
==== Front
Medicine (Baltimore)
Medicine (Baltimore)
MD
Medicine
0025-7974
1536-5964
Lippincott Williams & Wilkins Hagerstown, MD

MD-D-24-04992
00095
10.1097/MD.0000000000039328
3
4700
Research Article
Observational Study
Transforming healthcare performance monitoring – A cutting-edge approach with generalized additive profiles: GAMs for healthcare quality monitoring
https://orcid.org/0000-0002-1272-6904
Waqas Muhammad PhD ab
Xu Song Hua PhD cd
Aslam Muhammad Usman PhD a
Hussain Sajid PhD a
https://orcid.org/0009-0001-1608-3221
Masengo Gilbert PhD e*
a Department of Statistics, School of Mathematics and Statistics, Xian Jiaotong University, Xian, China
b Department of Statistics, University of Wah, Taxila, Pakistan
c Department of Health Management & Institute of Medical Artificial Intelligence, the Second Affiliated Hospital, Xi’an Jiaotong University, Shaanxi, China
d Yale University, New Haven, USA
e Department of Mechanical Engineering, Rwanda Polytechnic/Integrated Polytechnic Regional College (IPRC) Karongi, Kigali, Rwanda
* Correspondence: Gilbert Masengo, Department of Mechanical Engineering, Rwanda Polytechnic/Integrated Polytechnic Regional College (IPRC) Karongi, Kigali, Rwanda (e-mail: engemabert@yahoo.com).
13 9 2024
13 9 2024
103 37 e3932807 5 2024
25 7 2024
26 7 2024
Copyright © 2024 the Author(s). Published by Wolters Kluwer Health, Inc.
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial License 4.0 (CCBY-NC), where it is permissible to download, share, remix, transform, and buildup the work provided it is properly cited. The work cannot be used commercially without permission from the journal.

Recent findings indicate a growing trend in data analysis within healthcare using statistical process control. However, the diversity of variables involved necessitates the expansion of new process control methodologies. This study examined control chart applications in cardiology by using generalized additive models (GAMs) to construct profiles while involving multiple healthcare variables (08). Two distinct statistics: deviation (D), and Hotelling (T2) were employed for constructing control charts: a commonly used single-variable statistic for nonparametric profiles and an innovative multivariate statistic that assesses the contribution of each element to process changes. These statistics were tested for monitoring ischemic and hemorrhagic strokes in 1-year acute stroke (369) patients at the Faisalabad Institute of Cardiology. Demographic parameters (age, gender), vascular risk factors (diabetes, family history, sleep), socioeconomic variables (smoking, location), and blood pressure are included in the model. The research includes the computation of zero-state average run length (ARL) for assessing the performance of control charts. The characteristics of the proposed profile were analyzed, such as the T2 control chart, performing better than the D chart for medium-to-large shifts (δ ≥ 0.50). On the other hand, for small δ = 0.25, the D control chart produces smaller ARL values but more significant standard deviations. While both statistics contribute to profile monitoring, T2 is more effective at identifying and tracing medium and large shifts. In conclusion, such handy tools may aid healthcare performance monitoring, especially for complicated predictor–response relationships. Monitored profiles demonstrated that GAMs are useful for healthcare analysis and process monitoring.

applications
cardiology
healthcare data analysis
profile monitoring
statistical process control
OPEN-ACCESSTRUE
SDCT
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pmc1. Introduction

In healthcare, control charts are being used for a wide range of health departments to monitor various sickness phenomena.[1] Control charts can discover assignable reasons for process instability by monitoring stability.[2] Monitoring multiple measurements with control charts for each size may increase the margin of error. To solve this problem, employ a functional relationship or profile, to model many measurements instead of control charts for each response variable. Profiles assume measurements of 1 or more independent factors together with the outcome variable.[3] Profile monitoring enables a symbiotic relationship between statistical modeling and statistical process control (SPC), providing an opportunity to pool modeling and SPC techniques, potentially leading to synergistic benefits between the 2 approaches.

