Change Points Analysis for the Trend of Count Data

9 III https://doi.org/10.22214/ijraset.2021.33151 March 2021 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com Change Points Analysis for the Trendof Count Data Taghreed M. Jawa1, David Young2, Chris Robertson3 1 Department of Mathematics and Statistics, Faculty of Sciences, P.O.Box 11099,Taif University, Taif 21944, Saudi Arabia 2 Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland 3 Health Protection Scotland, Glasgow, Scotland Abstract: Introduction: Change point analysis is a technique for detecting change in trend over time. Seg- mented regression analysis and joinpoint analysis are used to try to determine the most important interventions which impact rates of healthcare associated infections (HAIs). AiMs: Use change point analysis to determine which interventions reduce rates of HAIs. Data and Methods: The data on HAIs was monitored by Health Protection Scotland (HPS) and includes staphylococcus aureus bacteraemia (SAB) and clostridium difficile infection (CDI). Since 2004, several interventions were implemented by NHS to reduce the rates and these were reported by Health Protection Scotland (HPS). Segmented regression and joinpoint models are investigated and developed to detect times when the indection rates changed significantly. Profile likelihood and bootstrapping are used to construct confidence intervals for the joinpoints. Results: Interventions which took place from April-June 2006, July-September 2008 and January-March 2011 appear to be associated with a significantly decreasing trend in MRSA. Joinpoint analysis suggested that from July-September 2007 and January-March 2012 there was a significant change in the trend of MRSA bacteraemia. The trend of MSSA bacteraemia did change significantly from January-March 2011, however, joinpoint analysis did not indicate any change in MSSA bacteraemia. A segmented model suggested interventions around October-December 2009 had an impact on the rates of CDI in patients over 65 years and joinpoint analysis showed from AprilJune 2008 and January-March 2011 the rates changed. Conclusion: Segmented regression analysis detects changes in rates associated with specific interventions. It appears from this that training of hospital staff in dealing with infection outbreaks and the implementation of an antibiotic policy are associated with an observed reduction in the rates of SAB and CDI in healthcare settings. Joinpoint analysis gives the most robust modelling to estimate significant change. Keywords: Segmented regression; joinpoint analysis; seasonal effect; bootstrap confidence interval; profile likelihood confidence interval; healthcare associated infections; MRSA; MSSA; CDI. I. INTRODUCTION Everything in the world tends to change over time such as the economy, education and epidemi- ology. It is of interest to know when changes happened to determine the cause. Change point analysis aims to detect a time point when a trend in data changes. A trend in data may havemultiple change points. The change point analysis addresses two aspects in the analysis of a trend - a hypothesis testing approach to decide if there are any change points and an estimation approach to locate the change. Detecting change points was investigated using different methods. Segmented regression analysis was used to discover change points where the rates change significantly after a specific intervention and thereby help improve the quality of the interventions [Wagner et al. (2002)]. Joinpoint analysis was used to identify change points at unknown times and to estimate the location of them. Using a joinpoint statistical software package [NCISR (2020)] the simplest joinpoint model (which in includes only a time variable) is fitted to the data. The minimum and maximum number of joinpoints is determined. The program starts with the minimum number of joinpoints and tests whether additional joinpoints are statistically significant using a permutation method. These are added to the model up to the maximum number. A grid search method has a discrete number of locations that are tested to find the best fitted model and joinpoints occur exactly at one or more of these locations (observed rate) [Kim (2001)]. A. Healthcare Associated Infections Healthcare associated infections (HAIs) are a major contributor to morbidity and mortality [Tong et al. (2009)]. These include staphylococcus aureus bloodstream (SAB) infections