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Journal of Combinatorial Optimization

, Volume 37, Issue 1, pp 248–270 | Cite as

Influencing factors analysis and modeling of hospital-acquired infection in elderly patients

  • Xiaohui Liu
  • Ni ZouEmail author
  • Dan Zhu
  • Dan Wang
Open Access
Article
  • 682 Downloads

Abstract

Hospital-acquired infection threatens the patients’ health and life and also impacts medical quality by decreasing the bed turnover rate, prolonging hospitalization, increasing hospital costs and bringing the patients the huge economic losses. Therefore, hospital infection management is the focus of today’s hospital management and one of the most prominent public health problems. The elderly patients are a special group of nosocomial infections as they often suffer from a variety of serious underlying diseases and their immune function are low so their incidence of nosocomial infection is also higher than the average population. This paper establishes model by the statistical analysis tools and analyzes the influencing factors of all kinds of nosocomial infections in elderly patients based on the investigation of incidence of nosocomial infection in Shanghai General Hospital.

Keywords

Hospital-acquired infections Elderly patients Statistical analysis Influencing factors 

1 Introduction

According to data from the sixth national census, China’s population was 13.328 billion, of which 1.776 million were over 60 years old, accounting for 13.33% of the total population. The World Health Organization estimates that between 2000 and 2050, the world’s population over 60 years old will double from 11 to 22% and the absolute number of people over 60 years old would grow from 605 million to 2 billion over the same period. Along with the acceleration of the pace of population aging, the problem of the elderly is becoming more and more prominent. Hospital-acquired infection (HAI) is an infection that is acquired in a hospital or other health care facility, including infection during hospitalization and infection in the hospital after being discharged. Such an infection can be acquired in hospital, nursing home, rehabilitation facility, outpatient clinic, or other clinical settings. HAI threatens the patients health and life and also impacts the hospitals medical quality by decreasing the bed turnover rate, prolonging hospitalization, increasing hospital costs and bringing the patients the huge economic losses. The elderly patients are a special group of nosocomial infections as they often suffer from a variety of serious underlying diseases and their immune function are low so their incidence of nosocomial infection is also higher than the average population. Therefore, this paper builds the model to research the influence factors of hospital-acquired infection in elderly patients aged 65 years or older to identify risk factors for HAI with emphasis on those most relevant to the elderly.

Hospital-acquired infection (HAI) is a global problem which currently affects approximately 10% of patients throughout the USA and Europe, causing respiratory, gastrointestinal, urinary tract, surgical site and blood-borne infections, complicating recovery and contributing to patient mortality. According to a report by Grand View Research, Inc., global hospital-acquired infections diagnostics market is expected to reach USD 11.6 billion by 2022. The global hospital acquired infections diagnostics market is projected to grow at a healthy CAGR during the period of 2015–2022. Advancing age of geriatric population is one of the main factors attributing to the growth of the market. In the United States, the Centers for Disease Control and Prevention estimated roughly 1.7 million hospital-associated infections (Klevens et al. 2007). In Europe, where hospital surveys have been conducted, the category of gram-negative infections is estimated to account for two-thirds of the 25,000 deaths each year.

As a hot topic, a large number of literatures have been studied related to the hospital-acquired infections. Mayon-White et al. (1988) put forward an international survey of the prevalence of hospital-acquired infection. Hussain et al. (1996) put forward a prospective survey of the incidence, risk factors and outcome of hospital-acquired infections in the elderly. Taylor and Oppenheim reviewed the incidence, risk factors and types of hospital-acquired infection in the elderly. Plowman (2000) studied the socio-economic burden of the hospital-acquired infection. Andersen and Rasch (2000) put forward a 3-year survey of hospital-acquired infections and antibiotic treatment in nursing/residential homes, including 4500 residents in Oslo and researched hospital-acquired infections in Norwegian long-term-care institutions. Ellidokuz et al. (2003) studies the hospital-acquired infections in elderly patients on the basis of results of a west Anatolian University Hospital surveillance. Brusaferroa et al. (2006) presented results from a 6-month prospective surveillance of hospital-acquired infections in four Italian long-term-care facilities (LTCFs). Durando et al. (2010) researched hospital-acquired infections and leading pathogens detected in a regional university adult acute-care hospital in Genoa, Liguria, Italy. Avci et al. (2012) determined the frequency, type, microbiological characteristics and outcome of HAIs in the elderly (age 65) and to compare the data with younger patients in a Turkish Training and Research Hospital. Laurent et al. (2012) investigated risk factors for HAIs, especially in the elderly, and described the relationship between comorbidities (number, severity, and specific diseases) and HAIs using a comprehensive inventory of comorbidities. Mehta et al. (2014) put forward the guidelines for prevention of hospital acquired infections. Redder et al. evaluated a system for automated monitoring of hospital-acquired urinary tract (HA-UTI) and bloodstream infections (HA-BSI) and reported incidence rates over a 5-year period in a Danish hospital trust. Hensley and Monson (2015) addressed the predominant resistant healthcare associated pathogens including methicillin-resistant Staphylococcus aureus, Clostridium difficile, and vancomycin-resistant enterococci to decrease the impact of these healthcare-associated infections. Wolkewitz et al. (2016) provided a case-cohort approach and showed that a full competing risk analysis was feasible even in a reduced data set. Boev and Kiss (2017) explored HAIs specific to risk factors, epidemiology, and prevention, and how nurses can work together with other health care providers to decrease the incidence of these preventable complications.

The rest of the paper is organized as follows. In Sect. 2, we analyze the quantitative characteristics from hospital departments, infective types, hospitalization days and patients’ ages of hospital-acquired infection. In Sect. 3, we clarify the influencing factors of elderly patients’ hospital-acquired infection, build the mathematical model, conduct the numerical experiments and sum up the result of the study and countermeasures. Finally, in Sect. 4, we come to some conclusions of this paper and put forward our future research directions.

2 The quantitative analysis of elderly patient’s hospital-acquired infection

A growing number of the global population is aging; accordingly a higher number of elderly patients are hospitalized for various causes. In this study, we collected the data of 307 elderly HAI patients cases from Shanghai General Hospital during the period from January 2015 to June 2017. In this section, we conduct the following four points of quantitative analysis of elderly patients hospital-acquired infection.

