The Effect of Provider Case Volume on Cancer Mortality Systematic Review and Meta-analysis

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• Published: 02 January 2022

Exploring relationships betwixt in-hospital mortality and hospital case volume using random forest: results of a accomplice study based on a nationwide sample of German hospitals, 2016–2018

• Felix Walther^1,2,
• Maria Eberlein-Gonskaⁱⁱ,
• Peter C. Scriba³,
• Ralf Kuhlen³,
• Jochen Schmitt¹ &
• Olaf Schoffer¹

BMC Wellness Services Enquiry volume 22, Commodity number:1 (2022) Cite this article

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Abstract

Background

Relationships betwixt in-hospital mortality and instance volume were investigated for various patient groups in many empirical studies with mixed results. Typically, those studies relied on (semi-)parametric statistical models like logistic regression. Those models impose strong assumptions on the functional grade of the relationship between outcome and case volume. The aim of this written report was to determine associations between in-infirmary mortality and infirmary case volume using random forest as a flexible, nonparametric machine learning method.

Methods

We analyzed a sample of 753,895 infirmary cases with stroke, myocardial infarction, ventilation > 24 h, COPD, pneumonia, and colorectal cancer undergoing colorectal resection treated in 233 German hospitals over the period 2016–2018. We derived partial dependence functions from random forest estimates capturing the relationship between the patient-specific probability of in-hospital death and hospital example volume for each of the half dozen considered patient groups.

Results

Across all patient groups, the smallest hospital volumes were consistently related to the highest predicted probabilities of in-hospital death. We establish stiff relationships between in-hospital bloodshed and infirmary case volume for hospitals treating a (very) minor number of cases. Slightly higher case volumes were associated with essentially lower bloodshed. The estimated relationships between in-hospital mortality and example book were nonlinear and nonmonotonic.

Conclusion

Our analysis revealed strong relationships between in-hospital mortality and hospital example volume in hospitals treating a pocket-sized number of cases. The nonlinearity and nonmonotonicity of the estimated relationships indicate that studies applying conventional statistical approaches like logistic regression should consider these relationships fairly.

Peer Review reports

Background

Volume-outcome relationships in inpatient intendance were investigated in a large number of studies for various patient groups [1,2,3,iv,5]. In research on patient outcomes in critical care and surgery, special accent has been placed on hospital mortality. Empirical analyses suggested that higher example volumes were related to lower mortality in patients with stroke [6, vii], acute myocardial infarction [8, 9], mechanical ventilation [10, 11], respiratory diseases [12, 13], and surgical interventions [fourteen,15,16,17,xviii,19]. However, show is inconclusive as the results of several studies bandage doubt on the proposed book-outcome associations [xx,21,22,23].

Typically, studies investigating relationships between case book and infirmary mortality applied (semi-)parametric statistical models similar logistic regression [four, 7, 10, 13]. A main advantage of those conventional approaches is that they facilitate adjustment for patient-specific chance factors while ensuring easily interpretable results in terms of effect sizes (e.g. due to estimation of odds ratios). Even so, this advantage comes at the price of flexibility in modeling book-issue relationships. Statistical models like logistic regression impose a specific functional form on the relationships betwixt event and covariates, including instance volume, east.g. via the logistic link office. This functional grade represents a strong assumption, peculiarly if case volume enters the regression every bit a continuous variable [2, 4]. In this instance, the relationship between the probability of outcome occurrence and case book is causeless to be logistic over the whole range of case volumes included in the data. Deviations from this assumption may result in biased estimates. Equally an alternative strategy, example book may be divided into groups, which then enter the regression as dissever indicator variables [2, vii, viii, 13]. Still, this approach involves the definition of thresholds for volume groups, which may be chosen in an capricious fashion. Importantly, inappropriate definition of those thresholds (e.yard. thresholds assigning also small or too large widths to specific book groups) may lead to inadequate results and conclusions.

Against that background, the objective of this study was to exploit advantages of random forest as a flexible, nonparametric motorcar learning method for estimating volume-consequence relationships. Random wood facilitates exploration of associations between in-infirmary mortality and hospital instance volume without presuming a specific functional relationship between outcome and risk factors. Instead, those relationships were explored by estimating partial dependence functions [24]. Inside the framework of the IMPRESS study ("Effectiveness of the IQM-PR procedure to improve in-patient care - a pragmatic cluster randomized controlled trial"), we aimed to determine associations between in-hospital bloodshed and hospital instance volume. Therefore, we analyzed a large sample of German hospital cases covering the menstruation 2016–2018. Based on random forest estimates, we derived fractional dependence functions capturing associations betwixt patient-specific probabilities of in-infirmary death and infirmary instance volume for patients with stroke, myocardial infarction, colorectal resection with cancer, ventilation > 24 h, COPD, and pneumonia.

