A mixture cure modeling framework for survival analysis of hospitalized COVID-19 patients: implications for hospital resource management

Abstract

Background

COVID-19 has caused substantial global morbidity and mortality, placing unprecedented strain on hospital systems. Understanding heterogeneity in survival outcomes and identifying subgroups with distinct mortality risk profiles are essential for improving preparedness in future pandemics. Traditional survival models do not account for the presence of patients who are effectively cured within a clinically meaningful window. Mixture cure models offer a framework for simultaneously estimating the probability of long-term survival and the time-to-event among uncured individuals. This study applies a mixture cure modeling approach to evaluate mortality risk factors among hospitalized COVID-19 patients and to derive statistical insights relevant to hospital resource planning.

Methods

Data were obtained from 1,998 patients enrolled in the Khorshid COVID Cohort (KCC), a prospective hospital-based study with one-year follow-up. The outcome was COVID-19 death occurring during hospitalization or within 12 months post-discharge. Patients who remained alive throughout the one-year follow-up window were classified as cured. The analysis accounted for exact, right-censored, and interval-censored event times within the mixture cure model. Feature selection was performed using random survival forests and binary random forests, followed by interaction identification with decision trees. The cure component was modeled using logistic regression, while Weibull and Cox proportional hazards models characterized time-to-death among uncured individuals.

Results

Older age was a strong predictor of mortality, with hazard ratios of 2.30 for ages 65–74 and 3.32 for ages > 74 compared with < 45 years. Lower baseline oxygen saturation (< 80%) increased the death hazard by 3.41-fold. Longer time to ICU admission increased mortality risk (HR = 1.17). Higher cumulative methylprednisolone dosage increased the odds of death by 2.06-fold, whereas cumulative ceftriaxone use reduced the death hazard by 49% among patients with oxygen saturation of 80–89%. Meropenem use—particularly without concurrent methylprednisolone—was associated with a significantly elevated hazard of death. Results were consistent across mixture cure and Cox models. Feature selection identified key predictive variables, including intubation duration, ICU duration, oxygen saturation, pulse and respiratory rates, BUN, and specific treatment interactions.

Conclusion

The mixture cure framework distinguished between patients with long-term survival potential and those at sustained risk of mortality, revealing clinically relevant factors associated with both cure probability and death hazard. Although descriptive—not causal—these findings highlight subgroups with high resource needs and may inform conceptual approaches to planning ICU capacity, ventilator demand, and treatment prioritization during future pandemics. Mixture cure models provide a flexible statistical tool for understanding heterogeneous survival patterns in acute infectious diseases.

Clinical trial number

Not applicable.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1186/s12911-026-03687-8.

Background

The COVID-19 virus spread widely across the world and caused significant negative impacts on both the global population and the economy. As the pandemic persists, hospitals are striving to find effective methods for managing patients with severe symptoms. Additionally, it is a major global public health challenge, causing high mortality worldwide. Therefore, it is necessary to gain additional knowledge about the epidemiology and clinical course of COVID-19 in order to create effective and efficient strategies for preventing and treating the disease.

Survival analysis is a statistical method that examines the time to an event of interest, such as death, the survival time of a transplant patient, or failure in mechanical systems [1]. Such methods are commonly used in engineering to study reliability and durability, as well as in economics to model duration outcomes, in sociology for event history analysis, and in biostatistics to model the disease-free or time-to-mortality of medical patients. To estimate survival probability and explore factors associated with death due to COVID-19, a wide variety of techniques have been proposed in the statistical literature [2–7]. Among them, some survival models such as the proportional hazard model [2], Kaplan-Meier [8], and proportional odds models [3] are commonly used to estimate the probability of an event occurring at any given time, as well as to examine the factors that may affect time-to-event. Kaso et al. [4] employed Kaplan-Meier and Cox regression methods to estimate survival probability and investigate predictors of COVID-19 death. In the context of survival analysis studies, censoring is an inherent challenge, where sometimes there can be a lack of complete information regarding the survival time of individuals being observed. Regarding censored observations, interval-censored data, where event times are only known to occur within specific finite intervals, are frequently encountered in medical studies [9–11].

With advances in medical research, a growing number of patients can now recover from diseases once known to be fatal, such as COVID-19 and certain cancers. This motivates the study of risk factors that are associated with both the likelihood of being cured and the survival patterns of the individuals who remain at risk. Cure rate models are a special type of survival models in which a fraction of individuals are cured and never experience the event of interest [7, 12, 13]. Some cure rate models, known as mixture cure rate models, assume that the population consists of two subgroups: susceptible (uncured) and insusceptible (cured) subjects. Such models are widely implemented in two main forms: the mixture cure model [6, 7] and the non-mixture cure rate model [14–16].

The mixture cure model is a statistical approach that takes into account both individuals who are susceptible to experiencing an event, such as COVID-19 death, and those who survive. The non-mixture cure rate model, which is also referred to as the bounded cumulative hazard model or promotion time cure model, determines an asymptote for the cumulative hazard and hence for the cure fraction. Several authors have also explored parametric, semi-parametric, and non-parametric methods to estimate the cure fraction [17–20]. Recent studies in cure rate models are more focused on semi-parametric mixture and non-mixture cure rate models [21–24].

Some studies on mixture cure models with interval-censored data primarily concentrate on the proportional hazards mixture cure (PHMC) model [25] and the proportional odds mixture cure (POMC) model [26]. In recent years, there has been significant interest in nonparametric estimation methods for predicting the cure rate and failure time distribution of uncured subjects in censored survival data. A study by López-Cheda et al. [27] provides a comprehensive review of these methods, particularly in the context of mixture cure models. They introduce a novel nonparametric estimator for the distribution of uncured subjects that relaxes previous assumptions made in other studies.

