An Experimental Framework for Compatibility- and Capacity-Aware Doctor-Patient Matching in Online Consultation

Summary

This protocol presents a scalable experimental framework for doctor-patient matching in online medical consultation platforms. By jointly integrating patient-centered clinical compatibility and physician-side service capacity into a hybrid scoring model, this method optimizes matching accuracy, minimizes patient wait times, and ensures a balanced distribution of physician workload.

Abstract

Large-scale online medical consultation platforms require effective algorithm-assisted doctor-patient matching to balance patient-centered fit and operational efficiency. Existing approaches often optimize either clinical compatibility or physician capacity independently, leading to prolonged waiting times and uneven workloads. This protocol presents a scalable experimental framework to jointly incorporate compatibility and capacity into a hybrid matching score. Using a simulated dataset comprising 240 physicians, 3,600 patient requests, and 9,785 candidate pairs, the method quantifies compatibility (e.g., specialty alignment, mode fit) and capacity (e.g., load ratio, estimated waiting time). The framework evaluates candidate pairs through a hybrid score and compares performance against rule-based, compatibility-only, and capacity-only benchmark strategies across 12 evaluation folds. Representative results demonstrate that the hybrid framework achieves superior matching quality, including a mean precision at rank 1 of 0.740 and an F1 score of 0.714. Furthermore, it yields high operational efficiency with a capacity fill rate of 0.825 and a short mean estimated waiting time of 5.52 h. By maximizing mean patient satisfaction (4.43/5.00) and minimizing load imbalance (0.195), this framework provides a practical protocol for intelligent consultation routing and platform management.

Introduction

Online medical consultation has become an increasingly important mode of healthcare delivery, extending access to medical services beyond conventional face-to-face encounters¹. In China, the expansion of internet telemedicine has been reinforced by policy development, market growth, and deeper integration with the broader healthcare system, making digital consultation an increasingly important component of healthcare organization². Large-scale evidence from internet hospitals further indicates that online consultation services are now operating at substantial scale, functioning as a meaningful part of routine service provision rather than a marginal supplement³. At the same time, asynchronous telemedicine has broadened the scope of remote care by allowing flexible interaction patterns, improving accessibility while concurrently increasing the operational complexity of digital consultation platforms⁴.

As these platforms expand, their performance cannot be judged solely by technical availability. Patient experience and service quality have become central outcomes of digital care delivery⁵. Recent research has shown that the use of online consultation systems is associated with measurable differences in patient experience, especially concerning access, convenience, and appointment processes⁶. However, digital consultation also generates additional physician workload, including message handling and work performed outside routine clinical hours, which makes capacity management a central operational concern⁷. This challenge is intensified by the uneven distribution of demand across physicians, because visible service cues such as reviews, ratings, and other profile information can channel patient traffic toward a limited subset of highly visible doctors⁸. Doctor-patient assignment on online consultation platforms is, therefore, not merely a patient-side search problem, as physicians may also show selective response preferences when facing heterogeneous consultation requests⁹.

From the patient's perspective, the choice of online consultation is inherently multidimensional. Users simultaneously weigh waiting time, physician qualifications, hospital level, service mode, and consultation cost when choosing care options¹⁰. Consistent with this complexity, a recent systematic review concluded that online medical consultation platforms require recommendation mechanisms capable of reducing information overload and better aligning patient needs with physician resources¹¹. Methodological studies have accordingly begun to introduce structured matching approaches, including dynamic stable matching under incomplete information, to improve doctor-patient allocation in online consultation environments¹². More recent recommendation research has further emphasized that doctor-patient matching should improve allocation efficiency while reducing excessive concentration of demand around highly visible physicians from top-tier hospitals¹³. Mixed-method evidence shows substantial heterogeneity in telemedicine preferences, indicating that a one-size-fits-all allocation logic is unlikely to be sufficient at platform scale¹⁴. Despite these advances, the existing literature tends to treat compatibility-related factors and physician capacity constraints as separate problems, even though online consultation platforms must manage both relational fit and service absorbability simultaneously¹¹.

