Review Reports - Joint Modeling of Longitudinal and Survival Data in Public Health and Biomedical Research: A Systematic Review

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is well written. The authors have done a comprehensive review of the literature. I have a minor comment. It would be helpful to show some numerical results on how the methods compare with each other through an example either from a simulated dataset or a real dataset.

Author Response

Comments 1: The paper is well written. The authors have done a comprehensive review of the literature. I have a minor comment. It would be helpful to show some numerical results on how the methods compare with each other through an example either from a simulated dataset or a real dataset.

Response 1: We thank the reviewer for the thoughtful and constructive comment. We agree that numerical comparisons through simulation studies or real-data applications can be highly informative when methods are designed to address the same research question under comparable assumptions.

However, the methods reviewed in this paper were developed for different scientific questions, data structures, and modeling assumptions (e.g., truncated or sparse longitudinal data, different event processes, varying association structures, high-dimensional biomarkers, etc.). As such, they are not directly comparable within a single simulation or application framework without substantially narrowing the scope of the review. Using just one example might unintentionally give the impression that the methods can be broadly ranked, which would be misleading since each was designed for a specific context and purpose.

To clarify this point, we have added a brief statement in the Discussion section noting that direct numerical comparison is beyond the scope of this review and that method selection should be guided by research questions and data characteristics. Now the paragraph reads as:

“We did not perform simulation studies or include a real-data application to numerically compare the reviewed methods. As discussed above, different joint modeling approaches are designed for different scientific settings, data structures, and research objectives. Because of these differences, they are not directly comparable within a single unified simulation or example without substantially narrowing the scope. Moreover, using only one example might give the impression that the methods can be broadly ranked, which would be misleading given their context-specific purposes. Therefore, direct numerical comparison is beyond the scope of this review, and method selection should be guided by the specific research question and characteristics of the data.” (Lines 600-608, p. 13-14).

Reviewer 2 Report

Comments and Suggestions for Authors

Major comments

The authors review methodological advances of joint longitudinal and survival models applied to public health by consulting the PubMed database. Such a review is very welcome, given that this area of statistical/methodological research is very active and, and the authors point out, joint modeling of this kind offers many important advantages.

The authors use only 3 keywords and leave out other, often used keywords such as “time-to-event.” This can greatly reduce the breadth of their review.

A single author (cf. line 98) did the title+abstract screening, and this should be recognized as a major, potential limitation.

Finally, although the authors provide a narrative synthesis of methodological advances, they are not very explicit about possible guidelines and advice to the users. They mention some in the Discussion, especially with respect to the survival model, but it would be extremely helpful to add subsections to the Discussion that provide recommendations on all 3 aspects (longitudinal submodel, survival submodel, and type of association) and also about future developments that are still needed and that appear promising.

Minor comments

Title: The title mentions “time-to-event,” which oddly was not one of the very keywords. The authors should replace with “survival.”

line 104: Why were the 9 studies on estimation algorithms excluded? That is potentially a major methodological advance, as Rizopoulos (2016) has shown with his Bayesian R package.

line 112: Given there was a single coder, what kind of discrepancies could have appeared?

line 135: The authors must mean that “epsilon_i (and not u_i) is the measurement error.

line 145. The symbole “w_i” did not come through correctly.

line 147: To be correct, “alpha” is the effect of the “true value” of the longitudinal variable on the risk of the event.

Table 1 is very hard to read. Could you increase its readability?

References

Rizopoulos, D. (2016). The R Package JMbayes for Fitting Joint Models for Longitudinal and Time-to-Event Data using MCMC. arXiv:1404.7625 [Stat], 72. https://doi.org/10.18637/jss.v072.i07

Author Response

Comments 1:

Major comments

The authors use only 3 keywords and leave out other, often used keywords such as “time-to-event.” This can greatly reduce the breadth of their review.

Response 1:

We thank the reviewer for the helpful and constructive suggestion. We have replaced the keyword “time-to-event” into “survival”, and the keywords now are “joint model; statistical methods; review; longitudinal and survival data; public health” (Lines 28-29, p. 1).

Comments 2:

A single author (cf. line 98) did the title+abstract screening, and this should be recognized as a major, potential limitation.

Response 2:

We appreciate the reviewer’s comment. We acknowledge that having a single author conduct the title and abstract screening may introduce potential selection bias and should be recognized as a limitation. We have added a statement in Section 4.2 (Limitations) to explicitly acknowledge this as a potential limitation of the review process (Lines 678-682, p. 15).

