Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors propose a method, inspired by the autocorrelation function used in Dynamic Light Scattering (DLS), to characterise sample turnaround time (TAT) and workflow performance in highly automated clinical laboratories. A function Gexp(t) is defined such that each sample contributes a value of 1 until its TAT is reached and 0 thereafter, with the normalised sum across samples yielding a decaying curve. A broken-line fitting function Gfit(t) is introduced, from which the authors derive descriptive parameters, principally TL50 (the midpoint of the constraint range) and TLV50 (the fraction of samples completed at TL50). Seven simulated scenarios, generated in Microsoft Excel, are presented (unimodal Gaussian, unimodal random with and without delay, and bimodal random variants), together with a simulated time course of TLV50 used to distinguish buffering from non-buffering systems.

The conceptual analogy is creative, the writing is generally clear, and the topic (real-time monitoring of laboratory automation) is relevant to the readership. However, several substantive issues should be addressed before the manuscript can be considered for publication.

Major comments

1. Relationship to the survival function and the question of novelty.
   On inspection, the term inside Equation (1), namely [|ti − τx| − (ti − τx)] / [2(|ti − τx| + ε)], reduces to an indicator that returns approximately 1 when t is below the sample TAT and 0 when t is above it. Consequently, Gexp(t) is the fraction of samples not yet completed at time t, which is the empirical survival function S(t) = P(TAT > t), equivalently one minus the empirical cumulative distribution function. The authors themselves invoke the survival-analysis analogy in the Introduction (Kaplan-Meier, log-rank, Cox). The manuscript would be considerably strengthened by stating this equivalence explicitly and early, then clarifying what the DLS framing and the proposed parameters add beyond a standard empirical survival or complementary cumulative distribution analysis. As written, the central object risks being a re-derivation of the survival function under new terminology. Please articulate the specific, demonstrable advantage of TLV50 over established tail metrics such as the 90% completion time, the median, or the survival function evaluated at a clinically chosen threshold.
2. Absence of real-world data.
   All results, including the buffering and non-buffering comparison in Figure 4, are generated from Excel RAND() values. The manuscript is therefore a proof of concept with no empirical demonstration on actual laboratory automation data. For a claim of a "novel tool for evaluating, monitoring, and comparing the performance of laboratory automation systems," at least one worked example using real intra-laboratory TAT records (for instance, a single analyser line or a defined laboratory section over a defined period) is needed to show that the parameters behave as claimed and reveal something not visible from conventional statistics. Without this, the practical contribution remains unproven.
3. The "fitting" procedure.
   Equation (2) is described as fitting nX(min) and nX(max). However, these quantities appear to be simply the counts of samples with TAT below and above TL50, which can be read directly from the data without any optimisation. Please specify precisely what is being fitted, by what algorithm, with what objective function, and over what free parameters. If no genuine fit is performed, the language of "fitted parameters" should be revised to "computed quantities," and the value added by Gfit(t) over Gexp(t) should be justified.
4. Definition and operational determination of TL50, τX(min), and τX(max).
   TL50 is defined as the midpoint of the range [τX(min) + τX(max)]/2 rather than the median of the observed distribution. As a result, TLV50 equals 0.5 only under symmetric distributions, and its interpretation depends entirely on how the two constraints are set. In the simulations these are fixed by design. In a real laboratory, how are τX(min) (theoretical minimum) and τX(max) (maximum admissible TAT) to be determined, and how sensitive are TLV50 and the reported intersections to these choices? A sensitivity analysis is warranted, since the headline metric is anchored to operator-selected constraints.
5. Figure 4 demonstrates a narrative rather than a result.
   The buffering and non-buffering trajectories are random TLV50 values arranged into labelled regions (A, B, C, C1, C2). Without a generative model of buffering dynamics or empirical observation, this figure illustrates hoped-for behaviour rather than demonstrating that the metric discriminates real buffering capacity. Please either provide a defined dynamic model from which these trajectories emerge, or replace the simulation with real monitoring data showing recovery and non-recovery episodes.
6. Claim of predictive, real-time, early-warning capability.
   The Discussion states that the method enables detection of deviations "even before the estimated time is reached." At any time t, Gexp(t) reports only the fraction already completed and the fraction already overdue; it is descriptive of the current state. Please clarify the mechanism by which the approach is predictive rather than contemporaneous, and distinguish it from a simple running count of in-process and overdue samples.
7. Statistical reliability threshold.
   Table 1 states that more than 30 samples suffice for statistical reliability, without justification. For characterising the tail of a skewed TAT distribution and for stable estimation of survival at a chosen time point, 30 observations may be inadequate. Please provide the basis for this threshold, ideally with a short analysis of estimator variance as a function of n.
8. Multiclass applicability.
   The requirement that TAT values of different classes not overlap is a strong constraint, as real laboratory TAT distributions for serum, plasma, and other matrices typically overlap substantially. Please discuss how the method performs under overlap, and temper the claims regarding routine multiclass deployment accordingly.
9. Terminology.
   "Correlation function" and "autocorrelation function" are, strictly, misnomers in this context, since no correlation between two signals is computed; the quantity is a completion or survival decay. Retaining the DLS analogy is reasonable for exposition, but the precise mathematical meaning should be stated so that readers from laboratory medicine are not misled. Relatedly, the title refers to "particle physics," whereas DLS and Brownian motion belong to soft-matter and physical chemistry rather than to particle physics; please reconsider the title for accuracy.
10. Situating the framework within healthcare workflow analytics.
    The Discussion advances claims about operational optimisation, performance monitoring, and cost-effectiveness in healthcare systems, but these claims are not anchored in the broader literature on healthcare workflow and operational analytics. The manuscript would benefit from connecting the proposed monitoring framework to prior work that characterises clinician and system workflow behaviour and operational performance in digital health settings. I recommend the authors cite the following relevant study, which examines workflow patterns, user engagement, and operational performance through mixed methods and provides a useful frame for interpreting performance-monitoring metrics in clinical operations:

