Effects of health and social care spending constraints on mortality in England: a time trend analysis

Objective Since 2010, England has experienced relative constraints in public expenditure on healthcare (PEH) and social care (PES). We sought to determine whether these constraints have affected mortality rates. Methods We collected data on health and social care resources and finances for England from 2001 to 2014. Time trend analyses were conducted to compare the actual mortality rates in 2011–2014 with the counterfactual rates expected based on trends before spending constraints. Fixed-effects regression analyses were conducted using annual data on PES and PEH with mortality as the outcome, with further adjustments for macroeconomic factors and resources. Analyses were stratified by age group, place of death and lower-tier local authority (n=325). Mortality rates to 2020 were projected based on recent trends. Results Spending constraints between 2010 and 2014 were associated with an estimated 45 368 (95% CI 34 530 to 56 206) higher than expected number of deaths compared with pre-2010 trends. Deaths in those aged ≥60 and in care homes accounted for the majority. PES was more strongly linked with care home and home mortality than PEH, with each £10 per capita decline in real PES associated with an increase of 5.10 (3.65–6.54) (p<0.001) care home deaths per 100 000. These associations persisted in lag analyses and after adjustment for macroeconomic factors. Furthermore, we found that changes in real PES per capita may be linked to mortality mostly via changes in nurse numbers. Projections to 2020 based on 2009-2014 trend was cumulatively linked to an estimated 152 141 (95% CI 134 597 and 169 685) additional deaths. Conclusions Spending constraints, especially PES, are associated with a substantial mortality gap. We suggest that spending should be targeted on improving care delivered in care homes and at home; and maintaining or increasing nurse numbers.


Conclusions
Spending constraints, especially PES, may have produced a substantial mortality gap. We suggest that spending should be targeted on improving care delivered in care homes and at home; and maintaining or increasing nurse numbers.

KEYWORDS
Health care, social care, spending, expenditure, mortality, PYLL, life expectancy, time trend

STRENGTHS AND LIMITATIONS
• Time trend analysis with projections of future outcomes and counterfactual analysis • Sensitivity analyses by using other outcomes: potential years of life lost and life expectancy • Analysis included potential effect modifiers and mediating factors • Results only imply association rather than causation • There might be other mediating factors beyond those identified in this study  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  coverage, is no exception. [1][2][3][4] Since 2010, the NHS in England has seen a real-term annual increase in public healthcare spending in England of 1.30% between 2010 and 2014, as compared to historical annual growth of around 4%. 4 During the same period, demand and healthcare cost inflation increased sharply, with medical advances and a growing and ageing population contributing. By 2020/21, a funding gap, between what is needed and what is available, has been predicted, unless major changes are implemented 4 Public-sector funding for social care in England has also suffered. 5 Such funds enable the provision of means-tested home care and care-home accommodation, 6 allowing, for example, hospitals to discharge frail patients who would otherwise have no adequate support. Real-term adult social care spending decreased by 1.19% annually between 2010 and 2014, reversing the annual increase of 3.17% between 2001 and 2009. This is despite increasing demand, with the group most likely to require social care -the over-85s -set to rise from 1.6 million in 2015 to 1.8 million in 2020. 7 This supply-demand mismatch has manifested in several ways. During the first week of 2017, more than four in 10 NHS hospitals declared a major alert. 8 Emergency medicine departments (A&E) saw 900,000 (4.6%) more attendances in 2015/16 compared with the previous year, and 4% more emergency hospital admissions. 9 Over the past two years, the number of elderly patients waiting 5 over 12 hours in A&E has trebled, and there has been a 31% increase in delayed hospital discharges. 9 While the funding gaps facing health and social care have been well-quantified, 10,11 the impact on population outcomes remains unclear.
Here we sought to model the past, present, and future impact of funding constraints experienced by the public health and social care system in England on mortality, to provide insights into the association between funding and health outcomes and inform future financial allocations.

