Identification of antibiotic consumption targets for the management of Clostridioides difficile infection in hospitals- a threshold logistic modelling approach

ABSTRACT

Background

This study aims to demonstrate the utility of a threshold logistic approach to identifying thresholds for specific antibiotic use associated with Clostridioides difficile infection (CDI) in an English teaching hospital.

Methods

A combined approach of nonlinear modeling and logistic regression, named threshold logistic, was used to identify thresholds and risk scores in hospital-level antibiotic use associated with hospital-onset, healthcare-associated (HOHA) CDI cases.

Results

Using a threshold logistic regression approach, an incidence greater than 0.2645 cases/1000 occupied bed-days (OBD; 85th percentile) was determined as the cutoff rate to define a critical (high) incidence rate of HOHA CDI. Fluoroquinolones and piperacillin-tazobactam were found to have thresholds at 84.8 and 54 defined daily doses (DDD)/1000 OBD, respectively. Analysis of data allowed calculating risk scores for HOHA CDI incidence rates exceeding the 85th percentile, i.e. entering critical incidence level. The threshold-logistic model also facilitated performing ‘what-if scenarios’ on future values of fluoroquinolones and piperacillin-tazobactam use to understand how HOHA CDI incidence rates may be affected.

Conclusion

Using threshold logistic analysis, critical incidence levels and antibiotic use targets to control HOHA CDI were determined. Threshold logistic models can be used to inform and enhance the effective design and implementation of antimicrobial stewardship programs.

KEYWORDS:

• Antibiotic consumption
• antimicrobial resistance
• threshold logistic
• Clostridioides difficile infection
• predictive models
• antimicrobial stewardship

1. Introduction

Clostridioides difficile infection (CDI) is a leading nosocomial infection, causing an increased burden on health-care systems and incurring significant direct and indirect costs [1–3]. Clostridioides difficile (C. difficile) is an anaerobic spore-forming bacterium that colonizes the large intestine and is transmitted among humans through the fecal – oral route [4]. C. difficile can cause conditions ranging from mild diarrhea to toxic megacolon, colonic perforation, and death and is associated with longer hospital stays and readmissions [2–5]. This bacterium can also be carried asymptomatically in the gut, providing a potential reservoir for onward transmission in health-care facilities [5]. Risks of CDI transmission in health-care setting and acquisition by patient are multifactorial. National UK guidelines on infection prevention and control and management of CDI inform hospital policies and high preventative standards. Important factors that increase the risk of CDI acquisition include antibiotic exposure, advanced age, underlying morbidity, and longer health-care admissions [4–9]. Of importance, antibiotic exposure remains an important modifiable risk factor for the CDI [4,8]. Antibiotic use can cause changes in the natural balance of indigenous colonic microbiota, leading to C. difficile proliferation [5]. A recent systematic review and meta-analysis updating the synthesis of evidence in relation to the risk of health-care facility-associated CDI showed that recent exposure to carbapenems, third- and fourth-generation cephalosporins, fluoroquinolones, clindamycin, and beta-lactamase inhibitor combination penicillin antibiotics was observed prior to developing CDI case [8].

Antimicrobial stewardship (AMS) aims to improve antibiotic prescribing in health-care settings. Balancing access to effective antimicrobials with the prevention of the emergence of antibiotic resistance is challenging. Complete restrictions of certain antibiotics in clinical practice require significant efforts to implement and may select for other resistance mechanisms due to the need to compensate with other antibiotics [10]. In a number of evaluations of the relationship between antibiotic use and resistance, analysis of data showed non-linear relationships and allowed determining a threshold of antibiotic use beyond which resistance would be triggered [11–16]. Recently, Aldeyab and Lattyak introduced a threshold-logistic modeling concept to improve our understanding of the relationship between antibiotic use and the incidence of resistant pathogens [17,18]. The threshold-logistic approach is a combination of nonlinear modeling and logistic regression, which we used to identify thresholds and risk scores in hospital-level antibiotic use associated with incidence rates of extended-spectrum β-lactamase (ESBL) producing Escherichia coli (E. coli), and meticillin-resistant Staphylococcus aureus (MRSA) [17,18]. For ESBL-producing E. coli and MRSA, we demonstrated a way to facilitate near real-time feedback on the effectiveness of antimicrobial stewardship models, and we provided an opportunity to perform ‘what-if scenarios’ using different levels of antibiotic use to assess the expected impact on pathogen incidence rates in future months [17,18].

This study aims to demonstrate the utility of the recently developed threshold logistic approach in identifying thresholds for specific antibiotic use in association with CDI in one teaching hospital in England. We used data from the same population for which we previously examined the incidence of ESBL-producing E. coli and MRSA [17,18]. This is to show a case for mapping high-risk antibiotics against important pathogens in one hospital, therefore, providing relevant antibiotic use targets and tailored recommendations to inform AMS.

