Measuring the level of compulsory hospitalisation in mental health care: The performance of different measures across areas and over time

Abstract Objective A variety of measures are used for reporting levels of compulsory psychiatric hospitalisation. This complicates comparisons between studies and makes it hard to establish the extent of geographic variation. We aimed to investigate how measures based on events, individuals and duration portray geographical variation differently and perform over time, how they correlate and how well they predict future ranked levels of compulsory hospitalisation. Methods Small‐area analysis, correlation analysis and linear regressions of data from a Norwegian health registry containing whole population data from 2014 to 2018. Results The average compulsory hospitalisation rate per 100,000 inhabitant was 5.6 times higher in the highest area, compared to the lowest, while the difference for the compulsory inpatient rate was 3.2. Population rates based on inpatients correlate strongly with rates of compulsory hospitalisations (r = 0.88) and duration (r = 0.78). 68%–81% of ranked compulsory hospitalisation rates could be explained by each area's rank the previous year. Conclusion There are stable differences in service delivery between catchment areas in Norway. In future research, multiple measures of the level of compulsory hospitalisation should ideally be included when investigating geographical variation. It is important that researchers describe accurately the measure upon which their results are based.

variation in the extent to which compulsory hospitalisation is used. A number of studies report practice variation when comparing the level of compulsory hospitalisation between countries (Hansson et al., 1999;Riecher-Rössler & Rössler, 1993;Salize & Dressing, 2004;Sheridan Rains et al., 2019;Zinkler & Priebe, 2002) and within areas regulated by the same legislation (Bindman et al., 2002;Engberg, 1991;Keown et al., 2016;Kjellin, 1997). For instance, the highest admission rates among mental health departments in the Veneto region in Italy 2000-2007 were 14 times higher than the lowest rates (Donisi et al., 2016), while in France in 2012, the rate of compulsory hospitalised patients in the highest 10th percentile of psychiatric sectors' catchment areas was 10 times higher than the 90th percentile (Gandré et al., 2018). Such large differences indicate that some areas might use more compulsion than necessary. If that is the case, it would constitute unwanted variation which is described as 'variation that cannot be explained on the basis of illness, medical evidence or patient preference' (Wennberg, 2010, p. 4). Geographical variation is commonly observed in most health service delivery and might reflect differences in local practice, culture or service dimensioning. Given the implications of compulsory interventions for personal autonomy, it is particularly important to detect potential geographical variation in such practice, as a precursor to identify ways of improving the organisation and delivery of services in the best interest of patients.
In order to establish the extent of geographical variation in compulsory hospitalisations, both within and between jurisdictions, reliable measures are required. Trustworthy measures are also needed to track compulsion use over time, which would be necessary to monitor progress towards reduced compulsion levels, following political ambitions. However, there is a long lamented lack of agreement on standardisation of measuring and reporting compulsory mental health care, both in national statistics and the research literature (de Stefano & Ducci, 2008;Høyer, 2008;Riecher-Rössler & Rössler, 1993;Sheridan Rains et al., 2019;Zinkler & Priebe, 2002).
This heterogeneity complicates comparisons, as different studies often employ different measures of the level of compulsory hospitalisation and also because the descriptions of how measures are operationalised is not always clear. Studies that compare measures from various sources or areas are therefore conventionally accompanied by a note of caution.
Based on our reading of the research literature we have categorised the most frequently used measures according to three concepts, which are also fundamental to general epidemiology (Rothman et al., 2008): events, individuals and duration. Event measures are most common and are usually based on counts of compulsory admissions (Riecher-Rössler & Rössler, 1993;Zinkler & Priebe, 2002). Some studies employ counts of individuals with minimum one compulsory hospitalisation (Gandré et al., 2018;Keown et al., 2016;Sheridan Rains et al., 2019;Weich et al., 2017). A number of studies include measures based on duration, normally the number of days between admission and discharge (Aguglia et al., 2016;Girolamo et al., 2008;Wierdsma & Mulder, 2009), although it varies whether studies include days of voluntary stay during an admission (Iversen et al., 2009;Kelly et al., 2018).
In order to make comparisons between countries, regions or institutions, raw numbers are often recalculated to populationbased rates per person year. Quotas or shares of compulsory hospitalisations/inpatients of the total number of hospitalisations/inpatients is sometimes used. While quotas can be useful when the population-at-risk is unknown, they are less suitable for comparison between areas, since they rely heavily on the total admission frequency, which is dependent on the available resources and coverage of mental health care in each country (Høyer, 2008;Riecher-Rössler & Rössler, 1993). Quotas are therefore not part of this study.
While a more nuanced picture of the level of compulsory hospitalisation is likely to emerge through the inclusion of multiple measures, data availability might restrict options. It is therefore important to understand whether and how the selection of measures impacts inferences drawn about the level of compulsory hospitalisation, to limit biases due to methodology and choice of operationalisation.
Increasingly comprehensive, reliable and accessible hospital registries with individual level data hold potential for more valid estimates of variation in health care delivery, including variation in the level of compulsory hospitalisation. The Norwegian Patient Registry (NPR) ranks among the world's most complete and reliable health registries (Bakken et al., 2020) and enables us not only to describe the level of compulsory hospitalisation within selected samples, but the entire population. This also makes it possible to apply different measures, over an extended period of time, and to compare them across health care regions regulated by the same legislation. We have not found any study that has investigated how the commonly used measures appear and diverge when applied to a whole population, over time and how the resulting picture of variation might depend on the choice of measure. Therefore, this will be the focus of our study. Specifically, we aim to answer the following Compulsory hospitalisation is regulated by the 1999 Norwegian Mental Health Act. The main legal criterion is the presence of severe mental illness. In addition, the patient's condition must be likely to deteriorate without treatment, or the patient poses an immediate danger to themselves or others. Section 3.2 permits compulsory observation in hospital, which may last 10 days, and can be extended for another 10 days. Section 3.3 permits compulsory mental health care. Here, no time limit applies, but there are legal requirements to assess whether the criteria are met every 3 months. Section 3.4 prohibits the compulsory detention of patients admitted voluntary, except when there is immediate and serious danger to the patient or others. A legislation change in 2017 restricted compulsory care to patients without the capacity to consent to treatment, unless there is immediate danger. As intended, compulsion numbers were reduced initially, but figures rose again the following year (Bremnes & Skui, 2020).