2.1 Hospital departments of HAI

Among 307 cases, the hospital departments and their numbers of HAI are as Table 1 and the probability plot of numbers is as Fig. 1.

The probability plot is usually used to evaluate the fit of a distribution to data, estimate percentiles, and compare different sample. In Fig. 1, the x-axis are the numbers of Hospital Departments of HAI and the y-axis are percentage of numbers in the cases that are less than or equal to it. We plot the x-axis versus the y-axis, along a fitted distribution line (middle line). From Fig. 1, we found that the mean numbers of the Hospital Departments of HAI is 13.35 and SD is 17.42. From Table 1 and Fig. 1, we found that about 60% of the HAIs occurred in the four departments, which are Internal Medicine ICU, Department of Gastrointestinal Surgery, Department of Neurosurgery and Department of Thoracic Surgery. It reminds us these four departments should be the key control objects of HAI.
Table 1

Hospital departments of HAI and their numbers

The hospital departments

Numbers

Internal Medicine ICU

73

Department of Gastrointestinal Surgery

47

Department of Neurosurgery

34

Department of Thoracic Surgery

31

Department of Hepatobiliary and Pancreatic Surgery

19

Department of Gastroenterology

13

Department of Medical Oncology

11

Department of Gynaecology

9

Department of Cardiology

8

Department of Urology

7

Department of Orthopaedics

6

Department of Orthopedics Trauma

6

Emergency Department

6

Department of Endocrinology and Metabolism

6

Department of Interventional Oncology

6

Department of Neurology

5

Department of Nephrology

5

Department of Cardio-Vascular Surgery

4

Department of Respiratory Medicine

4

Department of Radiation Oncology

2

Department of Ear–Nose–Throat and Head and Neck Surgery

2

Department of Hematology

2

Department of Breast–Thyroid–Vascular Surgery

1

Total

307

Fig. 1

Probability plot of numbers of hospital departments of HAI

Table 2

Infective types of HAI and their numbers

The infective types

Numbers

Lower respiratory tract (unrelated to catheter) infection

104

Surgical site infection (SSI)

71

Ventilator associated pneumonia (VAP)

41

Catheter associated urinary tract infection (CAUTI)

29

Bloodstream infection (unrelated to catheter)

26

Intraabdominal tissue infection

21

Urinary tract (unrelated to catheter) infection

20

Upper respiratory tract (except for colds) infection

20

Central line-associated bloodstream infection (CLABSI)

12

Skin and soft tissue infection

8

Gastrointestinal infection (except gastroenteritis and appendicitis)

6

Other site infection

5

Disseminated infection

3

Infectious diarrhea

1

Antibiotic associated diarrhea

1

Oral infection

1

Total

369

2.2 Infective types of HAI

Among 307 cases, the infective types of hospital-acquired infections and their numbers of HAI are as Table 2 and the probability plot of numbers is as Fig. 2.

In Fig. 2, the x-axis are the numbers of infective types of HAI and the y-axis are percentage of numbers in the cases that are less than or equal to it. From Fig. 2, we found that the mean numbers of the infective types of HAI is 43.41 and SD is 88.28. From Table 2 and Fig. 2, we found that about 60% of the HAIs occurred in the three types of infection, which are lower respiratory tract (unrelated to catheter) infection, surgical site infection (SSI) and ventilator associated pneumonia (VAP). It reminds us these types of infection should be the key control objects of HAI.

2.3 Hospitalization days of HAI

Among 307 cases, the hospitalization days and their numbers of HAI are as Table 3 and the dotplots of hospitalization days is as Fig. 3.
Fig. 2

Probability plot of numbers of infective types of HAI

Table 3

Hospitalization days of HAI and their number

Hospitalization days

Numbers

1–19

80

20–39

136

40–59

51

60–79

21

80–99

9

100–

10

Total

307

The picture of dotplots is usually used to assess and compare distributions by plotting the values along a number line. We use dotplots to compare distributions of hospitalization days of HAI. In Fig. 3, the x-axis for a dotplot is divided into many small intervals. Data of hospitalization days of HAI values falling within each interval are represented by dots. From Table 3 and Fig. 3, we found that about 45% of HAI patients were hospitalized between 20 and 39 days. We checked the original data and found that among the HAI patients who were hospitalized between 20 and 39 days, 34.81% of these patients were suffered from by lower respiratory tract infection. It validates the conclusion of 2.2 and reminds us that lower respiratory tract infection should be the key control object of HAI.
Fig. 3

Dotplots of hospitalization days of HAI

2.4 Patients ages of HAI

Among 97 samples, the patients ages of hospital-acquired infections and their numbers of HAI are as Table 4 and the histogram of patients ages is as Fig. 4.

The picture of histogram is usually used to examine the shape and spread of data. Histogram divide values into many intervals called bins. Bars represent the number of observations falling within each bin. In Fig. 4, the x-axis for the histogram is divided into several small intervals. Patients ages of HAI that fall exactly on each interval boundary are included in the interval to the right. From Table 4 and Fig. 4, we found that the distribution of ages of HAI elderly patients conform to the distribution of ages of hospital elderly patients.
Table 4

Patients ages of HAI and their numbers

Patients ages

Number

65–69

99

70–74

77

75–79

51

80–84

50

85–89

26

90–

4

Fig. 4

Histogram of patients ages of HAI

3 Influencing factors model and numerical experiments of elderly patients HAI

3.1 Influencing factors to hospital-acquired infection

Many factors promote hospital-acquired infection occurrence in hospitals. Some of these factors are present regardless of the resources available: prolonged and inappropriate use of invasive devices and antibiotics, high-risk and sophisticated procedures, immuno-suppression and other severe underlying patient conditions, insufficient application of standard and isolation precautions. Some determinants are more specific to settings with limited resources: inadequate environmental hygienic conditions and waste disposal, poor infrastructure, insufficient equipment, understaffing, overcrowding, poor knowledge and application of basic infection control measures, lack of procedure, lack of knowledge of injection and blood transfusion safety, absence of local and national guidelines and policies. On the other hand, factors influencing hospital-acquired infections include: age, infected patients, drug resistance, susceptible patients and surgical procedures. Usually neonates and elderly of extreme ages may acquire hospital infection because of their long stay in hospitals and inefficient immunity. And patient with community acquired or non-hospital infection due to pathogenic microorganisms may enter the hospital and spread the infection to close contents. The drug resistant organisms may show increased virulence or transmissibility as well as limiting the choice of therapy. Hospitalized patients with pre-existing diseases (diabetes, immunosuppression, patients in special care units or with prosthetic implants are at risk and more susceptible to hospital infections. The natural defense mechanisms of the body surface may be bypassed by injury or by a diagnostic or therapeutic intervention. We collected 307 patients case and concluded factors that were susceptible to infection as Table 5.
Table 5