In recent years, several advanced artificial-intelligence (AI)-based modelling frameworks have emerged that address multi-dimensional data, uncertainty, and long-term pandemic decision-making. For instance, systematic reviews have evaluated the performance of AI in predicting COVID-19 mortality [28], while deep-learning models incorporating vaccination data have been used to forecast pandemic waves [29]. In addition, a recent study proposed a comprehensive parametric model to analyze and predict pandemic casualties while optimizing vaccination policies according to age and priority groups [30].

Subsequent evaluations have further shown that many first-generation COVID-19 prediction models suffered from high risk of bias, limited generalizability, and inadequate calibration, underscoring the need for more rigorous patient-level modelling approaches and highlighting the limitations of models developed on heterogeneous or aggregated datasets rather than clinical cohorts [31]. Although these methods provide valuable insights for population-level forecasting and strategic planning, they primarily rely on aggregated data and fail to capture individual-level survival processes, cure fractions, or interval-censored event times—critical gaps that motivate the patient-level mixture-cure modelling approach advanced in this study.

Furthermore, Rezaei Ghahroodi et al. [32] analyzed the effects of hospitalization treatment strategies on longitudinal changes of COVID-19 symptoms in a hospital-based prospective cohort, using machine learning, generalized linear mixed models, and joint generalized estimating equations to account for confounding factors and predict symptom evolution. Subsequent deep-learning frameworks have integrated mobility patterns, temporal disease dynamics, and regional vaccination uptake to enhance epidemic-wave forecasting across heterogeneous populations.

However, despite these advances, such population-level models still lack the capacity to capture survival heterogeneity, censoring mechanisms, and the presence of cured or long-term survivor subgroups observed in clinical cohorts. Optimization-based models have likewise been developed to determine age- and priority-specific vaccine allocation under constrained supply, demonstrating the utility of parametric decision tools for real-time pandemic response [33]. However, these frameworks also operate at the population level and fail to account for the censoring mechanisms inherent in patient-level time-to-event data.

Recent deep-learning mortality prediction studies have demonstrated the value of incorporating laboratory trajectories, comorbidity histories, and clinical biomarkers into predictive pipelines, yet even these state-of-the-art systems do not include formal survival components capable of distinguishing cured from uncured individuals [34]. Taken together, these works underpin the growing role of AI, statistical, and machine learning-based predictive frameworks in pandemic preparedness and management. By situating our study in this context, we highlight how our cure-mixture and semi-parametric modelling approach complements this trend by focusing on survival outcomes under uncertainty and combining parametric and semi-parametric techniques. In addition, these limitations collectively underscore the need for statistical frameworks—such as mixture cure models—that explicitly incorporate censoring structures, latent cure fractions, and patient-specific heterogeneity in time-to-event outcomes, thereby offering insights that population-level AI forecasting tools cannot provide.

This paper applies a cure rate mixture model to perform a risk assessment for hospitalized patients diagnosed with COVID-19. The event of interest is death due to COVID-19 occurring anytime from hospital admission through one year after discharge. To demonstrate the methodology, the KCC dataset with 1998 patients is used [35]. Data analysis was performed using R version 4.3.2, developed by the R Foundation for Statistical Computing. The available packages “stats”, “survival” and, “icenReg” were used to estimate cure rate mixture model parameters.

In contrast to most existing research, which primarily assesses fewer primary risk factors for high-risk COVID-19 patients and often ignores the interaction of covariates and medications, this study takes a more comprehensive analytical approach and examines a large number of covariates and treatments. We utilize the mixture cure model to simultaneously investigate factors associated with both the probability of recovery (cure fraction) and the survival dynamics among non-cured patients. To our knowledge, this is the first study to apply a mixture cure model to in-hospital COVID-19 patients in conjunction with decision trees and random forest-based models for detecting influential covariates and interaction effects.

This integrative approach not only improves the interpretability of survival patterns but also reveals critical covariate–treatment interactions that may inform future hypothesis generation and research design. By identifying subgroups of patients with distinct survival trajectories and treatment responses, the model provides statistical insights that could support understanding of hospital patient outcomes and healthcare dynamics during and beyond pandemic crises.

This study makes several methodological and applied contributions. First, it provides the first application of mixture cure modeling to a large hospital-based COVID-19 cohort, enabling separation of cured and uncured subpopulations and providing a more realistic representation of long-term survival heterogeneity. Second, our approach integrates feature selection using random survival forests, followed by interaction detection using decision trees—an analytic pipeline that identifies complex nonlinear relationships between demographic, clinical, and therapeutic factors that traditional regression models may overlook. Third, the study incorporates interval-censored event times, an aspect often ignored in COVID-19 survival studies, allowing more accurate estimation of the survival distribution. Fourth, the analysis distinguishes the incidence (cure probability) and latency (time-to-death) components of the mixture cure model, offering insights into both short-term mortality and long-term recovery potential. Finally, although the model is descriptive and not causal, the identification of high-risk subgroups and treatment–covariate interactions provides statistical insights that can inform conceptual frameworks for hospital preparedness, resource prioritization, and future pandemic planning. These contributions position the study at the intersection of survival analysis, machine learning, and healthcare analytics.

Although the mixture cure model does not directly optimize resource allocation, it provides a statistically grounded characterization of patient subgroups with distinct survival trajectories. Patients classified as uncured represent individuals with sustained mortality risk who are more likely to require intensive hospital services such as mechanical ventilation, ICU admission, and prolonged monitoring. By quantifying the covariates associated with both the probability of cure and the time-to-death among uncured patients, the model offers descriptive insights that can support conceptual preparedness planning. These insights help identify high-burden clinical profiles that may generate disproportionate demand during future pandemics, thereby complementing broader hospital capacity planning frameworks.

The structure of the paper is as follows: In section “Materials and methods”, we provide a detailed description of the longitudinal dataset of the KCC, our approach to feature selection, and the methodology used for the cure rate mixture model. In section “Results”, we present the outcomes of our initial exploratory analysis and the results of assessing the factors associated with mortality and time-to-death. Discussion about these findings is presented in section “Discussion”.