Methods

The Print study

The IMPRESS study was a cluster-randomized controlled trial (cluster RCT) on the effectiveness of clinical peer review conducted in member hospitals of the German Initiative Qualitätsmedizin (IQM) on mortality in patients ventilated > 24 h. The cluster RCT was embedded in a prospective accomplice report, which provided the basis for exploratory analysis of adventure factors for in-infirmary bloodshed. Master consequence was in-hospital mortality in patients ventilated for more than 24 h. Secondary outcomes were in-hospital morality in patients with stroke, myocardial infarction, colorectal resection, COPD, and pneumonia. The report has been registered [25] and its procedures were described in particular elsewhere [26]. Here, we report exploratory results from the cohort study. Our analyses were based on data from 233 IQM member hospitals which agreed to participate in the Impress report, covering the period 2016–2018.

Outcome and patient groups

The outcome of this study was in-hospital bloodshed. Nosotros estimated relationships between in-hospital bloodshed and hospital case volume for patients with stroke, myocardial infarction, COPD, pneumonia, and patients with colorectal cancer undergoing colorectal resection. We identified these patients based on ventilation time, diagnoses co-ordinate to the German modification of the International Classification of Diseases (ICD-10-GM), and medical procedures co-ordinate to the Operation and Procedure Classification Organisation (OPS). Inclusion and exclusion criteria followed the corresponding German Inpatient Quality Indicators (G-IQI, version 5.0) [27] definitions (Tabular array 1). Parting from the 1000-IQI, we included patients with colorectal resection just if they had a documented diagnosis of colorectal cancer (ICD-10-GM: C18-C20) to ensure specificity and homogeneity of the underlying medical condition [eighteen, 19].

Table 1 Instance definitions

Total size table

Data sources and variables

The analysis was based on secondary data and did non involve human being participants. We gathered patient data of included IQM member hospitals co-ordinate to German law, §21 Krankenhausentgeltgesetz (KHEntgG). These data are collected by inpatient care providers for bookkeeping purposes and are harmonized at the national level. In addition, we used information on hospital characteristics from the German Hospital Directory (Deutsches Krankenhausverzeichnis).

Nosotros calculated yearly hospital instance volumes equally the number of patients with a specific indication (stroke, myocardial infarction, colorectal resection, ventilation > 24 h, COPD or pneumonia) treated in a specific hospital in a specific year. To accommodate for the influence of relevant patient characteristics, multivariable analyses included historic period (in years), sex (male; female person), and dummy variables for all 31 Elixhauser comorbidities [28]. In addition, nosotros used admission reason (referral; emergency case admission, transfer from other hospital) and intensive care unit (ICU) admission as proxies for urgency and disease severity. Regarding potentially relevant hospital characteristics, we accounted for urban/rural location (as defined by Bundesinstitut für Bau-, Stadt- und Raumforschung (BBSR) [29]), hospital ownership (public, non-turn a profit, private), and university infirmary condition.

Since the information sources provide full information on patient and infirmary characteristics, all participating hospitals and patients fulfilling the inclusion criteria could be included in our analysis.

Information protection and ethics

We obtained written consent on study participation from all included hospitals prior to the start of the IMPRESS study. The written report information trust site at Koordinierungszentrum für Klinische Studien (KKS) Dresden ensured anonymization of the data. These anonymized data were analyzed at the Eye for Evidence-Based Healthcare (ZEGV) Dresden. The ethics committee of the TU Dresden approved the study protocol on 24/04/2017 (registered at the Institutional Review Lath (IRB): Part for Human Enquiry Protections (OHRP); identification numbers: IRB00001473 and IORG0001076).

