Influence of Time (years) on Efficiency

The efficiency and bootstrap- efficiency scores appeared to be higher during recent years, when compared with previous years, and the influence was highly significant, as shown by the three estimation procedures (p-value<0.005). Consequently, this result supports the previous findings of both DEA analysis and Malmqusit Index.

6.9.9 Indirect and Total Effect

In terms of a direct effect, the results provided in Tables 6.27 and 6.28 confirmed that the females, who were above 60 years and less than 18, did not have any indirect impact through intervention variables of patients with GCS. For a total effect, the total influence of gender was -.0014 for inefficiency and -.0015 for bootstrap-inefficiency scores, with both producing significant relevance using ordinary and robust SE. Furthermore, the total influence of age>60 was 0.0010 for inefficiency and 0.0011 for bootstrap-inefficiency scores, where only robust SE resulted in a significant impact. Comparatively, no significant influence was seen for the ages of <18 within both inefficiency and bootstrap-inefficiency scores.

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Effect Structural model

SEM Ordinary procedure Ordinary Allowing for Heterosked- asticity Β p- value β p-value

Indirect effects Inefficiency

Female -.00008 .248 -.00008 .470 Age >60 years -.0013 .144 -.0013 .316 Age <18 years -.00009 .194 -.00009 .291

Total effects Inefficiency

Female -.0014 .019 -.0014 .037 Age >60

years .0010 .074 .0010 .019 Age <18

years -.0001 .780 -.0001 .685

Table 6.27: Indirect and total effect for inefficiency scores

Effect

Structural model

Ordinary

procedure Robust procedure

Β p- value β p- value Indirect effects Efficiency Female -.00008 .253 -.00008 .643 Age >60 years -.0001 .145 -.0001 .961 Age <18 years -.00009 .202 -.00009 .151

Total effects Efficiency

Female -.0015 .019 -.0015 .045 Age >60

years .0011 .068 .0011 .018 Age <18

years -.00009 .868 -.00009 .816

Table 6.28: Indirect and total effect for bootstrap-inefficiency scores

6.10 Conclusion

The aim of this chapter has been to examine the performance of HTI hospitals during the period 2009-2012. As indicated in Chapter 3, the DEA method does not require any prior assumptions in regards to the functional forms, nor any assumptions relating to organisation-

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specific effects. Therefore, it theoretically avoids imposing a wrong functional form on organisations, which is imperative when analysing hospitals, whose behavioural assumptions are not easily defined. Likewise, its capabilities of accommodating multiple inputs and outputs simultaneously, as well as not requiring input price data, also make the DEA the preferable method for measuring hospital efficiency. Hence, the current research employed the DEA method to measure efficiency, and the Malmquist productivity index to investigate the productivity growth of the HTI hospitals.

The choice of inputs and outputs for this empirical analysis of HTI hospital efficiency assessment was based on the postulated theory, the input- output selection from previous studies, the opinions of TARN managers, and the availability of data. The model specification was subsequently chosen with three measures of inputs and six measures of outputs. The inputs are the average number of doctors per patient, the average number of consultants per patient, and the total cost per patient. Moreover, they are the percentage of patients with minor injuries who recovered satisfactorily, the percentage of patients with moderate injuries who recovered satisfactorily, the percentage of patients with severe injuries who recovered satisfactorily, the average of the total period of stay per patient, the average number of total surgical operations per patient, and the average number of treatments provided by emergency services per patient.

Once the DEA method was used to examine the technical efficiency, it was ascertained that pure technical efficiency relatively increased during the period under consideration, from 90.74% in 2009 to 92.99% in 2012. The improvement analysis demonstrates that inefficient hospital managers’ are oriented toward decreasing the average number of doctors and total cost, and less oriented toward reducing the average number of consultants. In addition, HTI hospitals can be equally competitive in relation to pure technical efficiency, as neurosurgical unit hospitals and non- neurosurgical hospitals rank about the same, and no relationship exists between these hospital groups and its efficiency. Hence, there is no reason to believe that hospital performance differs in their ratings from a statistical perspective according to their operating style.

Furthermore, the results of the Malmquist productivity indices showed that the total factor productivity of HTI hospitals increased after a regress in the first pair of years. Overall, the progress of average productivity of 7.87% was mainly due to the technical efficiency improvement of 7.66% per year. The catching-up effect (i. e. improvement in technical

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efficiency change) was attributable to the positive change in both pure technical efficiency (1.77%) and scale efficiency (5.7%).

Overall, out of the seven environmental factors, three are considered to be important in directly affecting the efficiency of HTI hospitals, which are: the percentage of the age > 60 years old, together with the percentage of female groups and years. Comparatively, the indirect effects of these environmental factors on efficiencies through the 2 groups of the severity of patients was attributed to the percentage of both age groups: the age > 60 years and the age<18 years. However, following the consideration into the total effect of the environmental factors on the hospital efficiencies, only the age > 60 years and the female group demonstrated an important influence.

