A Systematic Literature Review of Efficiency Measurement in Nursing Homes

Background: As our population ages at an increasing rate, the demand for nursing homes is rising. The challenge will be for nursing homes to maintain efficiency with limited resources while not compromising quality. This study aimed to review the nursing home efficiency literature to survey the application of efficiency methods and the measurements of inputs, outputs, facility characteristics and operational environment, with a special focus on quality measurement. Methods: We systematically searched three databases for eligible studies published in English between January 1995 and December 2018, supplemented by an exhaustive search of reference lists of included studies. The studies included were available in full text, their units of analysis were nursing homes, and the analytical methods and efficiency scores were clearly reported. Results: We identified 39 studies meeting the inclusion criteria, of which 31 accounted for quality measures. Standard efficiency measurement techniques, data envelopment analysis and stochastic frontier method, and their specifications (orientation, returns to scale, functional forms and error term assumptions) were adequately applied. Measurements of inputs, outputs and control variables were relatively homogenous while quality measures varied. Notably, most studies did not include all three quality dimensions (structure, process and outcome). One study claimed to include quality of life; however, it was not a well-validated and widely used measure. The impacts of quality on efficiency estimates were mixed. The effect of quality on the ranking of nursing home efficiency was rarely reported. Conclusions: When measuring nursing home efficiency, it is crucial to adjust for quality of care and resident’s quality of life because the ultimate output of nursing homes is quality-adjusted days living in the facility. Quality measures should reflect their multidimensionality and not be limited to quality of throughput (health-related events). More reliable estimation of nursing home efficiencies will require better routine data collection within the facility, where well-validated quality measures become an essential part of the minimum data requirement. It is also recommended that different efficiency methods and assumptions, and alternative measures of inputs, outputs and quality, are used for sensitivity analyses to ensure the robustness and validity of findings.


Appendix 1 -Efficiency measurement
All production requires the use of resources such as equipment and buildings (often referred to as capital), personnel (as labour), and land and raw materials. We can regard production as a process by which these resources are transformed into goods or services.
Measures of efficiency can be defined as "ex post measures of how well firm managers have solved different optimisation problems" [1]. To measure how well a decision-making unit (DMU) perform in producing outputs (goods or services) from inputs (resources) and we need to know about their managerial behaviour (optimisation problems), for which the existing sets and functions has few implications for behaviour. For instance, revenue function does not mean that DMU managers will choose outputs in order to maximise revenues. Instead, different DMU managers tends to behave in different ways depending on what they can and cannot choose and on what they value. Some of the simplest optimisation problems that DMU managers face involve minimising inputs, maximising outputs, and/or maximising productivity [1].
Efficiency answers the question if any waste can be eliminated without worsening any inputs or outputs [2]. It is considered inefficient if the desired outcome can be achieved with less throughputs or the throughputs could produce more outcome desired.
Following are concepts of measuring efficiency which is also applied in health care: Economic efficiency, or overall efficiency, refers to an economic state in which objectives are achieved in relation to the inputs (economic resources) used. It is estimated by the value of inputs employed and value of outputs delivered. Economic efficiency can be measured when price information is available and optimisation assumption-eg. cost minimisation, profit/revenue maximisation-is appropriate [3]. When the objective is revenue maximisation, a production function or output-oriented approach can be used to estimate revenue efficiency.
When the cost minimisation is more appropriate, a cost function or input-oriented approach can be applied to measure cost-efficiency.
Technical efficiency refers to the measures of how well technologies are chosen and used [1]. It measures the ability of a DMU to avoid waste by minimising inputs as output level will allow or maximising outputs as input usage will allow. Technical efficiency can be categorised in terms of non-scale and scale effects. The former is considered as pure technical efficiency which technical efficiency under a variable return to scale (VRS) production technology. Scale efficiency measures the ability to eliminate waste by operating at the optimal productive scale.
It is about operation size and how various sizes influence productivity and efficiency of the DMU. A DMU is referred to be at optimal scale only when it attains the highest possible productivity (ratio of output to input) with the available technology.
Allocative efficiency reflects the ability of a DMU to use their available inputs in optimal proportions given the available production technology and their respective prices. It is about

Economic efficiency (EE)
• The value of inputs used in comparison with the value of outputs produced. • Including cost efficiency and revenue efficiency.

Allocative Efficiency (AE)
Ability to use optimal proportions of inputs to produce outputs given their respective prices.

CRS Technical Efficiency (TECRS)
• Ability to produce maximum possible quantity of output with given input, or use minimal possible quantity of input as output level will allow, when the production technology is assumed to be constant returns to scale.

Scale efficiency (SE)
Ability to increase productivity by operating at the most productive scale.

VRS technical efficiency (TEVRS)
Technical efficiency when allowing the production technology to exhibit variable returns to scale (increasing or decreasing).
choosing between technically efficient combinations of inputs used to produce the maximum possible outputs.
Two major methods to measure efficiency are non-parametric and parametric methods.
The non-parametric method is a piecewise-linear convex hull approach to frontier estimation originally proposed by Farrell [4], developed by Charnes et al. [5]; Banker et al. [6] and Fare et al. [7]. Data Envelopment Analysis (DEA), the predominant representative of nonparametric method, applies linear programming approach to estimate the production technology. DEA is often described as a non-parametric method as it does not involve any error terms. As such, it does not involve any assumptions about the functional form of the technology or the parameters (means, variances) of the distributions of those error terms. DEA requires assumptions regarding the regularity properties of the production frontier. For example, if the production possibilities set is not convex then the DEA model is known as a Free Disposal Hull model. DEA's assumption on functional form is that the cost or production frontier is locally linear.
The parametric method has stochastic frontier analysis (SFA) as the predominant representative. SFA involves the use of econometric methods to measure either primal or dual representations of the production technology. It was first developed simultaneously by Aigner et al. [8], Meeusen and Van den Broeck [9] and Battese and Corra [10]. Since then, SFA has evolved and become an increasingly popular method. SFA assumes the functional form of the frontier (e.g. translog or linear), the regularity properties of the frontier (e.g. monotonicity or concavity), and the distributions of error terms representing inefficiency and statistical noise (e.g. means or variances). The maximum likelihood method is usually used to estimate the unknown parameters of these functions and error distributions.