and clostridium difficile infection (CDI). SAB includes methicillin resistant staphylococcus aureus (MRSA) bacteraemia and methicillin sensitive staphylococcus aureus (MSSA) bacteraemia. The treatment of MRSA bacteraemia can be challenging because MRSA is resistant to the most antibiotics. Bacteraemia is a bloodstream infection associated with high risk of morbidity and mortality [(Wertheim, 2005)]. The surveillance programme in Scotland reported the occurrence of HAIs up to March 2017 which included data on staphylococcus aureus from January 2003 for MRSA bacteraemia and from April 2005 for MSSA bacteraemia [HPS (2017)]. © IJRASET: All Rights are Reserved 578 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com CDI data was reported from October 2006 in patients aged over 65 years and from April 2009 for patients aged 15-64 years [HPS (2017)]. Data was collected every three months and records the number of patients with MRSA bacteraemia, MSSA bacteraemia, CDI. The number of acute occupied bed days (AOBDs) in Scotland are based on the daily counts of occupied beds that are undertaken in every hospital at midnight [HPS (2007)]. Rates of infections are presented per 100,000 AOBDs and this gives an indication of the number of cases relative to the size of the population at risk (Notice: due to updated data from April 2017 was recorded for SAB generally and for CDI generally, data until March 2017 was usedin this paper [HPS (2020)]). To control infections, some healthcare interventions were implemented in Scottish hospitals from 2004 to 2011 (see Table 3 in Appendix) [HPS (2015)]. It is important in developing healthcare policy to know whether any of these interventions had an impact on reducing the rates of HAIs. This research uses different methods to detect changes in infection rates and identifies the number and location of change points. II. CHANGE POINT DETECTION METHODS Change points analysis uses several different models to find statistically significant change points associated with a rate change and identifies how many change points can be estimated [Chen andGupta (2011)]. A. Segmented Regression Analysis Segmented regression analysis is used to discover change points where the rates change after a specific intervention [Wagner et al. (2002)]. By using Poisson and quasi-Poisson distributions, the general segmented regression model for the rates of MRSA bacteraemia, MSSA bacteraemia, CDIin patients over 65 years and CDI in patients aged 15-64 years was obtained as: log(Cases(t)) ∼ offset(log(AOBDs(t))) + α0 + β0t(i) + γQu(t) + β1t∗(i), (1) where i is an indicator of the quarter when the intervention took place. Cases(t) is the number of patients at time t, log(AOBDs(t)) accounts for different population sizes in each period of time and t is the year. t∗(i) is a continuous variable counting the time after the intervention at quarter i, which is coded 0 before the intervention at quarter i and (t − t(i)) after the intervention. The coefficient α0 estimates the intercept (baseline level). The coefficient β0 estimates the change in the rate before the intervention at quarter i (baseline slope). The coefficient β1 estimates the change in the slope where the estimate of the slope after the intervention at quarter i is β0 + β1. Finally, the coefficient γ estimates the seasonal effect Qu(t). Two different selections of data points were used to fit segmented regression models. Specific change points were investigated at time points when interventions took place. The first method used all data points before and after each intervention at quarter i and looked for one or more interventions associated with rate changes. The residual deviance is used as a measure of goodness of fit. Change in deviance can be used to compare models since the same number of data points were used around each intervention to fit the model. Model (1) is fitted with all possible interventions and the model with least residual deviance (the biggest effect) is chosen. Evidence of additional significan interventions can then be considered until the final number of change points is chosen. The second method considers four years of data (8 data points before and 8 after each intervention at quarter i). For example, when the intervention took place at Qu4, October- December 2007, data from Qu1, January-March 2006 to Qu4, October-December 2009 is used to fit the segmented model. Using the same number of data points avoids bias