set may be post-treatment text. The impact of this dependence is unclear.\n\n- It is unclear how sensitive the performance of the proposed method is to the choice of pretrained zero-shot model, or whether we can expect better performance as the zero-shot model used scales up.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the thoughtful feedback. We address the reviewer’s questions and comments on our paper's weaknesses.\n\n> The significance of the empirical evaluation is limited due to synthetic and semi-synthetic experiments. The impact of the proposed method in realistic settings is hard to assess. While the evaluation of real settings is hampered by the lack of ground-truth, it may still be possible to synthesize data that is as realistic as possible so that the more realistic challenges of deploying such a method may be uncovered.\n\nWe thank the reviewer for this comment. We agree we should evaluate with the most realistic data possible. Yet, we believe our semi-synthetic experiments, which use real-world clinical notes from MIMIC-III, are the most realistic possible given our constraints. \n\nOn Line 276, we write \"In causal inference, empirical evaluation is difficult because it requires ground-truth labels for counterfactual outcomes of an individual under multiple versions of the treatment, data that is generally impossible to obtain Holland (1986); see Gentzel et al. (2019); Keith et al. (2023).\" We plan to expand that writing to make the constraints of empirical evaluation in causal estimation even more clear. Gentzel et al. (2019) and Keith et al. (2023) describe methods for evaluation that are more realistic than semi-synthetic evaluation if one has an RCT dataset and can downsample the RCT dataset to create an observational (confounded) dataset. However, for the proximal setting we investigated in this paper, we could not find an existing RCT that would contain a sufficient amount of text and was suitable for the proximal causal inference set-up. \n\nIn contrast, semi-synthetic experiments use real data for part of the DGP and then specify synthetic relationships for the remainder of the DGP. Semi-synthetic experiments have been used extensively for empirical evaluation of causal estimation methods; see [Shimoni et al., 2018](https://arxiv.org/abs/1802.05046); [Dorie et al., 2019](https://arxiv.org/abs/1707.02641); [Veitch et al., 2020](https://proceedings.mlr.press/v124/veitch20a/veitch20a.pdf). We will add additional writing clarifying our choice of semi-synthetic experiments in our camera ready paper upon acceptance. \n\n> Can the authors provide any intuition for what they expect to be the impact of using a language model that has been trained on post-treatment text data to infer proxies and plug them into the causal effect estimation?\n\nWe thank the reviewer for this thoughtful comment. In Appendix B, we describe that if one of the proxies is constructed using post-treatment text and the other proxy is constructed from pre-treatment text, then proximal causal inference conditions could still be satisfied. However, we agree with the reviewer that if both proxies are constructed using LLMs that have post-treatment pretreatment text, this could be potentially problematic. \n\n**(1) We believe MIMIC-III is not contaminated in the pre-training datasets of the LLMs we use in our semi-synthetic experiments.** \n\nIn our semi-synthetic experiments, we intentionally choose to use \"open\" LLMs, Flan-T5 and OLMo, in which the entire pretraining dataset is known and can be inspected. MIMIC-III is not available via a public URL (researchers have to sign-up and agree to a terms of service) so we do not believe it is contaminated in the pretraining data of either of these LLMs.  \n\nFlan-T5 is built upon T5 which uses C4 (Colossal Clean Crawled Corpus) as its pretraining data (Raffel et al. 2020). Dodge et al. 2021 explore and document C4 and provide a search index, https://c4-search.apps.allenai.org/. We sampled full sentences from MIMIC-III and searched for them in C4 and did not have any search hits. \n\nOLMo is built from an open pretraining dataset Dolma (Soldaini et al. 2024), which is a 3 trillion token English corpus. Soldanini et al. describe that the data is acquired from sources that are \"made accessible to the general public\" such as the Common Crawl, GitHub, Reddit, Semantic Scholar, and Wikipedia. Again, because MIMIC-III is not publicly available, we again believe it is very unlikely any of the individual data is in the pretraining data. \n\n**(2) Other applications (e.g., social media) that have individual post-treatment texts in the pretraining data may need to rely on temporal time stamps.**\n\nEven though we have established that our semi-synthetic experiments using MIMIC-III may not be contaminated or contain individual data, there are other applications in which there could be post-treatment individual text data in the pretraining data of a LLM.