Statistical methods

Nosotros characterized the distributions of hospital and patient characteristics by accented and relative frequencies in case of chiselled variables and by median and 1st and 3rd quartile (Q1; Q3) in case of continuous variables. For descriptive analysis, nosotros divided hospital instance volumes into ten categories (ane–9; 10–19; twenty–49; 50–99; 100–199; 200–499; 500–999; 1000–1999 and 2000+). Hospitals with zero cases per considered grouping were excluded. The smaller widths assigned to categories capturing lower volumes reflect that volume-outcome relationships may exist more pronounced at smaller case volumes [30]. For each volume category, we calculated the raw mortality rate across all hospitals and used bar charts to visualize its relationship with case book.

Descriptive, bivariate analysis of relationships betwixt mortality and example volume may be subject to uncontrolled confounding. Nosotros therefore modeled patient-specific bloodshed run a risk conditional on all patient and infirmary characteristics outlined in a higher place. In contrast to conventional statistical approaches, we used random forest classifier [24, 31]. Random forest is a tree-based machine-learning algorithm that constructs a multitude of determination copse based on bootstrapped samples of the original data. As a nonparametric statistical method, random forest does not make assumptions on the functional form of the relationships between issue and covariates. Thus, it allows for flexible, information-driven exploration of those relationships and even captures circuitous interactions between covariates. Based on random forest results, relationships between the effect and specific covariates may be explored by estimating the partial dependence office [24]. The partial dependence part represents the effect of a specific covariate on the outcome after bookkeeping for average effects of the other covariates. Due to the flexibility of random forest, estimated partial dependence functions can be highly nonlinear and may even include discontinuities. Since the analysis was conducted at the patient-level, we calculated and visualized fractional dependence functions capturing relationships betwixt the average patient-specific probability of in-hospital death and infirmary case volume for all considered patient groups. Statistical analysis was performed using the packages "ranger" [32] and "pdp" [33] in R version 4.0.2 [34].

Sensitivity analyses

We assessed the robustness of our results in multiple sensitivity analyses (see supplementary material). These included 1) aligning for type or severity of the considered indication, 2) exclusion of individuals belonging to more one of the considered patient groups, 3) estimation of volume-outcome relationships for patients ventilated > 24 h with specific medical conditions (stroke, myocardial infarction, and COPD).

Results

Hospital and patient characteristics

The full dataset included 12,140,587 cases treated in the participating hospitals in the period 2016–2018 (come across flow chart provided in the supplementary fabric). 753,895 of these cases fulfilled the inclusion criteria for at to the lowest degree one patient group. The resulting sample covered a broad range of average yearly hospital case volumes, which differed between indications (Table 2). While the median case volume was lowest for colorectal resection (35 cases), the highest median case volume was observed for pneumonia (189 cases). Almost hospitals were located in urban areas and more than 40% were privately owned. The sample included 8 university hospitals. Mortality was highest in patients with ventilation > 24 (overall mortality rate: 32.9%) and lowest in patients with colorectal resection (overall mortality rate: iii.two%). The median age of patients ranged betwixt 69 years (ventilation > 24 h) and 77 years (pneumonia). Beyond all indications, men accounted for the majority of cases. Compared to the other patient groups, patients with ventilation > 24 h had the highest median number of Elixhauser comorbidities. Most patients with stroke, myocardial infarction, and pneumonia were admitted every bit emergency case. The share of emergency cases was 48.v% in patients with ventilation > 24 h, 47.7% in patients with pneumonia, and 17.1% in patients with colorectal cancer undergoing colorectal resection. ICU admission was well-nigh frequent in patients ventilated > 24 h (44.7%).

Table 2 Hospital and patient characteristics

Full size table

Descriptive relationships betwixt in-infirmary mortality and hospital instance volume

With 2000 or more cases per yr, the largest infirmary-volumes were observed for stroke and ventilation > 24 h (Table three). Calculating the boilerplate mortality rates by instance book for each indication did not reveal clear patterns (Fig. 1). For most patient groups, hospitals with small volumes were characterized by relatively loftier mortality rates. Notwithstanding, the evolution of bloodshed rates across volume groups was not-monotonic. There was an increment in mortality rates in hospitals belonging to the highest volume groups for stroke, myocardial infarction, colorectal resection, and pneumonia. Contrary trends of mortality rates in high-volume groups were found for ventilation > 24 h and COPD.

