MissSurrogate R Package for Surrogate Evaluation

• MissSurrogate is an R package designed to estimate the proportion of treatment effect explained (PTE) when continuous surrogate measurements are incomplete in randomized trials.
• It implements both parametric (via Wang–Taylor linear regression) and nonparametric methods, utilizing inverse probability weighting (IPW) and semiparametric maximum likelihood estimation (SMLE) to correct bias.
• Empirical evidence demonstrates that these methods improve efficiency and reduce bias compared to complete-case analysis under typical MCAR or MAR missing-data scenarios.

Searching arXiv for the specified paper to ground the article in the cited source. MissSurrogate is an R package for evaluating surrogate markers in randomized clinical trials when the surrogate is missing for some participants. Its scope is the proportion of treatment effect explained (PTE) framework, with implementations of inverse probability weighting (IPW) for both parametric and nonparametric surrogate evaluation and semiparametric maximum likelihood estimation (SMLE) for the parametric framework. The package is designed for settings in which the primary outcome is observed, the surrogate is continuous and incompletely observed, treatment is randomized, and missingness is assumed to be missing completely at random (MCAR) or missing at random (MAR) rather than missing not at random (MNAR) (Lotspeich et al., 21 Mar 2026).

1. Definition, purpose, and scope

MissSurrogate addresses a specific inferential problem: estimating surrogate utility when a surrogate marker $S$ is missing for some trial participants. In the underlying framework, $S$ is an intermediate measurement intended to stand in for a harder-to-obtain primary clinical outcome $Y$, and treatment is represented by $Z \in \{0,1\}$. The central methodological concern is that standard surrogate-validation procedures are often applied only to complete cases, meaning subjects with both $S$ and $Y$ observed, even though deleting subjects with missing $S$ can be inefficient and, under many realistic missingness patterns, biased (Lotspeich et al., 21 Mar 2026).

The package is not presented as a generic missing-data package. It is software for a specific statistical task: estimating surrogate utility, especially the proportion of treatment effect explained, when surrogate measurements are incompletely observed. The paper states that the package is available at https://github.com/sarahlotspeich/missSurrogate and that supporting information and reproducible simulation code are available at https://github.com/sarahlotspeich/evaluate_missing_surrogates. The paper does not give exact function names, so no software interface beyond the methodology itself is specified.

A central clarification concerns the role of complete-case analysis. The paper’s position is not that complete-case analysis is always invalid. Rather, complete-case analysis is often inefficient, and under common MAR-type mechanisms it can become biased. The package therefore implements corrections intended to retain more of the information in the full trial and to reduce bias under a broader range of missingness mechanisms than complete-case analysis.

2. Statistical formulation of surrogate utility

The paper defines the primary outcome $Y$, the surrogate marker $S$, the randomized treatment indicator $Z \in \{0,1\}$, and an indicator $S$0 for whether the surrogate is observed: $S$1 Potential outcomes are denoted by

$S$2

The overall treatment effect on the primary outcome is

$S$3

The residual treatment effect after accounting for the surrogate is defined as

$S$4

where

$S$5

The surrogate utility measure of interest is then

$S$6

In the paper’s interpretation, $S$7 corresponds to a perfect surrogate, $S$8 to a useless surrogate, and intermediate values to partial explanation (Lotspeich et al., 21 Mar 2026).

Because $S$9 and $Y$0 are never jointly observed for the same individual, $Y$1 is not directly identified. The paper therefore assumes

$Y$2

Under (A1),

$Y$3

This is the identified form used operationally.

Within this framework, the package supports both parametric and nonparametric estimation. The parametric approach uses the Wang–Taylor linear model

$Y$4

With

$Y$5

the paper gives

$Y$6

$Y$7

and

$Y$8

This is a plug-in estimator: estimate $Y$9 and $Z \in \{0,1\}$0, then compute $Z \in \{0,1\}$1, $Z \in \{0,1\}$2, and $Z \in \{0,1\}$3.

