SyncTwin: Treatment Effect Estimation with Longitudinal Outcomes
Authors: Zhaozhi Qian
Yao Zhang
Ioana Bica
Angela Mary Wood
Mihaela van der Schaar
Venue: NeurIPS 2021 Poster (2021)
Keywords: Causal Inference
Healthcare
Interpretability

Abstract: Most of the medical observational studies estimate the causal treatment effects using electronic health records (EHR), where a patient's covariates and outcomes are both observed longitudinally. However, previous methods focus only on adjusting for the covariates while neglecting the temporal structure in the outcomes. To bridge the gap, this paper develops a new method, SyncTwin, that learns a patient-specific time-constant representation from the pre-treatment observations. SyncTwin issues counterfactual prediction of a target patient by constructing a synthetic twin that closely matches the target in representation. The reliability of the estimated treatment effect can be assessed by comparing the observed and synthetic pre-treatment outcomes. The medical experts can interpret the estimate by examining the most important contributing individuals to the synthetic twin. In the real-data experiment, SyncTwin successfully reproduced the findings of a randomized controlled clinical trial using observational data, which demonstrates its usability in the complex real-world EHR.

SyncTwin: Treatment Effect Estimation with
Longitudinal Outcomes
Zhaozhi Qian University of Cambridge 2 zq2240 cam. ac.uk
Yao Zhang University of Cambridge y25550cam. ac. uk
Ioana Bica University of Oxford The Alan Turing Institute ioana. wwc.aceng........... ox ac.uk
Angela Mary Wood University Cambridge
Mihaela van der Schaar University of Cambridge
amw79@meds ch cam ac. uk
UCLA The Alan Turing Institute mv472 7 cam ac uk
Abstract
Most of the medical observational studies estimate the causal treatment effects using electronic health records (EHR), where a patient's covariates and outcomes are both observed longitudinally. However, previous methods focus only on ad- justing for the covariates while neglecting the temporal structure in the outcomes. To bridge the gap, this paper develops a new method, SwnccTwin, that learns a patient-specific time-constant representation from the pre-treatment observations. SyncTwwn issues counterfactual prediction of a target patient by constructing a synthetic twin that closely matches the target in representation. The reliability the estimated treatment effect can be assessed by comparing the observed and synthetic pre-treatment outcomes. The medical experts can interpret the estimate by examining the most important contributing individuals to the synthetic twin. In the real-data experiment, Sync successfully reproduced the findings of a randomized controlled clinical trial using observational data, which demonstrates usability in the complex real-world EHR.
Introduction
Estimating the causal individual treatment effect (ITE) using observational data has become increas- ingly common in the medical literature due to the popularization of electronic health records (EHR). The EHR is longitudinal collection of records: it contains repeated measurements of patient's health condition over irregular time intervals. Although the treatments may also vary over time, many studies consider point treatment, where the treatment allocation performed some observed time Point treatment is widely applicable to problems involving one-off treatments (e.g. surgical operations) treatments that do not change frequently (e.g. long term medication for chronic disease). We will refer to the setting above as Longitudinal and Irregularly sampled data with Point treatment setting, or LIP. The LIP setting will be the focus of this work [ A).
and stays fixed during the study [12] 44 34 51
The LIP setting is different from the conventional settings in causal inference. This is because we observe the pre-treatment outcome y, over time leading to the treatment allocation. These pre- treatment outcomes may unveil the inherent temporal structure in the outcome time series (e.g. trend and seasonality), leading to better ITE estimation over time. In contrast, the conventional settings
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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A: problem setting
B: illustration of Sycn Twin
Potential Outcomes
Encode
Synthetize
3. Estimate
Outcomes
Target individual (treated)
Synthetic twin
ITE
Treatment
Contributors
Temporal Covariates
(control)
Time
Before
After Treatment
Treatment
Covariates
Rep. Vectors
Weights
Outcomes
Time
Figure 1: A: Illustration of the LIP setting. Yellow dots: the potential outcomes. B: Illustration of SynnTTwin
(shaded area: the time points after the treatment allocation). Temporal covariates are encoded representation vectors. 2. The synthetic twin of a treated target individual is constructed as the weighted average of the few contributors from the control group. 3. The difference between observed outcome the synthetic twin outcome estimates ITE. Similar procedures can be carried out for control or new individuals.
only consider the outcomes after treatment initiation 54 that deal with dynamic treatment allocations 40
52
36
43
This true even for works
35
A naive way incorporate pre-treas treatment outcomes into the standard ITE methods is to treat them as additional covariates. This approach is viable but inadequate: the pre-treatment outcomes are arguably much more closely linked to the outcomes after treatment than the covariates they hence deserve special considerations, e.g. modifying the architecture or loss function to reflect their importance. Without such modification, the ITE methods will not incorporate our prior belief the importance of the pre-treatment outcomes, which may lead to worse performance.
To bridge this gap, propose Swnn novel ITE estimation method tailored for the LIP setting. assume that the temporal outcomes are generated by individualized latent factors and time- varying latent trends. This assumption is similar the "factor model" assumption commonly used in Econometrics [T] and allows us to achieve the right balance between the parametric assumption and modeling flexibility. Figure [ illustrates the schematics of Sync using example with two treatment options (treated and control). Swin first uncovers the individualized latent factors using representation learning. For a target individual, SyncTTwin selects and weights few contributors based on their latent factors and sparsity constraint. It proceeds to construct a synthetic twin whose temporal outcomes the weighted average of the contributors. Finally, the ITE is estimated the difference between the target individual and the synthetic twin's 's outcomes.