Table 3 Number of hospital-years and cases by indication and volume group

Full size tabular array

Fig. 1

Descriptive relationships between in-hospital mortality and hospital case volume

Total size image

Partial dependence functions based on random forest estimates

In contrast to descriptive evidence, the fractional dependence functions derived from random forest estimations revealed clear and qualitatively similar patterns across most patient groups (Fig. ii). Delight note that book- and probability-scales are specific to each subfigure. The strongest relationships betwixt in-hospital decease and hospital case volume were revealed for those hospitals treating a small number of cases. The smallest case volumes were consistently related to the highest patient-specific probabilities of in-hospital death. In all patient groups, slightly higher case volumes compared to these smallest case volumes were associated with substantially lower predicted probabilities of in-infirmary decease. Notably, the estimated fractional dependence functions were relatively smoothen although they were calculated pointwise for specific infirmary volumes. In relative terms, estimated differences betwixt the lowest and the highest average predicted probability of in-hospital death exceeded fifty% for all indications except for ventilation > 24 h. In instance of the latter, the maximum absolute difference in the volume-specific predicted probabilities of in-hospital decease was approximately 10 percentage points. The fractional dependence functions also indicated increases in the probability of in-infirmary death for instance volumes exceeding certain, indication-specific thresholds. Again, the only exception was ventilation > 24 h for which this upwards tendency in partial dependence at higher case volumes was not observed.

Fig. ii

Fractional dependence functions capturing the relationship between the probability of in-infirmary death and infirmary case volume derived from random forest estimates

Full size image

Sensitivity analyses

As shown in the supplementary material, the results remained qualitatively stable when adjusting for additional risk factors (type or severity of indication) and when excluding individuals belonging to more than one of the considered patient groups. Volume-result relationships establish for the total population of patients ventilated > 24 h were as well revealed in subgroups of ventilated patients with stroke, myocardial infarction, and pneumonia, respectively.

Discussion

Volume-event relationships in inpatient care were explored and discussed controversially in a multitude of studies. Typically, estimation of those relationships relied on (semi-)parametric statistical models. The two main strategies of handling case volume in those analyses - treating example book as continuous variable or defining book groups - either impose strong assumptions on the functional form of the relationship between outcome and volume or rely on the definition of arbitrary volume thresholds.

Using random forest as a flexible, nonparametric statistical method, this study contributes to the literature past providing real-globe evidence on book-consequence relationships for half dozen patient groups without presuming a specific functional form. Using a sample of more than than 230 German hospitals over the menstruum 2016–2018, our results consistently signal that hospitals with pocket-sized case volumes were characterized by the highest predicted probabilities of in-hospital decease in patients with stroke, myocardial infarction, colorectal resection, ventilation > 24 h, COPD and pneumonia. Estimated book-outcome relationships were specially pronounced in small-volume hospitals. Slightly college volumes were associated with substantially lower bloodshed in the group of hospitals treating a (very) small number of cases. Thus, our findings propose that peculiarly hospitals with very small-scale case volumes showed deficient performance. This finding is in line with previous studies on volume-outcome relationships in like clinical settings [2]. Although the estimated fractional dependence functions were calculated pointwise for specific hospital volumes, they were notably smooth for all patient groups. This supports the notion of systematic relationships betwixt in-hospital bloodshed and hospital case volume.

Moreover, our results show that book-outcome relationships were nonlinear and non-monotonic. Except for ventilation > 24 h, nosotros constitute that the boilerplate predicted probability of in-hospital decease increased with case volume subsequently reaching a certain, indication-specific threshold. A possible caption for this finding is that hospitals with very high case volumes may exist characterized by a patient population that systematically differs from those of hospitals with lower case volumes in terms of disease severity [35]. If patients treated in hospitals with very high volumes were characterized by systematically higher illness severity that was non fully captured by comorbidities and admission reasons included in our analysis, this incomplete adjustment may result in increasing predicted probabilities of in-hospital death for higher case volumes. The fact that this upward trend in high-volume hospitals was not observed for ventilation > 24 h may reflect that protective volume effects outweigh incomplete aligning for affliction severity for this indication. Since long-term ventilation is a highly difficile chore that places loftier demands on equipment, skills and capabilities of medical personnel [36], effect improvements resulting from increased treatment experience and expertise may saturate at afterward stages. A complementary explanation for the finding of increasing mortality at high case volumes is that loftier-volume hospitals often have multiple departments treating patients with the same indication. Equally a result, each of those departments only accounts for a certain share of full infirmary volume. The existence of multiple departments may exist related to heterogeneity in operation and increment the risk of misallocation of patients, which, in turn, may exist reflected in higher mortality.