The nonparametric approach avoids specifying model (1). The overall effect is estimated by

$Z \in \{0,1\}$4

and the residual effect by

$Z \in \{0,1\}$5

where $Z \in \{0,1\}$6 is the empirical CDF in controls and $Z \in \{0,1\}$7 is the Nadaraya–Watson estimator

$Z \in \{0,1\}$8

Then

$Z \in \{0,1\}$9

This nonparametric formulation requires the support-overlap assumption

$S$0

The paper emphasizes that the nonparametric method can fail or be badly biased when surrogate distributions in the two treatment arms do not overlap well. It also notes that MissSurrogate is focused almost entirely on one surrogate criterion, the PTE $S$1, rather than functioning as a general surrogate-validation toolbox spanning principal stratification, meta-analytic surrogacy, or other paradigms.

3. Missing-data methods implemented in the package

The package is built around missingness in the surrogate $S$2, not in the primary outcome $S$3. The implemented methods assume MCAR or MAR missingness in $S$4, not MNAR (Lotspeich et al., 21 Mar 2026).

For IPW, the paper requires a correctly specified model for the probability that the surrogate is observed. If

$S$5

then the operational assumptions are MAR given the modeled variables and positivity: $S$6 If missingness depends only on treatment, the paper suggests nonparametric estimation: $S$7 More generally, if missingness depends on multiple variables, the paper suggests fitting a model using all subjects, such as logistic regression or generalized boosted models. The inverse-probability weights are

$S$8

and are used only for subjects with $S$9.

For the parametric PTE method, IPW is implemented by fitting the regression

$Y$0

using a weighted linear regression on complete cases with weights $Y$1. The treatment-arm surrogate means are estimated by weighted Horvitz–Thompson estimators: $Y$2 These are then substituted into equations (3)–(5).

For the nonparametric PTE method, $Y$3 is unchanged because $Y$4 is fully observed: $Y$5 The residual effect is reweighted as

$Y$6

with weighted kernel regression

$Y$7

Then

$Y$8

The paper attributes complementary properties to IPW. Its strengths are conceptual simplicity, computational speed, and relative flexibility in including additional predictors of missingness. Its limitations are dependence on correct specification of the weight model, instability when some observation probabilities are small, and lower efficiency than model-based methods because subjects with missing $Y$9 do not directly contribute to the surrogate regression or kernel fit.

SMLE is implemented only for the parametric PTE framework. The full-data joint distribution is factored as

$S$0

Here, $S$1 comes from the normal linear regression model in (1), while $S$2 is left nonparametric. Let $S$3 denote observed support points of $S$4 in treatment group $S$5, with probabilities

$S$6

satisfying

$S$7

Even when $S$8 is continuous, the nonparametric MLE places mass on observed support points.

The parameters $S$9 are estimated by EM. In the E-step, the paper computes posterior probabilities

$Y$0

via

$Y$1

In the M-step, the expected complete-data objective is maximized, with $Y$2 obtainable by weighted linear regression and the mass probabilities updated by

$Y$3

The initialization reported in the paper is

$Y$4

with convergence tolerance $Y$5.

After EM converges, arm-specific surrogate means are estimated by

$Y$6

and these are inserted into the parametric PTE formulas to obtain $Y$7, $Y$8, and $Y$9. SMLE requires correctness of the linear model in (1), MAR/MCAR-type missingness assumptions, and enough observed support in $S$0 within treatment groups to estimate $S$1 nonparametrically. The paper characterizes the method as more robust than a fully parametric likelihood because it avoids specifying a parametric model for $S$2, while also noting greater computational cost and potential difficulty under heavy missingness or sparse support.

4. Relation to complete-case analysis and simulation evidence

A central theme of the paper is that complete-case analysis is not uniformly biased, but it is often inefficient and becomes biased under some common MAR mechanisms. The simulation study compares gold-standard full-data estimators, complete-case parametric and nonparametric estimators, IPW parametric and nonparametric estimators, and parametric SMLE estimators (Lotspeich et al., 21 Mar 2026).

