Transfer Learning for Meta-analysis Under Covariate Shift

Zilong Wang; Ali Abdeen; Turgay Ayer

stat.MLApr 3, 2026

Transfer Learning for Meta-analysis Under Covariate Shift

Authors: Zilong Wang, Ali Abdeen, Turgay Ayer

Organizations: Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA

Abstract

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport framework that treats source-trial outcomes as abundant proxy signals and target-trial placebo outcomes as scarce, high-fidelity gold labels to calibrate baseline risk. A low-complexity (sparse) correction anchors proxy outcome models to the target population, and the anchored models are embedded in a cross-fitted doubly robust learner, yielding a Neyman-orthogonal, target-site doubly robust estimator for patient-level heterogeneous treatment effects when target treated outcomes are available. We distinguish two regimes: in connected targets (with a treated arm), the method yields target-identified effect estimates; in disconnected targets (placebo-only), it reduces to a principled screen--then--transport procedure under explicit working-model transport assumptions. Experiments on synthetic data and a semi-synthetic IHDP benchmark evaluate pointwise CATE accuracy, ATE error, ranking quality for targeting, decision-theoretic policy regret, and calibration. Across connected settings, the proposed method is best or near-best and improves substantially over proxy-only, target-only, and transport baselines at small target sample sizes; in disconnected settings, it retains strong ranking performance for targeting while pointwise accuracy depends on the strength of the working transport condition.

Figures & tables

	Performance				Calibration
Method	PEHE	ATE	$\tau$	Regret	Slope	R 2	ECE
TargetOnly	6.9	3.3	7.0	6.8	8.3	7.0	6.4
ProxyOnly	8.6	8.2	8.6	8.6	7.0	8.5	8.3
IPW-Transport	4.5	6.6	4.4	4.5	4.5	4.4	5.2
OM-Transport	3.7	5.7	3.5	3.7	3.2	3.4	4.2
EntropyBal	5.3	6.3	5.2	5.3	5.4	5.2	5.7

TABLE I: Average rank per metric across all sweeps (1 = best). Calibration: Slope (ideal=1), R 2 , ECE (Expected Calibration Error).

$p$	Method	50/0	150/100	550/500
10	TargetOnly	–	1.43 $\pm$ 0.39	1.38 $\pm$ 0.45
	ProxyOnly	2.34 $\pm$ 0.67	1.96 $\pm$ 0.66	2.10 $\pm$ 0.83
	IPW-Transport	1.80 $\pm$ 0.83	1.60 $\pm$ 0.70	1.82 $\pm$ 1.06
	OM-Transport	1.80 $\pm$ 0.83	1.60 $\pm$ 0.70	1.81 $\pm$ 1.06
	EntropyBal	1.81 $\pm$ 0.83	1.60 $\pm$ 0.70	1.82 $\pm$ 1.06
	AnchorOnly	–	1.46 $\pm$ 0.41	1.39 $\pm$ 0.46

TABLE II: PEHE across budget

(m_{0},m_{1})

and dimensionality

p

. Lower is better.

$C$	Method	50/0	150/100	550/500
2	TargetOnly	–	4.95 $\pm$ 1.18	4.46 $\pm$ 0.91
	ProxyOnly	5.67 $\pm$ 1.05	5.55 $\pm$ 1.37	5.19 $\pm$ 1.22
	IPW-Transport	3.64 $\pm$ 1.45	3.78 $\pm$ 1.85	3.74 $\pm$ 1.97
	OM-Transport	3.54 $\pm$ 1.45	3.59 $\pm$ 1.89	3.52 $\pm$ 1.98
	EntropyBal	3.76 $\pm$ 1.45	3.79 $\pm$ 1.85	3.73 $\pm$ 1.98
	AnchorOnly	–	5.01 $\pm$ 1.26	4.52 $\pm$ 0.94

TABLE III: PEHE across source sites

C

and budget. Lower is better.