but residual deviance cannot be used to compare models. Here percentage of deviance explained (PDE) is used to measure the goodness of fit where the best fitted model has the biggest PDE. PDE is calculated as: (1 - (deviance of the segmented model / deviance of the null model))× 100, where the null model is obtained as log(rate) = 1. Segmented regression detects the times when specific interventions took place. There may well be a lag period for an effect to be seen as the intervention was rolled out over a period of time across various health boards. The next method looks for the significant changes at all possible time points within the rate data. B. Joinpioint Analysis Joinpoint analysis is used to estimate the number and location of change points. The joinpoint regression model describes changes in the rate by connecting linear trends. Using similar ideas to [Kim et al. (2000)], a joinpoint analysis based on the Poisson distribution which incorporates seasonality was developed and confidence intervals estimated. The joinpoint function was writtenin R [R Core Team (2014)] as the standard joinpoint software [NCISR (2020)] did not allow for a seasonal factor. © IJRASET: All Rights are Reserved 579 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com 1) Joinpoint estimation The algorithm for the analysis is as follows: a) Set minimum (min) and maximum (max) number of joinpoints which satisfy max-min ≥ 2. b) Use Equation 1 to fit null models with the minimum number of joinpoints and alternative models with the maximum number of joinpoints to the data. c) Find the best fitted model of both (null and alternative) models by using a grid search method considering one time point of data between every possible joinpoint. d) Permute the residuals from the chosen null model (100 times) and use them to get permutedcounts. e) The permuted counts are calculated using Pearson residuals and are obtained as: permuted counts = expected values of null √ model + Pearson residuals × expected values of null model. f) Use permuted counts to fit an alternative model and find the smallest permuted deviances. g) The permutation test is calculated to find the p-value for accepting or rejecting the nullmodel.  Find the change in deviance from original data (X= deviance of null model - devianceof alternative model).  Find the change in deviance from permuted data (Y= deviance of null model - permuteddeviances of alternative model).  Calculate p-value of permutation test as ∑ I(Y > X)/(length(Y) + 1), I(Y > X) = 1; Y > X and 0; otherwise. h) If p < 0.05/(max-min), reject the null model and accept the alternative model then perform the same analysis using the same alternative model and set the null model as (minimum number of joinpoint +1). See Bonferroni correction in Kim et al. (2000). i) If p > 0.05/(max-min), accept the null model and reject the alternative model then perform the same analysis using the same null model and set the alternative model as (maximum number of joinpoint -1). j) Repeat the analysis until the distance between the null and alternative models becomes 1. k) The number of joinpoints and their locations can be then known from the last accepted model. C. Confidence Intervals for joinpoint Confidence intervals for joinpoints are constructed using a Profile likelihood method and boot-strapping. 1) Profile Likelihood Confidence Interval The profile likelihood confidence interval is based on the asymptotic chi-square distribution of the log-likelihood ratio test statistic. The confidence interval for one joinpoint can be computed by adding χ2 ( 0.95,1)= 3.84 to the minimum value of the deviance function which was calculated from each joinpoint model. The deviance is -2 multiplied by the log-likelihood value of null model minus the log-likelihood value of the saturated model [Royston et al. (2007)]. The residual deviances from joinpoint models were calculated and the curve of deviance function was plotted. This is U-shaped where deviances start to decrease and at the minimum deviance start to increase. A horizontal line based on the minimum deviance plus 3.84 was plotted and two points of intersection with the deviance function curve were obtained. These two points are the lower and upper confidence level of the estimated joinpoint. The deviance function of models with two or more joinpoints cannot be used to find confidence intervals so bootstrap confidence interval wereproduced. 