| Data inclusion
Data on all episodes of compulsory hospitalisation in the period 2014-2018 was obtained from NPR. The registry is person identifiable through unique patient numbers, which enabled us to follow individuals over time and across institutions. Only the population at risk of compulsory hospitalisation was included in the study, which was defined as all individuals between 18 and 65 years living in a Norwegian municipality during the study period. The age scope was primarily selected because services are organised differently for other age groups. Forensic admissions were not included, as this can be considered a distinct population, regulated through a different legal framework (Salize & Dressing, 2004).
Analyses were based on residency prior to each hospitalisation. This is likely to result in more homogeneous categories compared to analyses of where people were treated, since the numbers will not be impacted by service organisation (Wennberg, 2010). One percent of all patients relocated and were subsequently readmitted compulsory in a different area the same year. They were counted in both areas.
Population counts for municipalities, stratified by age and gender were collected from Statistics Norway (2020). Individuals without a Norwegian national identity number or missing values on residency were excluded (1% and <0.001% of persons compulsory hospitalised, respectively). The population of homeless people in Norway is small; 0.75 homeless per 1000 inhabitants (Dyb & Lid, 2017). Individuals in this category were included based on their last recorded residency.
Data completeness was in general good. The 11 catchment areas in Central Norway were excluded in 2014 due to incomplete reporting, but all areas were included in 2015-2018. In two cities, two CMHCs operate within the same urban district. Since we lacked sufficiently detailed information on residence for those living in these areas to determine to which CMHC they belonged, we combined the relevant two areas in both cities. The boundaries of some of the CMHC's catchment areas changed during the study period, so the  Compulsory inpatients were defined as individuals with at least one compulsory hospitalisation and this was counted for each calendar year.

