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Mapping Suicide in London A Brief Methodological Case Study on the Application of the Smoothing Technique Mohsen Rezaeian1,2, Graham Dunn2, Selwyn St Leger3, and Louis Appleby4 1
Social Medicine Department, Rafsanjan Medical School, Rafsanjan, Iran Biostatistics Group, School of Community Based Medicine, The University of Manchester, UK 3 Retired, formerly University of Manchester, UK 4 School of Community Based Medicine, The University of Manchester, UK
2
Abstract. Background: When one intends to globally smooth unstable rates, e.g., suicide rates in a region, one needs to consider whether it is better to smooth the rates toward the global mean of the country or toward the global mean of the same region. Aims: The present study aims to provide a methodological framework to answer this question by smoothing suicide rates within London boroughs. Methods: Based on the results of the spatial autocorrelation statistics, the noniterative empirical Bayes method of moments was chosen to globally smooth the suicide rate of each borough, first toward the global mean of England and Wales, and second toward the mean of the London region. Results: The results revealed that smoothing the suicide rates of the boroughs toward the global mean of England and Wales had a stronger influence in reducing the variability of suicide rates than smoothing toward the global mean of the London region. Conclusions: Smoothing the rates toward the mean of a region within a country acts somewhat between global and local smoothing. Keywords: mapping, suicide, London, global smoothing, local smoothing
Introduction One of the most important tasks within geographical epidemiology is disease mapping, which has been recognized as a basic tool in the analysis of public health data (Lawson et al., 1999). This is because maps often highlight spatial relationships that may be not easily be discovered in tables (Bell & Broemeling, 2000). As a result, they may be used for different descriptive purposes including: generating etiological hypotheses, recognizing high risk areas, aiding policy decisions, and allocating public health resources (Elliott & Wartenberg, 2004; Jerrett et al., 2003; Rezaeian et al., 2004). A problem arises when maps refer to small geographical areas, for example the administrative units of wards and local authorities. Events, e.g., suicides, may be sufficiently rare that observed numbers are subject to considerable random fluctuation. There are a number of approaches that help map producers to handle this problem (Rezaeian et al., 2007a). The first strategy is to combine smaller areas into larger areas in order to get more stable rates. However, because this approach yields sudden changes of geographical boundaries (Boyle, Muir, & Grundmann, 1989) and conceals deviation of rates among the smaller geographical areas (Rytkönen, 2004), it is not considered as the best choice. The other approach, which works far better, is to “smooth” or © 2011 Hogrefe Publishing
“shrink” those unstable local risk estimates based on the overall or local pattern of the observed rates (Bailey & Gatrell, 1995). The former is called global smoothing, which smoothes local estimates based on the overall mean of the map and the latter is called local smoothing, which smoothes local estimates based on the nearby areas (Olsen, Martuzzi, & Elliot, 1996). The choice of either global or local smoothing depends on the spatial dependency between rates (e.g., suicides) among nearby areas, i.e., whether the rates within neighboring areas are more related than those from more distant areas. (Tobler, 1970). Spatial dependency might occur if nearby areas have similar underlying cultural and socioeconomic characteristics that trigger suicidal behavior (Rezaeian et al., 2007a). Therefore, in the case of the spatial dependency between suicide rates, one has to apply local smoothing, otherwise global smoothing is the next best choice (Olsen et al., 1996). A question remains with respect to global smoothing. When mapping suicide rates at a subnational level, e.g., London region, is it better to smooth the rates for London boroughs toward the global mean at the national level, i.e., England and Wales, or toward the mean of a subnational level, i.e., the London region? This study aims to provide a methodological framework to answer this important question. Crisis 2011; Vol. 32(4):225–230 DOI: 10.1027/0227-5910/a000085
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Table 1. 1998 population estimate, the total observed number of suicides in (1996–1998), and different rates of suicide in London region (1996–1998) LONDON Inner London
Camden City of London
POP 981