2) Bootstrap confidence interval The algorithm for constructing bootstrap confidence intervals is as follows: a) Use original data sample to fit a joinpoint model of the rate of infection. b) Obtain the fitted values yˆi and Pearson residuals εˆi Re-sample the residuals to get a new response variable yi∗ by adding re√ sampled residuals tothe fitted values as yi∗ = yˆi + εˆi × yˆi. c) Round yi∗ to integer values. d) Use the new responses (bootstrap data) to fit joinpoint models which have the same number of joinpoints as in the original model. e) Save the location of joinpoints from the best fitted model. f) Repeat steps 3 to 6 B times (say 1000 times) to obtain bootstrap estimates of joinpoints. g) Calculate the 95% confidence interval for joinpoint by using the bootstrapped joinpointswith the function quantile at 0.025 and 0.975 in R © IJRASET: All Rights are Reserved 580 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com III. RESULTS Change points for MRSA bacteraemia, MSSA bacteraemia, CDI in patients aged over 65 years and CDI in patients aged 15- 64 years were estimated. Firstly, segmented regression analysis was used to detect change points when the specific interventions took place. Secondly, joinpoint analysis was used to estimate the number of change points and their locations. A. Segmented Regression Analysis Segmented regression uses the data to fit linear trends in log rates and interventions are assumedto have taken place at specific times when the trend changes. B. MRSA Bacteraemia Using all data before and after an intervention at quarter i, and assuming that only one significant intervention affects the rate, the Poisson fitted model (1) of MRSA bacteraemia with intervention at Qu2, 2006 gave least deviance (105.65 on 51 degrees of freedom). Assuming the time when the first intervention took place is Qu2, 2006, a second intervention at Qu3, 2008 gave a significantly improved model with two interventions. Given these two interventions, a third intervention at Qu1, 2011 gave a significantly better with residual deviance is 64.76 on 49 degrees of freedom. This implies three significant change points at which interventions affected the rates of MRSA. Using 8 points of data before and 8 after each intervention, the Poisson fitted model (1) on MRSAbacteraemia with intervention at Qu2, 2006 has the largest PDE= 0.6538, see Figure 1 and Table 1. Table 1: Change points by segmented regression analysis Infection Segmented points All data Segmented point 2 years B and A MRSA bacteraemia Qu2, 2006 Qu3, 2008 Qu1, 2011 DV:64.76, DF:49 Qu1, 2011 DV:105.66, DF:42 Qu4, 2009 DV:1405.52, DF:36 Qu4, 2009 DV:94.05, DF:26 Qu2, 2006 MSSA bacteraemia CDI in patients aged over 65 years CDI in patients aged 15-64 years PDE=0.6538 Qu2, 2008 PDE=0.1862 Qu4, 2009 PDE=0.9889 Qu4, 2009 PDE=0.8629 20 ●● ● 15 ● ● 5 10 ● ●● ●● ● ● ● ● ● ● ● ●●● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ● ●●● ●●● ●●● ●● ● ● ●● 0 Rate of MRSA bacteraemia 25 Qu: Quarter, Qu1: January- March, Qu2: April- June, Qu3: July- September, Qu4: October- December, DV: Residual Deviance, DF: Degree of freedom, A: After, B: Before. 2004 2006 2008 2010 2012 2014 2016 Year Figure 1: Change points in MRSA bacteraemia. Black circles are the observed rates, red line is the expected rates, the change points by segmented regression from all data observed at blue lines and the change points by joinpoint analysis with bootstrap confidence interval observed at green lines. © IJRASET: All Rights are Reserved 581 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com C. MSSA Bacteraemia Fitting segmented regression models using all data on MSSA rates before and after each inter- vention at quarter i and fitting quasiPoisson regression suggested one change point at Qu1, 2011 giving the smallest residual deviance of 105.66 on 42 degrees of freedom. However, by using two years of data before and two years after each intervention at quarter i and using Poisson regression, the significant change in the slope was observed at Qu2, 2008 with PDE= 0.1862, see Figure 2 and Table 1. D. CDI in Patients Aged over 65 Years For CDI in patients over 65 years, using all data before and after each intervention at quarter i and fitting segmented models with quasi-Poisson gave one significant change point at Qu4, 2009 with residual deviance of 1405.52 on 36 degrees of freedom. Segmented models with one change point and two years of data before and after each intervention at quarter i showed Qu4, 2009 had PDE=0.9889 with a significant change in the slope, see Figure 3 and Table 1. 