| Events, individuals and duration
Duration of compulsion excluded voluntary days during the admission, and was calculated in two ways: for the Compulsory Length of Stay (LoS) rate, the total number of days of compulsory hospitalisation was counted for each year. This included compulsory hospitalisations that commenced in earlier years, and hospitalisations that extended into the following year. This was done to ensure that compulsory hospitalisations that lasted more than 1 year were also included, providing a more valid estimate of prevalence. For median compulsory LoS and average compulsory LoS, number of days of compulsory hospitalisation was counted for each completed hospitalisation, after discharge, each year. This included days of compulsory hospitalisations that commenced in earlier years.

| Statistical analysis
In order to answer the first research question of the extent of geographic variation when measured in different ways, four analyses were conducted to test how much each measure varied between areas. First, the extremal quotient (EQ) was calculated to quantify the magnitude of difference, by dividing the highest with the lowest rate. Second, while the EQ is a popular measure, it is impacted by the number of cases compared (Kazandjian et al., 1989). Therefore, to reduce the influence of outliers, the ratio of the 90th percentile to the 10th percentile (EQ 90/10 ) of the distribution of each measure was also calculated (OECD, 2014).
Third, the coefficient of variation (CV), which is the ratio of the standard deviation to the mean was calculated. The CV is useful for comparing the different measures of the level of compulsory hospitalisation, since the CV is scale invariant and shows the relative variability. Fourth, while both EQ and CV might be impacted by unstable rates due to small populations and rare occurrences, the systematic component of variation (SCV), which is specifically developed to investigate geographical variation, subtracts the random component from the variance (McPherson et al., 1982). For the hospitalisation rate and the LoS rate, the adjusted formula for SCV suggested by Cain and Diehr (1992) and Diehr et al. (1993) was employed, which accounts for the extra Poisson variation introduced by individuals with multiple admissions.
For all variation measures, higher values indicate higher levels of variation between areas. Univariate scatter plots were created for each measure to aid in the analysis. These included average scores for each CMHC area, grouped by health region.
In order to answer the second research question on the relationships between measures, Spearman's rank order correlation coefficient was calculated to investigate the pairwise relationships between the different measures of compulsory hospitalisation.
The third research question concerning the ability to predict future ranked levels of compulsory hospitalisation was answered by ranking each CMHC area for each year according to each measure of compulsion. Linear regression was performed using each year's rank as independent variable, and the subsequent year's ranking as dependent variable. This procedure was repeated for each compulsion measure, and R 2 was used as measure of explained variance. As a further test of stability, we performed the same analysis with ranks from 2014 as independent variable, as well as ranks based on the average values from 2014 to 2017, to predict ranks in 2018.
To reduce the impact of random fluctuation, the average over the 5-year period for each area was used to answer research question one and two. In order to account for risk differences due to varying gender and age distribution, direct standardisation was performed for the rates, using the countrywide population as reference population (Ash et al., 2003). Expected cases were calculated based on six age categories (18-25, 26-33, 34-41, 42-49, 50-57, 58-65). Indirect standardisation using countrywide compulsory hospitalisation rates as reference was used for SCV. As robustness tests to avoid undue impact of unstable rates, all analyses were repeated without areas with less than 35,000 inhabitants, resulting in a reduction of catchment areas to 35-40.

| Ethics
The Research Ethics Committee deemed the study to fall outside    Some reduction in geographic variation occurred during the study period, particularly the hospitalisation rate.