Unlike conventional methods, SyncTwwin does not use the learned latent factors to directly predict the outcomes; instcad it uses these variables to find the contributors and their importance weights so as to construct the synthetic twin. This approach brings two bonus features; both are important to medical applications. (1) We can calculate an individualized estimation error bound based on the actual and the synthetic outcomes before treatment. In practice, the clinician can accept the recommended treatment when the error bound below a threshold and resort to expert knowledge otherwise. (2) We identify the most important contributors to estimate as the ones who receive the highest weights. The clinician can further examine these contributors (e.g. whether they are indeed similar to the target individual) validate and interpret the estimate.
Contributions. (1) We develop SyneTwin to leverage the temporal structure in the outcomes for better ITE estimation. (2) We provide theoretical justifications for each step involved in Sync'Twin and prove an individualized error bound that can be used to identify untrustworthy estimates. (3) In addition to extensive simulations, we conduct an observational study using real EHR data and successfully reproduced the findings randomized controlled clinical trial with Sync
Problem setting
We consider an observational study with N individuals indexed by E [N] = (1,..., NJ. Let E {0, 1} be the treatment indicator with a, = 1 if received the treatment at some time and a, 0

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otherwise We realign the time steps such that all treatments were initiated at time t = 0. Let I {i [N] a; 1} and Zo- {i [M] a, 0} be the set of the treated and the control individuals respectively. Denote No = [Zo| and Nı |Za| as the sizes of the groups.
Let X, [xs))e[[s.] be the temporal covariates consisting of sequence of observations X;s R Let M, m be the sequence of binary masking vectors mis E {0, 13 where [m; = indicates the tth clement of X,s is measured and [maa]d = 0 otherwise. The entire sequence X; contains S; E N observations taken before treatment at times T; [tulsE(S,)) lis O. The maximum sequence length S (S.)
The outcome y,, IR is observed time & E T Let {O...., H - 1} be the observation times before and after treatment allocation. We arrange the outcomes after treatment into H T-dimensional vector denoted as yı IakkET+ E R2 Similarly define pre-treatment outcome vector Y; [YakeT
(-M,.... ...., -11 and T+
R.
Using the potential outcome framework [+I, let y., E R denote the potential outcome at time t in world where i received the treatment as indicated by a.. Let y:(1) = [y,, E R and y, (1) = (ya RMM. Similarly, let (0) Iy (0))eTT and y, (0) = [ya The individual treatment effect (ITE) is defined as T; (1) - (.) E R
3 ITE estimation via SyncTwin
SyncTwwi estimates the ITE by predicting both potential outcomes y;(1) and y. and take the difference. Note that for an individual in the dataset i E [N], it is only necessary to predict the counterfactual outcome y; a,) because the factual outcome y: ya(a,) = y; is observed (under the consistency assumption to be discussed later). Without loss of generality, we will use estimating (0) as an example in the following sections. One can estimate (1) using the same method.
3.1 Assumptions
SyncTTwin relies on three assumptions. (1) Stable Unit Treatment Value Assumption 41 Y:.
Ya, Vi E [N], t E T UT+ (2) No anticipation, also known as causal systems 4 yır = Yı (1) = Ya (0), Vt E T , E [N]. (3) Data generating process (DGP). The DGP assumption involves two parts. First, the causal directed acyclic graph (DAG) is specified in Figure 2 37]. which involves a
latent factor e; R Secondly, we assume the potential outcomes have parametric form:
(0) q. + Exr, Vt WETUUT:
where q: E RRKKK K < min(M, H) is a weight vector and Eir is the white noise. Equation I is commonly referred to as a latent factor model with c, as the individualized latent factor and qi as the time-varying latent trend [10]. Without loss of generality, we require the weight vectors ||q:l|
VI E T UT+ [50]
Discussion. Swne differs from the nonparametric ITE estimation methods (27) because it assumes the paramet- ric form in Equation I In essence, it means that we can fully separate the time effect from the individual effect, We would like highlight two aspects of this assumption. First, the latent factor c, does not change over time. It provides constant link between the pre-treatment out- comes and the post-treatment outcomes. Secondly, the time-varying latent trend qi is common to all individuals. Together, they ensure that any linear combination of dif- ferent individuals' outcomes will automatically preserve q. i.e. E. b,y, (0) q. Σ, b,c, + Σ. b,Eu. for any weights b, E I,, Vi E [N]. For this reason, SyncTwin bypasses qı and directly finds the weights 6, 's to issue counterfactual predictions. As we will show later, doing so allows us to derive various theoretical results to inform the design of SyncTwwin also leads to checking procedure to validate estimation quality and improvements in interpretability.
E [N]
Latent Variable
Vit
a: Treatment
Xis
Outcomes
Covariates 8 [St]
E T UT+
Figure 2: The DAG of the assumed data generating model.
TWin can model more than treatment options, but we focus binary treatments for illustration.
3

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The DAG in Figure 2 different from the one commonly used in the static setting [41]. We assume the latent factor c, captures the physiological factors that impact both the outcome and the covariates. Here, the covariates from treatment to outcome, i.e. o; - X₁s - C; -> Yie [37. Based on the backdoor criterion [37], adjusting for the covariates Xis is sufficient to identify the treatment effect from observational data.
is "confounder" in general sense because it opens up a backdoor path
We compare our assumptions with those used in the related works in Appendix A.2 In particular, we show that our assumption is weaker than the one used by Synthetic Control, a widely-appliet method in Econometrics [2]. In Appendix A.5] we further demonstrate the plausibility of our assumptions in real-world scenarios. In the simulation study (Section 5.1 we show experimentally that SwnnTTwin performs well even when the data is not generated from the assumed DGP exactly but instead from a set of differential equations. Finally, and perhaps most importantly, we show that based on our assumptions, SyneTTwin able to reproduce the findings of large-scale randomized controlled trial using observational data (Section 5.2).