Various models were recently put forth for constructing profiles. To illustrate, Shewhart methodology has been commonly applied to track linear profiles in single- and multi-situational settings.[4,5] Additionally, other control methodologies, that is, EWMA, CUSUM, and Hotelling T2, have been adapted and applied for monitoring linear profiles,[6–10] monitoring and diagnosing high-dimensional variability in phase 1,[11] as well as circular and cylindrical profiles.[12] Recent cardiology research indicates a worldwide drive towards more advanced statistical approaches, as 70% of studies performed after 2018 to solve various healthcare issues by the confluence of year, chart type, variable, and nation. From clinical outcomes like mortality risk in Iran and China to efficiency measurements like Door-to-needle time in Switzerland and Sweden, studies conducted in several nations have used sophisticated statistical methods, including CUSUM charts, EWMA charts, and GAMs models. The application of risk-adjusted and adaptive control charts is also increasing.[13–18] These studies discussed that risk-adjusted control charts that account for the preoperative risk of patients have been widely used for monitoring of surgical outcomes. But the selection of the suitable control chart for specific health phenomena also matters in healthcare monitoring.[19,20] Generally, risk-adjusted control charts have been developed based on a binary classification of surgical outcomes. Overall, these multifaceted methods encompass patient-centered care as well as clinical effectiveness, reflecting the complex knowledge of surgical and cardiovascular health management. Using cutting-edge statistical methods and gaining understanding from a range of clinical settings, researchers hope to propel ongoing advancements in the provision of cardiac care globally see Table 1.

Table 1 A summary of existing control chart studies in cardiology departments in different countries.

Control charts applications in the Cardiology Department	
Study	Year	Control chart	Cardiology variable	Study phases	Country	
Bonetti, Waeckerlin[21]	2000	Run chart	Door-to-needle time	Phases I and II	Switzerland	
Coory, Duckett[22]	2008	CUSUM chart	Mortality rate	Phase I	Australia	
Woodall[23]	2018	CUSUM and EWMA charts	Emergency readmission rate, Mortality risk,	Phases I and II	UK	
Erfanian, Sadeghpour Gildeh[24]	2021	D and T2 chart, GAMs models	ischemic and hemorrhagic stroke patients	Phases I and II	Iran	
Jing, Li[25]	2022	Directional covariance matrix chart	Uterine contraction (UC) rate and fetal heart rate (FHR)	Phase II	China	
Rafiei and Asadzadeh[26]	2022	CUSUM chart	Patients of coronary artery bypass grafting surgery	Phases I and II	Iran	
Pakdil and Beazoglou[27]	2022	IMR chart	Length of stay of patients with acute myocardial infarction (AMI) disease	Phase II	USA	
Sabahno and Khoo[28]	2022	Cv and MCv chart	Blood pressure (BP) and Heart rate (HR)	Phases I and II	Sweden	
Asif and Noor-ul-Amin[13]	2022	Adaptive EWMA	Cardiac surgery patients record	Phases I and II	Pakistan	
Noor-ul-Amin, Khan[14]	2024	Risk-adjusted EWMA	Cardiac surgery patients record	Phase II	Pakistan	
Yeganeh, Johannssen[29]	2023	Risk-adjusted Auto_Encoder charts	ischemic and hemorrhagic stroke patients	Phases I and II	Iran	
Study Types; Retrospective and Longitudinal	

Various SPC variables in healthcare monitoring require different profiles for effective tracking.[30] Some research mentioned linear profiles as the simplest. Parametric and nonparametric nonlinear profiles require different monitoring strategies than linear profiles. Nonlinear parametric profiles can be monitored using techniques such as nonlinear regression,[31] mixed polynomial approach,[32] and nonlinear mixed model.[33] However, nonparametric profiles have been less studied, with limited systems such as nonparametric regression modeling,[34] incorporation of rank set methods, EWMA control scheme approaches,[35,36] and normal process with the heteroscedastic model being used for monitoring. GAMs, originally proposed by,[37] were subsequently employed by[38] for monitoring processes involving a partial additive models approach, and[24] practised the idea of GAM in cardiology. GAMs can model diverse measurement types as outcome variables depending on the associated explanatory variables. In comparison to earlier models, GAMs offer various forms of models, such as nonparametric, semi-parametric, or parametric. Notably, GAMs, especially for nonparametric terms, permit a breakdown of control charts every time, in contrast to earlier nonparametric profiles. In this paper, we employed several generalized additive models (GAMs) to construct profiles. We thoroughly discovered the various applications of GAMs and control charts.