To address this gap, this method aims to establish a scalable experimental framework for compatibility- and capacity-aware doctor-patient matching on large-scale online medical consultation platforms. The rationale behind this technique is that optimizing either clinical preference or physician service capacity in isolation leads to prolonged waiting times, uneven physician workloads, and suboptimal consultation experiences. The primary advantage of this hybrid strategy over alternative rule-based or single-objective allocation techniques is its ability to jointly model patient needs, physician characteristics, and dynamic service constraints to maintain workload balance and high patient satisfaction¹². By detailing the construction of the hybrid matching score and the fold-based evaluation process, this protocol provides a practical basis for intelligent consultation routing. Readers can leverage this methodological framework to determine whether a dual-aware matching logic is appropriate for optimizing triage, resource allocation, and workflow management in their specific digital health applications.

Protocol

The evaluation dataset used in this protocol was computationally simulated from aggregated, de-identified operational distributions and contained no actual or identifiable human participant data. Consequently, the study was deemed exempt from full ethical review by the Institutional Review Board (IRB) of NingboTech University (Exemption No. NT9918276).

1. Data preparation and cohort definition

1. Establish the physician pool containing 240 active online physicians across eight consultation specialties: Internal Medicine, Cardiology, Neurology, Dermatology, Pediatrics, Gynecology, Orthopedics, and Psychiatry.
2. Extract and define the following variables for each physician record: specialty, sex, professional title (Resident, Attending, Associate Chief, or Chief), hospital tier (Primary, Secondary, or Tertiary), years of practice, years of online consultation experience, consultation fee, nominal daily consultation capacity, current daily load, historical rating, mean first reply time, historical acceptance rate, follow-up service rate, and supported consultation mode (Text, Text plus Voice, or Text plus Voice plus Video).
3. Establish the patient request pool containing 3,600 consultation requests.
   NOTE: To contextualize the evaluation's temporal dimension, this pool is calibrated to represent a continuous 30-day operational period encompassing both standard weekdays and weekends. This timeframe is designed to capture routine cyclical variations in patient demand while explicitly excluding extreme atypical periods (e.g., major national holidays or peak epidemic outbreaks) to establish a stable, steady-state baseline for algorithmic performance evaluation.
4. Extract and define the following variables for each patient request: age, sex, target specialty, severity level (Low, Moderate, or High), urgency level (Routine, Urgent, or Priority), budget ceiling, preferred physician gender (Male, Female, or No Preference), preferred consultation mode (Text, Voice, or Video), prior platform visits, digital engagement level, comorbidity count, city tier, and preferred contact period.
5. Clean the dataset by excluding any records with missing values in specialty, consultation fee, daily capacity, current load, mean first reply time, severity, urgency, budget ceiling, preferred consultation mode, or preferred physician gender. Ensure all retained records are complete before proceeding to pair generation.

2. Candidate pair generation

1. Generate candidate doctor-patient pairs using a specialty-first retrieval rule. For each patient request, retrieve the first physicians who match the patient’s target specialty.
2. Expand the retrieval window to adjacent high-frequency specialties that remain active on the platform on the same day only if fewer than two active physicians with remaining consultation capacity are available in the initial target specialty.
   NOTE: In this protocol, "adjacency" is structurally defined by established clinical cross-referral patterns and anatomical or symptomatic overlap (e.g., routing a patient from Cardiology to General Internal Medicine), while "high-frequency" specifically refers to specialties ranking in the top quartile (top 25%) of historical daily consultation request volume on the platform.
3. Link each patient to two to four candidate physicians, aiming for an empirically derived mean number of approximately 2.72 candidates per request. Establish the final candidate-pair layer containing 9,785 pairs. See Figure 1 for the overall study workflow.

3. Pairwise variable operationalization

1. Define all pairwise variables used in score construction prior to benchmarking. Refer to Table 1 for the prespecified definitions, thresholds, and score mappings.
2. Code specialty match (S) as 1 when the physician specialty is identical to the patient target specialty, and 0 otherwise.
3. Code mode fit (M) as 1 when the physician’s supported mode fully covers the patient’s preferred mode, and 0 otherwise.
4. Code gender-preference fit (G) as 1 when the patient selects No Preference or when the physician's sex matches the stated preference, and 0 otherwise.
5. Code affordability fit (A) as 1 when the physician fee is less than or equal to the patient’s budget ceiling, 0.5 when the fee exceeds the budget by no more than 20%, and 0 when the fee exceeds the budget by more than 20%.
6. Normalize the physician historical rating using the observed physician-level range (minimum 4.10, maximum 4.98). Calculate the normalized quality score (Q) using the following formula:
      (1)
   Set values below 4.10 after truncation to 0, and values above 4.98 to 1.
7. Define urgency-response fit (U) based on the patient urgency and the physician's mean first reply time as specified in Table 1.
8. Calculate the physician load ratio by dividing the current daily load by the nominal daily capacity. Calculate remaining same-day slots by subtracting the current daily load from the nominal daily capacity.
9. Calculate the estimated waiting time (in hours) using the following formula:
   