Comments 3:

Finally, although the authors provide a narrative synthesis of methodological advances, they are not very explicit about possible guidelines and advice to the users. They mention some in the Discussion, especially with respect to the survival model, but it would be extremely helpful to add subsections to the Discussion that provide recommendations on all 3 aspects (longitudinal sub-model, survival sub-model, and type of association) and also about future developments that are still needed and that appear promising.

Response 3:

Thank you so much for the helpful comment. We have provided the recommendations by sections on the 3 aspects respectively in Discussion (Lines 485-579, p. 11-14). Now the text reads as follows:

“4. 1 Recommendations for sub-model choices

The findings of this review provide recommendations on the selection of sub-models in joint modeling. Although the longitudinal and survival components are estimated jointly, the considerations guiding their specification often differ depending on the characteristics of the repeated measurements, the event process, and the primary research objective. In particular, the distributional form, dimensionality, and temporal structure of the longitudinal outcomes mostly determine the choice of the longitudinal sub-model, whereas the nature of the event process and assumptions regarding the hazard function guide the choice of the survival sub-model. Based on the methodological developments identified in this review, recommendations are presented separately for the longitudinal sub-model, the survival sub-model, and the association structure.

4.1.1 Recommendations for the longitudinal sub-model

Methodological developments in joint modeling have focused extensively on the specification of the longitudinal sub-model. In practice, the choice of longitudinal sub-model should primarily be guided by the distributional characteristics of the longitudinal outcome(s), the dimensionality of the measurements, the presence of heterogeneity, and the research objective.

For continuous longitudinal outcomes that generally follow normal distribution, linear mixed-effects models remain the standard choice and the most widely used sub-model. Extensions such as robust linear mixed-effects models can provide improved robustness when the data contains outliers or follows heavy-tailed distributions. When the longitudinal outcome is non-Gaussian, generalized linear mixed-effects models provide flexibility for different outcome types, including binary, count, ordinal, or proportional. Examples include logistic models for binary outcomes, negative binomial or Poisson models for count data, and ordinal logistic models for ordered categorical outcomes. Quantile models can also be considered for skewed outcomes.

For longitudinal outcomes with excessive zeros or semicontinuous distributions, zero-inflated count models and two-part models combining logistic and continuous components are recommended. For proportion data bounded between 0 and 1, such as microbiome measures, beta regression models or zero-inflated beta models provide an appropriate distributional specification. When measurements are subject to detection limits, two-part joint models can be employed to account for left-censored observations. In situations where the longitudinal trajectories exhibit nonlinear patterns over time, nonlinear mixed-effects models, spline-based models (including B-splines or penalized splines), and piecewise mixed-effects models can capture complex temporal dynamics. Penalized approaches such as B-spline models combined with LASSO regularization can further improve variable selection and model flexibility when multiple covariates or time-varying effects are present.

When the study population presents substantial heterogeneity or different disease progression patterns, latent class models or latent variable approaches can be used to identify subgroups with different longitudinal trajectories. These methods are particularly useful in chronic diseases such as Alzheimer’s disease or cancer, where patients may follow different progression patterns. In addition, functional data approaches, including functional principal component analysis (FPCA) and multivariate FPCA, can effectively summarize complex longitudinal trajectories, especially when multiple biomarkers are measured repeatedly over time. For high-dimensional or multivariate longitudinal out-comes, several modeling strategies are available. Multivariate mixed-effects models, functional mixed models, and copula-based models allow joint modeling of multiple correlated biomarkers. In addition, spatiotemporal multilevel models can capture spatial dependence when measurements are collected across geographical locations. Overall, careful alignment between the characteristics of the longitudinal data, including outcome type, distribution, dimensionality, and temporal pattern, and the choice of longitudinal sub-model, is important for valid inference in joint modeling.