Data collection
Population mortality data for England were extracted from the UK's Office for National Statistics (ONS) 12 based on Medical Certificates of Cause of Death from the Registration Online system.
Age-standardized death rates (ASDR) were calculated with reference to a standard European population using mortality data split into ten age groups (see Supplementary Appendix).
Information on deaths by place of occurrence (care homes, hospice, home, hospital, and other establishments) was provided by Public Health England. Additionally, mortality data were collected for 325 lower-tier local authorities (LAs) based on 2010 boundaries with Cornwall and the Isles of Scilly combined, due to the small population of the latter. Data on life expectancy were obtained from the ONS, whereas data on potential years of life lost (PYLL), a measure of premature mortality from causes considered amenable to healthcare, were obtained from the UK Health and

Statistical analysis
For all analyses, we used 2001 as the start of the study period since complete population mortality data were available from this year onwards, as well as it being first year that ICD-10 was used.
Time-trend analyses were conducted using Poisson or quasi-Poisson regression models with either all-cause ASDR or rates of PYLL as the dependent variable and calendar year as the independent variable. Analyses were repeated for each sex, age group, place of death, and local government area. Further details are provided in the Supplementary Appendix.
Fixed-effects regression models were conducted using real PEH/PES per capita and controls for economic variation (unemployment 14 and the average annual consumer price index [CPI] 15 ) and average weekly pensions as the independent variables, and care home, home and hospital mortality as the dependent variables. These were repeated for 1-and 2-year lag periods.
To validate these results, we looked at two alternative health outcomes: life expectancy and PYLL.
To see whether the possible effects of the 2010 spending constraints were sensitive to age, we conducted time-series analyses for ten different age groups (Table S4). Higher-than-expected numbers of deaths were confined to those ≥60 years of age with all six ≥60 age groups showed excess deaths in 2013. By contrast, <60 age groups most often exhibited fewer deaths.
We next looked at place of death for all age groups, while stratifying them by age into <60 and those ≥60 years. Time-trend analyses revealed care-home and home deaths to be the first and second largest contributors, respectively, to excess deaths across age groups and in those ≥60 ( Figure 2, Figure S2 and Table S5), with a relative increase in these places of death over others during the study period. For every year analysed, lower-than-expected numbers of deaths occurred in hospitals. For those <60 years, hospitals were the most frequent place of death, and so the net result was a lower-than-expected number of <60 deaths. Time-series analyses by local government area (for time points up to 2013) revealed no correlation between changes in the number of expected deaths and deprivation (P=0.14, R S =0.08).

Longitudinal associations between spending and mortality
Over the study period, we found that £10 per capita declines in real PEH and real PES were associated with increases of 0.19 (0.01-0.38) (P=0.049) and 5.10 (3.65-6.54) (P<0.001) care-home deaths per 100,000 in England, respectively (Table 1). For PES, these relationships persisted at least two years after the initial change but became weaker for PEH. We next sought to demonstrate that these associations were independent of macroeconomic forces, such as unemployment (for younger age groups) and pensions (for older age groups), which have each been linked with increased mortality. 17,18 On adjusting the regression models for macroeconomic factors and the annual average of weekly pensions, we found real PES per capita and real PEH per capita, remained inversely associated with care-home mortality (Table 1). Next, we used a regression model with both real PES and PEH per capita as explanatory variables, and found only PES remained inversely associated with care-home mortality ( Table 1). The results for home deaths replicated those for care-home deaths (Table S6). To check whether PES was specifically related to care-home and home mortality rather than any place of death, we conducted the same set of analyses using hospital mortality as the response variable. In contrast to care-home and home mortality, real PEH per capita was more strongly related to hospital mortality than real PES per capita without adjusting for controls. However, on adjusting for macroeconomic forces, the relationship between PEH and hospital mortality was no longer apparent (Table S7).  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59

Identification of resources potentially mediating the spending-mortality relationship
To discern the most important resources mediating the relationship between real PES per capita and care-home and home mortality, we collected data on workforce and bed numbers, and performed mediation analyses.
We were able to gather complete 2001-14 data for ten relevant health and social care resources (see Supplementary Appendix). Using these data, we found that the numbers of NHS hospital and community nurses, and NHS health and social care clinical support staff were each associated with care-home mortality while alleviating the relationship between real PES per capita and care-home mortality at lag years 1 and 2, suggesting these staff numbers were the most important mediators of the spending-mortality relationship ( Table 2). When we looked at home mortality as the outcome, we found the number of nurses, but not clinical support staff, was suggested to be a mediator of the relationship between spending (both PEH and PES) and mortality rates for lag years 1 and 2 (Table   S8). On repeating these analyses for PEH, we again found the number of nurses to be the sole mediator of the relationships between PEH per capita and care-home mortality (Table S9), and PEH per capita and home mortality (Table S10) for all years. In this regard, from 2001 to 2010, the average annual change in nurse numbers was 1.61 % whereas from 2010 to 2014, the average annual change was over twenty-fold lower at 0.07% (Table S11).