35 ● ● ● ● 30 ● ● ● ● ●● ● ●● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● 25 Rate of MSSA bacteraemia ● ● ● ● ● ● ● ●● ● ● ● ● ● 2006 2008 2010 2012 2014 2016 ● ● 100 ● ● ● ● ● ● ● 150 ● ● ● ● ●●● 50 Rate of CDI in patients over 65 years Year Figure 2: Change points in MSSA bacteraemia. Black circles are the observed rates, red line is the expected rates and the change point by segmented regression from all data observed at blue line. ● ●● ●● ●● ● ● 2008 2010 2012 ●● ● ● ● ● ● ●●● ● ● ● ●● ●● 2014 2016 Year Figure 3: Change points in CDI in patients over 65 years. Black circles are the observed rates, red line is the expected rates, the change points by segmented regression from all data observed at blue line and the change points byjoinpoint analysis with bootstrap confidence interval observed at green lines. © IJRASET: All Rights are Reserved 582 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com 100 ● 80 ● 60 ● ● ● ● ●●● 40 ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●● ●● ● 20 Rate of CDI in patients aged 15−64 years E. CDI in patients aged 15-64 years Segmented models with Poisson regression were fitted to the data on CDI in patients aged 15-64 years. Using all data before and after each intervention at quarter i, produced one significant change point where the model with Qu4, 2009 has the smallest residual deviance 94.05 on 26 degrees of freedom. However, Figure 4 shows that by using two years of data before and after each intervention at quarter i, Qu4, 2009 has PDE= 0.8629 with significant change in the slope. SeeTable 1. 2010 2012 2014 2016 Year Figure 4: Change points in CDI in patients aged 15-64 years. Black circles are the observed rates, red line is the expected rates, the change points by segmented regression from all data observed at blue line and the change points by joinpoint analysis with bootstrap confidence interval observed at green lines. F. Joinpoints and Their Confidence Intervals Joinpoint analysis was to estimate change points at all possible data points. The joinpoint model is linear on the log rate and seasonality was considered to improve the model fit. G. MRSA and MSSA Bacteraemias There are two joinpoints detected on MRSA bacteraemia data using joinpoint software [NCISR (2020)] at Qu1, 2008 and Qu2, 2012, see Table 2. Adding a seasonal effect to the model gave two significant joinpoints at Qu3, 2007 and Qu1, 2012 with residual deviance 72.31 on 50 degrees of freedom, see Figure 1. 95% bootstrap confidence intervals for these joinpoints are (Qu2, 2007Qu1, 2008) and (Qu2, 2010- Qu3, 2013), see Table 2. No significant joinpoint was identified for the H. MSSA Data Table 2: Estimated change points by joinpoint analysis Infection JPs by MRSA bacteraemia CDI in patients over 65 years CDI in patients aged 15- 64 years Qu1,2008 Qu2, 2012 Qu4,2008 Qu2, 2011 Qu2, 2011 JPs Confidence interval for joinpoint NCISR Profile likelihood Qu3, 2007 (Qu2, 2007 - Qu1, 2008) Qu1, 2012 (Qu2, 2010 - Qu3, 2013) Qu2, 2008 (Qu1, 2008 - Qu3, 2008) Qu1, 2011 (Qu4, 2010- Qu2, 2011) (Qu2, 2010 - Qu1, 2011) Qu4, 2010 (Qu2, 2010 - Qu2, 2011) Bootstrap JPs: joinpoints, Qu:Quarter, Qu1: January- March, Qu2: April- June, Qu3: July- September, Qu4: October- December, DV: Residual deviance, DF: Degree of freedom. © IJRASET: All Rights are Reserved 583 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com I. CDI in Patients Aged Over 65 Years For the data on CDI in patients over 65 years, there are two joinpoints with model deviance 191.39 on 35 degrees of freedom. The first is at Qu2, 2008 with 95% bootstrap confidence interval (Qu1, 2008 - Qu3, 2008) and the second is at Qu1, 2011 with 95% bootstrap confidence interval (Qu4, 2010 - Qu2, 2011), see Figure 3 and Table 2. The joinpoint software [NCISR (2020)] detected the same number of joinpoints but at different locations, see Table 2. J. CDI in Patients Aged 15-64 Years Figure 4 shows there is one joinpoint in the data of CDI in patients aged 15-64 years in Qu4, 2010 with residual deviance 52.27 on 26 degrees of freedom. A 95% profile likelihood confidence interval is (30.45, 32.77) ≈ (Qu2, 2010 - Qu1, 2011) and a 95% bootstrap confidence interval is (Qu2, 2010 - Qu2, 2011), see Table 2. Joinpoint software [NCISR (2020)] detected the same number of joinpoint but at different locations, see Table 2. IV. DISCUSSION Change