Technical note: discussion of measurement of trends in deaths in custody - standardised mortality rates methodology
Source: data.gov.uk (2018-05-25)

Safety in Custody. Data on assaults, self-harm and assaults in prisons in England and Wales. Headline figures produced quarterly with more detailed figures produced annually in April.

Reporting of deaths in 
custody 
 
Ministry of Justice 
Technical note: discussion of 
measurement of trends in deaths 
in custody – standardised mortality 
rates methodology 
 
 
Published 28 July 2011 

Reporting of deaths in custody 
1 
                                           
Introduction 
In February 2010, Justice Statistics Analytical Services, Ministry of Justice 
published Safety in Custody, a statistics bulletin containing data on deaths 
in custody, including data on self-harm and assaults.  This was the first 
publication of this data and as such was well-received.  However, 
improvements to reporting methods have been under consideration since 
publication.   
 
Reporting trends in deaths in custody is problematic because the total 
number of deaths is relatively small and small changes year on year 
produce disproportionately large percentage increases or decreases.  Table 
1 which appeared in the first publication shows that in 2009, there were 168 
prisoners who died, out of a total average prison population of 83,461 
prisoners. In 2008, 165 prisoners died out of an average population of 
82,572 prisoners. 1   So the 2009 figure represents an increase of 1.8% on 
2008.  The crude death rate for the prison population was 0.20% for both 
2008 and 2009, the small increase of 0.0015% from 2008 to 2009 being lost 
when rounding to two decimal places.  In an effort to smooth the data, 3-
year rolling averages were produced.  
 
These averages were published in units of both 1,000 and 100,000.  This is 
because descriptive statistics of populations are typically expressed in units 
smaller than the total (the prison population being less than 100,000) while 
data in units of 100,000 was provided to facilitate comparison with wider 
population statistics.  Presenting the rates in units of 100,000 only serves to 
highlight the problems associated with small data sets. 
 
1 “Safety in custody statistics 2008/2009, Prisons and probation, Safety in custody,” Justice, 
Ministry of Justice, http://www.justice.gov.uk/publications/safer‐custody.htm (accessed 21 July 
2011). 

Reporting of deaths in custody 
 
Table 1: Summary statistics, Safety in Custody statistical bulletin 
2008/092 
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary 
stat
isti
cs, 
Safe
ty i
n Cu
stod
y st
atis
tical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
T
abl
e 1: Summary statistics, Safety in Custody statistical bulletin 2008/09Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Tab
le 
1: 
Sum
mar
y s
tat
ist
ics, Safety in
 C
us
to
dy
 s
ta
ti
st
ic
al
 bulletin 2008
/0
9
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/0
9
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Table 1:
 
S
u
m
m
a
r
y
 
statistics, Safety in Custody statistical 
bulletin 2008/09
0
Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
T
able
 1: 
Summ
ary 
stat
istics, Safety in Custody statistical bulletin 2008/09Table 1: Summary statistics, Safety in Custody statistical bulletin 2008/09
Tabl
e 1:
 Summary statistics, 
S
a
fety
 in 
Cust
ody 
stat
isti
cal 
bull
etin 2008/09
 
 
Comparison of data with the wider population requires more than common 
units of measurement.  Differences between populations such as age and 
sex need to be acknowledged and controlled for.  The Department of Health 
uses standardised mortality ratios (SMRs) to compare mortality rates in 
hospitals.3  An SMR has the advantage of summarising differences between 
populations in one statistic while controlling for differences in distribution of 
age and sex.   
 