Factors and codes of susceptible to hospital-acquired infection

Code

Factors

01

Diabetes

02

Cerebral vascular disease

03

Hepatopathy

04

Chronic obstructive pulmonary disease

05

Malignant tumor

06

Nephropathy

07

Hematopathy

08

Severe pancreatitis

09

Enterobrosis

10

Open injury

11

Coma

12

Long-term bed

13

Smoking history \(\ge \) 10 years

14

Hormone

15

Radiotherapy

16

Chemotherapy

17

Immunosuppressor

18

Anemia (hemoglobin < 90 g/L)

19

Hypoalbuminemia (serum albumin < 30 g/L)

20

White blood cell count < 1.5 \(\times \) 10\(^{9}\)/L

21

Urinary catheterization

22

Arteriovenous catheterization

23

Tracheal intubation or tracheostomy

24

Ventilator

25

Endoscopic operation (endoscopic endoscope and bronchoscope)

26

Hemodialysis and peritoneal dialysis

27

Operation

28

Vasectomy

29

Organ transplant

30

Implant

31

Operation time >3 h

32

Surgical incision for contamination (III, IV)

33

Use of third-generation cephalospores

34

Use of antifungal drug

35

The time of using antimicrobial agents > 2 weeks

36

Use of three or more antimicrobial agents

Table 6

Influencing factors to HAI and their numbers

Influencing factors to HAI

Numbers

Use of three or more antimicrobial agents

240

Hypoalbuminemia (serum albumin < 30 g/L)

222

Use of third-generation cephalospores

212

The time of using antimicrobial agents > 2 weeks

210

Arteriovenous catheterization

191

Urinary catheterization

190

Operation

187

Anemia (hemoglobin < 90 g/L)

162

Tracheal intubation or tracheostomy

122

Malignant tumor

120

Ventilator

111

Operation time > 3 h

82

Diabetes

74

Use of antifungal drug

64

Cerebral vascular disease

59

Coma

46

Endoscopic operation (endoscopic endoscope and bronchoscope)

42

Smoking history \(\ge \) 10 years

40

Implant

24

Chronic obstructive pulmonary disease

22

Vasectomy

19

Long-term bed

18

Nephropathy

17

Chemotherapy

17

Surgical incision for contamination (III, IV)

17

Enterobrosis

11

Open injury

10

White blood cell count < 1.5 \(\times \) 10\(^{9}\)/L

10

Hepatopathy

8

Hemodialysis and peritoneal dialysis

7

Hormone

4

Hematopathy

3

Severe pancreatitis

2

Radiotherapy

1

Among 307 cases, the influencing factors to hospital-acquired infections and the numbers that each susceptible factor leads to HAI are as Table 6 and the empirical CDF of numbers is as Fig. 5. Table 6 and Fig. 5 show that the top 3 factors causing HAI are use of three or more antimicrobial agents, hypoalbuminemia < 30 g/L and use of three generations of cephalospores.

The empirical CDFs graph is usually used to evaluate the fit of a distribution to data and compare different sample distribution, including an empirical cumulative distribution function of sample data and a fitted normal cumulative distribution function. In Fig. 5, the x-axis are the numbers of influencing factors to HAI and the y-axis are percentage of numbers in the cases. From Fig. 5, we found that the mean numbers of the influencing factors to HAI is 75.41 and SD is 79.07. From Table 6 and Fig. 5, we found that about 50% of the HAIs occurred by the six influencing factors, which are use of three or more antimicrobial agents, hypoalbuminemia < 30 g/L, use of third-generation cephalospores, the time of using antimicrobial agents > 2 weeks, arteriovenous catheterization, urinary catheterization. It reminds us these six influencing factors should be the key control objects of HAI.
Fig. 5

The empirical CDF of numbers of influencing factors to HAI

3.2 The mathematical model of influencing factors to HAI

This section we use the five-step method to build the hospital-acquired infection influencing factors.

Step 1 is to ask a question. The question must be phrased in mathematical terms. In the process we are required to make a number of assumptions or suppositions about the way things really are. We should not be afraid to make a guess at this stage. We can always come back and make a better guess later on. Before we can ask a question in mathematical terms we need to define our terms. Go through the problem and make a list of variables. Include appropriate units. Next make a list of assumptions about these variables. Include any relations between variables (equations and inequalities) that are known or assumed. Having done all of this, we are ready to ask a question. Write down in explicit mathematical language the objective of this problem. Notice that the preliminary steps of listing variables, units, equations and inequalities, and other assumptions are really a part of the question. They frame the question.