$s/p$	Method	$\Gamma$ =0	0.5	1.0
0.05	TargetOnly	4.41 $\pm$ 0.70	4.25 $\pm$ 0.53	4.30 $\pm$ 0.57
	ProxyOnly	4.97 $\pm$ 0.89	4.72 $\pm$ 0.68	4.84 $\pm$ 0.72
	IPW-Transport	2.79 $\pm$ 1.25	2.13 $\pm$ 1.02	2.20 $\pm$ 1.11
	OM-Transport	2.67 $\pm$ 1.26	2.04 $\pm$ 1.03	2.10 $\pm$ 1.13
	EntropyBal	2.80 $\pm$ 1.25	2.14 $\pm$ 1.02	2.21 $\pm$ 1.11
	AnchorOnly	4.45 $\pm$ 0.70	4.28 $\pm$ 0.53	4.34 $\pm$ 0.56

TABLE IV: PEHE under A5 violations:

s/p

=sparsity ratio,

\Gamma

=nonlinearity. Lower is better.

$m_{0}=25$
Method	$m_{1}{=}25$	$m_{1}{=}50$	$m_{1}{=}100$
TargetOnly	4.22 $\pm$ 6.07	5.45 $\pm$ 7.12	3.09 $\pm$ 3.97
ProxyOnly	3.33 $\pm$ 4.71	4.21 $\pm$ 5.59	2.36 $\pm$ 2.75
AnchorOnly	3.12 $\pm$ 4.32	3.88 $\pm$ 4.87	2.37 $\pm$ 2.57
IPW-Transport	3.69 $\pm$ 6.23	3.76 $\pm$ 5.55	2.29 $\pm$ 2.21
EntropyBal	4.87 $\pm$ 8.67	6.41 $\pm$ 13.96	3.55 $\pm$ 4.33

TABLE VI: IHDP connected regime: PEHE across target budgets (mean

\pm

SD, 50 realizations).

Method	25	50	100	200
ProxyOnly	2.64 $\pm$ 2.65	3.46 $\pm$ 4.88	3.50 $\pm$ 4.27	3.79 $\pm$ 4.53
IPW-Transport	2.30 $\pm$ 3.08	3.36 $\pm$ 5.84	4.87 $\pm$ 6.95	4.79 $\pm$ 6.95
EntropyBal	2.82 $\pm$ 3.02	3.61 $\pm$ 5.65	5.47 $\pm$ 7.99	5.63 $\pm$ 8.62
OM-Transport	2.28 $\pm$ 3.41	3.37 $\pm$ 6.43	4.18 $\pm$ 5.96	4.50 $\pm$ 6.64
Proposed-B	2.11 $\pm$ 3.44	3.19 $\pm$ 6.23	3.90 $\pm$ 5.88	4.33 $\pm$ 6.59

TABLE VII: IHDP disconnected regime (

m_{1}=0

): PEHE across placebo budgets (mean

\pm

SD, 50 realizations).

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

$p$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
10	TargetOnly	–	1.69 $\pm$ 0.49	1.43 $\pm$ 0.39	1.42 $\pm$ 0.38	1.38 $\pm$ 0.45
	ProxyOnly	2.34 $\pm$ 0.67	2.09 $\pm$ 0.66	1.96 $\pm$ 0.66	2.08 $\pm$ 0.68	2.10 $\pm$ 0.83
	IPW-Transport	1.80 $\pm$ 0.83	1.80 $\pm$ 0.75	1.60 $\pm$ 0.70	1.78 $\pm$ 0.77	1.82 $\pm$ 1.06
	OM-Transport	1.80 $\pm$ 0.83	1.81 $\pm$ 0.75	1.60 $\pm$ 0.70	1.78 $\pm$ 0.77	1.81 $\pm$ 1.06
	EntropyBal	1.81 $\pm$ 0.83	1.81 $\pm$ 0.75	1.60 $\pm$ 0.70	1.78 $\pm$ 0.77	1.82 $\pm$ 1.06
	AnchorOnly	–	1.71 $\pm$ 0.53	1.46 $\pm$ 0.41	1.44 $\pm$ 0.41	1.39 $\pm$ 0.46

Appendix

TABLE VIII: PEHE (mean

\pm

SD) across budget and

p

. Lower is better.