| Correlation between measures
Results from the correlation analyses are displayed in Figure 3.
The strongest correlations were found between the hospitalisation rate and the inpatient rate (r = 0.88), and the inpatient rate and the LoS rate (r = 0.78). Negative correlations were seen between

| Robustness test
The results of the robustness analyses without areas less than 35,000 can be seen in the Appendix Table A1. A reduction in geographical variation is observed, and predictions were improved.

| DISCUSSION
To our knowledge, this is the first study to quantify geographical variation in the level of compulsory hospitalisation in mental health care for an entire population and over time, using different measures based on events, individuals and duration. The observed geographical variation was relatively stable across the years, and the variation in compulsory hospitalisation rates can be considered high compared to reference procedures (OECD, 2014). Furthermore, all duration measures showed considerable variation, suggesting substantial practice variation in the extent to which people remain compulsory hospitalised over time.

| Inpatient rates vary less than hospitalisation rates
The number of compelled inpatients is necessarily less than or equal to the number of events in a period. Consequently, measures based on inpatient counts will by necessity never display more variation than measures based on hospitalisation counts when applied to the same dataset. How large the difference in variation will be is an empirical question which will differ between populations. In this study, population rates based on counts of inpatients displayed less than half the amount of geographical variation of rates based on hospitalisations and LoS according to the SCV, but the difference was reduced during the study period.
The variation in inpatient rates can be categorised as medium-to-high variation compared to reference procedures (OECD, 2014).
The scatter plot in the lower half of Figure 3 showed that in some areas the compulsory hospitalisation rate was roughly the same as the inpatient rate, which means that there were almost no compulsory readmissions each year in those areas. In contrast, the ratio of the hospitalisation rate to the patient rate was roughly 2.5 in the area with the highest hospitalisation rate. This means that every patient in that area on average had more than two compulsory hospitalisations each year. The consequences of whether rates based on events or individuals are used in research and official statistics is thus highly contingent on the practice of compulsory readmissions.
The extent of geographical variation was relatively stable over the years, particularly so for the compulsory inpatient rate, as displayed in Figure 2. Most geographical variation was seen in 2014 for most measures. Still, the extent of geographical variation regularly appears larger when considering numbers for each year separately, than the average for the whole period. This underlines the importance of caution when interpreting geographical variations based on numbers from a short time interval, since these might be impacted by fluctuation over time. By averaging over the 5-year period, the more extreme differences due to random outliers were smoothed out. Substantial differences remained, however, indicating that there are stable differences in service delivery between different catchment areas of CMHCs.
The observed geographical variation pales in comparison with findings from catchment areas in France, where EQ 90/10 for the inpatient rate was 10, and CV roughly 80% (Gandré et al., 2018). The EQ 90/10 is impacted by the number of areas compared (Kazandjian et al., 1989), which was much larger in France (N = 514), and this can explain some of the discrepancy. While the CV is also a function of sample size, such large differences are not expected solely on the basis of the differing number of areas compared.

| Inpatient rates correlate strongly with hospitalisation rates
Rates based on inpatients correlate strongly with rates based on hospitalisations in this study. In other words, areas where the level of F I G U R E 4 R 2 from OLS. The left part of the figure shows the amount of explained variance in ranked levels of compulsory hospitalisation, as predicted from the previous year's levels. The right part shows explained variance for 2018 predicted by levels from 2014, and from the average levels during 2014-2017 compulsory hospitalisation is ranked higher, as measured by rates of hospitalisations, also tend to rank higher when measured by rates of

| Compulsory hospitalisation rates predict future ranked levels of compulsory hospitalisation
The high amount of variance explained in ranked levels of compulsory hospitalisation, solely on the basis of last years ranking, suggest considerable stability over time. This has implications for efforts at reducing compulsion levels in high-ranking areas. If random fluctuation dominates ranking, it would be difficult to identify areas that could benefit most from interventions to reduce compulsion levels. In this study however, areas that ranked higher one year were very likely to be ranked higher the subsequent year, particularly when ranked by the compulsory hospitalisation rate.