   This construction serves as a heuristic estimate inspired by basic queuing theory principles, where a physician's baseline mean first-reply time is penalized by their real-time utilization rate (Current Daily Load / Daily Capacity).
   NOTE: The urgency adjustment factor is set to 0.80 for Priority requests, 0.90 for Urgent requests, and 1.00 for Routine requests. These adjustment factors are implemented as prespecified operational weights to enforce prioritized routing for severe cases, rather than empirically derived coefficients.

4. Matching score construction

1. Construct the matching framework using a compatibility module and a capacity module, as detailed in Figure 2.
2. Compute the compatibility score as a weighted linear combination of the patient-centered matching factors:
   (3)
3. Compute the capacity score from the load-ratio score (L), remaining-slot score (R), and waiting-time score (W). Assign the categorical scores for , , and based on the thresholds defined in Table 1. Calculate the capacity score as:
   (4)
4. Calculate the final hybrid score by integrating the compatibility and capacity components:
   (5)
5. Fix the 0.60–0.40 weighting scheme before evaluation.
   NOTE: This predetermined ratio is guided by a fundamental principle of healthcare services. Clinical appropriateness and patient-centered fit must serve as the primary routing criteria to ensure medical safety, while still applying a substantial mathematical penalty to severe capacity constraints, which aligns with established triage literature that prioritizes clinical suitability over operational throughput.
6. Do not tune these weights after outcome inspection to prevent overfitting and ensure reproducibility.
   NOTE: Researchers adopting this protocol are highly encouraged to conduct comprehensive sensitivity analyses or employ objective multi-criteria decision-making techniques (e.g., the Analytic Hierarchy Process [AHP] or entropy weighting) to tailor the framework to their platform's specific operational load.

5. Match selection and strategy benchmarking

1. Perform benchmarking over 12 repeated evaluation folds. For each fold, sample 300 patient requests without replacement from the full patient pool.
   ​NOTE: This simple random sampling approach is intentionally used to simulate the stochastic, unpredictable nature of patient arrival streams characteristic of real-time online consultation platforms, rather than imposing an artificial structural balance on incoming demand.
2. Retain all candidate pairs linked to those sampled requests within the respective fold.
3. Benchmark four distinct allocation strategies independently on the same fold-specific candidate-pair layer:
   1. For the rule-based baseline, rank candidates by exact specialty match, then by lower consultation fee, and finally by higher historical rating.
   2. For a compatibility-only strategy, select the candidate with the highest compatibility score.
   3. For a capacity-only strategy, select the candidate with the highest capacity score.
   4. For the hybrid strategy, select the candidate with the highest hybrid score.
4. Select the candidate physician with the highest final strategy-specific score as the final match for each patient request.
5. Resolve any ties (identical scores to three decimal places) by selecting the candidate with the lower estimated waiting time, followed by the higher compatibility score, and finally the higher historical rating.