4.1.2 Recommendations for the survival sub-model

The survival sub-models have also advanced significantly, with researchers increasingly looking for alternative methods than the standard Cox proportional hazards model. Recent studies have explored the use of semiparametric models, including accelerated failure time (AFT) models, frailty models, and competing risks models to better handle left truncated data, informative censoring, and multivariate survival outcomes. For studies involving multiple event types or competing risks, competing risk models are recommended for different causes of failure. Besides, multi-state Markov models are helpful for modeling transitions among multiple disease states, such as disease progression, relapse, and mortality. These models are especially useful for chronic diseases in which patients may progress through several stages over time. When greater flexibility in modeling the baseline hazard is needed, piecewise constant hazard models or B-spline baseline hazard models can capture the complex hazard shapes. These methods allow the hazard function to vary over time. When the time-to-event distribution can be assumed, parametric survival models, such as AFT models based on Weibull, exponential, or Gompertz distributions, may be considered. Parametric models are especially useful in clinical trials or mechanistic studies when the underlying hazard can be reasonably assumed. When recurrent events or clustered survival outcomes are present, shared frailty models can account for unobserved heterogeneity and within-cluster correlation. These models are particularly useful in multicenter studies. Further, models with time-varying coefficients or functional predictors allow covariate effects to change over time, making them helpful when the proportional hazards assumption does not hold. More recently, survival sub-models with machine learning approach, such as random survival forests, have also been explored in joint modeling for complex nonlinear relationships or high-dimensional predictors. Overall, the choice of survival sub-model should be guided by the characteristics of the time-to-event process, including the number of event types, whether having recurrent events or not, assumptions regarding the hazard function, clustering effects, or time-varying effects.

4.1.3 Recommendations for the Association Structure

The choice of association structure should reflect both the biological context and the relationship between longitudinal biomarkers and the survival outcome. For biomarkers with a direct and consistent effect on the event, such as CD4 count in HIV/AIDS or serum creatinine in kidney disease, the shared parameter model is generally recommended, capturing risk through current value or slope components. In the meantime, for complex, multistage diseases like Alzheimer’s disease or cancer, latent class association structures are recommended to account for distinct patient characteristics with varying biomarker-survival relationships. When dealing with skewed or non-normally distributed biomarkers, such as viral loads or microbiomes, copula-based structures can be used to capture non-linear dependencies. Finally, studies with many correlated biomarkers, functional or high-dimensional latent trait structures can help with identifying disease progression. Selecting an association structure that aligns with the clinical and statistical context ensures more robust, interpretable, and biologically meaningful inferences.” (Lines 485-579, p. 11-14).

Comments 4:

Minor comments

Title: The title mentions “time-to-event,” which oddly was not one of the very keywords. The authors should replace with “survival.”

Response 4:

Thank you so much for the helpful comment. We have replaced the “time-to-event” with “survival” in the title. Now the title reads as “Joint modeling of longitudinal and survival data in public health and biomedical research: A systematic review” (Lines 2-3, p. 1).

Comments 5:

line 104: Why were the 9 studies on estimation algorithms excluded? That is potentially a major methodological advance, as Rizopoulos (2016) has shown with his Bayesian R package.

Response 5:

Thank you so much for your question. We fully acknowledge that studies on estimation algorithms are essential methodological advancements in joint modeling. However, the focus of our current review is particularly on the development of longitudinal and survival sub-model methods, rather than on algorithmic or computational aspects of estimation. To clarify this scope, we have added a sentence in the manuscript acknowledging these significant contributions while explaining why studies on estimation algorithms were not included (Lines 87-91, p. 3).

Comments 6:

line 112: Given there was a single coder, what kind of discrepancies could have appeared?

Response 6:

We appreciate the reviewer’s comment. We acknowledge that having a single reviewer conduct the title and abstract screening may introduce potential selection bias, and this has been explicitly recognized as a limitation of the current study. We have added a statement in Limitations section of Discussion to clarify this point (Lines 687-689, p. 15). Nevertheless, we followed the PRISMA guidelines in designing, conducting, and reporting the review, including clearly specifying the search strategy, inclusion and exclusion criteria, and study selection process to enhance transparency and reproducibility.

Comments 7:

line 135: The authors must mean that “epsilon_i (and not u_i) is the measurement error.

Response 7:

We appreciate the reviewer bring this up. Yes, we apologize for the typo and have revised the measurement error into (Line 157, p. 5).

Comments 8:

line 145. The symbole “w_i” did not come through correctly.

Response 8:

Thank you so much for noticing this. We have modified it accordingly (Line 169, p. 5).

Comments 9:

line 147: To be correct, “alpha” is the effect of the “true value” of the longitudinal variable on the risk of the event.

Response 9:

We appreciate the input. We have modified the equation to make it in a more general form by removing α and introducing the term into , which is a function of all history of the true values of the longitudinal variable (Lines 166-172, p. 5).

Comments 10:

Table 1 is very hard to read. Could you increase its readability?

Response 10:

Thank you so much for the recommendation. We have reformatted the table by converting the survival parametric and non-parametric methods from wide to long format and changed the layout of the pages into landscape. Besides, we will work with the publisher to make it reader friendly (Lines 717-730).

Reviewer 3 Report

Comments and Suggestions for Authors

See attached.