3.2 Learning to represent temporal covariates
The latent factor c; plays an important role as it affects the covariates Xis and the outcomes Yıo SyncTwin uses deep neural networks to learn the representation é; as a proxy for c;.
SyncTwin is agnostic to the exact choice of architecture long as the network translates the irregularly sampled temporal covariates into a fixed-sized representation vector. For this reason, we use the well-proven sereennc-to-seqeenee architecture (Seq2Seq) [47 with a standard attentive encoder [9] and a LSTM decoder [26). The learned representation č (X, M, T;; 0c), where fe is the encoder with trainable weights 0e. The reconstructed covariates X, [a Tú; 0u), where Laa is the decoder with trainable weights 0g. To ensure the learned representation č; is a linear predictor the potential outcome (0) (Equation D. we introduce a trainable parameter Q E IR x and define (0) == Q č, Note that using a nonlinear function to map from č; to (0) will be inconsistent with the DGP and will not uncover the latent factor c; as desired.
We train the networks end-to-end by optimizing the loss function C = Xr + XpCa, where X, and Ap are hyper-pape Sapee--arametery"" balancing the supervised loss L, and the reconstruction loss Cy:
CD(Do)
Σ (0) -0.01) (D) IEDO
E 11 - o
(2)
iEDoUD
where Do C To and Dj I are training data, m; is the masking vector, @ represents element-wise product and || II is the L2 norm. In Proposition we show that minimizing the supervised loss L. will reduce the error bound on the learned representations, making them closer to the true latent factor C, The proof and the motivations for L, are shown in.A.I.
Proposition 1 (Error bound on the learned representations). Under the assumptions in Section 3.1 the total error on the learned representations for the control is bounded by:
E1e, 1c,,- 3L,
Σ 1.
JET
JET
where Lg is the supervised loss, ,3 is a constant depending on qu and Q, and &y is the white noise (Equation)) and
3.3 Synthesizing the twin
At this point, one may be temped to predict the counterfactual outcome (0) of treated individual i I, with the output of the neural network ý, (0). However, (o) is issued by black-box neural network, which is not easily interpretable. As a remedy, SyncTwii explicitly constructs a synthetic twin who matches the target in representations. As will show, this approach is able to control estimation bias and is more interpretable.
The synthetic twin of target individual is defined by set of weights b, = [buseee, E No, each associated with a contributor in the control group j E To (or treatment group when predicting ý: (1)).
'The hyperparamter sensitivity is studied in A.13 Xy and Ap do not significantly impact the performance.

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SwncTwin solves the following optimization problem to find the weights:
b. arg min Σ JEZO
C
s.t. bi 2 O, Vj E To and
bi 1,
(4)
b.
JEZZ
where čj is the representation learned by the encoder. Denote the loss function in Equation 4 as L. We will call C. the matching loss because indicates how well the synthetic twin matches the target individual in representations. Let de denote the optimal value of L. and let è; be the synthetic representation given by the solution by:
di :- ||č:
Σ b1, JEZI
è :=
Σ bire
JEZo
The optimization procedure detailed in Appendix A.8 Yzz (0) for a target individual i using the same weights be Vt E ET-UTT UT+.
SwncTwin predicts the potential outcome
(0) = Σ
biy (0)
bisYfe
(6)
JEZO
jEIn
where the last equality follows from the consistency assumption (Section 3.1 Denote ý,(0)
(0))eTT as the predicted potential outcomes after treatment initiation.
The estimator in Equation 6 follows directly from the DGP assumption (Equation I To see this, remember that yx((0) is linear in the latent factor c, Hence, if we find a set of weights bi to match the latent factor, i.e. C; = Σ, Diy Cj. the same set of weights will also match the outcome (0) up to random noise. In practice, since we do not observe C, we have to
(0) ~ Σ, (c)) perform matching on the learned representation č as Equation 4
Therefore we can see that the quality of the estimator yix (0) depends on two things: (1) whether the learned representation è is close the true latent factor с and (2) whether good matching weights b, can be found on the learned representation. SynccTwin attempts to fulfill the first condition by representation learning Section 3.2 The second condition facilitated by solving the optimization
problem in Equation 4 Proposition 2 formalizes this intuition and shows that when perfectly- matching twin is found, the estimation error only depends on the quality of the learned representations
(proved in A.IIII..
Proposition 2 (Bias bound on counterfactual prediction). Suppose that de = 0 for some i E Ii (Equation (and5), the absolute value of the counterfactual prediction bias for is bounded by:
[E); y:)l) = IT 17+1((cc -cill+
Σ 11e, (a,1),,1) e,1l)
jETa
Notes on Interpretability. In addition to reducing bias by learning and matching representations, SyncTwwn is also more interpretable. In particular, the weights b, can be interpreted as the "contribu- tion" "on""on or "importance" of a contributor j the target due to the optimization constraints. We can create shortlist of the most important contributors based on b; A domain expert can understand the rationale behind the estimate by examining the shortlist. For instance, they can check whether the important contributors share similar disease progression patterns as the target individual.
This procedure corresponds to the notion of data point interpretability example-based interpretabil- ity [45), where one explains the prediction by presenting the most relevant data points to the users. Note that the learned representations č; are internal to the algorithm; we do not intend show these representations to the user or to make interpretations on them.