Each simulation used $S$3 total subjects, split evenly between treatment and control, with continuous surrogate $S$4 and continuous outcome $S$5. The data-generating model for $S$6 was

$S$7

and, for Settings 1–4,

$S$8

The true effects were

$S$9

Bootstrap inference used $Z \in \{0,1\}$0 stratified bootstrap samples, with both Wald and quantile confidence intervals. The reported metrics were bias and percent bias, empirical SE (ESE), average estimated SE (ASE), coverage probability, and relative efficiency (RE) relative to the gold standard.

Under MCAR, with

$Z \in \{0,1\}$1

all methods were essentially unbiased, and coverage was near 95% throughout. The nonparametric complete-case estimator had bias $Z \in \{0,1\}$2, ESE $Z \in \{0,1\}$3, and RE $Z \in \{0,1\}$4, whereas nonparametric IPW had bias $Z \in \{0,1\}$5, ESE $Z \in \{0,1\}$6, and RE $Z \in \{0,1\}$7. The parametric complete-case and parametric IPW estimators both had bias $Z \in \{0,1\}$8, ESE $Z \in \{0,1\}$9, and RE $S$00. Parametric SMLE had bias $S$01, ESE $S$02, and RE $S$03. In this setting, the paper interprets the corrections primarily as efficiency improvements, with SMLE the best parametric method.

Under MAR depending only on treatment,

$S$04

all methods again remained unbiased. Parametric complete-case RE was $S$05, parametric IPW RE was $S$06, and parametric SMLE RE was $S$07. The paper treats this as an instance in which complete-case analysis happened to be valid, but SMLE recovered substantially more precision.

Under MAR depending on the outcome,

$S$08

complete-case analysis became biased. The nonparametric complete-case estimator had bias $S$09, percent bias $S$10, and coverage $S$11 for normal intervals and $S$12 for quantile intervals. The parametric complete-case estimator had bias $S$13, percent bias $S$14, and coverage $S$15 and $S$16. IPW corrected the bias: nonparametric IPW had bias $S$17 and coverage approximately $S$18, while parametric IPW had bias $S$19 and coverage approximately $S$20–$S$21. SMLE was also unbiased and more efficient than parametric IPW, with bias $S$22, ESE $S$23, and RE $S$24, versus ESE $S$25 and RE $S$26 for parametric IPW. This is the paper’s main practical argument for the package’s corrections: when missingness depends on observed outcome information, complete-case surrogate evaluation can be biased, whereas IPW and SMLE recover validity.

The paper also studies IPW misspecification. When the true missingness depended on

$S$27

several weight models were tried: $S$28 only, $S$29 only, $S$30, $S$31, and the correct model $S$32. Underfitting caused bias, omitting key terms made IPW nearly as biased as complete case, and including extra terms did not hurt much and could be slightly better. The paper therefore reinforces a standard point: IPW is sensitive to omission of important predictors of missingness.

A separate setting examined lack of overlap in the treatment and control distributions of $S$33, violating the nonparametric support assumption. In that case, nonparametric estimators were biased even with full data: the nonparametric gold-standard estimator had bias $S$34 ($S$35), the nonparametric complete-case estimator had bias $S$36 ($S$37), and the nonparametric IPW estimator had bias $S$38 ($S$39). Coverage was poor, whereas parametric methods stayed essentially unbiased. The implication drawn in the paper is precise: missing-data correction cannot rescue a surrogate estimator whose core identifying or smoothing assumptions are violated.

5. Empirical application to the DCCT diabetes trial

The paper illustrates MissSurrogate with the Diabetes Control and Complications Trial (DCCT), a multicenter randomized trial in Type 1 diabetes comparing intensive treatment aimed at near-normal glycemic control with conventional treatment used at the time (Lotspeich et al., 21 Mar 2026).