Comments for author File: Comments.pdf

Author Response

Comments 1:

Joint modeling of longitudinal and time-to-event data in public 2 health and biomedical research: A systematic review

overall assessment:

The manuscript attempts to cover a broad range of joint modeling of longitudinal and time-to-event data (JM) advances (longitudinal sub-models, survival sub-models, multivariate and latent-variable approaches, functional data, etc.) and to categorize them in a structured way. A contemporary systematic review of methodological advances in JM in environment and public health contexts is indeed timely and useful for methodologists and applied researchers. The authors clearly intend to provide guidance for method development and applied research, and to summarize method characteristics in tables.

Given the breadth of JM literature reviewed and the potential value to the field, a Major Revision is recommended. It requires substantial revisions to methods, clarity, and scope to become suitable for publication as a methodological/systematic review in this journal.

Major concerns preventing acceptance in its current form:

Methodological and reporting quality gaps undermine reproducibility and usefulness for

readers (see below).

Response 1:

Thank you very much for this important comment. We appreciate the reviewer’s concern regarding methodological and reporting quality and its impact on reproducibility and usefulness to readers. We acknowledge that having a single reviewer conduct the title and abstract screening may introduce potential selection bias, and this has been explicitly recognized as a limitation of the current study. We have added a statement in Limitations section of Discussion to clarify this point (Lines 687-689, p. 15). Nevertheless, we followed the PRISMA guidelines in designing, conducting, and reporting the review, including clearly specifying the search strategy, inclusion and exclusion criteria, and study selection process to enhance transparency and reproducibility.

Comments 2:

Critical methodological/structural gaps that limit the manuscript’s value for guidance in

environmental research and public health applications (notably, lack of discussion of multilevel JM, Poisson-based surrogate for the survival submodels, computation, and model-choice guidance).

Response 2:

We appreciate the reviewer’s concern regarding the manuscript’s practical value in environmental and public health research. Regarding model-choice guidance, we have included a dedicated set of recommendations in the Discussion section. In the revised manuscript, we have further strengthened this section by explicitly providing recommendations across three key components of joint modeling: (1) selection of the longitudinal sub-model, (2) selection of the survival sub-model, and (3) choice of the association structure. These additions aim to provide clearer, application-oriented recommendations for researchers working in public health and biomedical research contexts (Lines 485-579, p. 11-14).

Comments 3:

Notable gaps in review methodology (e.g., single-reviewer screening/extraction, absence of formal risk-of-bias/quality assessment).

Response 3:

We appreciate the reviewer’s concern regarding using a single coder for data collection. We acknowledge that having a single reviewer conduct the title and abstract screening may introduce potential selection bias, and this has been explicitly recognized as a limitation of the current study. We have added a statement in Limitations section of Discussion to clarify this point (Lines 687-689, p. 15). Nevertheless, we followed the PRISMA guidelines in designing, conducting, and reporting the review, including clearly specifying the search strategy, inclusion and exclusion criteria, and study selection process to enhance transparency and reproducibility.

Comments 4:

Some statements about assumptions (e.g., conditional independence given latent classes) are presented in a way that could misrepresent the literature (latent-class JM often allows various forms of dependence; needs accurate framing).

Response 4:

“In this particular study, the longitudinal biomarkers were assumed to be conditionally in-dependent of the survival outcome given latent class membership and correctly specified covariates [27]. This assumption is specific to this formulation and does not apply universally to all latent class joint models, which may allow more flexible dependence structures between longitudinal and survival processes” (Lines 241-245, p. 6).

Reference

Li, M., Lee, C. W., & Kong, L. (2020). A latent class approach for joint modeling of a time-to-event outcome and multiple longitudinal biomarkers subject to limits of detection. Statistical methods in medical research, 29(6), 1624–1638. https://doi.org/10.1177/0962280219871679

Comments 5:

Specific issues and concrete recommendations

Page 2, Line 90 – add “joint models” as a keyword

Issue: The search strategy uses keywords but omits “joint model/joint modelling” as a

keyword.

Recommendation: Include “joint model” and “joint modelling” (and variants like “joint

models”) as keywords, in addition to “joint modeling,” “longitudinal and survival,” and

“public health.” Consider adding “time-to-event,” “survival analysis,” and “multivariate

joint modeling” as keywords to improve discoverability.

Editorial note: Ensure consistent spelling (joint modeling vs joint modelling) with journal

style.