6. Outcome calculation

1. Calculate the primary outcomes: precision at rank 1, recall, and F1 score.
2. Assign ground-truth outcomes to all 9,785 candidate pairs before benchmarking using probability distributions derived from the empirical baseline dataset.
   NOTE: Use a fully labeled synthetic environment to enable calculation of precision and recall for all candidate pairs. A successful match is achieved if the consultation is completed, and patient satisfaction is 4.0 on a 5-point scale, and no 14-day revisit occurs due to dissatisfaction or mismatch.
3. Calculate precision at rank 1 as the proportion of selected final matches that meet the successful-match criterion.
4. Calculate recall as the proportion of all successful candidate pairs within a fold correctly selected by the strategy. Derive outcomes for non-selected candidate pairs from the fully labeled synthetic environment established in Step 6.2.
5. Ensure that the recall metric accurately captures the algorithm's ability to identify all theoretically viable matches within the simulated candidate pool.
6. Calculate the F1 score using the following formula:
      (6)
7. Calculate secondary outcomes: capacity fill rate, mean estimated waiting time, mean patient satisfaction, consultation completion rate, 7-day follow-up rate, and reported improvement rate.
8. Calculate the load imbalance index to evaluate the unevenness of the physician workload distribution within each fold:
      (7)
9. Average the 12-fold-specific estimates to obtain the strategy-level summary values using the original score assignments.
10. Conduct a multivariable logistic regression analysis within the subset of selected final matches to identify pair-level factors independently associated with successful matching.
11. Include the following prespecified independent variables based on theoretical relevance: compatibility score, capacity score, estimated waiting time, affordability fit, specialty match, gender-preference fit, severity level, and urgency level.
12. Employ a forced-entry variable selection strategy rather than a stepwise approach to preserve the model's theoretical structure.
13. Assess multicollinearity using the Variance Inflation Factor (VIF). Confirm that all VIF values remain below 5.0 before final model estimation.
14. Define statistical significance as a two-tailed p < 0.05, and report the results as adjusted odds ratios (aORs) with corresponding 95% confidence intervals (CIs).

Results

Baseline characteristics of the physician pool and patient request pool

The simulated analytic dataset comprised 240 physicians and 3,600 patient consultation requests. The baseline characteristics of both sides of the matching system are summarized in Table 2, and the platform-side distribution patterns are illustrated in Figure 3.

Among the 240 physicians, 128 (53.3%) were female. The cohort demonstrated a mean clinical experience of 9.34 years, a mean consultation fee of USD 68.08, a mean nominal daily consultation capacity of 18.52 consultations, a mean historical service rating of 4.63, and a mean first reply time of 5.47 h. Internal Medicine was the largest specialty (19.2%), followed by Orthopedics (15.0%) and Neurology (13.3%). Regarding consultation mode, 41.7% of physicians supported text plus voice, 37.1% supported text-only, and 21.3% supported full text, voice, and video consultations.

Among the 3,600 patient requests, 53.1% were submitted by female patients. The mean age was 36.49 years, and the mean budget ceiling was USD 47.30. Internal Medicine was the most frequent target specialty (20.0%), followed by Neurology (13.8%) and Cardiology (13.0%). Requests were classified by severity (45.7% moderate, 34.2% low, 20.1% high) and urgency (39.1% priority, 35.9% routine, 25.0% urgent). Text consultation was the most common preference (45.1%), and 78.7% of patients reported no physician gender preference. Collectively, these distributions indicate that the platform operated in a heterogeneous consultation environment, validating the need to evaluate both compatibility and capacity constraints within the matching system.

Candidate-pair structure and score separation

Following the specialty-first retrieval and restricted candidate expansion, 9,785 candidate doctor-patient pairs were generated (Table 3, Figure 4). Across the full candidate-pair layer, 3,085 pairs were selected as final matches, while 6,700 were not. Selected pairs exhibited a higher exact specialty-match proportion (99.2% vs. 95.3%) and a slightly higher gender-preference match (90.2% vs. 89.0%) than non-selected pairs.

More importantly, the main pairwise differences were concentrated in operational and composite scoring variables. Selected pairs demonstrated a higher mean compatibility score (0.853 vs. 0.829) and a higher mean capacity score (0.395 vs. 0.381). Consequently, the mean hybrid score was 0.707 among selected pairs compared with 0.686 among non-selected pairs. Selected pairs were also operationally more favorable, presenting a lower mean physician load ratio (0.628 vs. 0.642), more available same-day slots (6.99 vs. 6.65), and a shorter estimated waiting time (12.46 h vs. 12.79 h).

Among the 3,085 selected pairs, 2,584 consultations were completed (83.8% completion rate). The mean patient satisfaction was 4.29 out of 5.00. Defining successful matching as consultation completion, patient satisfaction 4.0, and no 14-day revisit, 1,644 selected pairs met this criterion (53.3% success rate). These results demonstrate that final selections were driven by the intersection of higher compatibility, lower load pressure, and better waiting-time conditions, consistent with the prespecified protocol logic.