In this application, treatment $S$40 is intensive versus conventional therapy, the surrogate $S$41 is blood glucose level measured as change from baseline to 4 years, and the primary outcome $S$42 is LDL cholesterol measured as change from baseline to 4 years. The trial included $S$43 participants, of whom 208 were missing the surrogate at 4 years, corresponding to approximately $S$44 missingness. The paper reports that the surrogate distributions by treatment arm did not fully overlap, making the nonparametric method potentially unstable or biased, while scatterplots suggested that the $S$45-$S$46 relationship was fairly linear, supporting the parametric approach.

The reported nonparametric estimates were: $S$47 for complete case, and

$S$48

for IPW.

The reported parametric estimates were: $S$49 for complete case,

$S$50

for IPW, and

$S$51

for SMLE.

The paper interprets these results as showing that missingness-adjusted estimates were broadly similar to complete-case estimates in this dataset, suggesting limited bias from missingness. At the same time, the SMLE confidence interval was 31% narrower than the IPW interval among the parametric methods, which is consistent with the simulation findings on efficiency. The authors conclude that blood glucose explained a moderate proportion of the treatment effect on LDL, but not enough to support it as a valid surrogate in this setting, because the lower confidence bounds were well below thresholds such as 0.5. For the package’s intended use, this example shows that missing-data correction can improve precision even when point estimates change little, and that method choice should reflect the structure of the data, especially support overlap.

6. Inference, practical use, and limitations

The paper gives more methodological detail than software syntax, but several package-facing implications are explicit. At minimum, the methods require a continuous primary outcome $S$52, a continuous surrogate $S$53 that may be missing, a binary randomized treatment indicator $S$54, and, for IPW, variables used to model $S$55, such as $S$56, $S$57, or other observed covariates. The missingness indicator $S$58 is implied by whether $S$59 is observed (Lotspeich et al., 21 Mar 2026).

The central outputs are the estimands

$S$60

According to the paper, the supported methods are:

• Parametric: complete case, IPW, and SMLE.
• Nonparametric: complete case and IPW.

SMLE is not developed for the nonparametric framework in this paper.

Inference is bootstrap-based for all methods. The procedure uses stratified bootstrap resampling by treatment arm with $S$61 resamples, re-estimating $S$62, $S$63, and $S$64 each time. The paper reports bootstrap variance or standard error, Wald-type normal-approximation confidence intervals

$S$65

and quantile bootstrap intervals

$S$66

It suggests that quantile intervals are more robust, especially in smaller samples.

The paper also offers clear operational guidance. IPW is the simpler and faster correction, roughly comparable in speed to complete-case fitting, and is the only missing-data correction available for both the parametric and nonparametric surrogate frameworks. SMLE is slower because it uses an iterative EM algorithm, but in the parametric framework it is often more efficient and avoids explicit modeling of the missingness probability. Nonparametric methods require bandwidth selection and, critically, sufficient support overlap across treatment arms. The paper explicitly notes that SMLE may struggle under heavy missingness if too few support points are available to estimate $S$67 nonparametrically.

The limitations are equally specific. The methods do not handle missing primary outcomes, are not valid under MNAR without further sensitivity analysis, and are developed in a setting with continuous $S$68 and $S$69. SMLE is only developed for the parametric framework, and no missing-data method beyond IPW is developed for the nonparametric framework. The paper identifies extension to multiple imputation as potentially useful, and notes that extending the SMLE nonparametric component to condition on more than $S$70 would require smoothing or sieves. A practical implication is that users must assess randomized treatment, continuous outcomes and surrogates, MCAR or MAR missingness in $S$71, positivity for IPW, correctness of the IPW weight model when weighting is used, correctness of the linear model when the parametric or SMLE route is used, and overlap of surrogate distributions by treatment arm when the nonparametric method is contemplated.

Taken together, these features place MissSurrogate in a narrow but technically important niche. It is a PTE-focused package for randomized trials with incomplete surrogate measurement, intended to replace default reliance on complete-case analysis with methods that are more valid under MAR and often more efficient, while preserving a clear distinction between the parametric and nonparametric assumptions that govern surrogate evaluation.