Response 5:

Thank you for this helpful suggestion. We added “joint model” as an additional search keyword (Line 28, p. 1), and the search results remained unchanged. We also included the keyword “longitudinal and time-to-event” to improve discoverability, although most additional records were not relevant to the methodological focus of this review. The revised search identified several additional joint modeling methods studies, and we have updated the Methods (Lines 98-100, p. 3), Results, and Discussion sections, along with the corresponding results tables (Lines 717-730).

We also reviewed the spelling of “joint modeling” throughout the manuscript to ensure consistency with journal style. The spelling “joint modelling” appears only in the titles of cited references and was therefore retained as originally published.

Comments 6:

Relevance assessment by a single reviewer

Issue: Screening/eligibility were performed by a single reviewer, with uncertainties

resolved by a senior reviewer.

Recommendation: Implement dual independent screening (titles/abstracts, then full text)

with a predefined protocol. Report inter-rater agreement (e.g., Cohen’s kappa) and how 2

disagreements were resolved (e.g., by a third reviewer). If dual screening is not feasible for

the revision, provide a transparent justification and re-run screening with a second

independent reviewer.

Editorial note: This affects the credibility of the study selection process; address in the

Methods and Limitations sections.

Response 6:

Thank you for this important comment. In this review, the initial title/abstract screening and data extraction were conducted by a single reviewer, with guidance and consultation from a senior reviewer throughout the process. This approach is commonly used in review studies where the focus is on identifying methodological developments rather than synthesizing quantitative outcomes. The senior reviewer provided oversight during the screening and selection stages to ensure consistency in the application of the eligibility criteria and to resolve any uncertainties regarding study inclusion.

We acknowledge that dual independent screening can further reduce the potential for selection bias. Due to the large number of records identified in the initial search and the methodological nature of the review, dual independent screening was not implemented in the present study. To maintain transparency, we have clarified the screening process in the Methods section and have added a statement in the Discussion section (Lines 687-689, p. 15) to acknowledge this as a limitation of the review. The manuscript now notes that the use of a single reviewer during the screening stage may introduce potential selection bias. Future systematic reviews may consider dual independent screening to further enhance methodology.

Comments 7:

Equation (1) – ?? as a random-effects vector and MVN

Issue: ??

is described inconsistently; suggested to be a vector (random intercept + random

slope) and MVN(D) to generalize.

Recommendation: Clarify the longitudinal sub-model notation. If robust residuals are used,

specify that ??(?) has a heavier-tailed distribution (e.g., t-distribution) with explicit degrees

of freedom.

Rationale: This aligns with standard JM notation and makes the model easy to compare

with the broader JM literature.

Response 7:

Thank you so much for your helpful suggestion. Because the manuscript presented the standard formation of a joint model, the random effects and measurement errors of the longitudinal sub-model both follow normal distribution. We have corrected notation and specify the are random effects and is the measurement error. We have also specified the distribution of the two terms (Lines 156-157, p. 5).

Comments 8:

Equation (2) – clarify notation on the left and right side of the survival sub-model (??(?) and ??(?)).

Recommendation: Choose a single, well-defined notation for the longitudinal history used

in the survival sub-model and be explicit about what it represents: For example,

ℎ?(?|??(?), ??) with ??(?) = history of ??(?) for ? ≤ ?, or ℎ?(?|??(?), ??) if using the

current value. Then define ??(?) and ??(?) at first use and maintain consistency

throughout.

Rationale: Clear, consistent notation reduces confusion and helps readers implement

models correctly.

Response 8:

Thank you so much for your insightful suggestions. We have revised accordingly to make the equation clearer. Now we simplified the survival sub-model and make it more general by introducing a function of ??(?) on the right side of the equation, and provided denotations (Lines 166-172, p. 5).

Comments 9:

Page 5 Lines 166–167 – residual vs u in Eq. (1); t-distribution

Issue: It is unclear which term follows the t-distribution (residual ??(?) or random effect ??).
Recommendation: explicitly state when a t-distributed residual is used to handle outliers,

cite the relevant reference and explain how degree of freedom of the t-distribution is

estimated.

Rationale: The current phrasing is ambiguous and could mislead readers about model

assumptions.

Response 9:

Thank you so much for your question and input. In that study, both the residual ?? and random effects ?? follows t-distribution, we have revised to make the clear. Now the paragraph reads as follows:

“The proposed model assigns heavier tails to the error distribution to manage isolated measurement errors, while t-distribution for the random effects to accommodate outlying patients who do not fit to general population trends. This effectively reduces the influence of outliers, preventing them from biasing the population-level estimates or the association with survival risk. The degree of freedom parameter was not fixed and can be time-varying.” (Lines 200-205, p. 5).