2. Methods

2.1. Study design and population

The study took place at Pinderfields General Hospital (PGH) (700 beds), Mid Yorkshire Teaching NHS Trust in West Yorkshire, England. The Trust, with three hospital sites including PGH, cares for nearly 500,000 people, providing medical and surgical services, intensive care, hematology/oncology, regional burns and spinal injuries units, and community services. The study included only adult inpatients admitted to PGH. Data were retrospectively collected for the study period from January 2015 to December 2021. The analysis methods for this study required a minimum of 5 years of monthly antibiotic use and microbiology data [17,18]. Considering the availability of the longest period of consistent antibiotic use and CDI data, the study analyzed 7 years of monthly data. We hypothesized that using carbapenems, second- and third-generation cephalosporins, fluoroquinolones, co-amoxiclav, piperacillin-tazobactam, macrolides, and clindamycin could explain variations in CDI incidence rates. These antibiotics were identified a priori based on published evidence of their role as risk factors for driving the incidence of CDI in health-care settings [8,9].

2.2. Microbiology and pharmacy data

A CDI case was defined as any adult inpatient (≥18 years), who was admitted to PGH between 1 January 2015 and 31 December 2021, and who had three or more episodes of loose stools (diarrhea) and fecal samples, conforming to Bristol Stool Chart 5–7 (essentially taking the shape of the container) with positive glutamate dehydrogenase (GDH) and toxin test for C. difficile during their admission. As per the hospital policy, stool samples must only be submitted for testing once an assessment has been undertaken to determine if any other cause (such as laxatives, enemas, or other preparations to stimulate the bowel, enteral feeding, inflammatory colitis, overflow, bowel disorders, bowel surgery, and medication) for diarrhea (Bristol stool chart type 5–7) is excluded. The hospital laboratory standard operating procedure mandates testing only samples that confirm to Bristol Stool Chart 5–7; laboratory reports both non-C. difficile infectious causes of diarrhea and C. difficile PCR and toxin. Only hospital-onset, healthcare-associated (HOHA) CDI cases were included for this study. HOHA CDI was defined as any NHS patient with diarrhea and fecal specimens taken on the third day of admission onwards (i.e. ≥day 3 when the day of admission is day 1). Duplicated positive cases were excluded, and an isolate from the same patient identified within 30 days of a previous isolate with the same identification was considered as the same case. An infection control software (ICNET; Clinical Surveillance Software NG 1.7.1.0, Baxter International Inc., UK) was used to obtain this data.

The hospital pharmacy information systems were used to obtain monthly antibiotic use data. The classification of antimicrobials for systemic use (J01) in the WHO/ATC index was used, and antibiotic data were then converted into Defined Daily Doses (DDD) and were expressed as DDD per 1000 occupied bed-days (OBD) [19].

2.3. Modelling and statistical analysis

Threshold-Logistic analysis was applied in modeling the relationship between antibiotic use and an elevated level of HOHA CDI [17,18]. Antibiotics suspected to increase the incidence rate of the studied pathogen were initially considered. HOHA CDI incidence rate was used as our response variable. Upon completing this initial analysis phase, we identified candidate antibiotic series with lagged positive cross-correlation to HOHA CDI incidence rates that were statistically significant at the 10% level or better (p ≤ 10). The latter significance level was chosen to perform an initial variable selection of candidate explanatory variables (univariate methods). Lags of 1–5 months were considered when examining the linear association of antibiotic usage with increased pathogen incidence rate. The maximum cross-correlation value was used to choose the optimal lag for the antibiotic series to be considered as candidate explanatory variables in this screening stage of drivers. In the next phase, we applied a threshold search algorithm to identify break points in levels of the candidate antibiotic series that resulted in an increased response over the overall linear relationship. By doing so, we expanded our individual candidate antibiotic series with a threshold dimension.

In the final analysis phase, we applied a multi-dimensional threshold-logistic search algorithm that evaluated the combination of all candidate antibiotic series, with respect to their potential lag and threshold adaptations; potential multicollinearity was tested. Since we applied a logistic approach, the HOHA CDI incidence rate was transformed into a binary event. This was accomplished within the multi-dimensional threshold-logistic search algorithm that partitioned the HOHA CDI incidence rate by various percentiles, specifically between the 50th and 85th percentiles, in search of the greatest separation of the binary class (1 = exceeding cutoff; 0 = below cutoff) and best classification accuracy. The 50th–85th percentiles were selected as a plausible target since this target would be defined in the upper 50% of the historical data and would include enough observations so as not to be considered a rare event. Akaike information criterion (AIC) and area under the curve (AUC) from the receiver operator characteristic (ROC) curve were used to select the 85th percentile (0.2645) of HOHA CDI as the critical level, defining the binary event as

Event = Ifelse (CDI incidence rate ≥ 0.2645, 1, 0).

It was at this cutoff for the binary event that dominated classification performance for both accuracy and number of modeled results in the top decile of accuracy measures.