From the data we collect from January 2015 to June 2017 in the hospital, we extract the independent variables including diabetes, cerebral vascular disease, hepatopathy, chronic obstructive pulmonary disease, malignant tumor, nephropathy as \(x_1, x_2, x_3\) and the variable (\(x_i=0, 1\)) was used to analyze the related factors of HAI by single factor and multifactor logistic regression. We extract the variables including lower respiratory tract (unrelated to catheter), surgical site infection (SSI), ventilator associated pneumonia (VAP) as \(y_1, y_2, y_3\) and the variable (\(y_i=0, 1\)) was used to analyze the infective types of HAI by single factor and multifactor logistic regression. The values of the independent variables are shown in the Table 7 and the values of the variables are shown in the Table 8.
Table 7

Susceptibility factors and assignment methods

Variables

Susceptibility factors

Assignment methods

\(x_1\)

Diabetes

\(x_1=0\), no; \(x_1=1\), yes

\(x_2\)

Cerebral vascular disease

\(x_2=0\), no; \(x_2=1\), yes

\(x_3\)

Hepatopathy

\(x_3=0\), no; \(x_3=1\), yes

\(x_4\)

Chronic obstructive pulmonary disease

\(x_4=0\), no; \(x_4=1\), yes

\(x_5\)

Malignant tumor

\(x_5=0\), no; \(x_5=1\), yes

\(x_6\)

Nephropathy

\(x_6=0\), no; \(x_6=1\), yes

\(x_7\)

Hematopathy

\(x_7=0\), no; \(x_7=1\), yes

\(x_8\)

Severe pancreatitis

\(x_8=0\), no; \(x_8=1\), yes

\(x_{9}\)

Enterobrosis

\(x_{9}=0\), no; \(x_{9}=1\), yes

\(x_{10}\)

Open injury

\(x_{10}=0\), no; \(x_{10}=1\), yes

\(x_{11}\)

Coma

\(x_{10}=0\), no; \(x_{10}=1\), yes

\(x_{12}\)

Long-term bed

\(x_{12}=0\), no; \(x_{12}=1\), yes

\(x_{13}\)

Smoking history \(\ge \) 10 years

\(x_{13}=0\), no; \(x_{13}=1\), yes

\(x_{14}\)

Hormone

\(x_{14}=0\), no; \(x_{14}=1\), yes

\(x_{15}\)

Radiotherapy

\(x_{15}=0\), no; \(x_{15}=1\), yes

\(x_{16}\)

Chemotherapy

\(x_{16}=0\), no; \(x_{16}=1\), yes

\(x_{17}\)

Immunosuppressor

\(x_{17}=0\), no; \(x_{17}=1\), yes

\(x_{18}\)

Anemia (hemoglobin < 90g/L)

\(x_{18}=0\), no; \(x_{18}=1\), yes

\(x_{19}\)

Hypoalbuminemia (serum albumin < 30 g/L)

\(x_{19}=0\), no; \(x_{19}=1\), yes

\(x_{20}\)

White blood cell count < 1.5 \(\times \) 10\(^{9}\)/L

\(x_{20}=0\), no; \(x_{20}=1\), yes

\(x_{21}\)

Urinary catheterization

\(x_{21}=0\), no; \(x_{21}=1\), yes

\(x_{22}\)

Arteriovenous catheterization

\(x_{22}=0\), no; \(x_{22}=1\), yes

\(x_{23}\)

Tracheal intubation or tracheostomy

\(x_{23}=0\), no; \(x_{23}=1\), yes

\(x_{24}\)

Ventilator

\(x_{24}=0\), no; \(x_{24}=1\), yes

\(x_{25}\)

Endoscopic operation (endoscopic endoscope and bronchoscope)

\(x_{25}=0\), no; \(x_{25}=1\), yes

\(x_{26}\)

Hemodialysis and peritoneal dialysis

\(x_{26}=0\), no; \(x_{26}=1\), yes

\(x_{27}\)

Operation

\(x_{27}=0\), no; \(x_{27}=1\), yes

\(x_{28}\)

Vasectomy

\(x_{28}=0\), no; \(x_{28}=1\), yes

\(x_{29}\)

Organ transplant

\(x_{29}=0\), no; \(x_{29}=1\), yes

\(x_{30}\)

Implant

\(x_{30}=0\), no; \(x_{30}=1\), yes

\(x_{31}\)

Operation time > 3 h

\(x_{31}=0\), no; \(x_{31}=1\), yes

\(x_{32}\)

Surgical incision for contamination (III, IV)

\(x_{32}=0\), no; \(x_{32}=1\), yes

\(x_{33}\)

Use of third-generation cephalospores

\(x_{33}=0\), no; \(x_{33}=1\), yes

\(x_{34}\)

Use of antifungal drug

\(x_{34}=0\), no; \(x_{34}=1\), yes

\(x_{35}\)

The time of using antimicrobial agents > 2 weeks

\(x_{35}=0\), no; \(x_{35}=1\), yes

\(x_{36}\)

Use of three or more antimicrobial agents

\(x_{36}=0\), no; \(x_{36}=1\), yes

Table 8

Infective types and assignment methods

Variables

Susceptibility factors

Assignment methods

\(y_1\)

Lower respiratory tract (unrelated to catheter) infection

\(y_{1}=0\), no; \(y_{1}=1\), yes

\(y_2\)

Surgical site infection (SSI)

\(y_{2}=0\), no; \(y_{2}=1\), yes

\(y_3\)

Ventilator associated pneumonia (VAP)

\(y_{3}=0\), no; \(y_{3}=1\), yes

\(y_4\)

Catheter associated urinary tract infection (CAUTI)

\(y_{4}=0\), no; \(y_{4}=1\), yes

\(y_5\)

Bloodstream infection (unrelated to catheter)

\(y_{5}=0\), no; \(y_{5}=1\), yes

\(y_6\)

Intraabdominal tissue infection

\(y_{6}=0\), no; \(y_{6}=1\), yes

\(y_{7}\)

Urinary tract (unrelated to catheter) infection

\(y_{7}=0\), no; \(y_{7}=1\), yes

\(y_{8}\)

Upper respiratory tract (except for colds) infection

\(y_{8}=0\), no; \(y_{8}=1\), yes

\(y_{9}\)

Central line-associated bloodstream infections (CLABSI)

\(y_{9}=0\), no; \(y_{9}=1\), yes

\(y_{10}\)

Skin and soft tissue infection

\(y_{10}=0\), no; \(y_{10}=1\), yes

\(y_{11}\)

Gastrointestinal infection (except gastroenteritis and appendicitis)

\(y_{10}=0\), no; \(y_{10}=1\), yes

\(y_{12}\)

Other site infection

\(y_{12}=0\), no; \(y_{12}=1\), yes

\(y_{13}\)

Disseminated infection

\(y_{13}=0\), no; \(y_{13}=1\), yes

\(y_{14}\)

Infectious diarrhea

\(y_{14}=0\), no; \(y_{14}=1\), yes

\(y_{15}\)

Antibiotic associated diarrhea

\(y_{15}=0\), no; \(y_{15}=1\), yes

\(y_{16}\)

Oral infection

\(y_{16}=0\), no; \(y_{16}=1\), yes

Step 2 is to select the modeling approach. Now that we have a problem stated in mathematical language, we need to select a mathematical approach to use to get an answer. Many types of problems can be stated in a standard form for which an effective general solution procedure exists. Most research in applied mathematics consists of identifying these general categories of problems and inventing efficient ways to solve them. There is a considerable body of literature in this area, and many new advances continue to be made.