Materials and methods

Dataset description

The dataset used in this study was obtained from the Khorshid COVID Cohort (KCC), a hospital-based prospective study comprising 1,998 COVID-19 patients admitted to Khorshid Referral Hospital in Isfahan, Iran, between February 2020 and February 2021. This study followed an open-cohort design, monitoring each patient from the time of hospital admission through one year after discharge. Follow-up assessments were conducted via telephone interviews during the first and fourth weeks after discharge, and in-person evaluations at the 12th week and one-year follow-up to record the clinical symptoms, and respiratory function [35] (Fig. 1).

Fig. 1.

The scheme of the Khorshid COVID Cohort (KCC) study

The KCC dataset provides a rich and diverse foundation for this analysis, comprising 45 variables that capture a comprehensive clinical profile of hospitalized COVID-19 patients. These variables span demographic characteristics such as age, sex, education, and occupation; socioeconomic measures; detailed medical history, including hypertension, diabetes, and cardiovascular disease; vital signs at admission; imaging findings; and a wide spectrum of laboratory biomarkers covering hematologic, metabolic, inflammatory, and hepatic parameters. The dataset is further strengthened by its inclusion of comprehensive information on prescribed treatments and cumulative medication dosages during hospitalization. This breadth of data enables a robust, multi-dimensional modeling of survival outcomes and ensures a representative spectrum of clinical severity.

The reliability of this data was upheld through several rigorous processes. Standardized collection protocols were implemented by trained clinical staff at a single referral hospital, with baseline variables obtained via structured interviews, calibrated instruments, and centralized laboratory assays featuring internal quality controls. To ensure consistent outcome ascertainment, follow-up assessments were conducted on a predefined schedule at weeks 1, 4, 12, and one year, a strategy that minimized loss to follow-up. Furthermore, data integrity was preserved through a proactive approach to handling missing data. The overall missingness was low, averaging 6.3% and occurring primarily in non-critical fields. After visual and statistical evaluation of the missingness patterns supported a Missing at Random (MAR) assumption, multiple imputation via chained equations was applied in accordance with established practice, thereby safeguarding the analytic reliability of the study [36].

Figure 2 demonstrates the four possible categories for patients’ time-to-death, measured as the duration (in days) from hospital admission to death or last follow-up, thus providing a clear time horizon for survival analysis. In this study, events with exact observed death times are labeled as ‘observed event (death)’ to clearly distinguish them from censored outcomes. This labeling avoids ambiguity and aligns with the event definition used in the statistical analysis. The dashed line represents unobserved exact time of the event, while solid lines indicate the fully-observed timeline for each individual. In this study, 1542 patients were discharged alive. Among the deceased patients, 265 had an observed precise time of death. Additionally, 24 patients died between the two specific finite time points and were classified as “interval censored”, with time points varying individually. Finally, 278 patients whose unknown time of deaths occurred after a certain number of days, classified as “right-censored,” aligning with the fourth line from the top in the Fig. 2.

Fig. 2.

Illustration of censoring types for time-to-death in the study cohort. The solid line represents the interval during which a patient is under observation, and the dashed line represents periods without observation. Red circles denote an observed event (death). Patients whose death times fell within a known interval are classified as interval-censored, while those who were still alive at the last follow-up are classified as right-censored

The ethics committee of the Isfahan University of Medical Sciences (IUMS) and the other national authorities approved the study (IR.MUI.MED.REC.1399.029). The experimental protocol was also conformed to the Declaration of Helsinki. Also, the entire subjects gave written informed consent to the experimental procedure. The written informed consent was given by the first relative family of patients with severe conditions. No minors participated in our study.

Cure rate mixture model

Mixture cure models assume that a proportion of individuals will never experience the event of interest within a clinically meaningful time horizon. Let denote the latent cure status, where for uncured individuals and for cured individuals. The population survival function is expressed as a mixture of the long-term survivors and those susceptible to the event:

1

where represents the incidence (uncured) probability, modeled using logistic regression, and is the conditional survival function of uncured patients, typically modeled using a parametric or semi-parametric survival distribution. Identifiability of the cure fraction requires a sufficiently long follow‑up period to observe a plateau in the survival curve, which is satisfied in our study with a 12‑month follow‑up window.

The likelihood combines contributions from exact, interval‑censored, and right‑censored observations, allowing flexible incorporation of different censoring mechanisms. Parametric assumptions (e.g., Weibull distribution) offer smooth hazard estimation, whereas semi-parametric Cox proportional hazards modeling preserves flexibility by leaving the baseline hazard unspecified. Together, the incidence and latency components jointly characterize heterogeneity in mortality risk and enable examination of covariates influencing both cure probability and time‑to‑event among uncured individuals. This dual structure provides a more nuanced representation of survival patterns compared with standard survival models.

In survival analysis, outcomes usually consist of two random variables of failure time  T and censoring time  C where only their minimum, , can be observed. The censoring status for the individual is represented by the Bernoulli indicators , , where if individual is left-censored, if individual is right-censored and if individual is interval censored. For all censored individuals, . In this study, patients who remained alive throughout the one-year follow-up are considered ‘cured,’ since no further COVID-19-related death events were observed beyond this period, providing a clinically plausible window for defining the cured fraction.