Mortality projections to 2020 and scenario modelling
To investigate the possibility of a future population mortality gap, we projected mortality rates to To determine what it would take to close this gap above planned health and social care spending to 2020/21, we modelled three different scenarios ( Figure 3 and Table S12). On top of the combined health and social care budget, the aggregate spending and efficiency combinations required to completely close the mortality gap would be: an additional £29.56 billion (£25.74-33.37 billion) for a conservative 0% annual efficiency gain; an additional £27.26 billion (£23.61-30.91 billion) for a moderate 1% annual efficiency gain, and an additional £23.03 billion (£19.67-26.39 billion) for an aggressive 3% annual efficiency gain ( Figure 3 with an annual breakdown in Table S12). Under an ideal scenario in which no additional spending would be needed to close the mortality gap, the annual productivity increase to 2020 would need to reach 10.79% (7.8 to 14.46). In these scenarios, efficiency gains reflect improvements across the system required to meet respective spending constraints, while avoiding excess mortality.

DISCUSSION
This study demonstrates that recent constraints in PEH and PES spending in England have been associated with nearly 45,000 higher-than-expected numbers of deaths between 2012 and 2014. If these trends continue, even when considering the increased planned funding, we estimate approximately 150,000 additional deaths may arise between 2015 and 2020. Combining these projected excess deaths and the observed deaths prior to 2015 translate to around 95,000 excess  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59   The associations observed between PEH, PES, and mortality were independent of macroeconomic changes that often co-occur with periods of reduced public-sector spending. However, adjustment for health and social care resources, and nursing numbers in particular, nullified the associations between PEH, PES, and mortality. Our study suggests that the number of NHS-qualified nurses is the strongest tested mediator of the relationships between spending, and care-home and home mortality; this is congruent with findings in other reports. 21 This study has several policy implications. First, it demonstrates that decelerated public health and social care funding increases in England may have adversely affected population mortality as demand increased and healthcare costs rose above inflation. This demonstrates that while health system design and ambition, such as delivery of universal coverage, is important, it must be adequately financed to ensure design translates into health improvement. Second, the finding that the elderly population and those in care homes were the most vulnerable to recent financial challenges, makes a strong case for targeted interventions to ensure adequate management of these patient groups. 4 This includes funding increases in social care, in addition to maintenance or rises in nursing numbers aligned with demand. Third, and perhaps most importantly, there remains a prospective cost to the current trajectory of system financing that entails a number of excess deaths.
While it would be presumptive to class these deaths as avoidable (we have used the terms 'additional' or 'excess' to describe higher-than-expected numbers), we have outlined several funding-efficiency scenarios that attempt to demonstrate how such a gap could be closed. Given that the health system has historically achieved 1-2% annual productivity improvements, and that current demand is unprecedented, it seems unlikely that greater annual improvements could be  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  JW, WW, GDS, PDR, and VAM conducted data formatting, and JW and WW carried out statistical analysis with input from LPK. All authors helped interpret the findings. JW, WW, and MM wrote the first draft of the manuscript with input from DM, CDZ, RR, and LPK; all authors provided input to subsequent drafts. All authors had full access to all of the data in the study and can take responsibility for its integrity and the accuracy of the data analysis.

FUNDING
No funding was received for this study.

COMPETING INTERESTS
MM serves as an advisor to NHS England and is co-founder of Cera. However, the views expressed in this manuscript are his own and not those of Cera or NHS England.

ETHICAL APPROVAL
Not required.
Therefore, we employed a quasi-Poisson model in all analyses, with the logarithmic link function preventing the prediction of negative rates. The model takes the following form: where E(M t ) is the estimated mortality rate for year t, α is the baseline mortality rate, and β is the estimated drift parameter. For increasing observation-base trends, the following non-linear prediction model proposed by Dyba and colleagues, 14 also assuming a Poisson or quasi-Poisson distribution, was used: The trend of a mortality rate was determined to be decreasing or increasing according to whether the geometric mean of the ratio of the annual percentage change was negative or positive, respectively.
Rate ratios for the observed and expected mortality rates were calculated. We also estimated the number of "excess" (higher-than-expected) or "prevented" (lower-than-expected) deaths in 2011,  We ran separate analyses using the above model for males, females, and both sexes. The agestratified time-trend analyses examined 10 age groups. The place-specific mortality rates used the same approach but were split into just two age groups, those 60 and over, and those less than 60 in addition to an all-age group analysis.
For the analyses of potential years of life lost, the same process was repeated but using the directly standardized rates of potential years of life lost as the outcome instead of mortality rates.