As statistical scientists studied and found, logistic multivariate nonlinear regression equation is the most suitable for multivariate regression equations. In the analysis of elderly patients hospital-acquired infection, we choose logistic multivariate nonlinear regression. Logistic multivariate nonlinear regression is one of the most widely used statistical techniques for analyzing observational data. The analysis of observational data typically requires a structural and multivariate approach. We use regression models to uncover the relationships between the Infective Types and other variables, especially the influencing factors to HAI.

Step 3 is to formulate the model. We need to take the question exhibited in step 1 and reformulate it in the standard form selected in step 2, so that we can apply the standard general solution procedure. It is often convenient to change variable names if we will refer to a modeling approach that has been described using specific variable names.

In this research, we handle the categorical variables and create dummy variables to represent the different groups. Then we use these dummy variables just like other explanatory variables in a regression model. And the following is the regression analysis of infective types versus influencing factors to HAI. We suppose that the probability of any one of the elderly patients being infected in the hospital is p, and the susceptibility factor (independent variable) has 36 linear combinations of 36 influencing factors.
$$\begin{aligned} y = a+\sum _{j=1}^mb_jx_j \end{aligned}$$
(1)
Then, logistics multivariate nonlinear regression equation is
$$\begin{aligned} p = \frac{\exp {y}}{1+\exp {y}}=\frac{1}{1+\exp {(-y)}} \end{aligned}$$
(2)
By (2), we can get:
$$\begin{aligned} \frac{p}{1-p}= & {} \exp {y} \quad y=\ln {\frac{p}{1-p}}\end{aligned}$$
(3)
$$\begin{aligned} \text {Define: }\log {{ it}p}= & {} \ln {\frac{p}{1-p}} \end{aligned}$$
(4)
By (4), (3) and (1), we can get:
$$\begin{aligned} \log {{ it}p}=\ln {\frac{p}{1-p}}=a+\sum _{j=1}^mb_jx_j \end{aligned}$$
(5)
By (5), we can get:
$$\begin{aligned} a=\ln {\frac{p_0}{1-p_0}}. \end{aligned}$$
(6)
Step 4 is to solve the model. We use the Minitab statistical package to obtain the regression line. To do this, first we entered the samples data into Minitab worksheet and enter the time index numbers t into another column. Then we used the pull-down menus to issue the command Stat > Regression > Regression and specified the data as the response and the time index data as the predictor. To get the prediction interval for, we selected the options button in the regression window and enter in the box labeled Prediction intervals for new observations.

Step 5, we have made conclusion shown as the Sect. 3.3.

3.3 The numerical experiments of influencing factors to HAI

By regression analysis of 16 infective types versus 36 influencing factors to HAI, we could get the influencing factors with significant influence to each infective type. Among the 16 infective types, 11 infective types had influencing factors with P value < 0.05. The results of likelihood ratio tests of these 11 infective types were shown in Table 9. Other five infective types were not found having any influencing factor with significance, such as upper respiratory tract (except for colds) infection, disseminated hyper infection, infectious diarrhea, antibiotic associated diarrhea, oral infection.
Table 9

Some likelihood ratio tests of all infective types

Infective type

Susceptibility factors and assignment methods

Model fitting criteria

Likelihood ratio tests

−2 Log likelihood of reduced model

Chi-square

df

Sig.