The possible impact of COVID-19 pandemic was also considered in the model by introducing a binary dummy variable consisting of 0’s prior to April 2020 and 1’s thereafter. The estimation of the threshold-logistic model has shown the impact of the COVID-19 pandemic period to be statistically insignificant at the 5% level.

After identifying and estimating the final threshold-logistic model, predicted probabilities (risk scores) of the threshold logistic regression model were generated. A coded alert signal (High, Medium, or Low risk) was created based on the MinMax transformation of the predicted probabilities (risk score) coming from the threshold logistic model.

$Z=\frac{prob-min\left(prob\right)}{max\left(prob\right)-min\left(prob\right)}$

This MinMax transformation is helpful to produce a heuristic alert signal (High-Med-Low) for policy purposes that categorize risk scores from unbalanced classification data. To maximize the overall distribution accuracy of a low signal, classifying an infection rate as being below the 85th percentile, and a high signal classifying an infection rate as being greater than the 85th percentile, we computed the cutoff ranks using a linear programming (LP) technique. To define Low, Medium, and High coded alert signals, the cutoff ranks optimized through LP were 0.0 to ≤0.30, >0.30 to <0.84, and ≥0.84 to 1.0, respectively. For the purpose of estimating the reduction in studied pathogens resulting from antibiotic use maintained below threshold values, the weighted difference between the mean incidence rates relative to antibiotic use threshold criteria (subgroups) was used. A 95% confidence range on the expected reduction of pathogen incidence rate was reported by computing the standard error of the mean (SEM) for each subgroup along with the standard error between paired subgroup means.

The SCA Statistical System version 8.2 (Scientific Computing Associates Corp., River Forest, Illinois, USA) and R software version 4.3.0 (R Foundation for Statistical Computing, Vienna, Austria) were used to perform analysis.

3. Results

Over the study period, 260 non-duplicated HOHA CDI cases were identified. The average monthly HOHA CDI incidence rate was 0.154 cases/1000 OBD (range: 0.00–0.500). Average fluoroquinolone use was 67.2 DDD/1000 OBD (range: 37.4–123.0), and average piperacillin-tazobactam use was 57 DDD/1000 OBD (range: 14.07–86.16). A plot of the relationship between the use of fluoroquinolones and piperacillin-tazobactam and the incidence of HOHA CDI cases is shown in Figures 1 and 2.

Figure 1. Monthly hospital-onset, healthcare-associated (HOHA) incidence (thick line, no. Of cases/1000 OBD) versus use of fluoroquinolones (thin line, DDD/1000 OBD), January 2015 to December 2021.

Figure 2. Monthly hospital-onset, healthcare-associated (HOHA) incidence (thick line, no. Of cases/1000 OBD) versus use of piperacillin-tazobactam (thin line, DDD/1000 OBD), January 2015 to December 2021.

3.1. Defining critical (high) HOHA CDI incidence as the binary event

Applying threshold logistic regression in a search algorithm, the 85th percentile (0.2645 cases/1000 OBD) of HOHA CDI incidence was selected as the cutoff percentile to define the critical (high) incidence rate (Figure 3).

Figure 3. The empirical cumulative distribution function for hospital-onset, healthcare-associated (HOHA) CDI historical data. The solid vertical line represents the 85th percentile (0.2645 cases/1000 OBD).

The impact of the COVID-19 pandemic on HOHA CDI was found to be insignificant (coefficient = 1.2209; p = 0.0787), and it was removed from the models to maintain parsimony.

3.2. Identified risk antibiotics and targeted consumption rates

Threshold logistic analysis showed that fluoroquinolones and piperacillin-tazobactam exhibited thresholds at 84.8 and 54 DDD/1000 ODB, respectively (Table 1). The model showed that for every one-unit increase in fluoroquinolone and piperacillin-tazobactam use above 84.8 and 54 DDD/1000 OBD, the average odds of HOHA CDI incidence rate exceeding the 85th percentile of historical levels increased by 13.1% and 10.3%, respectively (Table 1). The AUC measure for the ROC curve was 71% (Figure 4). Figure 5 shows the cumulative CDI incidence rates relative to fluoroquinolones and piperacillin-tazobactam being above or below their respective thresholds.

Figure 4. Receiver operator characteristic (ROC) chart showing the true positive classification rate against the false positive classification rate at different probability cutoff thresholds. The area under the curve (AUC) is an aggregate measure of performance across all possible classification thresholds.

Figure 5. The cumulative CDI incidence rates relative to fluoroquinolone and piperacillin-tazobactam use being above or below their respective thresholds.

Table 1. Threshold logistic results in modeling hospital-onset, healthcare-associated (HOHA) CDI incidence rate at the 85^th percentile, January 2015 to December 2021.