Comments 10:

Line 170, Page 5 – define causal mediation analysis

Issue: Vague reference to “causal mediation analysis” without specifying the causal

structure (treatment, mediator, outcome).

Recommendation: If causal mediation is discussed, specify: 1) The treatment/exposure (if any), the mediator (longitudinal biomarker trajectory or a derived mediator), and the

survival outcome. 2) The causal estimands: direct effect of treatment on the survival

outcome, indirect effect through the longitudinal mediator, and assumptions (no

unmeasured confounding of exposure-outcome, mediator-outcome, and exposure-mediator relationships; correct temporal ordering; etc.). If the mediation is within a joint-model framework, explicitly describe the mediation pathway and how it is estimated (e.g., via mediation formulas adapted to longitudinal mediators or through a counterfactual

framework).

Rationale: Readers need to know what is being claimed as causal mediation and under

what assumptions, especially in a JM context.

Response 10:

Thank you for your comments. We appreciate the detailed instruction. We agree that the description of the causal mediation framework should be clearer. In the revised manuscript, we clarified the causal structure based on the framework described in Zheng and Liu (2022). In the revised manuscript, we now specify that the treatment/exposure affects the survival outcome both directly and indirectly through a longitudinal mediator. We also clarify that the study quantified the direct effect of treatment on survival and the indirect effect through the longitudinal biomarker trajectory within a joint modeling framework. Now the paragraph reads as

“Nevertheless, one extension of joint modeling methods focusing on the univariate linear mixed-effect sub-model was to quantify the causal mediation effect of treatment between a longitudinal biomarker and the time-to-event outcome [14] (Table 1). In this study, the repeatedly measured biomarker trajectory was used as the mediator between the treatment/exposure and the survival outcome. Within the joint modeling framework, the total treatment effect on survival was decomposed into a natural direct effect and a natural in-direct effect through the longitudinal mediator trajectory. These effects were under the sequential ignorability assumption, including correct temporal ordering and no unmeasured confounding of the mediation relationships.” (Lines 188-197, p. 5).

Comments 11:

Page 6, Lines 201–203 – claim about conditional independence given latent classes

Issue: The manuscript states an assumption that longitudinal biomarkers are conditionally independent of the survival outcome given latent classes, and then says this may not be true.
Recommendation: Reframe this to reflect the literature accurately: Acknowledge that

latent-class joint models often allow explicit class-specific associations between longitudinal trajectories and survival outcomes; in some formulations, conditional independence may be assumed for tractability but more flexible specifications permit direct associations across longitudinal and survival processes within and across classes (cite relevant JM-LC literature). Provide a balanced discussion and correct citation.

Rationale: The current sentence may misrepresent the spectrum of latent-class JM

formulations.

Response 11:

Thank you for this important clarification. We agree that latent class joint models, in general, may allow various forms of dependence between the longitudinal and survival processes, and that conditional independence assumptions depend on the specific model formulation. We recognize that our wording may cause the confusion that this assumption applies universally to all latent class joint models. To avoid misrepresentation, we have revised the text to clarify this assumption specifically to Li et al. (2020) and alternative latent class formulations may allow different dependence structures. Now the paragraph reads as “In this particular study, the longitudinal biomarkers were assumed to be conditionally in-dependent of the survival outcome given latent class membership and correctly specified covariates [32]. This assumption is specific to this formulation and does not apply universally to all latent class joint models, which may allow more flexible dependence structures between longitudinal and survival processes.” (Lines 241-245, p. 6).

Comments 12:

Page 7 – duplicate latent class subsection

Issue: The manuscript includes a subtitle “Latent Class Analysis” under the same section, creating duplication.
Recommendation: Remove redundant subsection headings or consolidate into a single

coherent subsection titled “Latent Class and latent-variable joint models” with clearly

delineated univariate/multivariate and longitudinal/survival discussions.

Rationale: Improve clarity and avoid confusion of readers.

Response 12:

Thank you for the helpful comments. We have removed the redundant headings and consolidated the latent class and latent variables into one subsection (Line 313, p. 8).

Comments 13:

Missing coverage: multilevel joint models and computation efficiency

Issue: The review lacks dedicated discussion on (a) multilevel (multilevel/hierarchical) JM

and (b) computational efficiency and scalability.

Recommendation: 1) Add a clearly defined section on multilevel joint models (e.g., joint

modeling of longitudinal outcomes observed at multiple levels, nested data structures,

shared/cluster-specific random effects, multilevel survival structures) with key references.