01 Lower respiratory tract (unrelated to catheter)

02 Cerebral vascular disease

332.683

5.325

1

0.021

13 Smoking history \(\ge 10\) years

335.213

7.855

1

0.005

14 Hormone

333.159

5.801

1

0.016

25 Endoscopic operation (endoscopic endoscope and bronchoscope)

334.501

7.143

1

0.008

32 Surgical incision for contamination (III, IV)

334.276

6.918

1

0.009

34 Use of antifungal drug

332.063

4.705

1

0.030

02 Surgical site infection (SSI)

03 Hepatopathy

204.000

7.332

1

0.007

11 Coma

201.209

4.541

1

0.033

22 Arteriovenous catheterization

203.561

6.893

1

0.009

27 Operation

228.002

31.334

1

0.000

32 Surgical incision for contamination (III, IV)

204.481

7.813

1

0.005

03 Ventilator associated pneumonia (VAP)

05 Malignant tumor

123.939b

5.152

1

0.023

24 Ventilator

136.217b

17.430

1

0.000

36 Use of three or more antimicrobial agents

122.813b

4.026

1

0.045

04 Catheter associated urinary tract infection (CAUTI)

01 Diabetes

107.561b

6.937

1

0.008

13 Smoking history \(\ge 10\) years

109.171b

8.547

1

0.003

21 Urinary catheterization

119.428b

18.803

1

0.000

30 Implant

105.640b

5.016

1

0.025

05 Bloodstream infection (unrelated to catheter)

02 Cerebral vascular disease

109.617b

4.907

1

0.027

04 Chronic obstructive pulmonary disease

109.604b

4.894

1

0.027

07 Hematopathy

110.662

5.952

1

0.015

20 White blood cell (WBC) \(< 1.5^{*} 10^{\wedge }9/\hbox {L}\)

112.526

7.817

1

0.005

25 Endoscopic operation (endoscopic endoscope and bronchoscope)

108.772b

4.062

1

0.044

27 Operation

109.632b

4.922

1

0.027

06 Intraabdominal tissue

03 Hepatopathy

75.405b

7.183

1

0.007

05 Malignant tumor

73.376b

5.155

1

0.023

18 Anemia \(< 90\,\hbox {g}\)/L

72.531b

4.310

1

0.038

19 Hypoalbuminemia \(< 30\,\hbox {g}\)/L

72.070b

3.848

1

0.050

26 Hemodialysis and peritoneal dialysis

72.490b

4.269

1

0.039

35 Use antimicrobials time \(>2\) weeks

73.602b

5.381

1

0.020

36 Use of three or more antimicrobial agents

73.279b

5.058

1

0.025

07 Urinary tract (unrelated to catheter)

13 Smoking history \(\ge 10\) years

85.669b

4.872

1

0.027

33 Use of third-generation cephalospores

85.591b

4.795

1

0.029

09 Central line-associated bloodstream infections (CLABSI)

22 Arteriovenous catheterization

50.410b

4.845

1

0.028

34 Use of antifungal drug

50.376b

4.811

1

0.028

10 Skin and soft tissue

12 Long-term bed

29.848b

19.509

1

0.000

11 Gastrointestinal infections (except gastroenteritis and appendicitis)

01 Diabetes

12.922b

6.801

1

0.009

04 Chronic obstructive pulmonary disease

127.966b

121.845

1

0.000

10 Open injury

12.465b

6.344

1

0.012

11 Coma

14.529b

8.408

1

0.004

12 Long-term bed

10.407b

4.286

1

0.038

19 Hypoalbuminemia \(< 30\,\hbox {g}\)/L

10.623b

4.502

1

0.034

22 Arteriovenous catheterization

12.596b

6.475

1

0.011

23 Tracheal intubation or tracheostomy

97.704b

91.583

1

0.000

30 Implant

29.614c

23.493

1

0.000

12 Other site infection

28 Vasectomy

17.679c

17.679

1

0.000

From the results of likelihood ratio tests in Table 9, for lower respiratory tract (unrelated to catheter), six influencing factors had significant influence, which were cerebral vascular disease, smoking history \(\ge \)10 years, hormone, endoscopic operation (endoscopic endoscope and bronchoscope), surgical incision for contamination (III, IV) and use of antifungal drug. The estimates of regression coefficient and marginal coefficient of these six variables were significant at the test level 0.05.

For SSI, five influencing factors had significant influence, which were hepatopathy, Coma, arteriovenous catheterization, operation and surgical incision for contamination (III, IV). The estimates of regression coefficient and marginal coefficient of these six variables were significant at the test level 0.05.

For VAP, three influencing factors had significant influence, which were malignant tumor, ventilator and use of three or more antimicrobial agents. The estimates of regression coefficient and marginal coefficient of these six variables were significant at the test level 0.05.

For CAUTI, four influencing factors had significant influence, which were diabetes, smoking history \(\ge \) 10 years, urinary catheterization and implant. For Bloodstream infection (unrelated to catheter), six influencing factors had significant influence, which were cerebral vascular disease, chronic obstructive pulmonary disease, hematopathy, white blood cell (WBC) < 1.5 \(\times \) 10\(^{9}\)/L, endoscopic operation (endoscopic endoscope and bronchoscope) and operation. For intraabdominal tissue infection, seven influencing factors had significant influence, which were hepatopathy, malignant tumor, anemia < 90 g/L, hypoalbuminemia < 30 g/L, hemodialysis and peritoneal dialysis, use antimicrobials time > 2 weeks and use of three or more antimicrobial agents. For urinary tract (unrelated to catheter), smoking history \(\ge \) 10 years and use of three generations of cephalosporins had significant influence. For central line-associated bloodstream infections (CLABSI), arteriovenous catheterization and use of antifungal drug had significant influence.

For skin and soft tissue, long-term bed had significant influence. For gastrointestinal infections (except gastroenteritis and appendicitis), nine influencing factors had significant influence, which were diabetes, chronic obstructive pulmonary disease, open injury, coma, long-term bed, hypoalbuminemia < 30 g/L, arteriovenous catheterization, tracheal intubation or tracheostomy, implant. For other site infection, vasectomy had significant influence.

4 Discussion

In this study, we found that the top 10 factors causing HAI are use of three or more antimicrobial agents, hypoalbuminemia (serum albumin < 30 g/L), use of third-generation cephalospores, the time of using antimicrobial agents > 2 weeks, arteriovenous catheterization, urinary catheterization, operation, anemia (hemoglobin < 90 g/L), tracheal intubation or tracheostomy and ventilator. These influencing factors can be summarized in the following three aspects: antibacterial use, relevant clinical test, invasive surgery and operation.

Firstly, this study finds that in the rank of the influencing factors of elderly patients hospital-acquired infection, use of three or more antimicrobial agents, use of third-generation cephalospores and the time of using antimicrobial agents > 2 weeks respectively rank the first, third and fourth. It shows that the long-term exposure of antibiotics, frequent replacement of antibiotics and the unreasonable use of antibiotics are the high risk factors that lead to hospital infection. Long-term abuse of antimicrobial agents can lead to increased bacterial resistance, increased risk of secondary infections such as fungi, and damage to liver and kidney function. All of these factors will make the patient’s infection worsen, the cure rate drop, and also make the patients more exposed to the environment of the more advanced antimicrobials. These infection will increase the patient’s hospital stay, the hospitalization expenses of the patients, and the human cost of medical treatment and nursing and will lead to a vicious cycle of treatment.

Secondly, this study finds that in the rank of the influencing factors of elderly patients HAI, hypoalbuminemia (serum albumin < 30 g/L) and anemia (hemoglobin < 90 g/L) respectively rank the second and eighth. It hints that during the elderly patient’s hospitalization, the nutritional status of patients was correlated with subsequent hospital infection. When elderly patients blood albumin is low than normal, the defense barrier of the patients bodies is easy to be destroyed. This leads to a decrease in immunity and the body may be vulnerable to microbial injury such as surgery or trauma, which leads to infection. When the hemoglobin becomes lower than normal, oxygen in the blood carried by hemoglobin decreases obviously and the ability to resist microorganisms will also be loss or decline in the condition of oxygen deprivation in the body. Therefore, we conclude that the decline of serum albumin and hemoglobin should be monitored during the course of elderly patients hospitalization and intravenous infusion of human albumin and erythrocyte suspension should be applied timely in order to correct its hypoalbuminemia and anemia status. These measures are conducive to reduce the risk factors of HAI and will have realistic guiding significance for the prognosis of elderly patients.