\n\nFor example, one might be using our proximal causal inference with text data design to infer proxies from social media posts from a platform such as Reddit. Individual posts that are post-treatment may possibly be scraped and included in the pretraining data of LLMs. In this scenario, to avoid this issue, we recommend (1) using open LLMs, such as we do with Flan-T5 and OLMo, in which the pertaining data can be inspected, and (2) using temporal time stamps to ensure that the LLMs pretraining data cutoff date is prior to treatment. \n\n> It is unclear how sensitive the performance of the proposed method is to the choice of pretrained zero-shot model, or whether we can expect better performance as the zero-shot model used scales up. [...] Do the authors expect the performance of their method to improve as they use larger language models to infer proxies?\n\nWe thank the reviewer for this comment, and we will make this point even more explicit in the writing of our next draft. As the predictive performance of the zero-shot models improves, this will not affect the bias of causal estimates (the estimates will remain unbiased)  but it will **decrease variance (making confidence intervals narrower)**.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gDI72FvrmY", "reviewer": "Reviewer_uHfh", "summary": "The situation with unobserved confounding variables is quite common in applied research and makes causal inference complicated. To deal with such settings, the authors propose a new causal inference method that uses multiple instances of pre-treatment text data, estimates two proxies from two zero-shot models on the separate instances, and applies these proxies in the proximal g-formula. It is shown that the identification conditions are satisfied, The method is evaluated in a simulation study on synthetic and semi-synthetic data.", "questions": "- How credible / realistic are (P1) and that $T^1_pre$ is conditionally independent from $T^2_pre$ in typical applications (e.g. using electronic health records)?\n-  How could one use EHR to construct proxies? Are the assumptions fulfilled? (Might be questionable.. the example mentioned in the text is not convincing.)", "limitations": "Limitations are adressed adequately. As mentioned above, theoretical guarantees for the propsoed method might be very valuable.", "rating": 5, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "- The paper proposed a new innovative method for proximal causal inference utilizing text data.\n- The paper is well written and motivated.", "weaknesses": "- Literature review is incomplete. The idea of proximal inference goes back to Zvi Griliches (1977) who should get credit for it. As background reading the corresponding chapter in the textbook \"Applied Causal Inference Powered by ML and AI\" by Chernozhukov and coauthors (2024).\n- To overcome the completeness condition the paper \"Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach\" (arXiv:2103.14029) might be helpful.\n- The theoretical results (Prop 1-4) are all in some sense \"negative\" and straightforward / already known. What would be more interesting, would be some \"positive\" results about the proposed method, although I am aware that this might be quite challenging.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the thoughtful feedback. We address the reviewer’s questions and comments on our paper's weaknesses.\n\n> Literature review is incomplete. The idea of proximal inference goes back to Zvi Griliches (1977) who should get credit for it. As background reading the corresponding chapter in the textbook \"Applied Causal Inference Powered by ML and AI\" by Chernozhukov and coauthors (2024).\n\nThank you for pointing us to the paper. We are happy to point to it as a reference for causal inference with proxies in linear SEMs and that later works generalize this to non-linear settings.\n\n> To overcome the completeness condition the paper \"Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach\" (arXiv:2103.14029) might be helpful.\n\nThank you for the reference. We believe this work complements our own as it concerns estimation given a pair of valid proxies. In our work, we provide a way of generating proxies from unstructured text that first satisfy the structural assumptions—assumptions P1-P3 that are encoded in the causal DAG Figure 1(b) of our paper and Figure 1 of the suggested reference—that are needed for both classical estimators in the proximal causal inference literature as well as the estimators developed in the suggested reference. \n\nThe estimators in the reference depart from older proximal literature on assumption P4 of completeness. Importantly, however, the old and new estimators both require the $U \\rightarrow Z$ and $U \\rightarrow W$ edges to be real, i.e., the proxies must be at least weakly correlated with the unmeasured confounder. In our algorithm for generating proxies, when the zero-shot