3.4 Calculating individualized error bound with pre-treatment outcomes
Since Equation 6 applies to all time points before and after treatment, let y, (0) = |s (0))ee be the predicted pre- pre-treatment potential outcome vector. We define d' as the estimation error in the pre-treatment period:
d= =1 (0) y7 (0)l = Ily. (0) - 11,
(7)
where || ||1 is the vector & norm. The second equality allows d to be evaluated for all individuals. It holds because of the anticipation assumption (Section 3.1. Achieving small error d' implies
5

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Table 1: Problem settings considered in the literature. "Static": observed (or allocated) only once; "Regular": observed (or allocated) over time at a regular frequency; "Irregular": observed over time inregularly; "-": not observed modeled. can be extended to Irregular. can be extended to Regular. LIP: Longitudinal, Irregular, Point treatment.
Setting
Example
Pre-treatment
Treatment
Post-treatment
Nonlinear f:
X
y
y
y = f(X)
Static
Static
Static
Static
DT
Regular"
Regular
Regular
SC
Regular
Regular
Static
Regular
LIP (This work)
This work
Irregular
Regular
Static
Regular
that the synthetic twin è. matches well with the true latent factor c; due to the linearity between y; (0) and c, (Equation Since c; assumed be constant over time, the pre-treatnen mre-treatment error can be used to assess the post- trstttretteet error. We formalize this intuition in Proposition 3 and use dž to control the error the post-treatment period (proved A.I.II)
Proposition 3 (Error control under hidden confounders). Given any target error threshold 5 0. define the acceptance group of treated individuals as
As {i Inld S 8 I/TT'})
Under the assumptions in Section Vi E As.
3.1 the post-treatment estimation error [E[ý, E[y,
Proposition shows that we can control the estimation error to be below certain threshold d by rejecting the estimate if its error dă during the pre-treatment period is larger than 8|T / Alternatively, we can rank the estimation trustworthiness for the individuals based on dV. This is helpful when the user is willing to accept percentage of estimations which are deemed most trustworthy.
3.5 Training, validation and inference
We perform model training, validation and inference (testing) on three disjoint datasets. In summary, we train the encoder and decoder on the training data using the loss functions described in Section The validation data is then used to validate and tune the hyper-parameters of the encoder and decoder. Then, we solve the optimization problem Section t. to find the weights b, for the target individuals in the testing data. Finally, we compute the potential outcome estimator (Section 3.3) and the individualized error bound (Section 3.4). The pscudocode described in A.7
3.2
4 Related work
Synthetic Control. Similar to SyneTTwin, Synthetic control (SC) [1 and its extensions ITE based on synthetic outcomes. However, SC needs to flatten the temporal covariates [ into fixed-sized (high-dimensional) vector X; and use it to construct the twin. As result, SC does not allow the covariates to be variable-length or sampled at irregular frequencies (Table []] otherwise 's dimensionality will vary across individuals. This severely limits SC's usability in medical observational studies because such sampling irregularities are common in EHR. Moreover, SC assumes Ysu (0) qe x, + Eas i.e. the flattened covariates X; linearly predicts y., (0), which is
g estimate
special case of Sync s assumption (to be discussed later in Equation TT and seems unlikely in many medical applications (e.g. body mass index does not linearly relate to blood pressure).
Static nonparametric ITE estimation. Most ITE estimation methods the literature consider the static setting and do not pay special attention to the outcomes before treatment y, these outcomes are treated as standard covariates X,, if at all (Table However, the pre- treatment outcomes y, may encode certain temporal structure that will persist even on outcomes y; after treatment (e.g. trend and seasonality). Explicitly unveiling such temporal structure will be very beneficial to accurately estimating and validating the ITE after treatment. Moreover, these methods make no parametric assumption the data generating model [27) and they learn to predict the two potential outcomes

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using deep neural networks 43 54 22]. these methods are still in general less interpretable than the parametric models such as SyncTwin whose coefficients can be directly understood by an expert.
Despite the recent progress in interpretable machine learning.
ITE estimation for dynamic treatments. Several works consider ITE estimation for dynamic treatments (DT) [40]. In the DT setting (Table [.) multiple treatment decisions are made over time for each individual. ITE estimation is much more challenging for DT because prior treatment a;- may influence the temporal covariates Xx, which may in turn confound a latter treatment a. This problem known as temporal confounding. Marginal structural model [40] and related works 42 have been proposed to overcome temporal confounding. In comparison, our setting considers point treatment and therefore do not suffer from temporal confounding, As a result, although the works in the DT setting are applicable, they might be complicate for our problem. In addition. our previous discussion about the inadequacy leveraging pre-treatment outcomes also applies to DT methods.
Works with similar terminology. Several unrelated works in the literature use terms such "twin", which might cause confusion. We discuss these works in Appendix
A..4 A.4
5
Experiments
5.1 Simulation Study
Data generation In this simulation study, we evaluate SyncTTwin on the task of estimating the LDL loowergg effect of statins, a common drug prescribed to hypercholesterolammie patients. Following our convention, the individuals are enrolled at t O, the covariates are observed
in T = S- 0), where S E {15, 25, 45), and the ITE is to be estimated in the period T [0, 4]. We start by generating a covariate k." for from mixture distribution:
8.f.c + (1 8, ga; 5, ~ Bern(;))
(8)
where Bern(p) is the Bernoulli distribution with success probability p and f.z, gar are drawn from two different distributions (specified in A0. To introduce confounding bias, we vary p; for the treated and the control: P; = Po. Vi E To and = 1, Vi E Z1. The constant Po controls the degree of confounding bias (smaller Po. larger bias). We simulate the outcome y, using the widely adopted
Pharmacology model in the literature [6 53 32). It is obtained by solving the differential equation
9 and adding independent white noise c (O 0.1).