Predictor variable	Lag	Median (IQR)	Threshold (95% Confidence Limit)*	Relation to threshold	Coefficient (95% CI)	p-value	Odds Ratio (95% CI)
Constant	NA	NA	NA	NA	−2.849 (−4.010 to −1.687)	0.0034	0.058 (0.018 to 0.185)
Fluoroquinolones use (DDD/1000 OBD)	3	64.43 (53.58 to 76.39)	84.82 (83.25 to 84.82)	Above	0.123 (0.017 to 0.228)	0.0226	1.131 (1.017 to 1.256)
Piperacillin-tazobactam use (DDD/1000 OBD)	1	59.55 (48.48 to 67.50)	53.99 (43.80 to 70.08)	Above	0.098 (0.020 to 0.176)	0.0137	1.103 (1.020 to 1.192)

*95% confidence limit around the optimized threshold value derived using a one-at-a-time (OAT) sensitivity analysis approach; IQR, interquartile range; NA, not applicable.

3.3. Near real-time performance monitoring and feedback

The risk scores for 2020 and 2021, which were determined using the threshold logistic analysis for HOHA CDI incidence rates exceeding the 85th percentile (0.2645 cases/1000 OBD), are shown in Table 2. Probability risk scores were coded using three alert signal levels (Low, Medium, and High; Table 2).

Table 2. Risk scores for CDI incidence rate exceeding the 85th percentile for 2020 and 2021.

Date	HOHA CDI (cases/1000 OBD)	Fluoroquinolones use (DDD/1000 OBD) at Lag 3	Piperacillin- tazobactam (DDD/1000 OBD) at Lag 1	HOHA CDI Observed Above Median (0.1268 (cases/1000 OBD)	HOHA CDI Observed Above 85th Percentile (0.2645 (cases/1000 OBD)	Predicted Probability HOHA CDI > 85th Percentile	Coded Alert Signal
January 2020	0.3124	75.3486	51.5024	Above	Above	0.0548	Low
February 2020	0.0989	61.4988	53.0375	Below	Below	0.0548	Low
March 2020	0.1116	81.3046	55.5658	Below	Below	0.0633	Medium
April 2020	0.1536	81.9790	62.8667	Above	Below	0.1215	Medium
May 2020	0.0630	58.8139	70.0846	Below	Below	0.2190	Medium
June 2020	0.3647	96.5792	59.3821	Above	Above	0.2941	Medium
July 2020	0.3332	108.5938	59.7163	Above	Above	0.6531	High
August 2020	0.0534	61.1416	57.9710	Below	Below	0.0788	Medium
September 2020	0.0550	72.5963	53.9901	Below	Below	0.0548	Low
October 2020	0.2519	60.0117	54.9952	Above	Below	0.0601	Medium
November 2020	0.2516	51.1270	60.1860	Above	Below	0.0961	Medium
December 2020	0.1974	78.5231	61.9743	Above	Below	0.1124	Medium
January 2021	0.0944	58.2552	66.1878	Below	Below	0.1607	Medium
February 2021	0.3146	59.6880	59.7643	Above	Above	0.0926	Medium
March 2021	0.2520	52.6965	61.8441	Above	Below	0.1112	Medium
April 2021	0.1062	54.5710	69.8339	Below	Below	0.2149	Medium
May 2021	0.1452	37.3735	73.1200	Above	Below	0.2741	Medium
June 2021	0.0973	93.3579	63.6442	Below	Below	0.2987	High
July 2021	0.2843	68.8383	80.6035	Above	Above	0.4402	High
August 2021	0.1784	52.7838	67.7126	Above	Below	0.1819	Medium
September 2021	0.2323	59.8199	64.5071	Above	Below	0.1397	Medium
October 2021	0.4859	71.2120	70.4928	Above	Above	0.2260	Medium
November 2021	0.2748	50.1003	67.0806	Above	Above	0.1728	Medium
December 2021	0.5006	57.0937	83.6626	Above	Above	0.5148	High

HOHA: hospital-onset, healthcare-associated; CDI: Clostridioides difficile infection; DDD: defined daily doses; OBD: occupied bed-days.

3.4. HOHA CDI incidence projections

The threshold-logistic model included lagged relationships between antibiotic use and CDI incidence rate. This facilitated an opportunity to use the model to perform ‘what-if scenarios’ on future values of fluoroquinolone and piperacillin-tazobactam use to understand how the expected CDI incidence rate may change. In our example, the last historical observation for CDI incidence rate was December 2021. The risk score and coded alert signal were already predicted by the model for January 2022 which was based on fluoroquinolone use in October 2021 (lag 3) and piperacillin-tazobactam use in December 2021 (lag 1). It was a high alert signal, and although we were unable to affect the risk score, there would be a month based on the prediction to prepare mitigation responses to an increased level of infection. The model also had the information on fluoroquinolone use to predict risk scores for February and March 2022, but it does not yet have information on piperacillin-tazobactam use. This allowed the opportunity to permutate values for piperacillin-tazobactam use and evaluate its scenario effect on risk. Since piperacillin-tazobactam use has a one-month lag in the model, antibiotic use for January 2022 (not yet realized) and its effect on CDI incidence rate in February 2022 and subsequent months could be explored.