2) Add a subsection on computation: estimation methods (Bayesian vs frequentist),

software (JMbayes2, JM, JointModel in R, Stan-based approaches, etc.), convergence

diagnostics, computation time, and performance considerations for large-scale data.

Discuss approximate/inference techniques (e.g., variational inference, Laplace

approximations) where applicable.

Rationale: This is a major gap for readers who plan to apply JM to public health data, which are often hierarchical and large.

Response 13:

We agree that multilevel joint models and computational considerations are important, especially for public health data with hierarchical structures and increasing complexity.

In the revised manuscript, we added discussion of multilevel joint models, noting that some reviewed studies extended joint modeling to clustered or nested data through multilevel or cluster-specific random effects. We also expanded the computational discussion to summarize the main estimation approaches used in the reviewed studies, including likelihood-based and Bayesian methods, as well as common numerical techniques such as adaptive Gaussian quadrature, Laplace approximation, and MCMC for more complex models (Lines 580-589, p. 13).

We acknowledge that we did not perform a direct comparison of computational efficiency or scalability across methods. Because the reviewed approaches were developed for different data structures and research objectives, such comparisons were beyond the scope of this review. We have clarified this point in the Discussion section (Lines 600-608, p. 13-14).

Comments 14:

Guidance on choosing joint models in public health and environmental research

Issue: The manuscript provides methodological summaries but offers limited practical

guidance for selecting JM approaches in real public health/environmental contexts.

Recommendation:

o Add a practical decision framework or flowchart that helps readers decide:

▪ When to use a standard two-submodel JM vs a latent-class JM vs a

multivariate/multidimensional JM.

▪ Which survival sub-model (Cox PH, AFT, competing risks, multi-state) fits

the data.

▪ Which longitudinal sub-models (LMM, GLMM, non-linear, FPCA, latentvariable or factor-based) are appropriate given data distribution, sparsity, and measurement error.

▪ How to handle high-dimensional longitudinal data (COPULA approaches, FPCA, sparse functional data methods).

▪ How to assess model fit, predictive performance, and interpretability for

public health decisions.

o Include concrete examples or mini-case studies (e.g., Alzheimer’s disease

progression, HIV progression, cardiovascular risk) to illustrate the guidance.

Rationale: A practical decision framework would significantly increase the manuscript’s

value as a guidance resource for public health researchers.

Response 14:

Thank you for this helpful suggestion. We agree that providing more practical guidance would improve the usefulness of the review for researchers working with public health and environmental health data. In response to this comment, we revised the Discussion section (Section 4.1) to provide clearer guidance on selecting appropriate joint modeling sub-models based on the characteristics of the data and research questions (Lines 485-579, p. 11-14).

Specifically, we added a paragraph outlining key considerations for choosing joint models in practice, including the distribution and dimensionality of the longitudinal outcomes, the structure of the event process (e.g., competing risks, recurrent events, or clustered survival outcomes), and the biological relationship between the longitudinal biomarkers and the survival outcome. We also expanded the recommendations for the longitudinal and survival sub-models to clarify when commonly used approaches. These revisions provide more practical guidance for researchers in selecting joint modeling strategies while maintaining the methodological focus of the review. Now the text reads as follows:

“4. 1 Recommendations for sub-model choices

4.1.1 Recommendations for the longitudinal sub-model

4.1.2 Recommendations for the survival sub-model

4.1.3 Recommendations for the Association Structure

Comments 15:

Additional methodological and editorial improvements to consider

Risk of bias and quality assessment: Even though many JM methodological papers exist, a formal assessment of reporting quality or methodological quality (where possible) would

add value. At minimum, discuss limitations in study design (e.g., simulation studies vs real

data, sample sizes, handling of missing data) and potential biases in the included works.

Response 15:

Thank you for this helpful suggestion. We agree that discussing the reporting quality and potential methodological limitations of the included studies can provide additional context for interpreting the findings of this review. In response to this comment, we expanded the Limitations section to further discuss potential sources of bias and methodological variability in the reviewed studies, including differences between simulation-based methodological studies and empirical applications, variations in sample sizes, handling of missing data, and the limited reporting of computational performance or robustness assessments (Lines 678-682, p. 15).

Because the primary focus of this review is to summarize recent methodological developments in joint modeling rather than evaluate empirical study outcomes, a formal risk-of-bias assessment tool was not applied. However, we now explicitly acknowledge these methodological considerations and their potential implications for the interpretation and generalizability of the reviewed methods in the revised manuscript.

Comments 16:

Notation and consistency: Standardize notation across the manuscript.