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CHAPTER SEVEN:RESEARCH FINDINGS AND CONCLUSIONS

7.1 Introduction

In the previous chapters, performance measurement approaches have been introduced and the most appropriate procedures have been selected. Despite the fact that DEA has some pitfalls, it is still the most common method used by scholars. The current study uses the DEA approach to appraise the efficiency of HTI care in the UK with the purpose of reducing costs to a minimum. In order to deal with missing data, a new methodology in the DEA context has been suggested, and the majority of the published literature on hospital performance has been reviewed by the study, although challenges remain in certain measurements of hospital performance, such as how to deal with environmental factors. Thus, in order to deal with such factors, SEM has been proposed as an integrated method with the output of DEA, so that the effects of these factors on hospital efficiency can be investigated. Consequently, the current research may be considered to be the first study that has integrated SEM as an exploratory technique with the DEA method to incorporate uncontrollable factors with DEA scores. Certain conclusions have been exhibited from this chapter, which offer some recommendations to inform and direct future research, and the structure of this chapter is as follows. In Section 7.2, a summary of the research findings are presented; Section 7.3 contains recommendations for managers and discusses policy related implications; Section 7.4 relates to the contributions of the current study to the areas of DEA and health care. Section 7.5 provides some suggestions for future research; study limitations are presented in Section 7.6; and Section 7.7 presents an overall conclusion.

7.2 Overview of the Research Findings

7.2.1 First Stage Results

The data used in the current study represent information collected for a sample of patients who were hospitalised with trauma brain injury (TBI) in any of 114 hospitals during the period of 2009-2012. These data were kindly provided under confidentiality agreements by TARN, in conjunction with the University of Manchester.

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The method used to assess the performance of HTI care is the BCC approach, which incorporates 3 inputs and 6 outputs. The input variables in the assessment are the average number of doctors per patient, the average number of consultants per patient, and the total cost per patient. The outputs are the percentage of patients with minor injuries who recovered satisfactorily, the percentage of patients with moderate injuries who recovered satisfactorily, the percentage of patients with severe injuries who recovered satisfactorily, the average of the total period of stay per patient, the average number of total surgical operations per patient, and the average number of treatments provided by emergency services per patient.

Various values were absent, such as the ones related to the average number of doctors per patient, the average number of consultants per patient and the average number of total surgical operations per patient. Ultimately, the MICE approach was one method considered for replacing the missing variables, as comparing the distribution of data pre- and post- imputation demonstrated clear similarities between the distributions for each of the variables. Furthermore, it was noted that all the output variables increased during the study period. However, in regards to the long time period being analyzed, it was expected to be necessary to observe such increasing levels of productivity.

The results obtained from the input VRS-DEA model reveal that the average pure technical efficiency of all HTI hospitals during the study period of time is 91.7%, as based on the selected inputs and outputs. This percentage implies that there are considerable possibilities for increasing the level of technical efficiency by 8.3%. Moreover, the results demonstrate that the mean was relatively stable for the first two years and reached its highest level (93.0%) in 2012. Out of 114 hospitals, the number of efficient hospitals increased from 41 to 60 over this period. The standard deviation of the technical efficiency is negatively correlated with the average technical efficiency over the four years considered. Overall, the minimum score (46.7%) of the inefficient HTI hospitals was in 2009, which improved over the next two years until it reached 63.6% in 2011.

The empirical findings from the current study have answered the uncertainty into whether there is empirical evidence to support the assumption that the costs associated with HTI can be lowered while health care can be improved at the same time. The results have suggested that in order to achieve a high level of hospital performance, head trauma care managers are required to provide the priority to the total cost and the average number of doctors, while simultaneously reducing the average amount of consultants. Similarly, inefficient hospitals’

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managers should reduce, on average over the study period, the total cost by 36.8% to make their hospitals fully efficient. Managers also need to decrease, on average over the study period, their average number of doctors by about 18.0%, and their average number of consultants by 8.5%. However, the reduction of each input variable varies from one year to another.

In addition, the findings also reveal that the performances of neurosurgical unit hospitals and non-neurosurgical unit hospitals are similar. This was assessed by the Mann-Whitney test, which provides the result that there is no statistically significant correlation between a hospital's characteristics and its efficiency score. The bootstrap DEA method of Simar and Wilson (1998, 2000, 2007) was undertaken in order to investigate the consistency of the DEA results, with the mean of the bootstrap efficiency estimated at 91.7%, which is very close to the mean (91.1%) of the original efficiency score. The point of interest to note is that none of the efficient hospitals identified from the original DEA model change to be inefficient hospitals following correction for bias by the bootstrapping DEA approach. Moreover, the average DEA efficiency scores of hospitals for each year are included in the corresponding 95% confidence interval for the bootstrap efficiency score. Thus, it is confirmed that the original DEA model is robust. Likewise, the Spearman rank correlations between the efficiency scores was also analysed, which was generated by our original DEA model and the bootstrapping DEA model. The observed correlation is a large positive value that is statistically significant at the 5% level.

All these results from the robustness analysis confirm that our DEA model is consistent. To achieve further robustness analysis, the internal validity and external validity were investigated. The internal validity was tested by comparing the results obtained by adopting different selections of inputs and outputs, while the external validity was tested by determining the stability of the efficiency score estimates over a period of time. The Spearman rank correlation of the internal validity analysis results show a large positive correlation between the two models in each year, which confirms internal validity. Similarly, the Spearman rank correlation results of the external validity analysis were positive and statistically significant, although they were not always extensive. Consequently, there is stability of change in the relative performance of HTI hospitals between each pair of years. The Friedman's test result confirms that there is no statistically significant difference in HTI

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hospital efficiencies over the period of the study. Therefore, this validity analysis reveals that the DEA model was robust and stable during the study period.