1.1. Defining GAMs application in profile monitoring

The connection between the mean function and the variables may become more flexible when using the GAMs, which are modifications of generalized linear models (GLMs).[39] The definition of a GAM by Marra and Wood[40] is as

(E(Zi))= Yi∗ω∗+∑lsl(yli) (1)

wherever f(⋅) is a special link function. The outcome variable Zi   ∼   exp_dist_family, Yi∗ is the ith row of Y∗, sl  being smooth functions based on the covariates yl, that can serve as vector covariates and generally comprise parametric model factors, with comparing parameter vectors that result subject to identification criteria such as ∑lsl(yli)=0, for all values of 1.[40] Regression spline basing is used to depict the sl . Together with measurements of function roughness that are described by quadratic structures in the coefficients framework.[41] It is possible to estimate model (1) using the specified components as a GLM; however, penalized maximum likelihood estimation is needed to avoid overfitting. To control overfit, roughness metrics are used. Usually, by doing iterative minimization of such problem, GAMs fitted as

 concerning∥V[n](u[n]−Yβ2∥    +∑lλiβTSlβ, with respect toβ

where n is the number of iterations, u[n]=Yβn+Hn(z−μn), μin are the estimates derived from the model E(Zi). Hn is nominated as a diagonal matrix in a way that Hiin=h′(μin), where Vn is also a diagonal matrix written that Viin=1/[Hii[n]2W(μi[n])], where W(μi[n]) returns Var(Zi) with ∅ as a scale parameter of the response distribution. [Y, Y∗] symbolizes columns for smooth function spline base sl, other hand β comprises on ω∗ along with coefficient vectors representing the smooths. Sl   s are matrices with coefficients that quantify the ruggedness of smooth functions using summation variables. See the supplemental file for more details.

2. Methods

2.1. Statistical profiling by GAMs

We demonstrate how to use GAMs to make statistical profiles as well as provide 2 control charts for effective process control in the healthcare industry. We take into account several subgroups of the dataset, each with mj (j = 1, …, n) samples of diverse sizes, and estimate the response variable’s values together with matching values of more than 1 independent variable. A GAM, which is specified in equation (1), is used to model the functional connection between the outcome variable and the independent variables. All subgroups are presumed to share this GAM-based profile. We utilize 2 charts based on the D-statistic and Hotelling T2-statistic to build control charts for tracking these generalized additive profiles. These statistics are discussed in more detail in the following subsections.

2.2. Deviation statistic (D) chart

Let x^ij represent the fitting values of yij, where yij is the vector representing the values found of the variables that explain for observation i inside profile j, with i = 1,...,  mj and j = 1,..., n. The D statistic for each profile is calculated based on this fitted value.

Dj= 1mj∑mji=1(x^ij−x~i)2,wherej = 1,..., n, (2)

The baseline profile’s fitted value x~i, is used in equation (2) and discussed in reference.[4] An approximate normal distribution is available for the test imagination of γj, denoted as γ^j, based on a large sample size, as mentioned in reference.[41] This implies that the profile estimation ytγj at any arbitrary point y follows a normal distribution (see supplementary file, http://links.lww.com/MD/N372).

2.3. Hotelling T2-chart

In each profile for GAMs, the estimates of the coefficients for the parametric predictors denoted as ωj∗^ (wherej = 1,..., n) are obtained following the methodology explained above. Similarly, the vector of assessed smoothing parameters associated with explanatory nonparametric variables is represented as λj^(wherej = 1,..., n). It is possible to determine the vector of parameter estimates for profile j as follows:

γjt= [ωj∗^− ρ^j],wherej = 1,..., nandρ^j=log(λ⏞j)  (3)