p. p K."" k Pei d, = h de; y, = kd, + 1 Yr-
where y, is the derivative yf y, and a, is the indicator of statins treatment. The covariates includes X2 = [k]"m Y..p,.. The interpretation of all constants involved are presented in Appendix 10 Finally, we introduce irregular sampling by creating masks marBBen((m) where probability m (0.3, 0.5, 0.7, 1}. worth highlighting that the simulation data are not generated from SyncTwwin's assumed DGP ① but from domain-specific ODEs (
Benchmarks. From the Synthetic Control literature, we considered the original Synthetic Control method (SC) (2). Robust Synthetic Control (RSC) (7) and MC-NNM (8). From the dynamic treat- ment literature, we compared against Counterfactual Recurrent Network (CRN) [ and Recurrent Marginal Structural Network (RMSN) B5). Note that RMSN belongs to the family of Marginal Struc- tural Models (MSMs) and we use as representative of MSMs. We included modified CFRNet, which was originally developed for the static setting 43 We replaced its fully-connected encoder with the encoder used by SyncTwin to allow CFRNet model temporal covariates (Section B.2). We also included benchmark adapted from the counterfactual Gaussian Process (CGP) [42] in order to adjust for the patient level covariates. We use One-nearest Neighbour Matching (1 (INN) 46 as a
baseline. The implementation details of all benchmarks are available in Appendix A.9 We compared with two ablated versions of SwncTwin. SyncTwin-C, is trained only with reconstruction loss and SyncTwin-C, only with supervised loss.
'The implementation of SyneTwin and the experiment code are available at ht / http://yyootii---eeuree---22-22 or bctps://githur com/ orgs/ wanderschaarlaab//peeello......
7

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Table 2: Mean absolute ITE under different levels of confounding bias po. m and $ 25 used. Estimated standard deviations are shown the parentheses. The best performer is in bold. Additional quantitative results are shown in Appendix A.11
No 200
No 1000
Method
Po 0.1
Po 0.25
0.5
Po 0.1
Po 0.25
Po 0.5
SynnTwin-Full
0.323 (.039)
0.144 (.013)
0.128 (.008)
0.178 (,012)
0.106 (.006)
0.094 (.005)
SyncTwin-&C
0.353 (.040)
0.171 (.016)
0.135 (.010)
0.256 (.026)
0.146 (.013)
0.102 (.006)
SwinTwin-Ls
0.336 (.040)
0.171 (.015)
(.008)
0.145 (.013)
0.114 (.007)
0.127 (.010)
SC
0,341 (.041)
0.151 (.024)
0.149 (.018)
0.258 (.050)
0.166 (.034)
0.214 (.036)
RSC
0,842 (.045)
0.361 (.020)
0.322 (.019)
0.310 (.06))
0.298 (.014)
0.302 (.014)
MC-NNM
1.160 (.060)
0.612
0.226
0.527 (.029)
0.159 (.008)
0.124 (.007)
CERNet
0,903 (.077)
0.387 (.035)
0.291 (.003)
0.399 (.038)
0.178 (.013)
0.104 (.007)
CRN
0,809 (.050)
0.613 (.039)
0.335 (.023)
0.779 (.041)
0.589 (.040)
0.563 (.035)
RMSN
0,418 (.032)
0.391 (.029)
0.334 (.027)
0.478 (.039)
0.414 (.034)
0.390 (.02))
CGP
0,660 (.043)
0.610 (.039)
0,561 (.035)
0.826 (,056)
0.693 (.047)
0.602 (.038)
INN
1.866 (.099)
1.721 (.091)
1.614 (.078)
2.446 (.131)
1.746 (.106)
1.384 (.083)
(A)
(B)
Accepted
Sync Win
00.12
10%
RSC
73%
MAE
50%
CRN
25%
0.08
INN
10-1
0.05
0.12
0.2
0.4
Rejection threshold
Number omitted covariates
Figure 3: (A) The percentage of accepted estimates (red) and their MAE (blue) using various rejection thresholds 8 on d". Eg, setting = 0.12 gives 75% acceptance rate and MAE around 0.105. (B) Performance when certain covariates are omitted (hidden confounders). Shaded area: 95% confidence interval.
Evaluation metric. In many medical studies, the outcome of interest is measured with heavy- tailed non-Gaussian noise [30]. In these settings, the mean absolute error (MAE) is preferred over the mean squared error (MSH) an evaluation metric due its robustness the outliers (38). For this reason, we will evaluate the mean absolute error (MAE) on counterfactual prediction: [0) (-)0l).. Note that MAE is also directly comparable to the error bound in Proposition 3 (i.e. the L1 norm).
1 Ri=
Main results. Table T presents the results for various levels of confounding bias po. Additional results for different sequence length S and sampling irregularity m are shown in the tables in Appendix A.1I SyncTTwin achieves the best equally-best performance in all cases despite the assumed DGP does not exactly hold. The full Sync'Twin with both loss functions also consistently outperforms the versions trained only with L, or L. In comparison, SC, RSC and MC-NNM underperform because their assumption that the flattened covariates x, linearly predict the outcome is violated (Section()) 4.)
Error bound. SyncTwwin allows the user to reject untrustworthy estimates based on d", In Figure 3 (A) below, we show the scenarios of using various rejection thresholds on d² As expected from Proposition 3 when the user increases the threshold, more estimates will be accepted but they will have a higher MAE. The fact that the two curves in the figure share the similar increasing trend suggests d'' is good indicator of individual error: rejection based will lead to a flat line of MAE. In practice, the user can use Figure 3 (A) to calibrate the threshold in order to achieve balance between the accuracy and the workload. For instance, if the would like SyncTTwin to accept 75% of the estimate, or she should set threshold
non-informative criterion
0.12 according to the pre-treatment error d² and expect a MAE of around 0.105 for the post-treatment outcome.