$p$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
10	TargetOnly	–	0.19 $\pm$ 0.15	0.14 $\pm$ 0.10	0.10 $\pm$ 0.07	0.07 $\pm$ 0.06
	ProxyOnly	0.69 $\pm$ 0.52	0.56 $\pm$ 0.45	0.53 $\pm$ 0.48	0.69 $\pm$ 0.48	0.67 $\pm$ 0.48
	IPW-Transport	0.77 $\pm$ 0.56	0.74 $\pm$ 0.50	0.52 $\pm$ 0.42	0.64 $\pm$ 0.50	0.70 $\pm$ 0.57
	OM-Transport	0.77 $\pm$ 0.56	0.74 $\pm$ 0.50	0.52 $\pm$ 0.42	0.64 $\pm$ 0.49	0.70 $\pm$ 0.57
	EntropyBal	0.77 $\pm$ 0.56	0.74 $\pm$ 0.51	0.52 $\pm$ 0.42	0.64 $\pm$ 0.50	0.70 $\pm$ 0.57
	AnchorOnly	–	0.21 $\pm$ 0.16	0.13 $\pm$ 0.11	0.10 $\pm$ 0.09	0.08 $\pm$ 0.06

Appendix

TABLE IX: ATE (mean

\pm

SD) across budget and

p

. Lower is better.

$p$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
10	TargetOnly	–	0.80 $\pm$ 0.06	0.85 $\pm$ 0.04	0.86 $\pm$ 0.03	0.88 $\pm$ 0.03
	ProxyOnly	0.64 $\pm$ 0.15	0.68 $\pm$ 0.16	0.72 $\pm$ 0.15	0.71 $\pm$ 0.14	0.71 $\pm$ 0.20
	IPW-Transport	0.81 $\pm$ 0.17	0.77 $\pm$ 0.21	0.80 $\pm$ 0.19	0.78 $\pm$ 0.19	0.78 $\pm$ 0.25
	OM-Transport	0.81 $\pm$ 0.17	0.77 $\pm$ 0.21	0.80 $\pm$ 0.19	0.78 $\pm$ 0.19	0.78 $\pm$ 0.25
	EntropyBal	0.81 $\pm$ 0.17	0.77 $\pm$ 0.21	0.80 $\pm$ 0.19	0.78 $\pm$ 0.19	0.78 $\pm$ 0.25
	AnchorOnly	–	0.80 $\pm$ 0.07	0.85 $\pm$ 0.05	0.86 $\pm$ 0.04	0.87 $\pm$ 0.03

Appendix

TABLE X: Spearman (mean

\pm

SD) across budget and

p

. Higher is better.

$p$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
10	TargetOnly	–	0.20 $\pm$ 0.09	0.14 $\pm$ 0.05	0.13 $\pm$ 0.05	0.12 $\pm$ 0.05
	ProxyOnly	0.43 $\pm$ 0.25	0.36 $\pm$ 0.22	0.32 $\pm$ 0.22	0.35 $\pm$ 0.21	0.35 $\pm$ 0.27
	IPW-Transport	0.27 $\pm$ 0.25	0.28 $\pm$ 0.24	0.22 $\pm$ 0.20	0.27 $\pm$ 0.24	0.29 $\pm$ 0.37
	OM-Transport	0.27 $\pm$ 0.25	0.28 $\pm$ 0.24	0.22 $\pm$ 0.20	0.27 $\pm$ 0.25	0.29 $\pm$ 0.37
	EntropyBal	0.27 $\pm$ 0.24	0.28 $\pm$ 0.25	0.22 $\pm$ 0.20	0.27 $\pm$ 0.24	0.29 $\pm$ 0.37
	AnchorOnly	–	0.19 $\pm$ 0.08	0.14 $\pm$ 0.06	0.13 $\pm$ 0.06	0.12 $\pm$ 0.06

Appendix

TABLE XI: Regret (mean

\pm

SD) across budget and

p

. Lower is better.