As discussed, there are multiple options for estimating the smoothing parameters. When employing the REML method, a normal approximation for ωj∗^ and  ρ^j (where j = 1,..., n) is available for large sample sizes.[41] That enables the poof to effectively utilizing the Hotelling, T2 control chart. Established

Tj2= (γj− γ¯)tY−1(γj− γ¯),  j   =   1,   .   .   .   ,   n,  (4)

Hence, γ¯ and Y are estimated as,

γ¯= 1n0∑n0j=1γj0 (5)

Y= 1n0∑n0j=1(γj− γ¯)(γj− γ¯)t (6)

and in-control n0 estimates illustrated as γ10,..., γn00  for profiles in phase I. Phase I evaluates process stability, outliers, and in-control parameters. Phase II monitors online data to quickly discover process changes using phase I estimates. As per the study by Tracy et al,[42] the upper control limit (UCL) for phases I and II is as

{UCLphase I= (n−1)2nβα,b/2, (n−b−1)/2 andUCLphase II=b(n−1)(n+1)n(n−b)Fα, b, n−b} (7)

The variable “b” represents the T2 statistic’s element count and the crucial beta and Fisher distribution values are denoted as “β” and “F”, respectively. The next step after recognizing an OOC profile is to identify the problem element; for more, see the supplementary file, http://links.lww.com/MD/N372.

3. Results

Kaggle a popular dataset sharing platform, provided this research study’s dataset https://www.kaggle.com/code/jorgeromn/heart-failure-prediction-decisiontree-rf, which came from the Faisalabad Institute of Cardiology, a reputed cardiology and heart surgery center, consisting on 369 acute stroke patients with 87% ischemic and 13% hemorrhagic. The information comprises demographic variables, cardiovascular-related medical examinations, and other factors such as smoking and diabetes. The data is imported from the .sav file to R 4.2.2 to perform analysis.

3.1. GAM fitting

First, construct stroke-type models using a logistic GAM. The model includes dichotomous, categorical, and continuous explanatory variables, including demographic (age, gender), vascular risk (diabetes, family history, sleep), socioeconomic (smoking, locality), and blood pressure variables. The model (8) includes smooth functions for continuous variables like age and blood pressure as described in (1). At the same time, the remaining terms are allocated using ω∗, based on whether they are binary or categorical. Utilizing the reverse variable selection technique,[43] the model is first fitted by including all listed variables. Subsequently, the variable with a substantial P value (>0.05) is then eliminated, and the more appropriate model that results is iteratively fitted until all variables with considerable P values (<0.05) are conserved. This reduces the AIC as well. Consequently, the final fitted GAM for profile monitoring can be expressed as follows: Let Yi represent the stroke type for patient i, with probability pi for ischemic stroke and probability 1−pi for hemorrhagic stroke (i = 1,..., 369). The logistic model is expressed as

logit (pi)= ω0+ω1geni+ω2loci+ω3smki +ω4dibmi+ω5fhisti+ω6slpi+s1(agei)+s2(bpi) (8)

The model consists of an intercept ω0, along with parameters ω1, ω2, ω3, ω4, ω5, and ω6 that correspond to the indicators gender: male/female (gen), locality: urban/rural (loc), smoker/nonsmoker (smk), medical histories of diabetes (dibm), stroke history in the family (fhist), and sleep problem (slp), respectively. Additionally, 2 smooth functions s1 and s2 respond to age and blood pressure (bp) problem, respectively. The function logit is also defined in the model,

f(z)=log⁡(z(1−z)−1),z≥0for some values

From now on, we will consider model (8) fitted over all 369 observations as the baseline for constructing control charts. The patient data is divided into 11 subgroups constructed on the age brackets at registration. Chart profiles require fitting model (8) to subgroup data. Note that variables might vary between profiles, causing subgroup variances not due to intrinsic differences. This can be overcome by assuming the reference profile’s covariate values are y1,..., y369, where each yi represents the observed value associated with the covariate vector (gen,   loc,   smk,   dibm,   fhist,   slp,   bp) for case i, i = 1,..., 369, see Table 2.