| Ways of measuring: Events, individuals, duration
Researchers who are primarily concerned with the burden imposed on the hospitalised individuals in terms of infringed autonomy might emphasise different elements of the level of compulsory hospitalisation, than researchers who, for instance, set out to calculate costs associated with compulsory hospitalisations. The focus of each study might therefore impact the choice of measures.
Each compulsory hospitalisation will constitute additional breach of autonomy, so if the burden of compulsion experienced by patients in an area is under study, counts of events might provide better estimates than counts of individuals. Also, one individual who is subject to many events of compulsory hospitalisation might significantly impact the hospitalisation rate in an area, but not the inpatient rate.
It is, therefore, an advantage of inpatient based rates that they are less prone to random fluctuation, which means that they will be more stable, even when data is only available for shorter time periods (Bowers, 2000).
A limitation with measures based on both events and individuals is that they do not distinguish between longer and shorter durations; one hospitalisation counts as one event regardless of length. The number of days under involuntary confinement thus provides an alternative take on the level of compulsory hospitalisation, and has been recommended in the compulsion literature (Høyer, 2008)

| National registers of compulsory admissions
This study was possible because of the existence of a national comprehensive population-based registry (Bakken et al., 2020).
Comprehensive health registries are required to analyse variation in compulsory hospitalisation at national levels, but are not available, or not of sufficient quality in many countries. As compulsory hospitalisation might compromise individual autonomy, a lack of high quality registers could constitute a democratic as well as a methodological problem.

| The need for unambiguous terms
Høyer (2008)  admission rates or patient rates should be named accordingly.

| Further research
Further research is needed to establish the performance of measures of the level of compulsory hospitalisation in other populations.
While our study focuses on inpatient compulsion it is clearly of interest to consider the extent and variation of outpatient commitment as well, which is another area of research that would benefit from adopting more standardised measures (Rugkåsa, 2016).
It would be especially interesting to calculate continued duration of compulsion when inpatient stays result in discharge to outpatient commitment.

| Strengths and limitations
A considerable strength of this paper is that we had access to complete information about all compulsory hospitalisations from the whole population in Norway over a 5-year period. The data are routinely collected, which is simultaneously a strength and limitation with register data, since they are not primarily intended for research.
Differences in the way events are registered can exist between areas.
We rely on the evaluation of the NPR for the validity and completeness of the variables used. Furthermore, other risk factors that can be unevenly distributed, such as patient mix, were not accounted for. Consequently, it would not be right to label all the observed geographic variation as unwarranted.

| CONCLUSION
This study showed that measures based on events, individuals and duration, paint different pictures of the extent and geographical variation of the level of compulsory hospitalisation. The geographical variation was high for hospitalisation rates and duration measures, and was stable across the years. Future studies describing the level of compulsory hospitalisation are likely to yield a richer and more accurate picture by including multiple measures. Since inpatient rates can be significantly lower than hospitalisation rates, and display less geographical variation, it is important that measures are accurately described to reflect how they are constructed and what they are based on.

ACKNOWLEDGEMENT
The authors are grateful to the Research Council of Norway for funding the research project ReCoN-Reducing Coercion in Norway (Project number 273546), which this work is part of.

CONFLICT OF INTERESTS
The author declares that there is no conflict of interest.

AUTHOR CONTRIBUTIONS
This study forms part of a larger research program for which Jorun Rugkåsa, in collaboration with Olav Nyttingnes and Tonje L. Husum obtained funding and accessed data. Tore Hofstad, Jorun Rugkåsa, Solveig O. Ose and Tonje L. Husum designed the present study. Tore Hofstad designed and performed the data analysis and wrote the first draft of the manuscript. All authors revised the manuscript in several rounds and approved the final version.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from The Norwegian Patient Registry. Restrictions apply to the availability of these data, which were used under license for this study.