$C$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
2	TargetOnly	–	5.33 $\pm$ 0.92	4.95 $\pm$ 1.18	4.70 $\pm$ 0.75	4.46 $\pm$ 0.91
	ProxyOnly	5.67 $\pm$ 1.05	5.62 $\pm$ 1.06	5.55 $\pm$ 1.37	5.42 $\pm$ 1.16	5.19 $\pm$ 1.22
	IPW-Transport	3.64 $\pm$ 1.45	4.17 $\pm$ 1.88	3.78 $\pm$ 1.85	4.03 $\pm$ 1.94	3.74 $\pm$ 1.97
	OM-Transport	3.54 $\pm$ 1.45	4.01 $\pm$ 1.93	3.59 $\pm$ 1.89	3.86 $\pm$ 1.93	3.52 $\pm$ 1.98
	EntropyBal	3.76 $\pm$ 1.45	4.23 $\pm$ 1.87	3.79 $\pm$ 1.85	4.04 $\pm$ 1.94	3.73 $\pm$ 1.98
	AnchorOnly	–	5.39 $\pm$ 1.00	5.01 $\pm$ 1.26	4.75 $\pm$ 0.78	4.52 $\pm$ 0.94

Appendix

TABLE XII: PEHE (mean

\pm

SD) across sources

C

and budget. Lower is better.

$C$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
2	TargetOnly	–	0.49 $\pm$ 0.41	0.40 $\pm$ 0.35	0.31 $\pm$ 0.24	0.21 $\pm$ 0.15
	ProxyOnly	1.29 $\pm$ 1.05	1.16 $\pm$ 0.97	1.08 $\pm$ 0.96	1.20 $\pm$ 1.20	1.13 $\pm$ 0.94
	IPW-Transport	0.79 $\pm$ 0.63	1.13 $\pm$ 0.95	0.88 $\pm$ 0.64	1.12 $\pm$ 0.97	0.79 $\pm$ 0.66
	OM-Transport	0.79 $\pm$ 0.64	1.11 $\pm$ 0.93	0.88 $\pm$ 0.66	1.12 $\pm$ 0.97	0.80 $\pm$ 0.67
	EntropyBal	0.82 $\pm$ 0.63	1.14 $\pm$ 0.96	0.88 $\pm$ 0.64	1.13 $\pm$ 0.97	0.79 $\pm$ 0.66
	AnchorOnly	–	0.54 $\pm$ 0.46	0.38 $\pm$ 0.33	0.30 $\pm$ 0.23	0.21 $\pm$ 0.14

Appendix

TABLE XIII: ATE (mean

\pm

SD) across sources

C

and budget. Lower is better.

$C$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
2	TargetOnly	–	0.47 $\pm$ 0.08	0.60 $\pm$ 0.06	0.66 $\pm$ 0.05	0.68 $\pm$ 0.04
	ProxyOnly	0.34 $\pm$ 0.09	0.41 $\pm$ 0.10	0.45 $\pm$ 0.10	0.49 $\pm$ 0.10	0.49 $\pm$ 0.12
	IPW-Transport	0.78 $\pm$ 0.15	0.74 $\pm$ 0.19	0.78 $\pm$ 0.16	0.75 $\pm$ 0.19	0.77 $\pm$ 0.20
	OM-Transport	0.79 $\pm$ 0.15	0.75 $\pm$ 0.19	0.80 $\pm$ 0.17	0.77 $\pm$ 0.19	0.79 $\pm$ 0.20
	EntropyBal	0.77 $\pm$ 0.15	0.73 $\pm$ 0.19	0.78 $\pm$ 0.16	0.75 $\pm$ 0.19	0.77 $\pm$ 0.20
	AnchorOnly	–	0.46 $\pm$ 0.08	0.59 $\pm$ 0.06	0.65 $\pm$ 0.04	0.67 $\pm$ 0.05

Appendix

TABLE XIV: Spearman (mean

\pm

SD) across sources

C

and budget. Higher is better.