Life expectancy
A univariate autoregressive integrated moving average (ARIMA) model was fitted to life expectancy data available from 1998 to 2010, and used to predict data points for 2011 and 2012 as per a method by Torri and Vaupel 15 . In order to optimize the p, d, and q parameters, we conducted a model search and selected the parameterized model that minimized the Akaike Information Criterion (AIC) value, which is defined as:

Aggregating results across years
Aggregate central estimates of deaths across time-trend analyses of each projected year were calculated by addition. For 95% confidence intervals, the root-sum-of-squares method was used: where ݀ is the aggregate confidence intervals (lower and upper), ݀ is the aggregate central estimate, ݊ is the final year in the projected time series, ݀ ௧ is the central estimate for year ‫,ݐ‬ and ݀ ௧ is the confidence interval (lower or upper) for the year ‫.ݐ‬

Model selection
To assess the suitability of different regression approaches, we separately fitted pooled ordinary least squares (OLS), fixed-effects, and random-effects models to the real PEH per capita and population mortality data with sex as the time-invariant entity. The assumption of the randomeffects model that the error terms for unobserved or observed time-invariant variables such as sex are uncorrelated with the independent variables means that sex is therefore also able to serve as an independent variable. In fixed-effects models, this is not the case.
We therefore tested whether the consistent but inefficient fixed-effects model was more suitable than the potentially inconsistent but efficient pooled OLS and random-effects approaches by conducting Hausman tests, both of which were highly significant (P<0.001), leading us to reject the random-effects and pooled OLS approaches and their assumptions in favour of a fixed-effects model.

Regression model
We therefore used the following fixed-effects regression model: where H it is the response variable for which i is sex and t is time in years; X kit represents the independent variables; β k is the coefficient for the independent variables; and U it is the error term.
For population-based mortality, H was all-cause ASDR. For the regression analyses in which economic and health resource indicators were not controlled, X was just real PEH or real PES per capita in units of ten pounds sterling. To test whether our results were robust to variations in the economy, we added average annual consumer price index (CPI) 16 and unemployment rate 17 as independent variables to the model. For mediation analyses, each health and social care resource was added as an independent variable. 8-12

Lag analyses
We conducted 1-and 2-year lag analyses. For an ith year lag analysis, regression was performed using the mortality rate in year x and the value of the explanatory variables (real PEH or real PES per capita, etc.) in year x -i.  To do this, we first performed fixed-effects regression as before but instead using all-cause population ASDR as the outcome variable, and combined real PEH or PES per capita as the explanatory variable. From these analyses, an increase of £10 per capita real spending on health and social care is associated with 2.56 (2.10 to 3.01) lives saved per 100,000.

Mortality projections to 2020
To calculate the number of lives saved, l, for year t, which could be any year between 2015 to 2020, inclusive, we used the following formula: where p is the assumed annual efficiency change; r is the coefficient (or upper or lower bound of the 95% confidence interval); 100,000 is that the coefficient is for all-cause ASDR per 100,000; S t represents planned health and social care spending combined for year t and S 2014 denotes the combined health and social care spending outturn for 2014/15. The difference in spending is divided by 10 to acknowledge that the regression coefficient was obtained with units of £10 changes per capita. The percentage of lives saved was calculated using the number of excess deaths from the mortality projections for year t.
The additional spending needed to completely close the gap, i.e. make sure that 100% of lives were saved for year t, was computed as follows: where d t is the excess deaths calculated for t.
For each year between 2015 and 2020, we modeled three different scenarios, each assuming different values for p: 1) a conservative 0% annual efficiency change; 2) a moderate 1% annual efficiency gain (1% was the average efficiency to the nearest integer These productivities were defined by using historical and targeted efficiency changes in healthcare as a guide. 19 In addition, we asked what annual efficiency gain up to 2020 would be needed if there was no spending on top of the planned PEH and PES budgets. This was calculated as follows: of methodological assumptions (such as discount rate, study perspective). 20b Model-based economic evaluation: Describe the effects on the results of uncertainty for all input parameters, and uncertainty related to the structure of the model and assumptions. Characterising heterogeneity 21 If applicable, report differences in costs, outcomes, or costeffectiveness that can be explained by variations between subgroups of patients with different baseline characteristics or other observed variability in effects that are not reducible by more information.