Sensitivity to omitted covariates. Figure (B), we show the situation when some covariates are omitted from the analysis, thus making it harder to adjust for the confounding bias. In particular,

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Outcome after starts
(0)
(mimoits)
y1o)
The Terget Individusl
y(1)
Synthetic Twin
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Time (yeers)
Distance between pre-treatment outcomes:
Number individuals contributing to the synthetic twin
4000
The median between target individual and
2000
On average individuals out of 24357 in total contribute the synthetic twin
3000
synthetic twin:
Frequeng
1500
2000
randomly individuals:
between
1000
1000
500
0.0
0.5
1.0
1.5
2.0
0
10
30 Number individuals
20
40
50
Figure 4: Top: the outcomes (LDL) before and treatment a target individual and its synthetic twin. Bottom left: histogram of distance d (Equation 7) Bottom right: histogram of number of contributors used to construct synthetic twin.
set x, {k." Yv. Prt. x, (Ye, Pr} or x, {y,} (omitting 0,1,2 covariates). We observe that SwncTwin is still the best-performing model when some covariates are omitted.
5.2 Experiment real data
Few existing works in the literature validate the method by conducting real-world observational study to replicate the findings of randomized controlled trial (RCT), which is the gold standard of causal inference. Most existing works rely synthetic semi-synthetic data for validation, which may significantly under-represent the complexity of the real-world data.
To validate the usability of SyncTTwin in real-world medical problems, we conduct an observational study to emulate a large-scale RCT-Heart Protection Study (HPS) (21 20 Although most existing methods have been validated in synthetic or semi-synthetic experiments 43 I1, few of them have been demonstrated to successfully reproduce the findings of a RCT from observational data. Since RCT is the gold standard of treatment effect estimation, the ability to reproduce a RCT provides strong evidence about the method's 's usability in medical research and facilitates the method's s adoption in the medical community.
The HPS was conducted investigate the treatment effect of statins, a drug commonly used to lower the LDL Cholesterol (LDL). It reported an change of -1.26 mmol/L (SD=0.06) in LDL for participants randomised to statins versus placebo the end of the first year after treatment (39]. The study enrolled 20,536 individuals and lasted for eight years, making it one of the largest studies to investigate the treatment effect of statins.
Data Source. We used medical records from English National Health Service general practices that contributed anonymised primary care electronic health records to the Clinical Practice Research Datalink (CPRD), covering approximately 6.9 percent of the UK population [25). CPRD was linked secondary care admissions from Hospital Episode Statistics, and national mortality records from the Office for National Statistics. We defined treatment initiation as the date of first CPRD prescription and the outcome interest was the measured LDL. Known risk factors for LDL were selected as temporal covariates measured before treatment initiation: HDL Cholesterol, Systolic Blood Pressure, Diastolic Blood Pressure, Body Mass Index, Pulse, Creatinine, Triglycerides and smoking status. Our analysis is based on subset of 784 individuals who met the enrollment criterion of HPS (Appendix A.15). They were split into three equally-sized subsets for training, validation and testing, each with 17.371 treated and 24.557 controls.

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not able to Main findings. SyncTTwin estimates the average treatment effect as -1.55 mmol/L (SD 0.01) by averaging the estimated ITE on testing data Σ / The estimate is very close to the result reported in HPS, -1 -1.26 mmol/I. (SD==006), after taking into account the standard errors. In contrast, CRN and RMSN estimate the effect to -0.72 mmol/I. (SD 0.01) and -0.83 mmol/I. (SD 0.01) respectively, which are significantly smaller than the trial's finding. Other benchmark methods (e.g. SC, RSC and MC-NNM) either cannot handle irregularl- measurrd covariates or do not scale to the size of the dataset. Our result suggests Swnn is able to overcome the confounding bias in the complex real-world datasets. Note that SyncTTwin is also able to estimate ITE and the effect over different time horizons. However, since these results not reported in HPS, quantitatively evaluate them.
Qualitative evaluation of ITE over time. For each individual, we can visualize the outcomes before treatment and compare them with the synthetic twin to sense-check the estimate. The individual shown in Figure 4 (top) has sensible ITE estimate because the synthetic twin matches its pre- treatment outcomes closely. addition visualization, we can calculate the individualized error bound based du (Equation 7). From Figure a median 0.24 mmol/L (compared to the average between any two randomly chosen individuals 0.76 mmol/L). This means if the expert can only tolerate an error of 0.24 mmol/L on ITE estimation, half of the estimates (those with dă < 0.24 mmol/L) can be accepted (Section 3). As shown in Figure 4 (bottom right) average only 15 (out of 24,557) individuals contribute the synthetic twin (biy > 0.01). The medical experts can check these few contributors to interpret the estimate.
left) we can see in most cases de is small with
Conclusion and future work
We present SyncTwin, an ITE estimation method tailored for temporal outcomes with point treatment. SyncTTwin achieves interpretability and strong performance in both simulated and real data experi- ments. In future works, plan extend SyncTTwin the dynamic treatment setting and to model the outcomes continuous time. Developing additional assumptions to guarantee the robustness to certain types of unobserved confounders is also interesting avenue for future research.
Acknowledgments and Disclosure of Funding
We thank anonymous reviewers as well as members of the vanderschaar-lab for many insightful comments and suggestions. This work is supported by the US Office of Naval Research (ONR), the National Science Foundation (NSF Grant number: 1722516), the Alan Turing Institute (under the EPSRC grant EP/N510129/1), and GlaxoSmithKline (GSK).