In Table 3, we reviewed the result of a ‘what-if scenarios’ for February 2022, with piperacillin-tazobactam use set to 55 (DDD/1000) for January 2022 (Lag 1), and fluoroquinolone use in November 2021 (Lag 3, 66.4040) already known. This resulted in a Medium alert signal with a 6% probability that HOHA CDI incidence rate may exceed the 85^th percentile. Risk scores are shown for March and April 2022, controlling for levels of antibiotic use. If piperacillin-tazobactam use was maintained below the recommended threshold of 53.99 DDD/1000 OBD in February 2022 and given that fluoroquinolone use in December 2021 was below the recommended threshold of 84.82 DDD/1000 OBD, we could reduce the probability of a critical increase in HOHA CDI rate for March 2022. In contrast, a high coded alert signal was produced if we allowed fluoroquinolone use in January 2022 (Lag 3) and piperacillin-tazobactam use in March 2022 (Lag 1) to exceed thresholds.

Table 3. What-if threshold logistic model exploration.

Date	Fluoroquinolones use (DDD/1000 OBD) at Lag 3*	Piperacillin- tazobactam (DDD/1000 OBD) at Lag 1*	Predicted HOHA CDI Level	Predicted HOHA CDI Level + 1 Standard Deviation (SD)	Predicted Probability HOHA CDI > 85th Percentile	Coded Alert Signal
January 2022	73.7587	86.1628	0.2178	0.2381	0.5755	High
February 2022	66.4040	55.0000	0.1282	0.1486	0.0601	Medium
March 2022	75.1536	53.0000	0.1253	0.1457	0.0548	Low
April 2022	94.0000	63.0000	0.1877	0.2080	0.3020	High

*The cells that are highlighted in bold fonts represent months where we can substitute a range of possible lagged fluoroquinolone and piperacillin-tazobactam values since they have not yet been observed in the data history.

3.5. Case reduction estimates for HOHA CDI

We segmented HOHA CDI incidence rates using the antibiotic thresholds from the model and compared the difference in monthly means. Table 4 shows the incremental reduction in incidence rate when antibiotic use was maintained below the identified thresholds. The number of months in which historic antibiotic use was above or below threshold conditions is provided in the months column and the associated HOHA CDI average for the threshold condition is provided in the HOHA CDI (mean) column. The difference in HOHA CDI averages being above or below the threshold condition is also displayed. In order to compute the weighted difference in HOHA CDI average and the expected reduction in HOHA CDI cases for 2021, the number of months was converted into a proportion. The proportion of months in which fluoroquinolone use was less than or equal to the threshold was 85.2% compared to fluoroquinolone use greater than the threshold, which was 14.8%. These proportions were then normalized (41.1% + 18.6% + 40.2% = 100%). The weighted reduction in HOHA CDI mean (0.0485) was then computed using the sum product of the difference in means and the normalized proportion of months in which the threshold condition was observed. Finally, the expected reduction in HOHA CDI cases for 2021 was computed by multiplying the 63 reported HOHA CDI cases in 2021 with the 0.0485 weighted reduction in HOHA CDI rate.

Table 4. HOHA CDI incidence rate distribution when antibiotic use is below/above thresholds.

	Months	Months (%)	Normalized Months (%)	HOHA CDI (Mean)	HOHA CDI (SEM)^†	Difference in HOHA CDI Mean (σ)*	Expected Reduction in HOHA CDI Cases for 2021 (95% CI)**
Fluoroquinolones use (DDD/1000 OBD) ≤ threshold	69	85.2%	41.1%	0.151	0.012
Piperacillin-tazobactam use (DDD/1000 OBD) ≤ threshold	32	38.6%	18.6%	0.129	0.013
Both Antibiotics ≤ threshold	25	83.3%	40.2%	0.136	0.015
Fluoroquinolones use (DDD/1000 OBD) > threshold	12	14.8%	15.9%	0.167	0.034	0.016	0.16
Piperacillin-tazobactam use (DDD/1000 OBD) > threshold	51	61.4%	66.1%	0.168	0.016	0.038	1.59
Both Antibiotics > threshold	5	16.7%	17.9%	0.251	0.054	0.115	1.30
						4.85% (0.82%)	3.06 (2.04 to 4.07)

*σ is the estimated standard error.

**63 HOHA CDI cases reported in year 2021.

^†SEM is the standard error of the mean.

It was estimated that the number of cases could have been reduced by 3.06 with 95% CI (2.04 to 4.07) if antibiotics were maintained below identified thresholds. This represents a potential 4.85% (standard error (σ) = 0.82%) reduction in HOHA CDI cases.

3.6. Case reduction estimates for ESBL-producing E. coli and MRSA [17,18]

For the purpose of estimating the reduction in the incidence of studied pathogens in this hospital, Table S1 and Table S2 show the incremental reduction in the incidence of the previously examined ESBL-producing E. coli and MRSA incidence rates when antibiotic use was maintained below the identified thresholds [17,18]. It was estimated that the number of ESBL-producing E. coli and MRSA cases could have been reduced by 2.93 with 95% CI (2.08–3.77) and 1.70 with 95% CI (0.47–2.94), respectively, if the antibiotics were maintained below identified thresholds. This represents a potential 4.12% (σ = 0.60%) and 3.04% (σ = 1.12%) reduction in ESBL-producing E. coli and MRSA cases, respectively.