Thirdly, this study finds that in the rank of the influencing factors of elderly patients HAI, arteriovenous catheterization, urinary catheterization, operation, tracheal intubation or tracheostomy and ventilator respectively rank the fifth, sixth, seventh, ninth, and eleventh. This corroborates that both of invasive surgery and the process of operation and all kinds of intubation making the body interlinked with the outside world increase the body’s normal mucosa, blood vessels, skin, viscera exposed to the outside world or have the possibility of microorganisms of the internal environment, especially the sterile area damage status which provides a channel and carrier for microbial invasion. Therefore, sterile technical principles of operation must be strictly abided , the care of the tubes of the intubated and operated patients must be strengthened, VAP, CAUTI, CLABSI core prevention and control strategy must be adhere to and carried out. All of these measures are critical for the prevention and control of nosocomial infections.

By regression analysis of 16 infective types versus 36 influencing factors to HAI, we found 11 infective types had influencing factors with P value < 0.05. The cause analysis of the correlation between each infective type and their influencing factors were as follows.

Lower respiratory tract (unrelated to catheter) was significantly related to six influencing factors have significant influence, which were cerebral vascular disease, smoking history \(\ge \) 10 years, hormone, endoscopic operation (endoscopic endoscope and bronchoscope), surgical incision for contamination (III, IV) and use of antifungal drug. Patients with cerebral vascular disease usually had disturbance of consciousness, cough reflex loss or decrease, failure to automatic sputum excretion, which were high risk factors of respiratory infections. The oscillating ability of the lower respiratory mucosal cilia decreased in patients with smoking history \(\ge 10\) years, which could result in decrease of the ability of the respiratory tract to eliminate dust and pathogenic bacteria and lower respiratory tract infection and likely to occur lower respiratory tract infection. The use of hormones can cause decline of the body’s own immunity, which may cause various types of infections. Endoscopic operation, especially in the operation of bronchoscopy, if not be taken care of the principles of aseptic operation, can easily lead to the descending of upper respiratory tract infection, which can lead to lower respiratory tract infection. For incision type of contaminated wounds, the surgery itself exists invasion of pathogenic bacteria and the surgical site infection rate is extremely high. But there is no research for the correlation with lower respiratory tract infection, which can be confirmed in further correlation analysis with control group setup. The use of antifungal agents and the lower respiratory tract infections may be cause and effect mutually. The reason for use of antifungal drugs may be either the existing lower respiratory tract fungal infection, or the secondary fungal double infection caused by long-term antibiotics abuse. Both of them can lead to lower respiratory tract infections caused by pathogenic fungi.

SSI was significantly related to hepatopathy, coma, arteriovenous catheterization, operation and surgical incision for contamination (III, IV). Obviously, operation and surgical incision for contamination were undoubtedly high risk factors for surgical site infection. The patient was in a coma, indicating that the patient was in critical condition and the body’s ability to defense against infection decreased as well as suffered from surgical traumatic stress response, which were probably risk factors of surgical site infection. Arteriovenous catheterization were invasive operation. The patients using arteriovenous catheterization mainly depend on artificial intravenous channels for long-term hydration, which would easily lead to pathogen infection into bloodstream related to surgical site infection. However, there was no relevant report about the relationship between hepatopathy and surgical site infection, which needs further verification.

VAP was significantly related to malignant tumor, ventilator and use of three or more antimicrobial agents. The use of ventilator is undoubtedly a necessary factor in the occurrence of VAP. Use of three or more antimicrobial agents and upper respiratory tract infection may be cause and effect mutually. In case of VAP happened, use of three or more antimicrobial agents are probably necessary to control infection, which may cause double infection such as fungal infection and exacerbation of VAP. Malignant tumor may be associated with VAP, since the ratio of CD4/CD8 in patients with malignant tumors decreased and was susceptible to infection. However, the correlation with VAP should be further studied.

CAUTI was significantly related to diabetes, smoking history \(\ge \) 10 years, urinary catheterization and implant. Obviously, urinary catheterization is undoubtedly a necessary factor in the occurrence of CAUTI. The increase of inflammatory stress factors in patients with diabetes and smoking history can lead to the occurrence of various infections, no exception for CAUTI. Patients after transplantation should stay in bed for a long time and the urinary catheter should be imbedded in large proportion, so the incidence of CAUTI would increase.

Bloodstream infection (unrelated to catheter) was significantly related to cerebral vascular disease, chronic obstructive pulmonary disease, hematopathy, white blood cell (WBC) < 1.5 \(\times \) 10\(^{9}\)/L, endoscopic operation (endoscopic endoscope and bronchoscope) and operation. The majority of patients with WBC < 1.5 \(\times \) 10\(^{9}\)/L had blood system diseases such as Leukemia or lymphoma. The absence of white blood cells leads to a decrease in the body’s immunity, and is prone to bloodstream infections such as sepsis and septicemia. Endoscopic operation and operation were invasive operations. The human skin mucosa and organ tissues were subjected to mechanical destruction. If the aseptic operation was not notices or its own operation position was infective site, it would facilitate the opportunistic pathogen into blood, and cause bloodstream infection. However, the relationship between cerebral vascular disease, chronic obstructive pulmonary disease, hematopathy and bloodstream infection were not clear.