In the KCC dataset, death times can either be observed exactly, right-censored, or interval-censored. In this study, the event of interest is death due to COVID-19 occurring between the date of hospital admission (time zero) and up to one year following discharge. Patients who remain alive throughout this follow-up window are treated as censored. The death indicator is defined as with probability  p for patients who die, and otherwise. Accordingly, the time-to-event variable  T is finite only for individuals with . This decomposition allows individuals to be categorized into those who experience the event and those who are cured. Therefore, the mixture cure rate model can be written as

2

where denotes the model parameters, which include the coefficients of the covariates used in the cure rate mixture model. For dead patients with an exact death time

where is the cumulative distribution function (CDF) of . Consequently, the density function is

with

where is the density of uncured individual. For right-censored deaths

3

where is right-censoring time for censored individuals and is the survival function of . For interval-censored deaths

4

where is left-censoring time for censored individuals. Therefore, the likelihood function for the mixture cure rate model can then be written as

5

A fully parameterized distribution is assumed for ease of derivation and optimization (see Appendix A for details). Since the likelihood function in Eq. (5) can be divided into two components, one for time-to-death and the other for survival status, the cure mixture model can also be split into two parts. The first part involves logistic regression models that predict survival status, while the second part involves a parametric survival model, such as exponential or Weibull, to estimate the time-to-death. In R, the “glm” function (from the “stats” package) can be used for the survival status part, while “survreg” (from “survival”) and “ic_par” and “ic_sp” (from “icenReg”) can be used for the time-to-death part. Factorization of the likelihood enables the independent estimation of the two components, which can subsequently be combined to obtain the full model. In parametric survival analysis, as in GLMs, uncertainty is modeled via the assumed distribution of the outcome. However, a limitation of these models is that the distribution needs to be fully specified, which requires making several strong assumptions. In this study, the Cox proportional-hazards model [2] is employed to provide additional flexibility by leaving the baseline hazard unspecified, allowing the model to accommodate unknown hazard structures and mitigate the impact of strict parametric assumptions.

In the proposed mixture cure model, uncertainty originates from several sources, which we categorize as pertaining to model specification and data structure. Specification uncertainty includes the parametric assumptions for the incidence (logistic) and latency (survival) components, such as the choice of a Weibull versus exponential distribution for the baseline survival function. Structural uncertainty, conversely, arises from the data-generating process itself, including unobserved patient heterogeneity, random censoring, and measurement error in covariates. A critical source of this structural uncertainty is right-censoring. For a censored observation, the individual’s true status—whether they belong to the “cured” or “uncured” subpopulation—is inherently unknown, introducing ambiguity into the model’s latent class structure. This uncertainty is formally accounted for within the likelihood function, where the contribution of a censored observation is a mixture of the probabilities of being cured or uncured but not yet having experienced the event.

To mitigate these uncertainties without relying on strict parametric assumptions, our modeling framework incorporates flexibility through a semi-parametric approach. Specifically, the survival component for the uncured group can be specified using a Cox proportional hazards model, which leaves the baseline hazard function non-parametric. This design reduces the risk of misspecification from an incorrect parametric form and provides a more robust estimation framework. By embedding this flexibility within the maximum likelihood estimation procedure, the model accommodates the unknown structure of the data while providing stable and interpretable parameter estimates for both the probability of cure and the hazard of the event.

Feature selection for creating cure rate mixture models

This section describes the feature selection process for constructing cure rate mixture models and the application of the cure mixture model to the KCC dataset. Figure 3 provides an overview of the analytical workflow used in this study.

Fig. 3.

The statistical methods used in the survival analysis of COVID-19 patients

To identify influential predictors for the incidence (cure) and latency (survival time) components of the mixture cure model, we employed a structured feature selection pipeline combining machine learning and statistical modeling (Fig. 3). This process began by fitting two random forest models to capture complex, non-linear relationships. First, a Random Survival Forest (RSF) model was fitted using time-to-death to handle right-censoring and identify covariates affecting the timing of events. Second, a standard Random Forest (RF) model was fitted with a binary survival status (deceased vs. long-term survivor) to identify predictors of the eventual outcome. Variable importance from both models was quantified using permutation importance, and covariates exceeding a predefined importance threshold were retained. The RSF model highlighted key predictors for the timing of death, including demographic factors (sex, age), clinical intervention durations (intubation, ICU stay), admission laboratory values (ALP, Sodium, BUN), vital signs (systolic blood pressure, pulse rate, respiratory rate, oxygen saturation), and specific treatments (heparin use, cumulative doses of levofloxacin, meropenem, and ceftriaxone). Concurrently, the binary RF model identified strong predictors of mortality probability, such as oxygen saturation, initial body temperature, intubation status and duration, ICU duration, and cumulative doses of levofloxacin, methylprednisolone, enoxaparin, and doxycycline.

To further investigate higher-order relationships among the selected predictors, a decision tree was constructed using the 30 most important variables derived from the combined random forest outputs. This analysis revealed clinically plausible interaction structures, such as between oxygen saturation and intubation duration, and between BUN and specific treatments.

Finally, the identified interaction terms were formally incorporated into the final mixture cure model specification. This hybrid, machine-learning-guided approach ensured our final model was both statistically principled and clinically interpretable, effectively reducing dimensionality while capturing the complex interdependencies inherent in the data.

Results

Exploratory data analysis

Some exploratory results for the characteristics of hospitalized patients with COVID-19 in KCC are presented in Table 1. This table illustrates the frequency of some demographic characteristics of the admitted COVID-19 patients presented separately for the deceased and surviving groups. Moreover, the percentages of some signs and symptoms at the time of admission for dead and alive patients are reported in this table.

Table 1.