3.7. Overall case reduction estimates

The overall reduction in the incidence of pathogens, including HOHA CDI, ESBL-producing E. coli, and MRSA, is shown to be a combined 12.02% (σ = 2.54%) (Table 5) if the antibiotic use were maintained below identified thresholds.

Table 5. Estimated reduction in the number of cases of studied pathogens.

Pathogens	Total Cases in 2021	Expected Reduction in Cases	Expected Mean Incidence Reduction (σ)**
HOHA CDI	63	3	4.85% (0.82%)
MRSA	56	2	3.04% (1.12%)
Reduction in gram positives (HOHA CDI and MRSA)*			7.90% (1.94%)
ESBL-producing E. coli	71	3	4.12% (0.60%)
Overall reduction in the studied pathogens*			12.02% (2.54%)

*The reduction is weighted by the number of cases for each pathogen.

**σ is the estimated standard error.

4. Discussion

In this study, we aimed to identify thresholds for specific antibiotic use in association with HOHA CDI in hospitalized patients and to determine the probability of a hospital reaching a critical level of HOHA CDI in advance of such an event occurring. The findings showed that fluoroquinolones and piperacillin-tazobactam were associated with the incidence of HOHA CDI. The other assessed antibiotics were eliminated in the variable selection process because they could not be shown to have a statistically significant impact on CDI incidence rate. Using a threshold logistic regression approach, an incidence greater than 0.2645 cases/1000 OBD (85th percentile) was determined as the cutoff rate to define the critical (high) incidence rate of HOHA CDI. Threshold logistic analysis showed that fluoroquinolones and piperacillin-tazobactam were found to have thresholds at 84.8, and 54 DDD/1000 OBD, respectively, significantly increasing the probability of high pathogen incidence rate. Analysis of data allowed calculating risk scores for HOHA CDI incidence rates exceeding the 85^th percentile, i.e. entering high incidence level. The threshold-logistic model also facilitates performing ‘what-if scenarios’ on future values of fluoroquinolones use and piperacillin-tazobactam use to understand how HOHA CDI incidence rate may be affected.

CDI is commonly associated with the use of certain antibiotics. The antibiotic use disrupts the indigenous microflora of the colon, allowing C. difficile to overgrow and produce toxins [5]. The findings of this study were consistent with other published research that documented the association between fluoroquinolones, piperacillin-tazobactam, and the incidence of CDI [8,9]. Both fluoroquinolones and piperacillin-tazobactam are classified as Watch antibiotics (crucial for human medicine and at higher risk of resistance) according to the WHO Access, Watch, Research (AWaRe) classification [20]. These antibiotics should be subjected to close monitoring by the hospital AMS management team and their use should be reduced where appropriate (https://adoptaware.org/). However, it is important to consider the balance between how far we can reduce the use of these antibiotics to control resistance while we still provide access to them and avoid over-restriction undesirable effect [10].

In this study, a two-stage approach was used to determine relevant quantitative targets to limit identified antibiotic use and control HOHA CDI incidence rate. Firstly, a threshold value is an inflection point that is the start of an accelerated change in the pathogen’s incidence rate that is in response to an increase in antibiotic usage, relative to lower values of antibiotic usage. This inflection point does not indicate an immediate jump in the pathogen incidence rate that is outside normal variation. Therefore, the critical level of a pathogen incidence rate should be determined from the outset. A pre-defined cutoff value that defines a critical level of a pathogen incidence rate for hospitals, can be based on (i) a tolerance level set by government recommendation, that is the number of cases per 1000 OBD determined to be a high level of pathogen incidence outside the normal range of the national hospital system, or (ii) a hospital guideline, that is the hospital’s goal to keep the pathogen incidence rate below a certain number of cases per 1000 OBD, or (iii) an empirical analysis of historical pathogen incidence rate for a specific hospital. In this study, we used empirical analysis of historical HOHA CDI incidence rates to define when a critical level of HOHA CDI incidence rate was reached. Using a threshold logistic regression search algorithm, an incidence greater than 0.2645 cases/1000 OBD was selected as the cutoff value to define the critical incidence rate of HOHA CDI.