OBS2
SRR3
SMR4
GSSRR5
LSSRR6
166231
105
1.78
1.81
1.22
1.25
4688
4
4.54
2.25
1.02
1.08
Hackney
163391
65
1.17
1.18
1.04
1.09
Hammersmith & Fulham
138511
50
1.01
1.04
.97
1.02
Haringey
189917
79
1.31
1.20
1.01
1.11
Islington
155126
68
1.28
1.29
1.09
1.14
Kensington & Chelsea
151531
66
1.28
1.22
1.03
1.12
Lambeth
229986
94
1.22
1.19
1.06
1.13
Lewisham
207609
106
1.53
1.49
1.12
1.25
Newham
187918
63
.98
1.01
1.01
1.05
Southwark
195114
103
1.61
1.55
1.15
1.26
Tower Hamlets
150874
53
1.12
1.06
1.00
1.06
Wandsworth
232961
102
1.39
1.24
1.04
1.13
Westminster City of
1.17
199055
92
1.40
1.30
1.04
Outer London Barking & Dagenham
131456
34
.78
.79
.94
.95
Barnet
288590
68
.72
.69
.85
.91
Bexley
189094
62
.99
.98
.95
1.03
Brent
217277
83
1.14
1.10
.99
1.06
Bromley
261098
55
.62
.63
.83
.82
Croydon
292019
85
.85
.86
.96
.95
1.02
1.06
Ealing
260730
84
.90
Enfield
226474
67
.88
.93 .87
.91
.93
Greenwich
183434
71
1.11
1.11
1.00
1.07
Harrow
183655
50
.82
.81
.92
.95
Havering
201574
43
.62
.62
.89
.93
Hillingdon
217580
72
.98
.97
1.00
1.05
Hounslow
182139
54
.85
.85
.93
.92
Kingston upon Thames
129114
46
1.04
1.04
.98
1.06
Merton
159706
48
.90
.87
.94
1.00
Redbridge
200400
56
.84
.83
.93
.98
Richmond upon Thames
164408
43
.80
.76
.88
.95
Sutton
153146
50
.97
.96
.99
1.04
Waltham Forest 187535 69 1.07 1.08 1.02 1.06 Note. 11998 population estimation of people over 10 years, 2Total observed number of suicides (1996–1998), 3Standardized rate ratio, 4Standardized mortality ratio, 5Global smoothed standardized rate ratio, 6London smoothed standardized rate ratio.
Methods We used suicide data between 1996 and 1998, provided by the National Confidential Inquiry into Suicide and Homicide by People with Mental Illness (the NCI, 1999) and the corresponding population data provided by the Office for National Statistics (ONS; Chappell, 1999). In a previous article (Rezaeian et al., 2007b), which dealt with the ecological association between rates of suicide within London boroughs and hot spots of deprivation, we provided details of our suicide data and the corresponding population data. We refer the reader to said article for that information. Crisis 2011; Vol. 32(4):225–230
In that article (Rezaeian et al., 2007b), we explained that both direct and indirect standardization were used to produce standardized incidence rate ratios (SRR) and standardized mortality ratios (SMR). However, since both methods acted very similarly and some researchers have shown that mortality maps can be misleading when based on indirectly adjusted rates or a function of them (Julious, Nicholl, & George, 2001; Pickle & White, 1995), in the present article we have focused our further analyses only on the SRRs. To assess the spatial dependency between the SRRs in nearby boroughs we applied the two most commonly used spatial autocorrelation statistics for continuous data (Od© 2011 Hogrefe Publishing
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Table 2. Comparing the ranks of the London boroughs based on the different rates of suicide Rank1
SMR
SRR
GSSRR
LSSRR
1
Havering
Havering
Bromley
Bromley
2
Bromley
Bromley
Barnet
Barnet
3
Barnet
Barnet
Richmond upon Thames
Hounslow
4
Richmond upon Thames
Barking and Dagenham
Havering
Enfield
5
Barking and Dagenham
Richmond upon Thames
Enfield
Havering
6
Harrow
Harrow
Harrow
Harrow
7
Redbridge
Redbridge
Hounslow
Barking and Dagenham
8
Hounslow
Croydon
Redbridge
Richmond upon Thames
9
Croydon
Hounslow
Merton
Croydon
10
Merton
Enfield
Barking and Dagenham
Redbridge
11
Enfield
Ealing
Bexley
Merton
12
Ealing
Merton
Croydon
Hammersmith and Fulham
13
Sutton
Sutton
Hammersmith and Fulham
Bexley
14
Hillingdon
Newham
Kingston upon Thames
Newham
15
Bexley
Hillingdon
Sutton
Sutton
16
Newham
Bexley
Brent
Hillingdon
17
Kingston upon Thames
Hammersmith and Fulham
Greenwich
Kingston upon Thames
18
Hammersmith and Fulham
Kingston upon Thames
Hillingdon
Tower Hamlets
19
Tower Hamlets
Waltham Forest
Tower Hamlets
Waltham Forest
20
Waltham Forest
Greenwich
Haringey
Ealing Brent
21
Brent
Tower Hamlets
Newham
22
Greenwich
Brent
Ealing
Greenwich
23
Hackney
Hackney
City of London
City of London
24
Lambeth
Lambeth
Waltham Forest
Hackney
25
Haringey
Islington
Kensington and Chelsea
Haringey
26
Kensington and Chelsea
Kensington and Chelsea
Hackney
Kensington and Chelsea
27
Wandsworth
Haringey
Wandsworth
Lambeth
28
Islington
Wandsworth
Westminster City of
Wandsworth
29
Westminster City of
Westminster City of
Lambeth
Islington
30
Lewisham
Lewisham
Islington
Westminster City of
31
Southwark
Southwark
Lewisham
Lewisham
32
Camden
Camden
Southwark
Camden
33 City of London City of London Camden Note. 1Ranks of the local authorities in terms of suicide rate from the lowest to the highest.