Results of testing the independence of binary death status outcome and categorical predictor variables (numbers in bold are significant at the %5 level)

Patients characteristics	Frequency (%)			Treatment	Frequency (%): Use
	Dead Frequency (%)	Alive Frequency (%)	Odds Ratio (P-value)		Dead Frequency (%)	Alive Frequency (%)	Odds Ratio (P-value)
Total	450	1547		Heparin: Yes	269 (59.8)	642 (41.6)	2.083 (0.000)
Gender			1.282 (0.026)		181 (0.402)	900 (58.4)
Male	282 (62.7%)	874 (56.7%)		Methylprednisolone: Yes	263 (58.4)	595 (38.6)	2.242 (0.000)
Female	168 (37.3%)	668 (43.3%)			187 (41.6)	947 (61.4)
Underlying Diseases			1.091 (0.469)	Ceftriaxone: Yes	185 (41.1)	604 (39.2)	1.084 (0.476)
Yes	293 (65.1%)	973 (63.1%)			265 (58.4)	938 (60.8)
No	157 (34.9%)	569 (36.9%)		Hydroxychloroquine: Yes	140 (31.1)	473 (30.7)	1.021 (0.862)
Smoking status			0.598 (0.007)		310 (68.9)	1069 (69.3)
Yes	39 (13.0%)	252 (20.0%)		Doxycycline: Yes	153 (34.0)	366 (23.7)	1.655 (0.000)
No	261 (87.0%)	1010 (80.0%)			297 (66.0)	1176 (76.3)
Intubation Status			22.758 (0.000)	Enoxaparin: Yes	131 (29.1)	351 (22.8)	1.394 (0.007)
Yes	82 (18.3%)	15 (1.0%)			319 (70.9)	1191 (77.2)
No	366 (81.7%)	1527 (99.0)		Azithromycin: Yes	101 (22.4)	365 (23.7)	0.933 (0.613)
Signs and symptoms					349 (77.6)	1177 (76.3)
Fever			0.948 (0.640)	LevofloxacinTablet: Yes	129 (28.7)	325 (21.1)	1.506 (0.001)
Yes	311 (69.1%)	1083 (70.2%)			321 (71.3)	1217 (78.9)
No	139 (30.9%)	459 (29.8%)		Oseltamivir: Yes	79 (17.6)	207 (13.4)	1.373 (0.032)
Cough			0.879 (0.265)		371 (82.4)	1335 (86.6)
Yes	307 (68.2%)	1094 (70.9%)		Linezolid: Yes	94 (20.9)	179 (11.6)	2.012 (0.000)
No	143 (31.8%)	448 (29.1%)			356 (79.1)	1363 (88.4)
Shortness of Breath			0.968 (0.782)	Meropenem: Yes	119 (26.4)	148 (9.6)	3.389 (0.000)
Yes	277 (61.6%)	961 (62.3%)			331 (73.6)	1394 (90.4)
No	173 (38.4%)	581 (37.7%)		Vancomycin: Yes	100 (22.2)	110 (7.1)	3.717 (0.000)
Fatigue			1.026 (0.829)		350 (77.8)	1432 (92.9)
Yes	253 (56.2%)	857 (55.6%)		Interferon B: Yes	71 (15.8)	118 (7.7)	2.262 (0.000)
No	197 (43.8%)	685 (44.4%)			379 (84.2)	1424 (92.3)
Chills			0.850 (0.131)	Ceftazidime: Yes	53 (11.8)	107 (6.9)	0.558 (0.001)
Yes	234 (52.0%)	864 (56.0%)			397 (88.2)	1435 (93.1)
No	216 (48.0%)	678 (44.0%)		Caltera: Yes	49 (10.9)	99 (6.4)	1.792 (0.002)
Decreased Appetite			1.049 (0.664)		401 (89.1)	1443 (93.6)
Yes	193 (42.9%)	643 (41.7%)		Aspirin: Yes	27 (6.0)	89 (5.8)	1.042 (0.820)
No	257 (57.1%)	899 (58.3%)			423 (94.0)	1453 (94.2)
Vomiting			0.984 (0.948)	Tazocin: Yes	28 (6.2)	60 (3.9)	1.639 (0.037)
Yes	98 (21.8%)	340 (22.0%)			422 (93.8)	1482 (96.1)
No	352 (78.2%)	1202 (78.0%)		Warfarin: Yes	25 (5.6)	38 (2.5)	2.331 (0.002)
Headache			0.616 (0.000)		425 (94.4)	1504 (97.5)
Yes	110 (24.4%)	531 (34.4%)		Vitamn C: Yes	19 (4.2)	32 (2.1)	0.481 (0.016)
No	340 (75.6%)	1011 (65.6%)			431 (95.8)	1510 (97.9)
Chest Pain			0.684 (0.004)	Ciprofloxacin: Yes	13 (2.9)	22 (1.4)	2.079 (0.063)
Yes	88 (19.6%)	404 (26.2%)			437 (97.1)	1520 (98.6)
No	362 (80.4%)	1138 (73.8%)		CoAmoxiclav: Yes	5 (1.1)	22 (1.4)	0.777 (0.817)
Diarrhea			0.878 (0.343)		445 (98.9)	1520 (98.6)
Yes	98 (21.8%)	371 (24.1%)		Clopidogrel: Yes	5 (1.1)	15 (1.0)	1.144 (0.789)
No	352 (78.2%)	1171 (75.9%)			445 (98.9)	1527 (99.0)
Sore throat			0.915 (0.609)	Metronidazole: Yes	6 (1.3)	11 (0.7)	1.883 (0.241)
Yes	68 (15.1%)	251 (16.3%)			444 (98.7)	1531 (99.3)
No	382 (84.9%)	1291 (83.7%)		Cefepime: Yes	7 (1.6)	8 (0.5)	3.030 (0.054)
Weight Loss			0.859 (0.344)		443 (98.4)	1534 (99.5)
Yes	66 (14.7%)	257 (16.7%)		Ribavirin: Yes	5 (1.1)	7 (0.5)	2.463 (0.157)
No	384 (85.3%)	1285 (83.3%)			445 (98.9)	1535 (99.5)
Loss of Smell			0.663 (0.024)	Rivaroxaban: Yes	3 (0.7)	9 (0.6)	1.144 (0.739)
Yes	39 (8.7%)	193 (12.5%)			447 (99.3)	1533 (99.4)
No	411 (91.3%)	1349 (87.5%)		Clindamycin: Yes	3 (0.7)	6 (0.4)	1.718 (0.431)
					447 (99.3)	1536 (99.6)

The results reject the hypothesis of independence of death status and four variables, including gender, smoking status, intubation status, and some clinical signs and symptoms such as headache, chest pain, and loss of smell. From the results, it is observed that smoking patients have a significantly lower risk of death (approximately 60% less) compared to non-smoking patients. Additionally, males have roughly 1.3 times higher odds of death compared to females.