Pair-level factors associated with successful final matching

A multivariable logistic regression within the selected-match subset was performed to identify features associated with successful matching (Table 4, Figure 5). The compatibility score remained positively associated with successful matching (adjusted odds ratio [aOR] = 11.99; 95% CI, 1.81–79.46; P = 0.010), as did the capacity score (aOR = 2.08; 95% CI, 1.22–3.55; P = 0.007). Conversely, a longer estimated waiting time reduced the probability of a successful match (aOR = 0.953 per additional hour; 95% CI, 0.934–0.972; P < 0.001). Affordability also remained significant (aOR = 1.33; 95% CI, 1.12–1.57; P = 0.001). Exact specialty matching, gender-preference matching, priority status, and high severity did not remain independently significant. This indicates that matching success depends more on the combined strength of compatibility and absorbable capacity than on any single surface-level feature.

Benchmarking and robustness of the allocation strategies

Comparative benchmarking across the 12 evaluation folds is summarized in Table 5, Table 6, and Figure 6. The proposed hybrid strategy achieved the most favorable overall profile. It produced the highest mean precision at rank 1 (0.740), recall (0.691), and F1 score (0.714), outperforming the rule-based baseline, the compatibility-only strategy, and the capacity-only strategy.

Operationally, the hybrid strategy achieved the highest capacity fill rate (0.825) and the shortest mean estimated waiting time (5.52 h). Patient-centered performance was also optimized, with the hybrid approach yielding the highest mean patient satisfaction (4.43) and the lowest load imbalance index (0.195), indicating a highly even physician workload distribution. Subgroup analyses (Table 7, Figure 6) confirmed that this stable performance pattern was maintained across different urgency strata and hospital tiers, proving the framework's robustness even in highly capacity-constrained settings.

Figure 1: Overall study workflow. (A) Construction of the physician pool and patient request pool. (B) Specialty-first candidate retrieval process with restricted expansion when fewer than two active physicians with remaining capacity are available in the requested specialty. (C) Generation of candidate doctor-patient pairs and derivation of pairwise variables. (D) Construction of the compatibility score, capacity score, and hybrid score. (E) Final physician selection, fold-based benchmarking across four allocation strategies, and calculation of performance outcomes. Please click here to view a larger version of this figure.

Figure 2: Architecture of compatibility and capacity-aware matching framework. (A) Compatibility module, including specialty alignment, consultation-mode fit, gender-preference fit, affordability fit, physician historical rating, and urgency-response fit. (B) Capacity module, including physician load ratio, remaining same-day slots, and estimated waiting time. (C) Score normalization and weighted score aggregation for compatibility score and capacity score. (D) Integration of the two modules into the final hybrid score. (E) Final ranking and tie-breaking logic used to determine the selected doctor-patient match. Please click here to view a larger version of this figure.

Figure 3: Baseline distribution patterns of physician and patient characteristics in the analytic dataset. (A) Specialty distribution of the physician pool. (B) Professional title and hospital-tier distribution of physicians. (C) Specialty distribution of patient consultation requests. (D) Severity and urgency distribution of patient requests. (E) Distribution of preferred consultation mode and preferred physician gender among patient requests. Note: All data distributions presented in this figure are derived directly from the finalized analytic dataset (n = 240 physicians; n = 3,600 patient requests) and are fully consistent with the summary statistics reported in Table 2. Please click here to view a larger version of this figure.

Figure 4: Pair-level score distributions and separation between selected and non-selected candidate matches. (A) Distribution of compatibility scores in selected and non-selected pairs. (B) Distribution of capacity scores in selected and non-selected pairs. (C) Distribution of hybrid scores in selected and non-selected pairs. (D) Estimated waiting time (in hours) by selection status. (E) Joint distribution of compatibility score and capacity score, with selected and non-selected pairs shown separately. Please click here to view a larger version of this figure.

Figure 5: Multivariable analysis of factors associated with successful final matching among selected pairs. (A) Forest plot of adjusted odds ratios for compatibility score, capacity score, estimated waiting time (in hours), affordability fit, specialty match, gender-preference fit, severity level, and urgency level. (B) Marginal probability of successful matching across the observed range of compatibility score. (C) Marginal probability of successful matching across the observed range of capacity score. (D) Inverse association between estimated waiting time (in hours) and probability of successful matching. Please click here to view a larger version of this figure.