Objective
Since 2010, England has experienced relative constraints in public expenditure on healthcare (PEH) and social care (PES). We sought whether these constraints have affected mortality rates.

Methods
We collected data on health and social care resources and finances for England from 2001 to 2014.
Time-trend analyses were conducted to compare the actual mortality rates in 2011 to 2014 with the counterfactual rates expected based on trends before the spending constraints. Fixed-effects regression analyses were conducted using annual data on PES and PEH with mortality as the outcome, with further adjustments for macroeconomic factors and resources. Analyses were stratified by age group, place of death, and lower-tier local authority (N=325). Mortality rates to 2020 were projected based on recent trends.

Results
Spending constraints between 2010-2014 were associated with an estimated 45,368 (95% confidence interval (CI): 34,530-56,206) higher-than-expected number of deaths compared to pre-2010 trends. Deaths in those aged ≥60 and in care homes accounted for the majority. PES was more strongly linked with care-home and home mortality than PEH, with each £10 per capita decline in real PES associated with an increase of 5.10 (3.65-6.54) (P<0.001) care-home deaths per 100,000.
These associations persisted in lag analyses and after adjustment for macroeconomic factors.
Furthermore, we found that changes in real PES per capita, may be linked to mortality primarily via changes in nurse numbers. Projections to 2020 suggested that planned health and social care

Conclusions
Spending constraints, especially PES, are associated with a substantial mortality gap. We suggest that spending should be targeted on improving care delivered in care homes and at home; and maintaining or increasing nurse numbers.

KEYWORDS
Health care, social care, spending, expenditure, mortality, PYLL, life expectancy, time trend

STRENGTHS AND LIMITATIONS
• Time trend analysis with projections of future outcomes and counterfactual analysis • Sensitivity analyses by using other outcomes: potential years of life lost and life expectancy • Analysis included potential effect modifiers and mediating factors • Variations may exist at the local level which were not identified by the study • There may be other mediating factors beyond those explored in this analysis Although the role of social determinants in health is increasingly acknowledged, 5 there is underinvestment in social care in many high-income countries such as the United States. 6 In England, public-sector funding for social care has also suffered. 7 Such funds enable the provision of means-tested home care and care-home accommodation, 8  This supply-demand mismatch has manifested in several ways. During the first week of 2017, more than four in 10 NHS hospitals declared a major alert. 10 Emergency medicine departments (A&E) saw 900,000 (4.6%) more attendances in 2015/16 compared with the previous year, and 4% more emergency hospital admissions. 11 Over the past two years, the number of elderly patients waiting over 12 hours in A&E has trebled, and there has been a 31% increase in delayed hospital discharges. 11 While the funding gaps facing health and social care have been well-quantified, 12,13 the impact on population outcomes remains unclear.
Here we sought to model the past, present, and future impact of funding constraints experienced by the publicly financed health & social care system in England on mortality, to provide insights into the association between funding and health outcomes and inform future financial allocations.

Population mortality, PYLL and life expectancy
Annual population mortality data for England were extracted from the UK's Office for National Statistics (ONS) 14 based on Medical Certificates of Cause of Death from the Registration Online system. Age-standardized death rates (ASDR) were calculated with reference to a standard European population using mortality data split into ten age groups (see Supplementary Appendix).
Information on deaths by place of occurrence (care homes, hospice, home, hospital, and other  19 ) and average weekly pensions as the independent variables, and care home, home and hospital mortality as the dependent variables. For a given year, population mortality on the same year was the outcome whereas spending data for a financial year starting at the given year was used as the main predictor. Since population mortality was collected annually and spending data is reported for each financial year (starting 1 April in the UK), we repeated our analysis using 1-and 2-year lag periods.
We additionally incorporated both PEH and PES in the same model.
Effects of public spending on resources such as staff or infrastructure have been documented 20 and these resources have also been linked with health outcomes. 21 Therefore, we explored resources of health and social care as potential mediating factors by running fixed-effects regression models with real PEH/PES per capita and each resource variable as the independent variables; and care home/home mortality as the dependent variable. Resource variables that were associated with the dependent variable, resulted in weaker associations between PEH/PES and the dependent variable,     (Table S1).
To validate these results, we looked at two alternative health outcomes: life expectancy and PYLL.
To see whether the possible effects of the 2010 spending constraints were sensitive to age, we conducted time-series analyses for ten different age groups (Table S4). Higher-than-expected numbers of deaths were confined to those ≥60 years of age with all six ≥60 age groups showing excess deaths in 2013. By contrast, <60 age groups most often exhibited fewer deaths.
We next looked at place of death for all age groups, while stratifying them by age into <60 and those ≥60 years. Time-trend analyses revealed care-home and home deaths to be the first and second largest contributors, respectively, to excess deaths across age groups and in those ≥60   Figure S2 and Table S5), with a relative increase in these places of death over others during the study period. For every year analysed, lower-than-expected numbers of deaths occurred in hospitals. For those <60 years, hospitals were the most frequent place of death, and so the net result was a lower-than-expected number of <60 deaths. Time-series analyses by local government area (for time points up to 2013) revealed no correlation between changes in the number of expected deaths and deprivation (P=0.14, R S =0.08).