Table 2 shows a summary table similar to Table 1 but with the addition of 
SMRs and 3-year rolling averages replaced by a single year annual 
average, as published in the Safety in Custody bulletin in July 2011:- 
                                            
2 “Safety in custody statistics 2008/2009”, Ministry of Justice, 
http://www.justice.gov.uk/publications/safer‐custody.htm (accessed 21 July 2011). 
3 “Template for Calculating Age‐Standardised Mortality Rates (Direct standardization),” London 
Health Observatory, London Health Observatory, 
http://www.lho.org.uk/viewResource.aspx?id=9275 (accessed 21 July 2011). 
2 

Reporting of deaths in custody 
 
Table 2: Summary statistics, Safety in Custody statistical bulletin 
20104 
Table 2: Summary 
stat
isti
cs, 
Safe
ty i
n Cu
stod
y st
atistical bulletin 
2010
58
5
1
 
 
Standardised mortality ratios (SMRs) 
Major differences between the general population and the prison population 
are total size and age and sex distributions.  The prison population data in 
Figure 15 is presented on a scale of units of 5,000 whereas the general 
population data in Figure 26 is presented in units of 5,000,000 because the 
population of England and Wales is nearly 900 times the size of the prison 
population.   Age and sex distribution also differs considerably between the 
prison and general population.  The prison population by definition only 
covers prisoners aged 15 years and over.  It also has considerably fewer 
prisoners aged 60 years and over.  Female prisoners constitute 5% of the 
total prison population compared with 51% of the general population of 
England and Wales. 
 
                                            
4 “Safety in custody statistics 2010”, Ministry of Justice, 
http://www.justice.gov.uk/publications/safer‐custody.htm (accessed 28 July 2011). 
5 Derived from data in Table A1.1, “Population, Offender management caseload statistics 2010 
tables”, Ministry of Justice, http://www.justice.gov.uk/publications/statistics‐and‐data/prisons‐
and‐probation/oms‐quarterly.htm (accessed 28 July 2011). 
6 Data from “England and Wales population estimates and projections 1961‐2083, The interactive 
population pyramid” Office for National Statistics, 
http://www.statistics.gov.uk/populationestimates/flash_pyramid/default.htm (accessed 21 July 
2011). 
3 

Reporting of deaths in custody 
Figure 1:  Total prison population of England and Wales, as at 30 June 
2010 
F
igure
 1:  T
otal p
rison 
population of England and Wales, as at 30 June 2010
Figure 1:  Total prison population of England and Wales, as at 30 June 2010
Figure 1:  Total prison population of England and Wales, as at 30 June 2010
 
 
Figure 2:  Population of England and Wales, 2010 
F
igure 2: 
 Population of England and Wales, 2010
Figure 2:  Population of England and Wales, 2010
Figure 2:  Population of England and Wales, 2010
 
 
Standardising total mortality ratios for age and sex factors out differences 
between age and sex distributions.  Selecting the general population of 
England and Wales as the standard population and the population in prison 
in England and Wales as the index population, estimated deaths in the 
prison population have been calculated in Table 2 using indirect 
standardisation by multiplying numbers of the index population categories 
by death rates in the standard population for both sexes.  The indirect 
method was chosen because of the relatively small size of events in the 
index population. 
4 

Reporting of deaths in custody 
Table 2:  SMR calculations  
Table 2:
  SMR
 calculatio
ns
 
F
o
rmula
F
o
r
m
u
l
a
 
          = 1.25 
 
If the index and standard populations had the same mortality rates, the SMR 
would be 1.0.  To understand whether an SMR indicates a statistically 
significant difference between the mortality rates of the index and standard 
populations requires calculation of upper and lower bounds7 for the 95% 
confidence interval defined as:- 
 
Formula
F
o
r
m
u
la
 
            = 1.11 
                                            
7 N. E. Breslow and N. E. Day, "Statistical Methods in Cancer Research, Vol. 2: The Design and 
Analysis of Cohort Studies."  International Agency for Research on Cancer Scientific Publications, 
no. 82 (1987).  http://www.iarc.fr/en/publications/pdfs-online/stat/ (accessed 21 July 2011). 
5 

Reporting of deaths in custody 
 
Formula
F
ormula
F
o
r
m
u
l
a
 
           = 1.41 
 
Since the value of the 2010 SMR is between 1.11 and 1.41, an interval 
which does not include 1, the difference between the death rate of the 
general population and the population in custody is statistically significant at 
the 95% confidence interval. Figure 3 shows the SMR and confidence 
intervals since 2002. 
 