Strengths and limitations of this study

A main strength of this study is the assay of data on more than 753,000 cases of patients treated in more 230 hospitals covering the menstruum 2016–2018. This wide dataset allowed for reliable nonparametric estimation of volume-effect relationships for six indications. By using a nonparametric machine-learning approach, our study complements conventional statistical approaches to estimate volume-outcome relationships and, thus, likewise makes an important methodological contribution to the literature.

Every bit a chief limitation, our results do not support a causal interpretation due to the use of secondary, observational information. In fact, the estimated partial dependence functions reflect the relation of predicted patient outcomes to infirmary instance book. Since experimental studies on volume-effect relationships are difficult to realize, this limitation is shared with the vast majority of related studies.

For descriptive analysis, we divided infirmary volumes into volume groups. Equally already mentioned above, definition of those book groups is arbitrary and different definitions may have led to different descriptive evidence on the relationship between in-hospital mortality and infirmary volume. To overcome this shortcoming, we practical random woods, which does not rely on definition of volume groups and does not impose a specific functional form on the relationship between in-hospital mortality and hospital example volume. A limitation of random forest analysis is that it does non accept the multilevel nature of the information (i.eastward. nesting of patients inside hospitals) into account. Consequently, nosotros could not derive valid uncertainty estimates (east.chiliad. confidence intervals) for partial dependence functions. Although hospitals with pocket-size instance volumes were consistently characterized by the highest mortality estimates, these estimates are based on a relatively pocket-size number of patients treated in these hospitals. This relatively modest number of patients may induce low precision of partial dependence estimates that cannot be captured past our methodological approach. Still, the fact that nosotros estimated the highest mortality rates for minor-book hospitals across all six considered indications suggests reliability of our findings. Moreover, missing doubt estimates practise non affect the validity of the signal estimates of the partial dependence functions, which allowed us to explore relationships between in-infirmary mortality and case book in a flexible way.

Our data do non include all possibly relevant hospital characteristics similar team/surgeon volumes [37], information apropos certifications [38,39,40], staffing, and qualification [41]. This is likewise true with respect to patient-specific chance factors. This may result in incomplete adjustment in the framework of statistical analysis and may explain the estimated upward trend in the fractional dependence between in-hospital mortality and instance volume for the largest hospitals in our sample. Withal, our results remained robust confronting inclusion of additional, indication-specific adventure factors available in our data and the exclusion of patients belonging to more one of the considered patient groups (run into supplementary material). Since the focus of our analysis was on hospital volume, nosotros did not account for the existence of multiple specialized departments in high-volume hospitals. Consequently, we could not capture intra-hospital heterogeneity in terms of volume and, mayhap, performance.

Coding bias and differences in coding practices between hospitals may limit the validity of our results [42, 43]. Nonetheless, this limitation is simply relevant to the extent as coding practices are systematically related to infirmary case volume. Since this report focused on mortality, nosotros did not consider other relevant patient outcomes. The main advantage of using mortality as outcome is that data on in-hospital death has high validity. Extending this assay to outcomes other than mortality would crave careful exam and discussion whether these outcomes can exist operationalized with sufficient validity using administrative hospital data [44]. Finally, our assay did not signal causes of the estimated volume-outcome relationships. In addition to learning-by-doing, such relationships may be explained past selective referral [45]. Gaining a deeper agreement of the underlying causes therefore is an of import chore for further research.

Conclusions

The results of this report support previous evidence on the beingness of volume-upshot relationships in inpatient intendance of patients with stroke, myocardial infarction, ventilation > 24 h, COPD, pneumonia, and patients with colorectal cancer undergoing colorectal resection. From a policy perspective, these results suggest that patient outcomes may be systematically worse in pocket-sized-volume hospitals and, thus, support arguments for centralization or regionalization of care of specific patient groups [46, 47].

The nonlinearity, nonmonotonicity, and indication-specific shape of the estimated relationships suggest that hereafter studies should pay special attention to the valid specification of statistical models. We found the most pronounced volume furnishings at small case volumes. Hence, equally a general recommendation, empirical studies using (semi-)parametric methods similar logistic regression should assign simply small widths to low-volume groups or use appropriate transformations of volume data to model these relationships adequately.