Table 2 Displays the outcomes of the model (8), which was fitted for a given value z that is greater than or equal to 0. Additionally, Figure 1 depicts the smooth terms of the model, illustrating the smoothed relationship between age, blood pressure, and predicted logits. The brief lines down the X-axis, commonly referred to as the rug, reflect the covariate scores of each observed smooth.

	Estimate	Std. Error	t value	P value	
Intercept	0.970	0.064	15.104	<.001	
gen	−0.729	0.081	−8.990	<.001	
loc	0.298	0.051	5.746	<.001	
slp	−0.199	0.043	−4.585	<.001	
smk	0.326	0.053	6.144	<.001	
dibm	0.057	0.046	1.245	.214	
fhist	−0.304	0.052	−5.799	<.001	
s^1(age)	4.449	5.47	2.248	.047	
s^2(bp)	7.553	8.43	13.785	<.001	

Figure 1. Smooth plot of age and blood pressure by estimation from model (8). The estimated impact is shown by a solid line having 95% confidence depicted bounds by the dashed line.

To start, the covariate values y1,..., y369 are assigned to all subgroups. Then, the stroke class is set according to the original detected case (yi) for every subgroup, if yi was originally part of that subgroup. If not, it is established to the expected value y~i estimated from the model (8) for yi. It is worth noting that equation (8) is a logistic model, so the predicted values are p tilde sub i prime s, e predictions expected values equivalent to yi ′ s. To achieve the correspondent y~i ′ s, u ROC curve is applied Figure S1, Supplemental Digital Content, http://links.lww.com/MD/N374 (supplementary file), where p~i ′ s are predictor values and yi ′ s are response measures. The AUC is 0.883, besides the optimum cutoff is selected based on somewhere sensitivity result and specificity result of the curve gained the equivalent and highest values. The subsequent F-measure is noted as 0.603, with sensitivity values of 0.571 and specificity of 0.804.

4. Discussion

4.1. Statement of principal findings

To evaluate the process and stability and identify any unusual profiles, D and T2 control charts were utilized during phase I analysis. D statistics were calculated using the formula provided,

Dj= 1m∑mi=1( p^ij− p~i), i=1,..., m;  j=1,..., n

where p^ij is jth profile estimated value for yi. T2 statistics were computed using (3) with γjt=(ω^0, ω^1, ω^2, ω^3, ω^4, ω^5,ω^6, ρ^1,ρ^2). The monitoring outcomes for both charts are presented in Figure 2. Our analysis includes the computation of zero-state ARL for these control charts. Zero-state ARL, which measures the expected number of points plotted on a control chart before an out-of-control (OOC) signal is given when starting in the in-control state, provides crucial insights into the initial performance of the control charts. Compared to steady-state ARL, which assumes the process has been running for a while and has reached a steady state, zero-state ARL often provides a more immediate perspective on the responsiveness of control charts Haq and Woodall.[44]

Figure 2. T2 and D charts constructed on Faisalabad Institute of Cardiology (FIC) data.

T2 chart monitored 3 observations that were out of the upper limit which were noted and kept for the identification phase, but since none of the points surpassed the threshold point, so overall process to be declared as in-control shown. If the process is stable and only a few observations are over the UCL but below the threshold point, it may not be too concerning. The mechanism may still be in control, and the observations are random changes within its normal variability. However, to maintain stability and control, the process should be closely monitored and data collected. Observing covariate-controlled stroke-type logits in the subgroups using T2 control charts show no significant differences. Where the D-chart detected 2 points out of control and slipping away from the threshold point, it may indicate that process variability is changing or that the T2 chart is unable to identify certain data patterns. Therefore, no observations need to be removed at the moment, and both charts will be compared using ARLs. For phase II usage, anticipated estimations and control limits have been kept. The limits (LCL, UCL) of control were designed to offer in-control ARLs, which is a key aspect to remember. of approximately 370 (equal to α = 0.0027).