Longitudinal associations between spending and mortality
We found that £10 per capita declines in real PEH and real PES were associated with increases of 0.19 (0.01-0.38) (P=0.049) and 5.10 (3.65-6.54) (P<0.001) care-home deaths per 100,000 in England, respectively (Table 1). For PES, these relationships persisted at least two years after the initial change but became weaker for PEH. We next sought to demonstrate that these associations were independent of macroeconomic forces such as unemployment (for younger age groups) and pensions (for older age groups), which have each been linked with increased mortality. 23,24 On adjusting the regression models for macroeconomic factors and the annual average of weekly pensions, we found real PES per capita and real PEH per capita to remain inversely associated with care-home mortality (Table 1). Next, we used a regression model with both real PES and PEH per capita as explanatory variables and found only PES remained inversely associated with care-home mortality ( Table 1). In this model, the variance inflation factor between PEH and PES was 4.15, suggesting that multicollinearity was not a problem. The results for home deaths replicated those for care-home deaths (Table S6). In contrast to care-home and home mortality, real PEH per capita was more strongly related to hospital mortality than real PES per capita without adjusting for controls. On adjusting for macroeconomic forces, the relationship between PEH and hospital mortality was no longer apparent (Table S7).

Identification of resources potentially mediating the spending-mortality relationship
We found that the numbers of NHS hospital and community nurses, and NHS health and social care clinical support staff were each associated with care-home mortality. These factors alleviated the relationship between real PES per capita and care-home mortality at lag years 1 and 2, suggesting these staff numbers were important mediators of the spending-mortality relationship ( Table 2). We found the number of nurses, but not clinical support staff, was suggested to be a mediator of the relationship between spending (both PEH and PES) and home mortality rates for lag years 1 and 2 (Table S8). We also found the number of nurses to be the sole mediator of the relationships between PEH per capita and care-home mortality (Table S9), and PEH per capita and home mortality (Table   S10) for all years. From 2001 to 2010, the average annual increase in nurse numbers was 1.61% whereas from 2010 to 2014, the average annual increase was over twenty-fold lower at 0.07% (Table S11).

Mortality projections to 2020 and scenario modelling
We projected mortality rates to 2020 using two observation bases:   To determine what it would take to close this gap above planned health and social care spending to 2020/21, we modelled three different scenarios (Figure 3 and  Figure 3 with an annual breakdown in Table S12). Under an ideal scenario in which no additional spending would be needed to close the mortality gap, the annual efficiency increase to 2020 would need to reach 10.79% (7.8 to 14.46). In these scenarios, efficiency gains reflect improvements across the system required to meet respective spending constraints, while avoiding excess mortality.