point analysis is necessary to detect significant interventions which impact rates of healthcare associated infections. Segmented regression with different sets of data was used to identify change points in HAIs (MRSA bacteraemia, MSSA bacteraemia, CDI in patients over 65 years and CDI in patients aged 15-64 years). Using all available data to fit segmented regression has some advantages. Segmented models can be estimated more accurately when there is a long period of time for analysis since the variance of the slope is then smaller. Since the same data was used each time when fitting different models, models with more than one interven- tion can be fitted and likelihood ratio test used to test the significance of nested models. The residual deviance can then be used to compare different models at different interventions. The limitation of using all the data is that segmented regression is fitting linear trends before and after an intervention and the linear trend does not describe the date well over a long period of time. Specifying the number of data points before and after each intervention to be two years of data (8 points) ensures there is enough residual degrees of freedom since each model has linear effect of time and a seasonal effect. This has the benefit that there are approximately equal variances of the slope before and after the intervention since the same number of data points are considered. The smallest variance then estimates the best fitting model. Also, since segmented regression is fitting linear trends before and after an intervention, the model is more likely to be linear and symmetric over this short period of time. On the other hand, the segmented model can be less accurate with lower power and precision because a short period of time was used. The residual deviance cannot then be used to compare fitted models so PDE was used to measure the goodness of fit. This compares each model with its null model and the model with a significant change in the slope after the intervention and the largest PDE is best. The trend of MSSA bacteraemia has one change over time but joinpoint analysis did not identify this. However, segmented regression of MSSA rates indicate one change where the rate starts to increase. It would appear that none of the interventions had a significant impact on the rates of MSSA. Joinpoint software [NCISR (2020)] does not allow modelling the effect of seasonality. The soft- ware was modified to include seasonality allowing more flexibility. Adding seasonality to MRSA, CDI in patients over 65 years and CDI in patients aged 15- 64 years, did not change the number of joinpoints but did change the locations suggesting that seasonality does influence infection rates. Confidence intervals for joinpoints can be constructed using the limiting distribution with large samples [Bai (1997)]. Profile likelihood and bootstrap are non-parametric approaches used to construct confidence intervals for joinpoints with unknown distributions. Using the profile likelihood method to construct confidence intervals for joinpoint does not work well, especially with small sample sizes. This is due to the residual deviance of joinpoint models being similar to each other. There can also be more than one minimum turning point or the horizontal line may not intersect with the curve. This can happen when the difference between the maximum and inimum points of deviances is less than χ2 ( 0.95,1) = 3.84. The profile likelihood cannot be applied when the model has more than one joinpoint because a single value of deviance describes these points and the curve of the deviance function cannot be plotted. As a result, profile likelihood confidence intervals do not perform well when the sample size is small or the model has more than one joinpoint. In such cases the bootstrap method can be used to construct confidence intervals, however, these intervals are wider and need much more computation than profile likelihood confidence intervals. © IJRASET: All Rights are Reserved 584 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com The research aimed to detect the time point and the specific intervention which reduces the rates of HAIs. Segmented regression analysis showed that the change in the rate of MRSA bacteremia occurred in 2006 and the first of these was the initiation of standard infection control precautions [RCN (2005)]: 1) Cover all cuts with clean waterproof dressing. 