Second, using threshold logistic models, thresholds for fluoroquinolones and piperacillin-tazobactam that would accelerate HOHA CDI incidence rates and increase the probability of reaching critical levels were identified. Fluoroquinolones and piperacillin-tazobactam were found to have a threshold at 84.8, and 54 DDD/1000 OBD, respectively. The identification of the cutoff value for critical HOHA CDI incidence and the thresholds of the latter antibiotics provide targets for the AMS team and the hospital policymakers. Adhering to the provided thresholds will allow for a decrease in average HOHA CDI incidence rates over time as future months of HOHA CDI incidence are going to be below the identified critical incidence rate. This will eventually lead to controlling the incidence rate of HOHA CDI, allowing for the fact that reducing high risk antibiotic use is one of several components to reducing overall CDI rates. The threshold logistic models, used in this study, also allowed calculating risk scores or probabilities of HOHA CDI incidence rates exceeding a critical level. This has the utility of providing near real-time feedback to prescribers on their performance of keeping antibiotic use below identified thresholds. We showed this utility via a sample scorecard with risk scores being coded into alert signals of low, medium and high risk. Providing regular feedback to prescribers is essential to maintain the effectiveness of implemented antibiotic policies. Importantly, threshold logistic models facilitate predictive analysis, resulting in ‘what-if scenarios’ based on varied antibiotic usage scenarios to assess the expected impact on the studied pathogen. In the present work, the AMS and infection prevention and control (IPC) management teams will have the predicted probability of approaching the critical HOHA CDI incidence, based on their antibiotic use, months in advance (depending on the identified fluoroquinolone and piperacillin-tazobactam lags). This will help the AMS and IPC teams in their risk assessment and forward plans to determine the best countermeasures to mitigate the risk of an increase in the incidence rate of HOHA CDI.

It is also important to note that the threshold logistic model can be used to strictly identify the association of the explanatory variables to the binary response, in this case, pathogen incidence rate in the upper 85^th percentile. There is less utility for the model to identify associations of the explanatory variables at lower percentiles of pathogen incidence rate. Furthermore, the model demonstrates the statistical significance of threshold levels of fluoroquinolone and piperacillin-tazobactam use on increased pathogen incidence rate. The consistency of the effect of antibiotic threshold levels on increased incidence rate (>50^th percentile) is also demonstrated in the difference between incidence rates when partitioned with respect to the condition of antibiotic use above or below identified thresholds (Figure 5). Undoubtedly other important explanatory variables may exist that increase the overall predictive power of the model above the adequate predictive power of the current model (AUC > .70),

Due to the evolutionary nature of resistant pathogens to adapt to changing environmental conditions, it is challenging to model and forecast AMR. In a recent article by Pei et al. (2023) [21], the authors discussed such challenges and highlighted the absence of real-time forecasting models for antimicrobial-resistant organisms and emphasized the need for improved predictive intelligence to better estimate the emergence and spread of population AMR in health-care settings. Addressing the time-varying effects of explanatory variables on the response function and considering changes in the structural form of the relationship between the explanatory variables and the outcome variable is essential to generate results that can inform health-care policies [22]. The use of threshold transfer function modeling, which includes Autoregressive Moving-Average (ARMA) components, aims to help address such issues by identifying locally linear relationships in the data. In this case, the threshold indicates where there is a change in response (e.g. AMR correlates to a consistently higher incidence rate or higher probability of entering a period of critical-level infection rate when the predictor variable exceeds a given threshold). It is within the locally linear conditions of the model that are associated with higher incidence rates and lower predictive error rates. Whereas the above characteristics of nonlinear threshold models can help, model recalibration also comes into play. First, because the models are parametric, the model parameters can be re-estimated after a new observation is recorded. In this sense, only the parameters are updated to reflect the new information, and no change in the structural form of the model would occur. However, the structural form of the model may need to be modified when the statistical significance of a model parameter falls below a defined confidence level. Second, the usefulness of the predictive model can be monitored by evaluating predictive error to a base. For a threshold-logistic model, the AUC can be used to assess the predictive power of the model and its ability to differentiate classes (binary events). In practice, model estimation, assessment, and the forecasting accuracy can be automated. The frequency of model recalibration is dependent upon the stability of the identified relationships in the model and the degree of observed AMR evolutionary changes [22].

In this study, threshold logistic analysis showed that fluoroquinolones and piperacillin-tazobactam were found to have a threshold in association with HOHA CDI at 84.8 and 54 DDD/1000 ODB, respectively. In a previous assessment of two other pathogen incidence rates [17,18], threshold logistic models identified thresholds for (i) fluoroquinolones (61.1 DDD/1000 OBD) and third-generation cephalosporins (9.2 DDD/1000 OBD) to control hospital ESBL-producing E. coli incidence, and (ii) fluoroquinolones (55.96 DDD/1000 OBD) and co-amoxiclav (312.19 DDD/1000 OBD) to control hospital MRSA incidence. Importantly, the assessment of the three pathogens, i.e. HOHA CDI, ESBL-producing E. coli, and MRSA, took place in the same study site hospital using the same study period and population. The findings of this study helped with mapping antibiotics that are known to promote resistance against certain alert pathogens in hospitalized patients. To control HOHA CDI, ESBL-producing E. coli, and MRSA, the AMS management team at Pinderfields General Hospital needs to monitor the following antibiotics and to adhere to the identified thresholds, that is, fluoroquinolones (<56 DDD/1000 OBD), third-generation cephalosporins (<9 DDD/1000 OBD), co-amoxiclav (<312 DDD/1000 OBD), and piperacillin-tazobactam (<54 DDD/1000 ODB). Regarding fluoroquinolones, it was associated with the three pathogens, and the lowest identified threshold was considered to set targets for informing antibiotic policies.