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13


Reviews:
[{"review_id": "dulimuGPgwZ", "reviewer": "Reviewer_n3BB", "summary": "The paper proposes a representation learning approach to model counterfactuals in longitudinal data with point interventions over time. Their approach, SyncTwin is thus suited to situations where an intervention is made on a temporal dataset at an instance of time or as a continuous exposure by treating all points post the intervention as the potential outcomes under treatment. \n\nThey compare the performance of their model against several counterfactual estimation baselines originally proposed to model static observational data with interventions.", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "The problem of identifying the *Individual Treatment Effect* in temporal settings is a challenging one due to issues of identifiability of the potential outcome over time. In this paper, the authors assume a simple setting with a binary treatment or intervention, such that all points post the intervention are considered as sampled from the distribution under treatment. Furthermore, at each time step the treatment is considered the same (the current approach does not model the effect of time-varying interventions) \n\nTheir main innovation is that at test time, the counterfactual outcome is determine by modelling it as mixture model over the observed time-steps (in the paper they refer to the weights of this mixture as $b_{ij}$ ). \n\n## Strengths\n\n- Interesting problem of counterfactual inference with longitudinal data. \n- Some theoretical insights around the latent factor model maybe interesting to the readers. \n- Extensive experimental evaluation against multiple baselines on synthetic and real world datasets.\n\n## Major Concerns / Weaknesses\n\n- The authors frequently confuse the term, *Data Generation Process* (DGP) and the *Modeling Assumption*.(Ex. lines 135-136) The DGP that there is a latent factor $c_i$ that causes the outcome and covariates jointly, is different from the modeling assumption that the relationship is linear. The authors should reconcile this terminology and clearly differentiate between the modeling assumptions and the data generation process.\n\n- The representation $c_i$ is frequently referred to as a *latent variable*. For $c_i$ to be a latent variable, there needs to be some explicit distributional assumption on $c_i$, which is not the case in the assumed model. The authors should thus instead call it a representation, not a latent variable. \n\n- The authors motivate the use of their mixing weights $b_i$ from an optimization perspective. In the DAG notation however, the $b_i$ s are mixing weights or probabilities. The authors should reconcile the proposed model clearly specifying the modeling assumptions via another DAG, (ideally separate from the DGP in figure 2) that includes $b_i$ as a *latent variable* over the time-steps. \n\n-  The final concern this reviewer has is that the current framework does not allow the model to represent the potential outcome $Y(1)$ or $Y(0)$ with a non-linear function of the representation $c_i$. The authors mention that this would be \"inconsistent with the DGP\" (ln 135)\". Firstly, as noted above, this is a modelling assumption, not the DGP. Secondly, this reviewer believes that this assumption is not required per se under the proposed model, if the authors were to remodel $c_i$, factual outcomes $y_i$ and mixing weights $b_i$ as true random variables (with explicit probabilistic interpretation). The Matching Loss and Reconstruction Loss would thus be easily modified as a likelihood in that case. \n\nOverall this reviewer believes that although the proposed approach is interesting, in its current form the paper requires substantial revision to:\n- present and motivate the approach in a formal probabilistic sense, including the mixing weights $b_i$ and the representation $c_i$\n- De-confound the DGP from the Modeling Assumptions. \n\n## Other concerns: \n\nAn important baseline that seems to be omitted when benchmarking performance is the Causal Effect-VAE (CEVAE) (citation [35] in the paper). I would recommend the authors to explicitly compare SyncTwin against CEVAE with an LSTM based encoder-decoder (to obtain the latent $c_i$)\n\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "I would encourage the authors to rephrase the Societal Impact section by focussing on how accurate counterfactual estimation can better help policy making for decision support in critical scenarios such as healthcare. \n\n", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "2"}, "extra_text": {}}, {"review_id": "WZ1p0g-pEe", "reviewer": "Reviewer_tEce", "summary": "This paper proposes a method, SyncTwin, to estimate treatment effects in Longitudinal and Irregularly sampled data with Point treatment (LIP) setting. The idea is to create a synthetic twin from controls that closely matches a treated target in representation. By using the pretreatment time samples of the twin to estimate temporal trend, SyncTwin can predict the outcome of the target when no treatment is administered. The method is applied to simulated and real data with lower prediction error shown.\n", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "Originality\nNot sure if the combined idea of creating a synthetic twin and using pretreatment outcome is novel since Synthetic Control at a high level seems to be doing that as well.\n\nQuality\nThe method seems sound, and the results on both simulated and real data are solid. A couple of question comes to mind. First, are there studies where no matched control data are collected during post-treatment period (which is used as ground truth in the current paper)? Second is what happens if we directly use the outcome prediction without creating a twin, since SyncTwin provides such output?\n\nClarity\nThe paper is mostly clear with good motivation provided for the proposed method, i.e. better use of pretreatment outcomes. Also, dividing the paper into sections on problem statement, assumptions, etc. make the paper easy to read. The problem statement is clear, but would suggest labeling Figure 1 with variable names. Also, the sentence “the pre-treatment outcomes are arguably much more closely linked to the outcomes after treatment than the covariates— they hence deserve special considerations, e.g. modifying the architecture or loss function to reflect their importance” is a bit unclear without proper context in the Introduction.\n\nSignificance\nBeing able to predict treatment outcome is of broad interest. The method provides both outcome prediction and error estimates to inform clinicians. For others to adopt this method, the authors will need to describe in more details on what kind of data are applicable, i.e. this method would not be needed if we have data from matched controls taking placebo. \n\nSummary Post Author Response\nI have read through the reviews and responses. I will keep my original score, which was mainly based on the results. My main concern was real world applications. It might be worth adding a bit more details on how to select a matched control group for executing the proposed method when data are not from well designed experiments, i.e. a random set of controls might not match well with all patients.