land, 1988), i.e., the I statistic (Moran, 1948) and the Geary’s c statistic (Geary, 1954), the results of which have already been published in Rezaeian et al., 2007b, and revealed that there is no spatial dependency between suicide rates in London boroughs. In the present study, guided by the results of spatial autocorrelation, we smoothed the SRRs toward the global mean applying the noniterative empirical Bayes method of moments proposed by Marshall (1991), which is capable of estimating the relative risks of a given disease in a similar, but less complicated way to the fully Bayesian approach (Rezaeian et al., 2007a). We have chosen to smooth each sex and age-specific rate individually (prior to standardization), rather than to seek a more sophisticated estimate of all of them taken together (Bailey & Gatrell, 1995). However, in using © 2011 Hogrefe Publishing
Southwark
this technique two scenarios were considered. First, the SRRs were smoothed toward the global mean of England and Wales, and second, the SRRs were smoothed toward the mean of the London region. For brevity the former one is called GSSRR (global smoothed standardized rate ratio), and the latter LSSRR (London smoothed standardized rate ratio). All analyses were carried out within the Stata Release 6.0 environment (StataCorp, 1999).
Results Table 1 shows the 1998 population estimate, the total observed number of suicides in (1996–1998), plus different Crisis 2011; Vol. 32(4):225–230
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Figure 1. Line plot depicting different rates of suicide in London region (excluding the City of London). rates of suicide (1996–1998), i.e., SMR, SRR, GSSRR, and LSSRR, across separate boroughs of London. This table shows that there are greater values for different rates of suicide for the inner boroughs in comparison to the outer boroughs. The other striking finding is the very low numbers of suicides and the estimated population over 10 years in the City of London and as a result of this, both SMR and especially SRR are very high for this area. This table also shows that while SMR and SRR convey practically the same information, GSSRR and LSSRR, as would be expected, are not perfectly associated with the other two indices. They are, however, perfectly associated with each other. After excluding the City of London, because of its unusual SRR and SMR, all the boroughs were sorted according to the value of their SRR. Figure 1 presents data on the value of SRR, SMR, GSSRR, and LSSRR for each borough. This Figure clearly shows the effect of globally smoothing SRR in each borough. The rate of suicide in those boroughs with very low or very high rates of suicide shrinks toward the global mean. However, it seems Crisis 2011; Vol. 32(4):225–230
that the effects of smoothing toward the global mean of England and Wales in reducing the variability of SRR tends to be more than that of smoothing toward the London region mean. One can also investigate the relationships between these four kinds of suicide rates by looking at the rank of each local authority using each rate and compare it with its rank for the other rates. Thus, in Table 2 the ranks of the London boroughs are compared. In this table Rank 1 suggests the lowest rate of suicide and Rank 33 suggests the highest rate of suicide. This table depicts that although the effects of smoothing toward the global mean of England and Wales on the rank of each borough are more or less similar to the smoothing toward the London region mean, there are some discrepancies. For instance, based on the GSSRR Lambeth, Islington, Lewisham, Southwark, and Camden (in an increasing order of rate) are the boroughs with the highest rates, while based on the LSSRR Islington, Westminster City of, Lewisham, Camden, and Southwark (in an increasing order of rate) have the highest rates. © 2011 Hogrefe Publishing
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Discussion
References