Estimation of number of HOHA CDI, ESBL-producing E. coli, and MRSA cases reduction, if the antibiotic use kept below identified thresholds, showed an annual decrease of 4.85% (3 cases), 4.12% (3 cases), and 3.04% (2 cases), respectively. This provided a total annual reduction of 12.02% (σ = 2.54%) in these gram-positive and gram-negative pathogens if antibiotics kept below identified thresholds. These pathogens are associated with significant costs to health-care systems. In a meta-analysis of 42 studies to estimate the financial impact of CDI in the US, the average cost for CDI case management per case was found to be $42,316 with an attributable cost per case of $21,448 [23]. Hospital-onset CDI-attributable cost per case was $34,157 [23]. A cost modeling of HCAI 2016/17, estimated the total annual cost of £2.7 billion, with 7.1 million bed days needed for NHS England [24]. It was reported that CDI accounts for 5.6% of all infections within NHS England [25]. A retrospective cohort study of 134 E. coli bacteremias in an Italian hospital estimated the mean cost per case for ESBL bacteremia to be €13,709 and non-ESBL to be €8,683 [26]. A larger cohort study in China of 580 patients found that costs were for ESBL bacteremia to be $8,048.68, compared to non-ESBL of $7,476.84 [27]. Costs of MRSA may vary in different places [28]. A study in the US examining the whole hospital excess costs of MRSA indicated adjusted costs of $51,252 to $84,436 for MRSA [29].

The study has the strength of using robust analysis methods. The data that were used for this study were routinely collected for all adult inpatients, therefore selection and information bias are unlikely. The study has some limitations. The hospital has a policy on the prevention and management of CDI which is aligned to national guidance and addresses various aspects of infection prevention and control (IPC) guidance surrounding CDI. The hospital has established AMS activities and reports on national measures such as Commissioning for Quality and Innovation (CQUIN) scheme. Overall, the hospital policy on the IPC of CDI, and the hospital AMS measures were consistently applied throughout the study period. Nevertheless, the analysis can be improved by including other explanatory factors, for example proxy measures for patient case mix, infection prevention and control activities, and factors adjusting for community antibiotic and resistance potential impact, if possible [30–32]. In addition, this work was done in one hospital and warrants being evaluated in a multi-center study.

5. Conclusion

Through the application of the threshold logistic concept, we provided an approach that can be utilized to inform and enhance the effective design and implementation of antimicrobial stewardship programs. A Threshold Logistic modeling approach was used to (i) define target critical pathogen incidence rates, (ii) derive threshold values of consequence that antibiotic usage should not exceed, (iii) provide probability scores to inform the ‘risk’ of entering a month of high pathogen incidence rate, (iv) address ease of monitoring policy using near real-time feedback and heuristic risk score levels (Low-Med-High) as alert signals, and (v) provide an opportunity to perform ‘what-if scenarios’ using different levels of antibiotic use to assess the expected impact on the predicted incidence rate of pathogens for future months; a high-risk alert signal should manifest into increased ‘preparedness’ to control the pathogen incidence rate. The threshold logistic model is a classification process in which classification accuracy can be monitored and components of the model (thresholds, coefficients, etc.) can be assessed over time for changes in pathogen response via the technical management team. Although our proposed models were created using real hospital datasets, the findings of these predictive models have not yet been implemented and tested in hospitals so that their operational utility can be assessed in daily clinical practice, an area that warrants further research.

Article highlights

• Balancing access to effective antimicrobials with the prevention of the emergence of antibiotic resistance is challenging.

• The non-linear relationship between antibiotic use and resistance creates a threshold of antibiotic use beyond which resistance would be triggered.

• Threshold logistic analysis provided the critical pathogen incidence level and antibiotic use targets to control resistance.

• Threshold logistic analysis provided near-real time performance feedback and future projections to control resistance.

• Threshold logistic models can be used to inform and enhance the effective design and implementation of antimicrobial stewardship programs.

Declaration of interest

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

Reviewer disclosures

Peer reviewers on this manuscript have no relevant financial or other relationships to disclose.

Author contributions

Conceptualization and design, M Aldeyab and W Lattyak; methodology, all authors; software, W Lattyak; data acquisition and investigation: all authors; formal analysis, M Aldeyab and W Lattyak; W Lattyak was the principal analyst; writing – original draft preparation, M Aldeyab; writing – review and editing, all authors. All authors have read and agreed to the published version of the manuscript.

Supplemental data

Supplemental data for this article can be accessed online at https://doi.org/10.1080/14787210.2023.2263642.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

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Funding

This paper was not funded.