Response 16:

Thank you for this suggestion. We have reviewed the manuscript and standardized the notation throughout to ensure consistency across sections.

Comments 17:

Scope and balance

o The abstract and introduction emphasize public health relevance, but several

sections read as a primarily methodological catalog. Strengthen the public-health

perspective by:

▪ Tying methodological advances to concrete public-health research questions (e.g., public health surveillance, environmental exposure assessment, chronic disease progression).

▪ Including a short section that translates JM concepts into public-health decision-making implications (risk prediction, policy-relevant interpretation of longitudinal-survival associations).

Language about limitations: The Limitations section should explicitly acknowledge the

primary limitation you’ve identified (single-reviewer screening) and any other biases

(database scope, English-language restriction). This helps readers gauge generalizability.

Response 17:

Thank you for these helpful suggestions. We agree that emphasizing the public health relevance of joint modeling would strengthen the manuscript. In response, we revised the Introduction and Discussion sections to more clearly connect methodological developments with practical public health research questions. Specifically, we expanded the discussion of real-world applications of joint modeling across multiple disease areas (e.g., Alzheimer’s disease, HIV/AIDS, cancer, cardiovascular disease, and kidney disease) to illustrate how longitudinal biomarkers and time-to-event outcomes are jointly analyzed to study disease progression, treatment response, and risk prediction in public health and biomedical research.

Regarding limitations, we have revised the Limitations section to more explicitly acknowledge the methodological limitations of the review process, including the use of single-reviewer screening with senior author supervision, the restriction to the PubMed database, and the inclusion of English-language articles only (Lines 678-681, 687-69, p. 15). These clarifications have been added to help readers better assess the scope and generalizability of the findings of the present study.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors present a systematic review of contemporary methodological developments in joint models for the analysis of longitudinal data and time-to-event outcomes in public health research. The study highlights the superiority of these models in reducing bias and improving predictive accuracy compared with traditional two-stage methods.

This systematic review is a scientifically rigorous work, offering a comprehensive overview of recent methodological developments in the joint modeling of longitudinal and time-to-event data.

Comments

The authors should include a brief comment justifying the selection of the time period considered.
All vectors/matrices should be presented in bold
For reasons of consistency, I believe that the term univariable should be replaced with the term univariate.
The tables are not adequately referenced in the text, with only a single general reference provided.
Line 137: u_i should be replaced by ε_i
Line 145: w_i should be replaced by w_i

Author Response

Comments 1:

The authors should include a brief comment justifying the selection of the time period considered.

Response 1:

Thank you so much for the valuable suggestion. We have added a sentence in the Methods section to justify the selection of the time period: “The search period (January 1, 2021 to January 30, 2025) was chosen to focus on the most recent methodological developments in joint modeling, as earlier foundational work has been reviewed in prior literature” (Lines 102-104, p. 3).

Comments 2:

All vectors/matrices should be presented in bold

Response 2:

Thank you so much for the comment. We have revised the formulas and notations accordingly (Lines 140-172, p. 4-5).

Comments 3:

For reasons of consistency, I believe that the term univariable should be replaced with the term univariate.

Response 3:

Thank you for this helpful suggestion. We agree that using consistent terminology improves clarity. We have revised the manuscript accordingly and replaced the term “univariable” with “univariate” throughout the manuscript for consistency (Line 176, p. 5; Line 217, p 6).

Comments 4:

The tables are not adequately referenced in the text, with only a single general reference provided.

Response 4:

Thank you for this helpful comment. We have revised the manuscript to reference the tables in the Results section to improve clarity (p. 5-11).

Comments 5:

Line 137: u_ishould be replaced by ε_i

Response 5:

Thank you so much for pointing this out. The notation has been corrected as suggested (Line 157, p. 4).

Comments 6:

Line 145: w_i should be replaced by w_i

Response 6:

Thank you for the suggestion. This has been revised accordingly (Line 169, p. 5).

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have been extremely responsive to all of my previous queries. I would like to thank them for a very thorough revision, especially in terms of recommendations to choosing an appropriate specification of joint longitudinal + survival model. I think this review can be quite helpful to researchers with repeated measures and time-to-event data.

Author Response

Comment 1:

Response:

We sincerely thank the reviewer for the positive and encouraging feedback. We are grateful for your constructive comments throughout the review process, which have helped us improve the clarity and practical relevance of the manuscript, particularly in strengthening the recommendations for selecting appropriate joint sub-modeling approaches. We are pleased to hear that the revised manuscript is helpful for researchers working with longitudinal and time-to-event data.