$C$	Method	(50,0)	(100,50)	(150,100)	(250,200)	(550,500)
2	TargetOnly	–	1.18 $\pm$ 0.24	0.92 $\pm$ 0.28	0.79 $\pm$ 0.18	0.71 $\pm$ 0.19
	ProxyOnly	1.58 $\pm$ 0.51	1.50 $\pm$ 0.45	1.39 $\pm$ 0.56	1.34 $\pm$ 0.60	1.23 $\pm$ 0.50
	IPW-Transport	0.50 $\pm$ 0.42	0.67 $\pm$ 0.55	0.55 $\pm$ 0.56	0.63 $\pm$ 0.56	0.56 $\pm$ 0.57
	OM-Transport	0.48 $\pm$ 0.41	0.63 $\pm$ 0.55	0.51 $\pm$ 0.55	0.60 $\pm$ 0.57	0.52 $\pm$ 0.59
	EntropyBal	0.52 $\pm$ 0.42	0.68 $\pm$ 0.54	0.55 $\pm$ 0.56	0.63 $\pm$ 0.56	0.55 $\pm$ 0.57
	AnchorOnly	–	1.20 $\pm$ 0.30	0.93 $\pm$ 0.28	0.82 $\pm$ 0.17	0.75 $\pm$ 0.21

Appendix

TABLE XV: Regret (mean

\pm

SD) across sources

C

and budget. Lower is better.

$s/p$	Method	$\Gamma=0.0$	$\Gamma=0.5$	$\Gamma=1.0$
0.05	TargetOnly	4.41 $\pm$ 0.70	4.25 $\pm$ 0.53	4.30 $\pm$ 0.57
	ProxyOnly	4.97 $\pm$ 0.89	4.72 $\pm$ 0.68	4.84 $\pm$ 0.72
	IPW-Transport	2.79 $\pm$ 1.25	2.13 $\pm$ 1.02	2.20 $\pm$ 1.11
	OM-Transport	2.67 $\pm$ 1.26	2.04 $\pm$ 1.03	2.10 $\pm$ 1.13
	EntropyBal	2.80 $\pm$ 1.25	2.14 $\pm$ 1.02	2.21 $\pm$ 1.11
	AnchorOnly	4.45 $\pm$ 0.70	4.28 $\pm$ 0.53	4.34 $\pm$ 0.56

Appendix

TABLE XVI: PEHE (mean

\pm

SD) under A5 violations. Lower is better.

$s/p$	Method	$\Gamma=0.0$	$\Gamma=0.5$	$\Gamma=1.0$
0.05	TargetOnly	0.22 $\pm$ 0.14	0.21 $\pm$ 0.17	0.16 $\pm$ 0.12
	ProxyOnly	0.92 $\pm$ 0.75	0.91 $\pm$ 0.74	0.98 $\pm$ 0.79
	IPW-Transport	0.80 $\pm$ 0.60	0.65 $\pm$ 0.51	0.61 $\pm$ 0.47
	OM-Transport	0.79 $\pm$ 0.58	0.65 $\pm$ 0.50	0.60 $\pm$ 0.47
	EntropyBal	0.80 $\pm$ 0.60	0.65 $\pm$ 0.51	0.61 $\pm$ 0.46
	AnchorOnly	0.20 $\pm$ 0.14	0.19 $\pm$ 0.14	0.15 $\pm$ 0.12

Appendix

TABLE XVII: ATE (mean

\pm

SD) under A5 violations. Lower is better.