Patients with intubation have approximately 22.76 times higher odds of death compared to patients without intubation. The mean age of hospitalized patients is 58.67, with significant differences (T-test = 2.78; P-value = 0.005) in the mean age for those who died (60.58) or survived (58.123) during the study.

Table 1 reveals that patients experiencing chest pain or loss of smell upon admission have a considerably lower risk of death (about 70% less) compared to patients without these symptoms. Table 1 also gives the counts and percentages of surviving or deceased COVID-19 patients who have been prescribed medicine during the hospitalization period. The most frequently prescribed treatments for COVID-19 patients are heparin (46%), methylprednisolone (43%), ceftriaxone (40%), and hydroxychloroquine (30%). About 60% of COVID-19 patients who died had taken heparin, while approximately 42% of COVID-19 patients who survived used this medicine during the hospitalization period. However, vancomycin use was slightly higher among patients who died (22%) compared to those who survived (7%). Overall, patients receiving treatments such as heparin, methylprednisolone, doxycycline, enoxaparin, levofloxacin tablets, oseltamivir, linezolid, meropenem, vancomycin, interferon B, Caltera, tazocin, and warfarin showed higher odds of mortality; however, this association most likely reflects greater disease severity at admission and confounding by indication, rather than any treatment-related causal effect.

To properly assess the association between critical interventions and mortality while avoiding potential immortal time bias, we performed a landmark analysis [37, 38] with the landmark set at day 5 of hospitalization. Figure 4 shows the subsequent survival of patients stratified by their ICU admission (right panel) and intubation status (left panel) during the first 5 days. The analysis reveals a pronounced disparity in outcomes. Patients who required critical interventions (ICU and/or intubation) within the first 5 days had significantly poorer survival after the landmark time compared to those who did not. This finding supports that these intensive interventions are powerful markers of severe disease and high subsequent mortality risk. The use of a landmark analysis ensures that this conclusion is not an artifact of the biased time-to-event structure inherent in a naïve baseline stratification.

Fig. 4.

Landmark analysis of survival stratified by ICU admission and intubation status. Kaplan-Meier curves depict survival probabilities from hospital day 5 (landmark time) onward. Patients were stratified based on whether they had experienced admission to the ICU (right) or endotracheal intubation (left) at any time during the first 5 days of hospitalization. This landmark approach eliminates immortal time bias by starting follow-up for all patients at a common time point after the exposure window has passed

To examine the relationship between laboratory findings and death status, Fig. 5 was generated. In this figure, the actual values of certain laboratory measurements such as platelet count, ALT, AST (aspartate aminotransferase), and ALP were divided by 10 to account for their substantially higher magnitudes compared to other laboratory variables. For white blood cell count and LDH, their actual values are divided by 100 to have a similar scale to the other laboratory findings.

Fig. 5.

95% confidence intervals for the difference in the mean laboratory findings between dead and alive patients at admission time

Based on the results of Fig. 5, there are significant differences in the mean values of several laboratory findings at the time of admission between dead and alive patients. Significant differences were observed for neutrophil, lymphocyte and platelet counts, PCO2, HCO3, Ca, K, P, Cr, AST, LDH, ESR, and BUN values. Lymphocyte, and platelet counts, as well as PCO2, and HCO3 levels, were significantly lower in dead patients compared to alive patients, whereas neutrophil counts, AST, LDH, and BUN levels were significantly higher in dead patients. No significant differences were observed in the mean value of other laboratory findings, including white blood cell count, hemoglobin, ALT, ALP, Na, Mg, PH, and Bili, between dead and alive patients at the time of admission.

Interpretation of cure rate mixture model results

To identify potential risk factors associated with the probability of death among COVID-19 patients, Table 2 presents the results of the logistic regression models. By using a feature selection algorithm, important covariates were chosen using random forests. After selecting the influential variables as inputs for the logistic regression, potential interactions among these covariates were identified using a decision tree.

Table 2.

The Results of fitting logistic regression model for the death status outcome (numbers in bold are significant at the 5% level)

Explanatory Variables	Coefficient (Odds Ratio)	SE	P-value
Constant	-6.931 (0.000)	2.210	0.001
Intubation duration	0.159 (1.172)	0.081	0.049
ICU duration	0.102 (1.107)	0.021	0.000
Intubation Status: Yes	4.564 (95.96)	0.691	0.000
Initial body temperature	0.121 (1.128)	0.058	0.039
oxygen saturation (Baseline: 90–100)	-	-	-
80–89	0.226 (1.253)	0.138	0.102
< 80	0.465 (1.592)	0.196	0.017
Drug Cumulative Dosage
Levofloxacin, tablets of strength 500 mg	0.059 (1.060)	0.015	0.000
Methylprednisolone	0.722 (2.058)	0.221	0.001
Enoxaparin	-0.001 (0.999)	0.000	0.003
Doxycycline	0.025 (1.025)	0.014	0.075
Interaction Effect
ICU duration* Intubation Status: Yes	-0.333 (0.716)	0.081	0.000
BUN * Methylprednisolone: Use	0.006 (1.006)	0.006	0.324
BUN * Methylprednisolone: Un-Use	0.017 (1.017)	0.005	0.001
AIC	1840.5

The results of Table 2 show that higher cumulative dosages of methylprednisolone significantly raise the odds of death by approximately 2.06 times. Patients who require a longer duration of intubation seem to face higher odds of death, approximately 1.107 times higher. The odds of death for patients who require intubation are approximately 96 times higher compared to patients who do not need intubation. Patients with low oxygen saturation levels (less than 80%) have a significant mortality risk that is approximately 1.59 times greater than patients with high oxygen saturation levels (90–100). The odds of death for patients who require intubation and have a longer stay in the ICU are actually about 70% lower compared to patients who do not require intubation and have a longer stay in the ICU.