DISCUSSION
This study demonstrates that recent constraints in PEH and PES spending in England have been associated with nearly 45,000 higher-than-expected numbers of deaths between 2012 and 2014. If these trends continue, even when considering the increased planned funding as of 2016, we estimate approximately 150,000 additional deaths may arise between 2015 and 2020. Combining these projected excess deaths and the observed deaths prior to 2015 translate to around 120,000 excess The associations observed between PEH, PES, and mortality were independent of macroeconomic changes that often co-occur with periods of reduced public-sector spending. However, adjustment for potential mediating factors, nursing numbers in particular, nullified the associations between PEH, PES, and mortality. Our study suggests that the number of NHS-qualified nurses is the strongest tested mediator of the relationships between spending, and care-home and home mortality; this is congruent with findings in other reports. 27 This study has several policy implications. First, it demonstrates that decelerated increases in public expenditure on healthcare and social care, in England, may have adversely affected population mortality as demand increased and healthcare costs rose above inflation. This demonstrates that while health system design and ambition, such as delivery of universal coverage, is important, it must be adequately financed to ensure design translates into health improvement. Second, the finding that the elderly population and those in care homes were the most vulnerable to recent financial challenges, makes a strong case for targeted interventions to ensure adequate management of these patient groups. 4 This includes funding increases in social care, in addition to maintenance or rises in nursing numbers aligned with demand. Third, and perhaps most importantly, there remains a prospective cost to the current trajectory of system financing that entails a number of excess deaths. While it would be presumptive to class these deaths as avoidable (we have used the terms 'additional' or 'excess' to describe higher-than-expected numbers), we have outlined several funding-efficiency scenarios that attempt to demonstrate how such a gap could be closed. Given that the health system has historically achieved 1-2% annual productivity improvements, and that current demand is unprecedented, it seems unlikely that greater annual improvements could be expected. After factoring planned Government spending, and the £2 billion funding increase to  to subsequent drafts. All authors had full access to all of the data in the study and can take responsibility for its integrity and the accuracy of the data analysis.

FUNDING
No funding was received for this study.

COMPETING INTERESTS
MM is a co-founder of Cera, a technology-enabled homecare provider.

ETHICAL APPROVAL
Not required.

Mortality and potential years of life lost
Given that consistent mortality data were available from 2001 onwards, and that the reductions in Depending on whether overdispersion was observed (where the variance exceeds the mean), we resolved to use either a Poisson or quasi-Poisson regression model, the latter of which incorporates a scaling parameter in order to address overdispersion. In every dataset for which we conducted time-series modelling, the variance of the mortality rates exceeded the mean rate.  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60   F  o  r  p  e  e  r  r  e  v  i  e  w  o  n  l  y Therefore, we employed a quasi-Poisson model in all analyses, with the logarithmic link function preventing the prediction of negative rates. The model takes the following form: where E(M t ) is the estimated mortality rate for year t, α is the baseline mortality rate, and β is the estimated drift parameter. For increasing observation-base trends, the following non-linear prediction model proposed by Dyba and colleagues, 14 also assuming a Poisson or quasi-Poisson distribution, was used: The trend of a mortality rate was determined to be decreasing or increasing according to whether the geometric mean of the ratio of the annual percentage change was negative or positive, respectively.
Rate ratios for the observed and expected mortality rates were calculated. We also estimated the number of "excess" (higher-than-expected) or "prevented" (lower-than-expected) deaths in 2011, 2012, 2013 and 2014 by finding the difference between the observed number of deaths and the number of deaths predicted by the 2001-2010-based time-series models above. 95% confidence intervals were computed using the standard errors of the fitted mortality rate estimates.
We ran separate analyses using the above model for males, females, and both sexes. The agestratified time-trend analyses examined 10 age groups. The place-specific mortality rates used the same approach but were split into just two age groups, those 60 and over, and those less than 60 in addition to an all-age group analysis.
For the analyses of potential years of life lost, the same process was repeated but using the directly standardized rates of potential years of life lost as the outcome instead of mortality rates.

Aggregating results across years
Aggregate central estimates of deaths across time-trend analyses of each projected year were calculated by addition. For 95% confidence intervals, the root-sum-of-squares method was used: where is the aggregate confidence intervals (lower and upper), is the aggregate central estimate, is the final year in the projected time series, is the central estimate for year , and is the confidence interval (lower or upper) for the year .

Model selection
To assess the suitability of different regression approaches, we separately fitted pooled ordinary least squares (OLS), fixed-effects, and random-effects models to the real PEH per capita and population mortality data with sex as the time-invariant entity. The assumption of the randomeffects model that the error terms for unobserved or observed time-invariant variables such as sex are uncorrelated with the independent variables means that sex is therefore also able to serve as an independent variable. In fixed-effects models, this is not the case.

Regression model
We therefore used the following fixed-effects regression model: where H it is the response variable for which i is sex and t is time in years; X kit represents the independent variables; β k is the coefficient for the independent variables; and U it is the error term.
For population-based mortality, H was all-cause ASDR. For the regression analyses in which economic and health resource indicators were not controlled, X was just real PEH or real PES per capita in units of ten pounds sterling. To test whether our results were robust to variations in the economy, we added average annual consumer price index (CPI) 16 and unemployment rate 17 as independent variables to the model. For mediation analyses, each health and social care resource was added as an independent variable. 8-12

Lag analyses
We conducted 1-and 2-year lag analyses. For an ith year lag analysis, regression was performed using the mortality rate in year x and the value of the explanatory variables (real PEH or real PES per capita, etc.) in year xi.