$s/p$	Method	$\Gamma=0.0$	$\Gamma=0.5$	$\Gamma=1.0$
0.05	TargetOnly	0.68 $\pm$ 0.04	0.67 $\pm$ 0.04	0.67 $\pm$ 0.04
	ProxyOnly	0.54 $\pm$ 0.09	0.55 $\pm$ 0.08	0.55 $\pm$ 0.08
	IPW-Transport	0.87 $\pm$ 0.11	0.91 $\pm$ 0.08	0.91 $\pm$ 0.08
	OM-Transport	0.88 $\pm$ 0.11	0.92 $\pm$ 0.08	0.92 $\pm$ 0.08
	EntropyBal	0.87 $\pm$ 0.11	0.91 $\pm$ 0.08	0.91 $\pm$ 0.08
	AnchorOnly	0.67 $\pm$ 0.04	0.66 $\pm$ 0.04	0.66 $\pm$ 0.04

Appendix

TABLE XVIII: Spearman (mean

\pm

SD) under A5 violations. Higher is better.

$s/p$	Method	$\Gamma=0.0$	$\Gamma=0.5$	$\Gamma=1.0$
0.05	TargetOnly	0.71 $\pm$ 0.15	0.68 $\pm$ 0.14	0.70 $\pm$ 0.15
	ProxyOnly	1.11 $\pm$ 0.40	1.02 $\pm$ 0.33	1.08 $\pm$ 0.31
	IPW-Transport	0.32 $\pm$ 0.29	0.20 $\pm$ 0.19	0.22 $\pm$ 0.22
	OM-Transport	0.30 $\pm$ 0.28	0.19 $\pm$ 0.19	0.20 $\pm$ 0.22
	EntropyBal	0.32 $\pm$ 0.29	0.20 $\pm$ 0.20	0.22 $\pm$ 0.22
	AnchorOnly	0.73 $\pm$ 0.16	0.71 $\pm$ 0.14	0.72 $\pm$ 0.15

Appendix

TABLE XIX: Regret (mean

\pm

SD) under A5 violations. Lower is better.

	p=10			p=20			p=50			p=100
Method	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE
TargetOnly	1.18	0.72	0.40	1.38	0.57	0.76	1.56	0.37	1.21	1.45	0.20	1.47
ProxyOnly	1.13	0.54	0.73	1.36	0.40	1.03	1.57	0.24	1.52	1.53	0.13	1.79
IPW-Transport	0.94	0.69	0.65	0.95	0.70	0.87	0.96	0.75	0.99	0.96	0.75	1.18
OM-Transport	0.94	0.69	0.66	0.95	0.70	0.87	0.97	0.75	0.98	0.97	0.76	1.14
EntropyBal	0.94	0.69	0.66	0.94	0.70	0.87	0.95	0.74	0.99	0.91	0.71	1.30

Appendix

TABLE XX: CATE Calibration: Dim Sweep at budget (150,100). Slope (ideal=1), R 2 (higher=better), ECE (lower=better).

	C=2			C=5			C=10			C=20			C=50
Method	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE
TargetOnly	1.48	0.36	1.24	1.50	0.35	1.20	1.48	0.36	1.20	1.54	0.35	1.23	1.50	0.35	1.20
ProxyOnly	1.43	0.22	1.48	1.47	0.23	1.34	1.57	0.24	1.54	1.50	0.22	1.44	1.52	0.22	1.54
IPW-Transport	0.84	0.66	1.32	0.88	0.69	1.18	0.97	0.71	1.14	0.97	0.76	0.86	0.99	0.74	0.96
OM-Transport	0.87	0.69	1.25	0.92	0.71	1.09	0.99	0.73	1.11	0.98	0.77	0.84	0.99	0.74	0.95
EntropyBal	0.84	0.66	1.32	0.87	0.68	1.20	0.95	0.70	1.15	0.95	0.75	0.88	0.99	0.73	0.97

Appendix

TABLE XXI: CATE Calibration: Sources Sweep at budget (150,100). Slope (ideal=1), R 2 (higher=better), ECE (lower=better).