To ensure impartial evaluations in phase II, all control charts must have similar ARL0. This study calculates ARLs constructed on 10,000 simulation repetitions, wherever profiles = 370, are independently generated for each. OOC samples are replicated by independently generating n observations from a Bernoulli distribution with μ  +  δσ , where (µ) is the mean value and (σ) is the standard deviation (SD) value of  p^i in the reference model, i = 1,..., 369. Shifts are determined by δ values of (0.25, 0.5, 0.75, 1, 1.5, 2, 2.50, and 3). The performance assessment of the designed control charts is evaluated based on the run length distributions In addition to reporting mean and standard deviation, several percentiles (10th, 25th, median, 75th, and 95th) are also recommended due to the right-skewed distribution of run lengths. Table 3 reports the average run length (ARL), standard deviation run length (SDRL), and coefficient of variation (CV) values. At the same time, Figure 3 presents boxplots for the 10th percentile, 25th percentile, median, and 75th and 95th percentiles.

Table 3 ARLs for both control charts at different shifts.

Chart		δ=0.25	δ=0.50	δ=0.75	δ=1.00	δ=1.50	δ=2.00	δ=2.50	δ=3.00	
D	ARL	181.793	136.215	79.741	48.004	30.317	13.183	6.595	3.782	
SDRL	5.504	5.816	6.536	7.317	12.563	20.733	33.164	75.877	
CV	0.423	0.413	0.391	0.367	0.319	0.280	0.169	0.109	
Hotelings   T2	ARL	272.548	108.252	29.571	6.554	1.019	1	1	1	
SDRL	0.728	0.892	0.971	0.994	1	1	1	1	
CV	0.346	0.171	0.074	0.004	0.000	0.000	0.000	0.000	

Figure 3. T2 and D, ARLs-based boxplot at different shift values and percentiles.

It is widely accepted that the ARL is an essential indicator of the control charts’ performance, and it is generally known that control charts for D and T2 are intended to have comparable ARLs aimed at specific values of the process shift parameter, which are approximately equal. Table 3 displays the results of the ARL evaluation. The ARL values in Table 3 indicate that the T2 control chart performs better than the D chart for medium-to-large shifts (δ ≥ 0.50). In fact, for δ values of 1.50, 2.00, 2.50, and 3, the T2 ARLs are 1.000, meaning that they detect 100% of shift cases, making their performance ideal. On the other hand, for minor shifts (δ = 0.25), the D control chart produces smaller ARL values, but more significant standard deviations. This trend is more noticeable in the values of the coefficient of variation. The CV values at δ = 0.25 are particularly higher for the deviation chart, and such a trend remains unchanged for the remaining δ values. Figure 3 presents more comprehensive results regarding the achieved ARLs at δ=   (0.25,   0.50,   1.00).

The ATS is calculated as the product of the ARL and the sampling interval (h), it provides the average time until an OOC signal is generated, that is ATS=ARL∗h. The D-chart shows varying ATS values, indicating faster detection times for larger shifts but with higher SDATS, suggesting greater detection variability. In contrast, the T2 chart consistently detects shifts quickly (ATS) and with minimal variability (low SDATS), highlighting its reliability for identifying significant process changes across different shift magnitudes, see Table S1, Supplemental Digital Content, http://links.lww.com/MD/N373.

4.2. Strength and limitations

A key strength of this study is its potential for expansion. It allows control chart analytics to handle asymptotic distributions and small sample sizes. Using mixed models GAMs to create profiles and control statistics seems promising. This research addresses the issues of large and geographically dispersed healthcare data systems by addressing the growing requirement for statistical process control in big data analysis. This study is limited by using data from a single healthcare institution, limiting generalizability. Implementing GAMs may require additional resources and expertise due to their complexity. Real-time, dynamic big data is crucial for healthcare applications, but the research does not address it.

4.3. Interpretation

The purpose of this research is to present a novel method for monitoring variations in the mean function of the outcome variable using a profile control chart with the inclusion of multiple variables. This chart is based on multiple GAMs, which enable the modeling of complex relationships between predictor variables and the response variable. The study employs 2 statistics, D and T2, which are utilized to develop the phase-I and -II process control charts. The methodology is expedited on the heart stroke data, where it is used to track the age bracket-wise acute stroke cases by considering stroke types. The model considers various personal characteristics of the patients and utilizes a logistic GAM to a analyze the relationships between the predictors and the response variable. The results of the study compare the proficiency of deviation statistics and T2 statistics to detect shifts in the mean function of the response variable, with a particular focus on their performance in detecting different magnitudes of shifts. The study shows that both statistics perform well in general, but T2 can trace the source of identified shifts and tends to be more sensitive to detecting medium and large shifts.