Figure 6: Comparative benchmarking of four doctor-patient matching strategies and subgroup performance of the hybrid framework. (A) Precision at rank 1, recall, and F1 score across the four strategies. (B) Capacity fill rate, mean estimated waiting time, and mean patient satisfaction across the four strategies. (C) Load imbalance index across the four strategies. (D) Fold-level performance ranges of the hybrid strategy across 12 repeated evaluation folds. (E) Hybrid strategy subgroup performance heatmap. Note: All values presented in this figure have been cross-validated with the corresponding results reported in Table 5 to ensure absolute consistency. Please click here to view a larger version of this figure.

Table 1: Operational definitions, thresholds, and scoring rules for the matching framework. Abbreviations: SD = standard deviation. Please click here to download this Table.

Table 2: Baseline characteristics of the physician pool and patient request pool. Section, characteristics, and comparative basic statistics of the analytic dataset prior to matching. Please click here to download this Table.

Table 3: Pair-level comparisons between selected and non-selected matches. This table aggregates the pairwise variables and descriptive statistics detailing the structural separation between the final selected matches and non-selected candidates. Please click here to download this Table.

Table 4: Multivariable logistic regression analysis of factors associated with successful final matching among selected pairs. Model information: Dependent variable = successful final match among selected pairs. A successful match was defined as consultation completion, patient satisfaction 4.0/5.0, and no 14-day revisit due to dissatisfaction or mismatch. Please click here to download this Table.

Table 5: Comparative performance of four matching strategies. Summary of comparative strategy-level benchmarking across 12 repeated folds. Please click here to download this Table.

Table 6: Stability and fold-level variability of the hybrid strategy. Summary of fold-level performance ranges of the hybrid strategy across 12 repeated evaluation folds. Please click here to download this Table.

Table 7: Subgroup performance of the hybrid strategy. Detailed subgroup performance of the hybrid strategy based on urgency levels and hospital tiers. Please click here to download this Table.

Discussion

The present protocol demonstrates a compatibility- and capacity-aware doctor-patient matching framework in a large-scale online medical consultation setting. The hybrid strategy achieved the most balanced overall performance across matching accuracy, waiting time, capacity utilization, patient satisfaction, and workload distribution. This result is crucial because digital consultation not only expands access but also shifts clinical work into after-hours activity, increasing the hidden workload when allocation logic overlooks service absorbability. Recent evidence shows that greater digital demand is associated with increased physician work outside scheduled hours, reinforcing the practical importance of incorporating capacity constraints into matching systems rather than treating them as secondary operational variables⁷. Furthermore, compatibility alone is insufficient when demand is unevenly distributed. In internet hospitals, patient choice is strongly shaped by visible physician characteristics, structurally driving demand concentration around highly visible or higher-status physicians. This dynamic explains why the compatibility-only strategy in this protocol preserved relatively strong matching quality but performed poorly regarding waiting times and load balance¹⁵.

In our evaluation, the binary classification of a successful match served as a stringent threshold to filter out failed clinical encounters, whereas the mean patient satisfaction score allowed us to evaluate the nuanced distribution of user-perceived quality across different matching strategies. Furthermore, to address concerns regarding potential circularity, the secondary performance outcomes in this study were evaluated independently of this binary status, providing a broader assessment of the framework’s impact on platform-wide service quality rather than merely validating its own classification criteria. The higher patient satisfaction observed under the hybrid strategy aligns with the broader telemedicine literature, sharpening it by demonstrating that satisfaction is deeply tied to the quality of allocation rather than mere digital access. Recent work identifies professional treatment planning, accurate understanding of patient concerns, comprehensive replies, and the avoidance of templated responses as key drivers of user satisfaction. Thus, optimal matching systems must direct patients to physicians who can respond within acceptable time windows and provide individualized interaction patterns^16,17. This dynamic also underscores our operational rationale for constraining the generated candidate pool to two to four physicians per request (mean 2.72). This specific threshold was empirically calibrated to strike an optimal balance between preserving patient autonomy and preventing "choice overload"- a well-documented cognitive bottleneck in digital health choice architectures that delays decision-making and degrades user experience. From an implementation perspective, this matching model should be embedded within a broader service workflow. Crucially, while the current experimental protocol evaluates the framework using a static, fold-based batch assignment, the underlying algorithmic logic is intrinsically adaptable to continuous-time dynamic scenarios. Because capacity variables—such as the current daily load and remaining same-day slots—are designed to be updated iteratively, the hybrid score can be efficiently recalculated in real-time to accommodate sequential patient arrivals and fluctuating physician availability. Research indicates that training, familiarity with technology, communication quality, and workload are critical implementation factors, and stakeholders recommend concrete mechanisms to reduce physician burden. Consequently, while the hybrid framework improves allocation performance, its real-world effectiveness relies heavily on supportive workflow design, platform governance, and operational support^18,19.