Table 3 presents the modeling results for time-to-death and clarifies how various risk factors are associated with the death hazard rate. Semi-parametric methods such as the Cox proportional hazard model and the mixture cure model using exponential, Weibull, and lognormal are employed. One approach toward model selection is to use Akaike’s Information Criterion (AIC). AIC evaluates the extent of information loss in a model; a lower AIC value indicates less information loss and better model fit. The Cox proportional hazards model has the lowest AIC (1356.525) between the parametric and semi-parametric models, and among parametric models, Weibull (1523.2) had the lowest AIC. More details of the results of all estimation models are given in Appendix A.

Table 3.

Results of the Cox proportional hazard model and mixture cure model with Weibull distribution (numbers in bold are significant at the 5% level)

Explanatory Variables	Death Hazard Ratio (Cox Regression)	SE	P-value		Death rd RatioHaza (Weibull)	SE	P-value
Constant					11.914	2.294	0.000
Gender: Female	1.399	0.216	0.120		1.396	0.216	0.061
Age (Baseline: < 45)					-	-	-
45–54	1.069	0.474	0.887		0.986	0.484	0.972
55–64	0.758	0.376	0.461		0.718	0.432	0.354
65–74	1.990	0.371	0.063		2.296	0.387	0.009
> 74	3.034	0.405	0.006		3.323	0.399	0.000
Intubation duration	1.268	0.087	0.006		1.283	0.069	0.000
Time to ICU	1.128	0.035	0.000		1.169	0.038	0.000
Laboratory findings at admission time
ALP, U/L	1.001	0.000	0.228		1.000	0.000	0.000
Na, meq/L	1.023	0.015	0.131		1.022	0.015	0.088
BUN, mg/dL	1.031	0.006	0.000		1.032	0.005	0.000
Vital Symptoms
Systolic blood pressure, mm Hg	0.991	0.004	0.042		0.993	0.004	0.051
Pulse Rate, /min	1.013	0.005	0.021		1.009	0.005	0.034
Respiratory Rate, /min	1.037	0.016	0.024		1.032	0.015	0.010
oxygen saturation (Baseline: 90–100)				-	-	-	-
80–89	1.261	0.316	0.463		1.303	0.333	0.335
< 80	3.129	0.314	0.000		3.413	0.350	0.000
Treatment use
Heparin	0.700	0.270	0.187		0.655	0.279	0.066
Drug Cumulative Dosage
Levofloxacin, tablets of strength 500 mg	0.936	0.026	0.011		0.936	0.023	0.000
Meropenem, 1 g vial	0.979	0.012	0.075		0.984	0.009	0.051
Ceftriaxone	0.949	0.038	0.017		0.943	0.036	0.049
Interaction Effect
BUN * Methylprednisolone: Use	0.987	0.008	0.102		0.986	0.007	0.025
BUN * Intubation duration	0.996	0.001	0.015		0.997	0.001	0.001
Oxygen Saturation (80–89) * Intubation duration	0.898	0.073	0.142		0.879	0.061	0.012
Oxygen Saturation (< 80) * Intubation duration	0.850	0.076	0.034		0.834	0.064	0.000
Meropenem (Use)* Methylprednisolone (Unuse)	4.314	0.422	0.000		3.758	0.403	0.000
Meropenem (Use)* Methylprednisolone (Use)	5.606	0.425	0.000		5.337	0.386	0.000
Oxygen Saturation (90–100) * Ceftriaxone (Use)	0.971	0.590	0.960		1.027	0.609	0.956
Oxygen Saturation (80–89) * Ceftriaxone (Use)	0.497	0.409	0.087		0.490	0.425	0.042
Oxygen Saturation (< 80) * Ceftriaxone (Use)	0.634	0.469	0.332		0.538	0.488	0.123
Log (scale)					0.192	0.065	0.003
AIC	1356.525				1523.2

The results of the Weibull model reveal that age plays a crucial role in mortality, with older people facing a significantly higher risk. The death hazard rate for individuals aged 65–74 significantly increases by 2.3 times, while those aged over 74 face a 3.3 times higher risk compared to the reference group (< 45 years). As the time until ICU admission increases, the risk of death also increases by 1.17 times. Notably, the findings indicate that when oxygen saturation falls below 80%, the death hazard rate significantly increases by 3.41 times compared to the reference group (90–100%).

Increasing the cumulative dosage of levofloxacin and ceftriaxone leads to a slight decrease in the death hazard rate by 5–6%. However, the death hazard rate significantly increases by 5.34 times for individuals using meropenem and methylprednisolone. Furthermore, individuals using meropenem without methylprednisolone also experience a significant increase in the death hazard rate by 3.76 times. As noted previously, the use of methylprednisolone and meropenem was associated with higher odds of mortality, likely reflecting greater disease severity and confounding by indication rather than a direct treatment effect.

Also, the use of ceftriaxone for individuals whose oxygen saturation falls between 80 and 89%, reduced the death hazard rate by 49%. When oxygen saturation falls below 80% or between 80 and 89%, the risk of death decreases (0.83, 0.88, respectively) as the duration of intubation increases. Results from the Cox and Weibull models closely align and lead to similar conclusions.

Discussion

Prompt identification of patient mortality risk and prediction of time-to-death patterns can provide physicians with valuable insights into patient trajectories within a strained healthcare system. The objective of this study was to validate personalized mortality risk factors and specifically examine how treatment protocols affect the risk of mortality and death hazard rate for COVID-19 patients who are hospitalized.