4.4. Implication for policy practice and research

The following section demonstrates how Hotelling T2 may be utilized in real life for practice and research for the OOC items diagnosis using the approach developed by.[45] This approach breaks down the T2 statistic through factors that demonstrate the relative contributions of every single variable.[2] Let T2 represent the statistic’s present value, squares represent the statistic’s value encompassing every set of variables included in the process, but other than the ith component (i = 1,...,p; in which p signifies the statistic’s component value). Then

Δi = T2−Ti2 (9)

where i=1,...,   p will measure the proportional contribution from the ith variable in the total statistic. The values of Δi are obtained, and larger values of Δi will be evaluated when any OOC pulse is noticed. We use 1 of the OOC scenarios identified in the simulation outcomes detailed in the preceding section as a case study when we execute this procedure. At first, a single of the δ with 0.25, 0.5, 0.75, 1, 1.5, 2, and 3 is randomly chosen. Next, 1 of the replications within the OOC message is randomly chosen from the produced data for the specified shift. Here, the eventual T2 value determined is 20.52. By adopting (9), the estimated values (1–9) of the intercept term, gender, locality, sleep, smoke, diabetsm, family history, age and blood pressure in (8) are given by ΔT=(Δ1,   Δ2,   .   .   .   .,   Δ9). Each of the components in ΔT is compared to the upper limit of   χα,12. When we set α=   0.01, we see that χ0.01,12=6.634 and Δ9=19.785 go to the upper bound. As a result, blood pressure is considered responsible for OOC, where other potential contributors identified include age and locality factors that have changed profile since this demonstrates that Δ3(locality),Δ8(age),Δ9(bp) are a significant contributor.

5. Conclusion

In conclusion, this research advocates that GAMs could be a useful option in healthcare performance monitoring, particularly when complex relationships between predictor variables and the response variable need to be considered. The findings also suggest that T2 is the preferred option for monitoring shifts within the mean function regarding the outcome variable. The services of such monitoring systems might be useful in saving the lives of many patients from cardiology and many other healthcare fields, since the importance of control charts in healthcare, especially cardiology, is increasing every year. Such studies are also extendable to other healthcare settings with single or multiple datasets. The studies on adaptive control charts is also increased in recent years, which are implemenetable from engineering to healthcare sector.[46,47] Furthermore, the utilization of autoencoders Yeganeh, Johannssen[29] or other advanced computational frameworks can also yield advantages.

Acknowledgments

The author thanks the Department of Health Management & Institute of Medical Artificial Intelligence, The Second Affiliated Hospital, and School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an China, and the University of WAH for offering research facilities.

Author contributions

Conceptualization: Muhammad Waqas.

Data curation: Muhammad Waqas.

Formal analysis: Muhammad Waqas.

Methodology: Muhammad Waqas.

Software: Muhammad Waqas.

Supervision: Song Hua Xu.

Writing – original draft: Muhammad Waqas.

Writing – review & editing: Muhammad Usman Aslam, Sajid Hussain, Gilbert Masengo.

Supplementary Material

Abbreviations:

ARL average run length

CUSUM cumulative sum

CV coefficient of variation

EWMA exponentially weighted moving average

GAMs generalized additive models

MEWMA multivariate EWMA

SDRL standard deviation run length

SPC statistical process control

The authors have no funding and conflicts of interest to disclose.

Ethical approval is not applicable in the study, because our research did not directly involve in field experiments or record collection from patients. Moreover, the data used in this research was already publicly available.

The datasets generated during and/or analyzed during the current study are publicly available.

Supplemental Digital Content is available for this article.

How to cite this article: Waqas M, Xu SH, Aslam MU, Hussain S, Masengo G. Transforming healthcare performance monitoring – A cutting-edge approach with generalized additive profiles: GAMs for healthcare quality monitoring. Medicine 2024;103:37(e39328).
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