Mortality projections to 2020
For the 2020 projection analysis, two projections were performed each with a different  To do this, we first performed fixed-effects regression as before but instead using all-cause population ASDR as the outcome variable, and combined real PEH or PES per capita as the explanatory variable. From these analyses, an increase of £10 per capita real spending on health and social care is associated with 2.56 (2.10 to 3.01) lives saved per 100,000.

Scenario modelling
To calculate the number of lives saved, l, for year t, which could be any year between 2015 to 2020, inclusive, we used the following formula: where p is the assumed annual efficiency change; r is the coefficient (or upper or lower bound of the 95% confidence interval); 100,000 is that the coefficient is for all-cause ASDR per 100,000; S t represents planned health and social care spending combined for year t and S 2014 denotes the combined health and social care spending outturn for 2014/15. The difference in spending is divided by 10 to acknowledge that the regression coefficient was obtained with units of £10 changes per capita.
The percentage of lives saved was calculated using the number of excess deaths from the mortality projections for year t.
The additional spending needed to completely close the gap, i.e. make sure that 100% of lives were saved for year t, was computed as follows: where d t is the excess deaths calculated for t. Describe what outcomes were used as the measure(s) of benefit in the evaluation and their relevance for the type of analysis performed. Measurement of effectiveness 11a Single study-based estimates: Describe fully the design features of the single effectiveness study and why the single study was a sufficient source of clinical effectiveness data. 11b Synthesis-based estimates: Describe fully the methods used for identification of included studies and synthesis of clinical effectiveness data. Measurement and valuation of preference based outcomes 12 If applicable, describe the population and methods used to elicit preferences for outcomes.

Estimating resources and costs
13a Single study-based economic evaluation: Describe approaches used to estimate resource use associated with the alternative interventions. Describe primary or secondary research methods for valuing each resource item in terms of its unit cost. Describe any adjustments made to approximate to opportunity costs. 13b Model-based economic evaluation: Describe approaches and data sources used to estimate resource use associated with model health states. Describe primary or secondary research methods for valuing each resource item in terms of its unit cost. Describe any adjustments made to approximate to opportunity costs. Currency, price date, and conversion 14 Report the dates of the estimated resource quantities and unit costs. Describe methods for adjusting estimated unit costs to the year of reported costs if necessary. Describe methods for converting costs into a common currency base and the exchange rate. Describe all analytical methods supporting the evaluation. This could include methods for dealing with skewed, missing, or censored data; extrapolation methods; methods for pooling data; approaches to validate or make adjustments (such as half cycle corrections) to a model; and methods for handling population heterogeneity and uncertainty.

Study parameters 18
Report the values, ranges, references, and, if used, probability distributions for all parameters. Report reasons or sources for distributions used to represent uncertainty where appropriate. Providing a table to show the input values is strongly recommended. Incremental costs and outcomes 19 For each intervention, report mean values for the main categories of estimated costs and outcomes of interest, as well as mean differences between the comparator groups. If applicable, report incremental cost-effectiveness ratios. Characterising uncertainty 20a Single study-based economic evaluation: Describe the effects of sampling uncertainty for the estimated incremental cost and incremental effectiveness parameters, together with the impact of methodological assumptions (such as discount rate, study perspective). 20b Model-based economic evaluation: Describe the effects on the results of uncertainty for all input parameters, and uncertainty related to the structure of the model and assumptions. Characterising heterogeneity 21 If applicable, report differences in costs, outcomes, or costeffectiveness that can be explained by variations between subgroups of patients with different baseline characteristics or other observed variability in effects that are not reducible by more information.

Discussion
Study findings, limitations, generalisability, and current knowledge 22 Summarise key study findings and describe how they support the conclusions reached. Discuss limitations and the generalisability of the findings and how the findings fit with current knowledge.

Other
Source of funding 23 Describe how the study was funded and the role of the funder in the identification, design, conduct, and reporting of the analysis. Describe other non-monetary sources of support.

Conflicts of interest 24
Describe any potential for conflict of interest of study contributors in accordance with journal policy. In the absence of a journal policy, we recommend authors comply with International Committee of Medical Journal Editors recommendations.