The principal findings of this study are as follows: (i) older individuals, particularly those aged 65–74 and above 74, face significantly higher risks compared to the reference group (< 45 years). This highlights the importance of age as a predictor of mortality. (ii) The longer the time until ICU admission, the higher the risk of death. This suggests that early and timely access to critical care can potentially improve survival outcomes. (iii) When oxygen saturation falls below 80% or between 80 and 89%, the risk of death decreases (0.83, 0.88, respectively) as the duration of intubation increases. This indicates that prolonged intubation may improve survival outcomes for patients with lower oxygen saturation levels. (iv) Increasing the cumulative dosage of levofloxacin and ceftriaxone leads to a slight decrease (94%) in the death hazard rate. This suggests a potential beneficial effect of these drugs in reducing mortality. The observed association between treatments such as methylprednisolone and meropenem and higher mortality risk likely reflects the underlying severity of illness among patients requiring these medications, rather than a direct causal effect of the treatments. This further strengthens the association between these treatments and an increased risk of death, likely due to the severity of the underlying health conditions requiring their use. The use of ceftriaxone for individuals with oxygen saturation between 80 and 89% appears to reduce the death hazard rate by 49%. This suggests a potential beneficial effect of ceftriaxone in mitigating mortality risk in patients with lower oxygen saturation levels. Therefore, identifying associations between treatment protocols and survival outcomes can improve understanding of clinical response patterns and may inform future research or guideline refinement. These findings highlight the complex interplay between age, timing of ICU admission, oxygen saturation, specific treatments, and mortality risk. They provide valuable insights for understanding and potentially improving patient outcomes in critical care settings.

According to the findings of Heras et al. [39] and Rieg et al. [40], older COVID-19 patients and those with higher LDH levels are at a greater risk of mortality. The literature also supports our findings, indicating that older age, lower oxygen saturation, and higher blood urea nitrogen (BUN) levels are primary risk factors that significantly contribute to mortality rates [41]. Predicted mortality for patients with low oxygen saturation, supporting previous studies that connect hypoxemia to higher mortality rates. The effect of treatment protocols and upper limit of steroid dose for hospitalized COVID-19 patients has not been sufficiently evaluated [42]. A previous study by Ro et al. [43] found that COVID-19 patients up to their early 70s who received methylprednisolone pulse therapy survived, but patients in their late 70s and older did not survive. This suggests that the younger group may have seen positive effects from the pulse therapy, while the older group did not seem to benefit from it. Meropenem is a widely used beta-lactam antibiotic in the intensive care unit (ICU) due to its broad activity against various pathogens and relatively low toxicity. Peng et al. [44] present a pharmacometric multistate model for analyzing survival outcomes in critically ill patients receiving meropenem treatment. Their study has important implications for cross-endpoint bridging, patient selection, and dose optimization in the field of antimicrobial therapy.

This study has some limitations that should be acknowledged. First, as an observational analysis, the identified associations between treatments and outcomes should not be interpreted as causal, as residual confounding may persist despite our extensive data. Future studies leveraging randomized trial data or quasi-experimental designs would be valuable for establishing causality. Second, although the KCC cohort includes extensive clinical and laboratory information, it does not contain differentiated cause-of-death data, preventing the use of formal competing-risk models. Third, our model treated all covariates as time-fixed, measured at baseline or during hospitalization; future work could extend this framework by incorporating time-varying treatments and laboratory values to better capture dynamic clinical pathways, though this would require careful handling of immortal time bias. Fourth, although missing data were limited and addressed using multiple imputation, some laboratory variables may still be subject to measurement error or selective testing. Fifth, the dataset originates from a single referral hospital, which may limit generalizability to other settings with different clinical protocols or patient characteristics. Finally, although the one-year follow-up period is clinically appropriate for defining a cured fraction in COVID-19, there remains a possibility of late post-COVID-19 complications beyond the study horizon. These limitations should be considered when interpreting the findings.

In summary, our analysis highlights key clinical and treatment factors associated with mortality risk among hospitalized COVID-19 patients, providing a nuanced understanding of patient trajectories. These insights, derived from the mixture cure model, can inform hospital preparedness, resource allocation, and future research aimed at optimizing care for high-risk subgroups.

Conclusion

This study presents a mixture cure model to effectively describe the diagnosis and treatment protocol of health services during hospital admission, as well as significant clinical outcomes like patient discharge from the hospital or death while undergoing therapy. Our findings contribute to a more accurate characterization of survival and mortality dynamics among hospitalized COVID-19 patients. While the mixture cure model is inherently descriptive and not intended as a resource optimization or clinical decision-making tool, its results provide valuable information relevant to hospital preparedness. By distinguishing between cured and uncured subgroups and identifying factors associated with high mortality risk, the model highlights patient profiles that may require greater resource intensity during hospitalization. For example, individuals with severe hypoxemia, prolonged intubation, advanced age, or specific treatment interactions represent subgroups with elevated risk of adverse outcomes and likely higher demand for ICU beds and advanced respiratory support. These findings do not prescribe clinical actions but offer evidence-based insights that can inform conceptual frameworks for anticipating resource needs, guiding triage strategies, and strengthening preparedness plans for future epidemic waves.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Conceptualization: Zahra Rezaei Ghahroodi, Roxana Darvishi, Abdollah Safari, Firoozeh Haghighi, Marjan Mansourian. Data curation: Marjan Mansourian, Zahra Rezaei Ghahroodi. Design and development: Zahra Rezaei Ghahroodi, Roxana Darvishi, Abdollah Safari. Writing–original draft: Zahra Rezaei Ghahroodi, Roxana Darvishi, Firoozeh Haghighi. Writing–review & editing: Zahra Rezaei Ghahroodi, Roxana Darvishi, Abdollah Safari, Firoozeh Haghighi, Marjan Mansourian.

Funding

Not applicable.

Data availability

Not applicable.

Declarations

Ethics approval and consent to participate

The ethics committee of the Isfahan University of Medical Sciences (IUMS) and the other national authorities approved the study (IR.MUI.MED.REC.1399.029). The experimental protocol also conformed to the Declaration of Helsinki. In addition, all subjects provided written informed consent for participation in the study. Written informed consent was obtained from the first-degree relatives of patients with severe conditions. No minors participated in this study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.