To assess the generalizability of our findings, additional studies applying flexible estimation of volume-issue relationships in similar settings would be valuable. Further indication-specific evidence on the shape of relationships between in-hospital mortality and example volume would exist an of import contribution to the literature and may let for derivation of robust implications for targeted improvement of hospital outcomes. This may include reliable, indication-specific estimation of volume thresholds for sufficiently high outcome quality.

Availability of information and materials

Information are not publicly available due to legal restrictions (German law). The data sets used and/or analyzed during the current study are bachelor from the corresponding author on reasonable request.

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Acknowledgements

The authors thank Jochen Strauß, Claudia Winklmair, the IQM executive lath, and all participating hospitals.

Funding

Open Access funding enabled and organized past Projekt DEAL. The IMPRESS study was funded by the Innovation Fund of the Articulation Federal Commission (Gemeinsamer Bundesausschuss, G-BA), Germany. Funding number: 01VSF16013.

Author information

Affiliations

1. Center for Prove-based Healthcare, Academy Infirmary Carl Gustav Carus and Medical Faculty at the Technische Universität Dresden, Fetscherstr. 74, 01307, Dresden, Frg

   Martin Roessler, Felix Walther, Jochen Schmitt & Olaf Schoffer

2. Quality and Medical Adventure Management, University Hospital Carl Gustav Carus Dresden, Dresden, Germany

   Felix Walther & Maria Eberlein-Gonska

3. IQM Initiative Qualitätsmedizin e.V., Berlin, Germany

   Peter C. Scriba & Ralf Kuhlen

Contributions

MR and OS designed the modeling strategy. MR conducted the empirical analysis. FW and JS, 1000000, PC, and RK contributed to interpretation and discussion of findings and revised drafts of the manuscript. All authors read and canonical the final manuscript.

Corresponding writer

Correspondence to Martin Roessler.

Ethics declarations

Ideals approval and consent to participate

The ethics commission of the TU Dresden approved the study protocol on 24/04/2017 (registered at the Institutional Review Board (IRB): Role for Human Inquiry Protections (OHRP); identification numbers: IRB00001473 and IORG0001076). We obtained consent to participate from the included hospitals earlier the kickoff of the Impress written report. Due to the employ of secondary, routine care information, patient consent to participate was not required every bit confirmed past the ideals committee of the TU Dresden (reference number: EK 186052017). The study adheres to all relevant ethical standards and guidelines, including the Declaration of Helsinki, the Memorandum on the Balls of Good Scientific Exercise of the German Inquiry Foundation (Deutsche Forschungsgemeinschaft, DFG), the Memorandum 3 "Methoden für die Versorgungsforschung" of the Deutsches Netzwerk Versorgungsforschung and the guideline "Skillful practice secondary data analysis" (GPS) of the German Society for Epidemiology (Deutsche Gesellschaft für Epidemiologie, DGEpi) [48].

Consent for publication

Not applicable.

Competing interests

Peter C. Scriba and Ralf Kuhlen are members of the scientific advisory lath of IQM. Maria Eberlein-Gonska serves as an external practiced for IQM. The other authors declare that they accept no disharmonize of involvement.

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Supplementary Information

Additional file 1: Tabular array S1

: Additional, indication-specific risk factors. Effigy S1: Partial dependence functions capturing the human relationship betwixt the probability of in-hospital death and hospital instance volume derived from random forest estimates including boosted, indication-specific risk factors. Table S2: Cases excluded due to membership in multiple patient groups. Figure S2: Fractional dependence functions capturing the human relationship between the probability of in-hospital death and infirmary case book derived from random wood estimates excluding cases belonging to multiple patient groups. Figure S3: Partial dependence functions capturing the relationship between the probability of in-hospital death and hospital case volume derived from random forest for patients ventilated > 24 h with specific indications.

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Roessler, M., Walther, F., Eberlein-Gonska, M. et al. Exploring relationships betwixt in-hospital bloodshed and hospital instance volume using random forest: results of a cohort written report based on a nationwide sample of German language hospitals, 2016–2018. BMC Health Serv Res 22, 1 (2022). https://doi.org/10.1186/s12913-021-07414-z

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• Received: 20 April 2021

• Accepted: 14 December 2021

• Published: 02 Jan 2022

• DOI : https://doi.org/x.1186/s12913-021-07414-z

Keywords

• Hospital mortality
• Volume-outcome relationship
• Accomplice study
• Gamble factors
• Random Forest
• Nonparametric modelling

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