One of the most important issues in mapping relatively rare phenomena such as suicide is that sometime the rarity of suicide, and also the very low population of some of the administrative units, made both the SRRs and the SMRs unstable (Rushton, 2003). In fact, these observed rates, which are the maximum likelihood estimates (MLE) for the underlying rates in each administrative unit, might not represent the best set of estimations (Efron & Morris, 1977). Therefore, one should consider the variation in population size as a source of random noise (Hertz-Picciotto, 1998) and try to overcome this problem, based on the extent of the spatial dependency between rates of nearby areas, with application of either a global or a local smoothing technique. We have shown that in the case of the London region, based on the fact that there is not a spatial dependency between suicide rates within neighboring boroughs, one should adopt a global smoothing approach. However, in doing that we have tested two different scenarios and revealed that smoothing the SRRs toward the global mean of England and Wales has a stronger influence in reducing the variability of the SRRs than smoothing toward the global mean of the London region. Why does this occur? It seems that, at least partially, this might happen because of the “edge effects” phenomenon. Edges are the external boundaries of the study area that may have a substantial effect on the estimates when methods are used that borrow information from adjacent areas (Lawson & Williams, 2001). In fact, when (based on the existence of spatial dependency) one smoothes the rates locally, the variability of rates within each area correlates with the area’s number of neighbors. It means that if one is to calculate the variability of smoothed rate estimates near to the peripheral boundary of the study region, one will find that the rate is elevated. This occurs because around the edge regions there is little information accessible to make the variability smaller (Vidal Rodeiro & Lawson, 2002). In our study, those boroughs located at the periphery of the London region have fewer nearby boroughs, when we smooth the rates toward the mean of the London region, compared with when we smooth the rates toward the mean of England and Wales. Therefore, this might explain why smoothing the rates toward the mean of the London region has less influence on the variability of the SRRs. Therefore, it can be concluded from the results of this methodological case study that smoothing the rates toward the mean of a region within a country performs actually somewhere between globally (i.e., smoothing toward the mean of country) and locally (i.e., smoothing toward the mean of neighboring areas).
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Rezaeian, M., Dunn, G. S., Leger, S., & Appleby, L. (2007b). Do hot spots of deprivation predict the rates of suicide within London boroughs? Health Place, 13, 886–893. Rushton, G. (2003). Public health, GIS, and spatial analytic tools. Annual Review of Public Health, 24, 43–56. Rytkönen, M.J. P. (2004). Not all maps are equal: GIS and spatial analysis in epidemiology. International Journal of Circumpolar Health, 63, 9–24. STATACorp. (1999). Stata statistical software: Release 6.0. College Station, TX: Author. Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(Suppl.), 234–240. Vidal Rodeiro, C. L., & Lawson, A. B. (2002, December). An analysis of edge effects in disease mapping. Presented at GeoHealth 2002. Victoria University of Wellington.
of Psychiatry (University of London, UK) from 1979 to 1996 and was appointed as Professor of Biomedical Statistic at the University of Manchester at the end of 1996. He is the author of several applied statistics textbooks and was a founding editor of the international review journal Statistical Methods in Medical Research. A. S. St Leger, retired, was a senior lecturer in Epidemiology and Consultant in Public Health Medicine based at the University of Manchester, UK. He is currently an honorary senior lecturer and tutor for an online course unit in advanced epidemiology for the MPH of the University of Manchester.
Received October 14, 2009 Revision received November 22, 2010 Accepted November 25, 2011 Published online July 8, 2011
Louis Appleby was recently appointed National Clinical Director for Health and Criminal Justice in the UK. The aim of his new post is to reduce mental illness in prisons and to improve collaboration between mental health services and the criminal justice system. Since 1996 he has been Professor of Psychiatry at the University of Manchester, UK, and since 1991 a consultant psychiatrist in Manchester. He was awarded a CBE for his services to medicine in 2006.
About the authors
Mohsen Rezaeian
Mohsen Rezaian is associate professor of epidemiology in the Social Medicine Department of Rafsanjan Medical School, Iran. His major interest lies in the epidemiology of suicide and its association with geography, socioeconomic status, cultural background, and religion.
Social Medicine Department Rafsanjan Medical School Rafsanjan University of Medical Sciences Rafsanjan Iran Tel. +98 391 5234003 E-mail
[email protected]
Graham Dunn worked as an academic statistician at the Institute
Crisis 2011; Vol. 32(4):225–230
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