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors mentioned extension to dynamic treatment settings and model outcomes in continuous time. The authors also mentioned, in practice, the clinician can accept the recommended treatment when the error bound is below a threshold and resort to expert knowledge otherwise. The question is how reliable/robust is the error bound to outlier subjects/measurements.", "review_text": "", "extra_scores": {"ethical_concerns": "The paper does not seem to have ethical issues.", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "6"}, "extra_text": {}}, {"review_id": "L7qAyqvu9Fh", "reviewer": "Reviewer_Hv4x", "summary": "The paper proposes an individual treatment effect estimation method called SyncTwin, which learns synthetic twins of target patients via the use of representation learning for counterfactual predictions. The proposed method is used on longitudinal data such as electronic health records. The paper is concerned with the setting of longitudinal and irregularly sampled data with point treatment. The paper describes the proposed method, offers some theoretical guarantees, and demonstrates the utility of the method on both synthetic and real-world data.", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "I think the paper makes efforts to address an important problem in causal inference, i.e. individual treatment effect estimation from longitudinal data. The proposed method is concerned with a specific, relatively simple setting (compared to dynamic treatment ) without unobserved confounders.\n\nOriginality: I think the proposed method is original, in terms of deriving solutions tailored to the specific setting proposed in the paper. The proposed method is also closely related to several lines of research in causal inference but different from those in various ways.\n\nQuality: I think the proposed method presents solutions to deal with various important challenges under the specific setting. Theoretical characterization is provided in the paper, and the analysis of experimental results on both synthetic data and real-world data is detailed.  I am somewhat unconvinced by the interpretability provided by the method. While the linear combinations of contributors provide some convenience to interpretability, such contributors are learned latent representations, which potentially are difficult to interpret. While the proposed method is validated on real-world data, the authors use the fact that the average treatment effect learned by the method is close to the one reported in RCT as an important argument to justify the effectiveness of the proposed method. I am not sure if such a justification suffices. For one thing,  it is unclear whether the population in the observational study is comparable to that in the RCT (despite the authors used the admission criteria of the RCT for the observation study).  It is also unclear whether the observational study meets the LIP setting, satisfies the assumptions made in the paper, and whether all confounders are appropriately adjusted. Based on these concerns, I am somewhat skeptical about the reliability of the results from real-world data. \n\nClarity: I think the paper is clear. Notation are well defined and used.\n\nSignificance: I believe the paper has certain significance based on the setting that it deals with and the difference it has compared to other related work. It's also a good attempt at tackling more challenging causal inference problems from longitudinal data.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "I think the authors can discuss more the limitation of the proposed method and understand the failure mode of the proposed method better.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "2"}, "extra_text": {"ethical_concerns": "I am somewhat concerned about the depolyment of the method in the real world because of the nature of individual treatment effect estimation. The reliability of such methods should be held to a high standard and guidelines and failsafe should be considered to make sure that the results of the proposed method are used responsibly in decision making."}}, {"review_id": "6wc5HaG-jXB", "reviewer": "Reviewer_CDQY", "summary": "The paper introduces a latent variable model (SyncTwin) for estimating time-varying individualized (point-) treatment effects (ITE) given temporal irregularly sampled pre-treatment covariates and outcomes. Theoretical results justifying the proposed approach include upper bound errors on the learned representations and counterfactual predictions. Experimental results on synthetic and real-world datasets show SyncTwin outperforms baselines per mean absolute error (MAE) on ITE and recovering RCT findings, respectively.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "", "main_review": "Overall I enjoyed reading this paper; the reviewer appreciates the clarity and organization. \n\n**Strengths**\n- The formulated latent variable model encodes interpretability by leveraging representation learning and a matching algorithm for counterfactual prediction.\n- The theoretical analysis for upper bounds on the learned representations and counterfactual predictions justify the proposed formulation.\n-  The paper shows SyncTwin recovers RCT findings on a challenging, large-scale real-world EHR dataset, something rarely done in most machine learning papers.\n\n*Below are the limitations.*\n\n**Technical limitations**\n- The paper seems like a straightforward extension of Synthetic control (SC), albeit accounting for irregularly sampled covariates. Also, the performance gains over SC seem marginal given the complexity of the proposed approach.\n- Unlike approaches such as CFRNet, SyncTwin is memory inefficient as it requires the storage of learned representations from the training datasets for the matching algorithm at test time.\n- Given that the matching algorithm is key to SyncTwin, empirical/theoretical analysis of best or worse case scenarios would strengthen the paper.\n\n**Weak experiments**\n-  Experimental findings on the real-world dataset are missing baseline results from SC or I-NN?\n-  Also, the paper should provide qualitative results from synthetic datasets showing predicted $y_t$ against ground truth.\n- Comparisons with propensity weighted approaches would be interesting.\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The discussion on limitations needs to be expanded.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes a new approach to estimating conditional average treatment effects based on longitudinal data. Overall, authors were responsive to criticism raised by reviewers. However, prior to publication two critical revisions should be made. First, explicitly state the key assumption that if the latent confounders are able to predict pretreatment then they will also be able to predict post treatment (this is somewhat implied by proposition 3, but never explicitly stated). Stating this assumption clearly is critical to ensuring that approach is not inappropriately applied in the future. Second, the authors deviate from the norm in this community reporting MAE in lieu of PEHE (or MSE), without providing a justification. In the revision, please include both MAE and MSE results, or provide a clear justification for why MSE results are omitted. 
Decision: Accept (Poster)