These results represent an optimization of platform routing rather than evidence that virtual consultations can replace all forms of care. While virtual consultations improve efficiency, evidence remains mixed regarding safety and equity; therefore, this framework is best understood as a front-end allocation tool, not a substitute for clinical triage or referral pathways²⁰. The current protocol has several limitations. First, while the evaluation dataset was constructed using variables and distribution patterns that strictly mirror real-world operational conditions, it fundamentally remains a simulated cohort designed for controlled platform evaluation. We acknowledge that the absence of supplementary, independent real-world datasets limits the external validity of the current findings. To robustly establish the generalizability of the proposed hybrid matching method, future studies must prioritize validating this experimental framework using large-scale, real-world consultation logs across diverse digital healthcare platforms and extended longitudinal timeframes. Evaluating the model's resilience and dynamic routing capabilities under extreme temporal demand shocks—such as peak flu seasons or public health emergencies—remains critical. Second, the outcomes emphasized consultation completion and patient satisfaction, excluding clinician-adjudicated diagnostic appropriateness or longitudinal health outcomes. Third, fold-based evaluation relied on simple random sampling rather than k-fold cross-validation or stratified sampling. While this captured the volatility of natural patient flow, it may occasionally compromise the uniform representativeness of specific minority subgroups. Future algorithmic evaluations should incorporate stratified sampling by severity, urgency, and hospital tier to ensure consistent performance across all patient subpopulations. Fourth, the estimated waiting time derived from this protocol serves as a structural proxy rather than a rigorously calibrated predictive model. Due to the lack of continuous, real-world timestamp logs, we were unable to perform strict correlation analyses or compute calibration errors against actual clinical waiting times. Future research should leverage large-scale empirical operational logs to validate and fine-tune these heuristic wait-time parameters. Fifth, the weighting scheme combining compatibility and capacity was prespecified heuristically rather than derived through objective mathematical modeling. While this fixed a priori approach prevents post hoc data fitting, it lacks the rigor of objective weighting methods such as AHP or entropy weighting. Future iterations of this framework should incorporate these objective multi-criteria decision-making methods to dynamically determine the optimal weighting ratio. Finally, the framework operates at a one-to-one allocation level and was evaluated under static batch assignment conditions, without modeling team-based consultations or continuous-time dynamic reprioritization (e.g., handling sudden demand spikes or real-time schedule cancellations). Future research should expand this framework into a fully dynamic queuing simulation and extend matching algorithms from initial physician selection to communication-aware routing and post-match interaction support²¹.

Overall, this protocol successfully moves the doctor-patient matching paradigm away from a single-objective logic. In large-scale online platforms, effective allocation must jointly address clinical-service fit and the physician's operational absorbability under current workload conditions, without degrading timeliness or patient experience. Compared with rule-based, compatibility-only, and capacity-only strategies, the compatibility- and capacity-aware hybrid framework achieved a superior overall balance across matching precision, recall, F1 score, waiting time, capacity fill rate, and workload distribution. By treating doctor-patient matching neither as a purely preference-based recommendation task nor a throughput-driven scheduling problem, this approach provides a highly practical and scalable basis for intelligent consultation routing, platform resource coordination, and the future optimization of digital healthcare services.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Candidate doctor-patient pairs	Study-generated	N/A	Pairwise variable derivation and match selection (9,785 candidate pairs)
IBM SPSS Statistics	IBM Corp.	https://www.ibm.com/products/spss-statistics	Statistical analysis (Version 27)
Microsoft Excel	Microsoft Corporation	https://www.microsoft.com/microsoft-365/excel	Data management and descriptive summary (Version 2021)
Patient request records	Study-generated	N/A	Baseline patient-side characteristics and preference parameters (3,600 consultation requests)
Physician records	Study-generated	N/A	Baseline physician-side characteristics and capacity parameters (240 active physicians)
Python	Python Software Foundation	https://www.python.org	Simulation, score construction, and benchmarking (Version 3.11)