		$\Gamma$ =0			$\Gamma$ =0.5			$\Gamma$ =1
$s/p$	Method	Slope	R 2	ECE	Slope	R 2	ECE	Slope	R 2	ECE
0.05	TargetOnly	1.69	0.48	1.33	1.75	0.47	1.32	1.68	0.47	1.26
	ProxyOnly	1.51	0.32	1.37	1.54	0.33	1.36	1.53	0.32	1.45
	IPW-Transport	0.95	0.78	0.92	0.97	0.85	0.71	0.98	0.85	0.64
	OM-Transport	0.97	0.80	0.89	0.98	0.86	0.69	0.99	0.86	0.62
	EntropyBal	0.95	0.78	0.93	0.97	0.85	0.71	0.98	0.85	0.64

Appendix

TABLE XXII: CATE Calibration under A5 Violations. Slope (ideal=1), R 2 (higher=better), ECE (lower=better).

Causal Inference

Causal inference studies how interventions and counterfactuals reveal cause-and-effect relationships beyond observed associations.

See all 309 papers

Mar 19, 2026

Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment

Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose CALM (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source's features into a common representation space. OS outcome models are transferred to the RCT embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate CALM in two forms: a closed-form linear version, CALM-Lin, and a neural representation-learning version, CALM-NN. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while CALM-NN wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies CALM-NN delivers the largest gains over the trial-only baseline.

Amir Asiaee, Samhita Pal

Department of Biostatistics, Vanderbilt University Medical Center, TN 37203, USA

Causal Effect Estimation Causal Representation Learning Conditional Average Treatment Effect Estimation Causal Inference Individualized Treatment Effect Estimation

Ask PDF

Mar 7, 2026

TEA-Time: Transporting Effects Across Time

Treatment effects estimated from a randomized controlled trial are local not only to the study population but also to the time at which the trial was conducted. The literature on generalizing experimental findings to new populations is extensive, yet transporting effects across time has received far less attention, and even defining the target estimand is nonobvious. We formalize the transported average treatment effect under a separable temporal effects assumption, derive two identification strategies: replicated trials and common arm, and develop doubly robust, semiparametrically efficient estimators for each. Applied to a large archive of headline A/B tests, the common arm strategy is substantially more precise but exhibits systematic bias when the temporal factor depends on the gap between intervention and measurement rather than on measurement time alone, while the replicated trials strategy, which allows this dependence, tracks the ground truth more faithfully. Simulation studies investigate when each strategy is reliable and when it silently fails.

Harsh Parikh, Gabriel Levin-Konigsberg, Dominique Perrault-Joncas +1

Amazon SCOT, Seattle, USA · Yale University, New Haven, USA · Duke University, Durham, USA

Causal Effect Estimation

Ask PDF

Aug 16, 2026

Inferential Evaluation of Surrogate-Derived Models under Covariate Shift

In transfer-learning settings, a model derived from abundant surrogate labels may be deployed in a target population where gold-standard outcomes are unobserved. Evaluating its target performance is essential for determining whether decisions based on the model remain reliable, yet it is difficult when gold labels are scarce, and covariate distributions differ across data sources. We study a three-sample setting with a small gold-labeled source, a larger surrogate-labeled source, and an unlabeled target. Under conditional transportability, we evaluate the surrogate-derived model against the latent gold-standard outcome in the target population. We propose cross-fitted estimators that transport information from the two labeled sources through source-specific density ratios. We also combine outcome-regression augmentation with a kernel correction for estimating the model near a threshold, accounting for uncertainty from all three samples. We establish asymptotically linear inference for TPR and FPR, consistency and pointwise inference for the ROC curve, and asymptotically normal inference for AUC. Simulations assess bias, coverage, and sensitivity to bandwidth and relative sample sizes. A retrospective temporal validation on Chatbot Arena and a semi-synthetic ACS-Income study provide validation in real-world AI applications.

Longtian Shi, Molei Liu, Doudou Zhou

Department of Statistics and Data Science, National University of Singapore · Department of Biostatistics, Peking University Health Science Center, Peking University, Beijing, China · Beijing International Center for Mathematical Research, Peking University, Beijing, China

Distribution Shift Robustness Covariate Shift

Ask PDF

Abstract

Causal Inference

Explore similar work

Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment

TEA-Time: Transporting Effects Across Time

Inferential Evaluation of Surrogate-Derived Models under Covariate Shift