Intraabdominal tissue infection was significantly related to hepatopathy, malignant tumor, anemia < 90 g/L, hypoalbuminemia < 30 g/L, hemodialysis and peritoneal dialysis, use antimicrobials time >2 weeks and use of three or more antimicrobial agents. According to the statistical results, hepatopathy and malignant tumor in patients were risk factors for intraabdominal tissue infection. Decreased liver function and malignant tumors in the abdominal cavity would result in intraabdominal tissue infection. Anemia and hypoalbuminemia were the first found to be associated with intraabdominal tissue infection. It might because that the lack of nutrition and the decline of the nutritional condition of the body caused by gastrointestinal surgery or operation provided the possibility for microbial invasion, which lead to intraabdominal tissue infection. In the case of patients with hemodialysis or peritoneal dialysis, the majority of them were attacked by renal function injury or uremia, and renal failure reduced the ability of toxin excretion. Meanwhile, the patients with peritoneal dialysis had long retained abdominal tubes, which also provided an invasive window for microbes. If the abdominal permeability pipeline was not properly managed and the aseptic operation was not strict, it would also lead to intraabdominal tissue infection. Use of antimicrobials time > 2 weeks, use of three or more antimicrobial agents and intraabdominal tissue infection may be cause and effect mutually.

Urinary tract (unrelated to catheter) was significantly related to smoking history \(\ge \) 10 years and use of three generations of cephalosporins. The increase of inflammatory stress factors in smoking patients can lead to various infections, including urinary tract infection. Urinary tract infection and use of three generations of cephalosporins might be cause and effect mutually. When urinary tract infection occurred, the three generations of cephalosporins might be used for bacterium infection control, and long-term use of the three generations of cephalosporins would also increase resistance, which would promote the double infection such as drug-resistant or secondary fungus infection, and lead to the urinary tract infection happen or aggravate.

CLABSI was significantly related to arteriovenous catheterization and use of antifungal drug. Obviously, arteriovenous catheterization is undoubtedly a necessary factor in the occurrence of CLABSI. Among CLABSI, some of the pathogens are fungal infections, so it is possible to use antifungal agents against infection. However, use of antifungal agents is not always risk factor of CLABSI.

We have identified some areas of future work. We see the health economics analysis of elderly patients hospital-acquired infection as an interesting and challenging future direction. Additionally, this work can also be extended to a larger scale, such as all public hospitals in Shanghai and can be enhanced by using individual patient data, such as patients of all ages.

Notes

Acknowledgements

This research was supported by Young Teachers Training and Research Project Behavior Game Research of Hospital Supplies Supply Chain Alliance Based on Big Data (B50YC150005P4) from Shanghai Polytechnic University in 2017 and Construction Project of Cultivate discipline “Management science and engineering” (XXKPY1606) from Shanghai Polytechnic University in 2017.

References

  1. Andersen BM, Rasch M (2000) Hospital-acquired infections in Norwegian long-term-care institutions. A three-year survey of hospital-acquired infections and antibiotic treatment in nursing/residential homes, including 4500 residents in Oslo. J Hosp Infect 46(4):288–296CrossRefGoogle Scholar
  2. Avci M, Ozgenc O, Coskuner SA, Olut AI (2012) Hospital acquired infections (HAI) in the elderly: comparison with the younger patients. Arch Gerontol Geriatr 54(1):247–250CrossRefGoogle Scholar
  3. Boev C, Kiss E (2017) Hospital-acquired infections: current trends and prevention. Crit Care Nurs Clin North Am 29(1):5165CrossRefGoogle Scholar
  4. Brusaferroa S, Silvestrob A, Vidottob L (2006) Incidence of hospital-acquired infections in Italian long-term-care facilities: a prospective six-month surveillance. J Hosp Infect 63(2):211–215CrossRefGoogle Scholar
  5. Durando P, Bassetti M, Orengo G, Crimi P, Battistini A, Tiberio G, Bellina D, Talamini A, Dodi F, Ansaldi F, Alicino C, Iudici R, Sticchi L, De Florentiis D, Viscoli C, Icardi G (2010) Hospital-acquired infections and leading pathogens detected in a regional university adult acute-care hospital in Genoa, Liguria, Italy: results from a prevalence study. J Prev Med Hyg 51(2):80–86Google Scholar
  6. Ellidokuz H, Ukub R, Uysal Ü, Abacolud H (2003) Hospital-acquired infections in elderly patients: results of a West Anatolian University Hospital surveillance. Arch Gerontol Geriatr 37(3):259–263CrossRefGoogle Scholar
  7. Hensley BJ, Monson JRT (2015) Hospital-acquired infections. Surgery (Oxford) 33(11):528–533CrossRefGoogle Scholar
  8. Hussain M, Oppenheim BA, ONeill P, Trembath C, Morris J, Horan MA (1996) Prospective survey of the incidence, risk factors and outcome of hospital-acquired infections in the elderly. J Hosp Infect 32:117–126CrossRefGoogle Scholar
  9. Klevens RM, Edwards JR, Richards CL, Horan TC, Gaynes RP, Pollock DA, Cardo DM (2007) Estimating Healthcare-associated infections and deaths in U.S. Hospitals, 2002. Public Health Rep 122(2):160–166CrossRefGoogle Scholar
  10. Laurent M, NhiBories P, Thuaut AL, Liuu E, Ledudal K, Bastuji-Garin S, Paillaud E (2012) Impact of comorbidities on hospital-acquired infections in a geriatric rehabilitation unit: prospective study of 252 patients. J Am Med Dir Assoc 13(8):760.e7–760.e12CrossRefGoogle Scholar
  11. Mayon-White RT et al (1988) An international survey of the prevalence of hospital-acquired infection. J Hosp Infect 11(Suppl A):43–48CrossRefGoogle Scholar
  12. Mehta Y, Gupta A, Todi S, Myatra SN, Samaddar DP, Patil V, Bhattacharya PK, Ramasubban S (2014) Guidelines for prevention of hospital acquired infections. Indian J Crit Care Med 18(3):149–163CrossRefGoogle Scholar
  13. Plowman R et al (2000) The socio-economic burden of the hospital-acquired infection. Euro Surveill 5(4):49–50CrossRefGoogle Scholar
  14. Wolkewitz M, Palomar-Martinezb M, Olaechea-Astigarraga P (2016) A full competing risk analysis of hospital-acquired infections can easily be performed by a case-cohort approach. J Clin Epidemiol 74:187–193CrossRefGoogle Scholar

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Shanghai Polytechnic UniversityShanghaiChina
  2. 2.Shanghai General HospitalShanghai Jiaotong UniversityShanghaiChina

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