models generate even weakly predictive proxies, they automatically satisfy completeness and therefore the alternative assumptions suggested in the reference since in the discrete case the assumptions in the reference are strictly weaker (and so if completeness holds, these assumptions also hold). Thus, the estimators developed in the reference could be directly applied to the proxies generated by our algorithm. It would be interesting to see what would happen if one were to try and use zero-shot models to predict continuous proxies—in this case completeness and the assumptions listed in the reference are incomparable, which would necessitate the use of different estimators depending on what conditions were more likely to hold. \n\nWe are happy to add a short discussion on this with the additional space granted in the camera ready if the paper is accepted.\n\n> The theoretical results (Prop 1-4) are all in some sense \"negative\" and straightforward / already known. What would be more interesting, would be some \"positive\" results about the proposed method, although I am aware that this might be quite challenging.\n\nWe respectfully push back on this. Propositions 1-3 are indeed “negative” in that they correspond to results that show what cannot be done in order to obtain unbiased causal effect estimates. This is the same sense in which non-identification/completeness results in causal inference and missing data are negative results — they inform the reader about datasets/data collection procedures that would lead to biased estimates, e.g., [Shpitser and Pearl, 2006](https://ftp.cs.ucla.edu/pub/stat_ser/r327.pdf) and [Nabi et al, 2020](https://arxiv.org/pdf/2004.04872). Further, while Propositions 1-3 appear simple, they are not obvious: We have, for example, encountered [applied work](https://arxiv.org/pdf/2307.03687) that treats machine learned predictions as direct plug-ins for unmeasured variables—this is the same sense in which collider bias can be obvious, but only to those who know it and are already looking for it.\n\nProposition 4 on the other hand is a “positive” result that shows identification and unbiased estimates are possible when following our algorithm. While these conditions may not always be fulfilled (just as with any other identification conditions) we also propose an odds ratio heuristic to check for violations of these conditions. The semi-synthetic results (Table 2 and Fig 3)  that use real-world text data from MIMIC-III also provide positive results (estimates with low bias) for the theory we propose.\n\n> How credible / realistic are (P1) and that $T^1_{pre}$ is conditionally independent from $T^2_{pre}$  in typical applications (e.g. using electronic health records)?\n\nWe address this issue in our paper: In line 302-303, we write “We hypothesize that notes written by different individuals will satisfy $T^{pre}_1 \\perp T^{pre}_2 | U, C$ since each individual will write a conditionally independent realization of 304 the patient’s status”. That is, this independence is more likely to hold if you use different clinical notes from different departments, in social media use different posts perhaps. We also propose the odds ratio heuristic as a way for the analyst to safeguard against violations of this condition.\n\n> How could one use EHR to construct proxies? Are the assumptions fulfilled? (Might be questionable.. the example mentioned in the text is not convincing.)\n\nWe refer the reviewer to our semi-synthetic experiments in Section 5 that use real EHR data and clinical notes from MIMIC-III to do exactly this. Table 2 and Fig 3 shows the success of our proxy generation process as well as the success of the odds ratio heuristic as a safeguard when the assumptions are not fulfilled. We have also added an illustrative figure of our proxy generation process that can be found in the rebuttal PDF and that we would be happy to add to the camera ready if the paper is accepted.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We thank the reviewers for their thoughtful comments and suggestions on improving our paper. We respond to each reviewer individually and address each reviewer’s questions point by point. We also include in our rebuttal a PDF with a figure that shows our proposed proximal causal inference with text design for our semi-synthetic pipeline (which uses real-world clinical notes from MIMIC-III). This figure specifically responds to reviewer dab7’s comment, and we intend to, given more space in a camera-ready version, add this figure to our paper.

If anything can be further clarified, please let us know. We look forward to further discussions.

Meta-review: This paper treats causal inference in the setting where there is an "unobserved" confounder, but there is a proxy variable available in the form of text. The reviewers appreciated the problem setting, the principled approach, and the clarity of communication.
Decision: Accept (poster)