Sumner, J.; Shankar, R.; Bundele, A.; Yap, A.; Mohamed Ali, J.; Teng, G.G.; Phang, K.F.; Yip, A.W.; Lim, Y.W. Insights from high and low clinical users of telemedicine: A mixed-methods study of clinician workflows, sentiments, and user experiences. International Journal of Medical Informatics 2025, 184, 106044. https://doi.org/10.1016/j.ijmedinf.2025.106044

Incorporating this reference in the Discussion would strengthen the positioning of the proposed metric within established approaches to monitoring and interpreting workflow performance in healthcare systems.

11. Reproducibility.
    Given that the entire manuscript rests on simulation, the random seeds, the exact transformation functions applied to RAND() for each of the seven cases, and the code or spreadsheets used to generate Figure 4 should be provided as supplementary material. "Available on request" is insufficient for a methods paper whose contribution is the simulation itself.
12. Sensitivity to the smoothing constant ε.
    The constant ε is introduced to avoid indeterminate values at ti = τx, but its magnitude and its effect on the curve near the transition are not reported. Please state the value used and demonstrate that conclusions are insensitive to it.

Minor comments

1. The keyword "statistical parametric mapping" appears in the abstract keyword list but the concept is never used in the manuscript. Please remove it or address it in the text.
2. Several typographical and grammatical corrections are needed, including: "for a for a single class" (repeated phrase in the captions of Figures 1, 2, and 3); "smaller particle diffuse more rapidly" (line 128) should read "particles diffuse"; "allow evaluation the system's" (line 143); "50% of sample will have complete their TAT" (line 187) should read "samples will have completed"; "total number of sample" (Table 2) should read "samples"; "hepararinized plasma" (line 217) should read "heparinized"; and "Total Automaton" in reference 3 should read "Total Automation."
3. The symbol for the second sample class (β) does not render in several locations in Sections 3.2.3 and in Table 4, appearing as a blank. Please correct throughout.
4. Subscript formatting for TATX, τX(min), and τX(max) is inconsistent across the text, tables, and figure captions. Please standardise.
5. Equation (1) and Equation (2) would benefit from a worked numerical example for a small set of samples, which would help readers verify the reduction to a step function described in major comment 1.
6. In Table 1, "Number of objects required for statistical reliability" lists 10^3 to 10^13 for DLS against more than 30 for the proposed method; please ensure the comparison is like for like, since these refer to different statistical objects.

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper introduces the correlation function concept from dynamic light scattering (DLS) theory into real-time monitoring of clinical laboratory sample turnaround time (TAT), establishing a mathematical model and parameter system (e.g., TLV50). Simulation data demonstrate its capacity to identify sample delays and differentiate system buffering capacity, offering a dynamic perspective for laboratory workflow management distinct from conventional statistical indicators.

The reviewer has the following issues for the authors to consider.

1. For Equation (2), the manuscript only visually compares fitted curves with raw correlation function curves, without standardized quantitative goodness-of-fit metrics such as R², RMSE, and 95% confidence intervals. No residual distribution or model bias analysis is provided, making it impossible to quantitatively evaluate the fitting accuracy of the piecewise polyline model. The authors should supplement quantitative analysis on how model fitting errors affect key conclusions.
2. Established TAT monitoring approaches including percentile charts, CUSUM, Kaplan-Meier, and discrete event simulation can all facilitate delay early warning. This study fails to quantitatively compare the warning sensitivity, interpretability, and computational efficiency of different methods, so the superiority of the proposed method cannot be verified. Comparative simulations of multiple methods under identical scenarios should be supplemented.
3. Table 1 claims the method is compatible with all TAT distributions, yet Equation (2) only fits subgroups using τmin and τmax and discards distribution features including kurtosis, long tails, and outliers. There exists inconsistency between the simplified model assumptions and the claimed application scope in the table. The authors should quantify calculation biases induced by this simplification and clarify the range of applicable distributions for the model.
4. The concluding statement ‘enabling early identification of deviations from expected performance’ lacks comparative data on advance warning timeliness; the claim of a ‘versatile method’ is also unsupported by test results across diverse scenarios, resulting in subjective conclusions. Corresponding quantitative experimental data should be added to substantiate concluding arguments.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thank you for carefully addressing my comments and revising the manuscript. I find that my concerns have been satisfactorily addressed, and I have no further comments. In my opinion, the manuscript is suitable for publication in its current form.