2) Keep hand hygiene every time. 3) Shake off any waste safely. 4) Do not transfer unnecessary patient between wards. 5) Arranged time for patient to avoid crowding. 6) Isolate patients who have infection. The second intervention was to introduce hand hygiene policy which includes [RCN (2005)]: a) Hands should be cleaned before and after contact with patients. b) Using soap and water for dirty hands and dried hands after that. c) Using alcohol if hands are clean. In addition, health improvement, efficiency, access and treatment (HEAT) was introduced with the expectation of a 30% reduction in SAB by 2010 [HPS (2006)]. Finally, MRSA screening practices changed to include all patients at admission, discharge and transfer. Staff who test positive for MRSA are also screened [RCN (2005)]. Joinpoint analysis showed the changes in rates of MRSA in 2007 when the Scottish patient safety programme (SPSP) was declared. SPSP aimed to improve healthcare safety and reliability in all health care settings [SPSP (2005)]. The rates of CDI in patients over 65 years changed in 2009 when the first healthcare environ- ment inspectorate (HEI) was carried out across the NHS in Scotland [HIS (2009)]. The hospital infection incident assessment tool (HIIAT) also started in 2009. This provides all tools that are needed to know about hospital infection [HPS (2011)]. However, joinpoint analysis showed that the change occurred in 2008 when quality improvement Scotland (QIS) was launched. QIS covers the issues relating to provision of patient-focused care and treatment [HIS (2008)]. Also in 2008, transmission based precautions(TBPs) commenced and was a requirement of staff. TBPs are control measures that should be implemented in addition to standard infection control precautions to infected patients [ICT (2015)]. In conclusion, the change point problem is an important analysis to detect the presence and locations of changes in trends of data. Segmented regression and joinpoint analysis have approx- imately similar results in terms of the location of such points. Segmented regression analysis depends on specific (known) time points, i.e. exact times when interventions took place. The process then looks at times when the pattern changes significantly after and intervention. Joinpoint analysis detects changes at unknown times and this approach looks for changes over a period of time and gives the most significant change points within all the data. It is more accurate than segmented regression because it is rare for an intervention to impact rates immediately - usually it takes time to affect the rates of HAIs. The joinpoint method detects the time not only at intervention points but also at points after interventions took place. The joinpoint analysis was also able to account for the impact of seasonality on rates. The idea in this research was to detect the times and interventions that reduced the rate of healthcare associated infections. The work suggests that improving the implementation of some healthcare interventions such as hand hygiene, training courses for hospital staff in dealing with infection, screening MRSA and MSSA in patients prior to hospital admission and applying antibiotic policy have helped to reduce and prevent infection in hospitals and healthcare systems. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] Bai, J. (1997). Estimation of a change point in multiple regression models. Review of Economics andStatistics, 79(4):551–563. Chen, J. and Gupta, A. K. (2011). Parametric statistical change point analysis: with applications to genetics, medicine, and finance. Springer. 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Quarterly epidemiological data on clostridioides difficile infection, escherichia coli bacteraemia, staphylococcus aureus bacteraemia and surgical site infection in Scotland. Jan- uary to March (Q1) 2020. Available at https://www.hps.scot.nhs.uk/search?q=Quarterly+ epidemiological#searchForm. [Accessed: 14-7-2020]. ICT, I. C. T. (2015). Transmission based precautions literature review: Definitions of trans- mission based precautions. Available at http://www.documents.hps.scot.nhs.uk/hai/ infection-control/ic-manual/tbp-lr-definitions-v1.0.pdf. [Accessed: 5-1-2015]. Kim, H.-J. (2001). Permutation tests for joinpoint regression with applications to cancer rates. Statistics in Medicine, 20(4):655–655. Kim, H.