 
Figure 3: SMR for Prison Population in England and Wales, 2002-2010 
Fig
ure
 3:
 SM
R f
or 
Pri
son
 Po
pul
ati
on i
n En
glan
d an
d Wa
les,
 200
2-
2010
Figure 3: SMR for Prison Population in England and Wales, 2002-2010
Figure 3: SMR for Prison Population in England and Wales, 2002-2010
 
 
Units of measurement 
 
The dictionary definition of a rate is, “a measure, quantity, or frequency, 
typically one measured against another quantity or measure.”  Rates of 
deaths in custody were published as both the number of deaths per 1,000 
and 100,000 prisoners.  The rate per 1,000 was chosen because the prison 
population is less than 100,000 but the rate per 100,000 was provided to 
facilitate comparison with other population statistics.  Population statistics 
for the UK are reported in units of 100,000 because the total population is 
larger than 100,000.   
6 

Reporting of deaths in custody 
7 
 
While there is no rule governing use of units of measurement for deaths or 
population statistics, deaths statistics published on the internet are more 
commonly reported as actual figures.  The Office for National Statistics 
(ONS) website reports rates of death for circulatory diseases, cancer and 
respiratory diseases and standardised mortality rates using units of 
1,000,000.  Elsewhere, ONS standardised mortality rates are reported using 
units of 100,000 when subdivided into cause.   The Eurostat website reports 
actual data as well as crude death rates using units of 100,000 and 
standardised death rates in terms of the average European mortality rate.  
The World Heath Organisation website reports age-specific rates of 
registered deaths by cause using units of 100,000.   
 
Rates for smaller populations such as infants and national data broken 
down by age-specific categories use units of 1,000.  Appendix A contains a 
brief survey of mortality rates as published on the internet. 
 
 
Conclusion 
 
Standardised mortality ratios for the prison population together with 
confidence intervals provide context to differences between mortality rates 
in custody compared to the UK population.  Publication of an annual SMR 
provides a more consistent measure of change than actual data or a three-
year-rolling average.   
 
Rates other than standardised mortality ratios could be published per 
100,000 in line with other population statistics but the numbers could be 
construed as misleading due to the fact that they describe a unit larger than 
the total population in custody.  Since the prison SMR uses UK population 
data as part of the calculation, direct comparison of data with ONS 
population statistics is unnecessary.  As the total prison population is less 
than 100,000, to avoid highlighting small year-on-year changes, rates 
should be published per 1,000 prisoners.  
    
As an area for future research we intend to look more closely at the 
reporting of self-inflicted deaths to enable more detailed analysis. 
 
 

Reporting of deaths in custody 
Appendix A  
 
Survey of online sources of mortality rates 
Survey of online
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of mortal
ity 
rates
Survey of online sources of mortality ratesSurvey of online sources of mortality rates
Survey of online sources of mortality rates
Survey of onlin
e sources of mortality rates
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urvey of online sources of mortality rates
Survey of online sources of mortality ratesSurvey of online sources of mortality ratesSurvey of online sources of mortality rates
Su
rv
ey 
of online sources of mortality rates
 
 
8 

Reporting of deaths in custody 
9 
 
  
 
Contact points for further information 
Press enquiries should be directed to the Ministry of Justice press office: 
Tel: xx-xxxx-xxxx 
 
Other enquiries about these statistics should be directed to: 
Alison Walker 
Ministry of Justice 
Justice Statistics Analytical Services 
7th Floor 
102 Petty France 
London 
SW1H 9AJ 
Tel: xx-xxxx-xxxx 
 
General enquiries about the statistical work of the Ministry of Justice can be 
e-mailed to: xxx@xxx.xx 
Other National Statistics publications, and general information about the 
official statistics system of the UK, are available from www.statistics.gov.uk 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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