-J., Fay, M. P., Feuer, E. J., and Midthune, D. N. (2000). Permutation tests for joinpoint regression with applications to cancer rates. Statistics in medicine, (19):335–51. NCISR (2020). 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Improved hospital-level risk adjustment for surveillance of healthcareassociated bloodstream infections: aretrospective cohort study. BMC infectious diseases, 9(1):145. Wagner, A., Soumerai, S., Zhang, F., and Ross-Degnan, D. (2002). Segmented regression analysis of interrupted time series studies in medication use research. Journal of clinical pharmacy and therapeutics, 27(4):299–309. Wertheim, H. F. L. (2005). Staphylococcus aureus infections; Lead by the nose. PhD thesis, Erasmus MC: University Medical Center Rotterdam. APPENDIX: INTERVENTIONS PROVIDED BY HPS Health protection Scotland (HPS) provided the information about when interventions took placefrom 2004 to 2011. Table 3: Interventions provided By HPS Month Intervention May 2004 control. March 2005 NHS Scotland Code of Practice on HAI management published.February 2005 July 2005 January 2006 February 2006 April 2006 April 2006 March 2007 December 2007 January 2008 March 2008 May 2008 July 2008 August 2008 August 2008 October 2008 January 2009 January 2009 March 2009 April 2009 April 2009 CNO letter on alcohol based handrubs and infection CNO requested that all G Grade Sisters/ Charge Nurses (Senior Charge Nurses) undertake the Cleanliness ChampionsCourse commenced. New IC structure in Boards, including ICM funding. August 2005 Antimicrobial Prescribing Policy and Practice in ScotlandRecommendations for good antimicrobial practice in acute hospitals. Hand hygiene national campaign announced/launched. Standard Infection Control Precaution model policiesfirst launched. HEAT targets introduced- target of 30% reduction in SAB by 2010asked of all boards. MRSA guidelines issued in Journal of Hospital Infection (although not Scottish initiative, widely recognised by infectioncontrol world)- screening practices changed. Scottish Patient Safety Programme (SPSP) announced-no intervention at this point. First national hand hygiene compliance report issued. HPS care bundles related to interventions first launched (SPSP). Launch of QIS standards (followed by visits to Boards related to these- from 2008).March 2008 HPS CDI bundle launched. Transmission Based Precaution model policies first launched.July 2008 SAPG guidance control of 4Cs antibiotic policy Cleanliness champions uptake at 2000 members of staff. Letter to CE in Scotland outlining roles and responsibilities for HAI(performance management push). National action plane for CDI. Credit card flyer issued (ABHR message).December 2008 National CDI guidance issued. Cab Sec announcement on zero tolerance tonon compliance with hand hygiene. HAIRT template introduce for hospital reporting atboards bi monthly. Second Wave of NHS staff materials (with mandate from SGHD for compulsory placement). Revised HEAT targets announced- CDI one introduced. Public health act (inclusive of reporting SAB and CDI) implemented. © IJRASET: All Rights are Reserved 586 International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.429 Volume 9 Issue III Mar 2021- Available at www.ijraset.com Month Intervention September 2009 September 2009 January 2010 March 2010 March 2011 First HEI inspection carried out. Second Wave of NHS staff materials reissued.December 2009 HIIAT issued for managing outbreaks. SAB 90 day programme launched. MRSA Screening changes in all Boards- targeted universal in specialties interimpolicy. MRSA screening changes to CRA. SAB: Staphylococcus aureus bacteraemia, CDI: Clostridium difficile infection, NHS: National Health Service, HAI: Healthcare associated infection, SAB: CNO: Chief nursing officer, IC: Infection control, ICM: Intensive care medicine, HEAT: Health improvement, efficiency, access and treatment, MRSA: Methicillin-resistant staphylococcus aureus, SPSP: Scottish patients safety program, HPS: Health Protection Scotland, QIS: Quality improvement Scotland, SAPG: Scottish antimicrobial prescribing group, 4Cs Antibiotic: Broad-spectrum antibacterials including clindamycin, co-amoxiclav, cephalosporins and fluoroquinolone, CE: Chief Executives, ABHR: Alcohol based hand rub, HAIRT: Healthcare Associated Infection Reporting Template, SGHD: Scottish Government Health Directorate, HEI: Healthcare environment inspectorate, HIIAT: Hospital infection incident assessment tools, CRA: Clinical risk assessment. © IJRASET: All Rights are Reserved 587