Two towns, Oakridge and Pinehurst, are being compared using crude death rates.
Crude death rate = (number of deaths / total population) x 1000
(a)State what a crude death rate tells you about a population.(1)
(b)Oakridge has a population of 25,000 and recorded 200 deaths last year. Calculate the crude death rate for Oakridge.(2)
(c)Pinehurst has a population of 10,000 and recorded 150 deaths last year. Calculate the crude death rate for Pinehurst.(2)
(Total for Question 1 is 5 marks)
2
Pinehurst has a much older population than Oakridge: a far higher proportion of Pinehurst's residents are aged 65 and over.
(a)Using the crude death rates found in Question 1 (Oakridge = 8 per 1000, Pinehurst = 15 per 1000), write down which town has the higher crude death rate.(1)
(b)Explain why comparing these two crude death rates alone might not fairly reflect which town's population is actually less healthy.(2)
(Total for Question 2 is 3 marks)
3
To compare mortality between areas fairly, statisticians often use a standard population with known age-specific death rates. The table below shows the standard population's age-specific death rates used throughout this pack.
Age band
Standard age-specific death rate (per 1000)
Under 40
1
40-64
5
65 and over
50
(a)Explain why simply comparing two areas' crude death rates can be misleading if their populations have different age structures, and state what problem standardisation is designed to solve.(2)
(b)State what is used, alongside a local area's own population figures, to calculate its expected number of deaths in this method.(1)
(Total for Question 3 is 3 marks)
4
The standardised mortality ratio (SMR) compares the observed number of deaths in an area with the number of deaths that would be expected if the area had the standard population's age-specific death rates.
(a)Which of the following is the correct formula for the SMR?(1)
A) (Expected deaths / Observed deaths) x 100
B) (Observed deaths / Expected deaths) x 100
C) (Observed deaths / Total population) x 1000
D) (Observed deaths - Expected deaths) x 100
(b)Write down the value that an SMR is always compared against.(1)
(Total for Question 4 is 2 marks)
5
Denby district has a population of 20,000, split by age band as shown.
Age band
Population
Standard age-specific death rate (per 1000)
Under 40
10,000
1
40-64
6,000
5
65 and over
4,000
50
The expected number of deaths in each age band is found by multiplying the age band's population (in thousands) by its standard age-specific death rate.
(a)Calculate the expected number of deaths in the Under 40 age band.(1)
(b)Calculate the expected number of deaths in the 40-64 age band.(1)
(c)Calculate the expected number of deaths in the 65 and over age band.(1)
(d)Work out the total expected number of deaths in Denby.(2)
(Total for Question 5 is 5 marks)
6
Denby's expected number of deaths, found in Question 5, was 240. Denby actually recorded 300 deaths that year.
(a)Calculate the SMR for Denby.(2)
(b)Interpret what an SMR of 125 means for Denby.(2)
(c)State whether an SMR above 100 indicates more or fewer deaths than expected.(1)
(Total for Question 6 is 5 marks)
7
The table shows the age-band populations (in thousands) of three small towns. Using the standard population's age-specific death rates (Under 40 = 1 per 1000, 40-64 = 5 per 1000, 65 and over = 50 per 1000), complete the table by calculating the expected number of deaths in each town.
Town
Under 40 (000s)
40-64 (000s)
65 and over (000s)
Expected deaths
Hollow Green
7
3
2
?
Marsh End
4
4
4
?
Top Fenwick
2
2
6
?
(Total for Question 7 is 3 marks)
8
Sandmoor district also has a population of 20,000, split by age band as shown.
Age band
Population
Standard age-specific death rate (per 1000)
Under 40
5,000
1
40-64
7,000
5
65 and over
8,000
50
Sandmoor recorded 396 actual deaths that year.
(a)Calculate the total expected number of deaths in Sandmoor.(3)
(b)Calculate the SMR for Sandmoor.(2)
(c)Interpret the SMR value found in part (b).(1)
(Total for Question 8 is 6 marks)
9
The table summarises the crude death rate and SMR for Denby and Sandmoor, both found in earlier questions.
District
Crude death rate (per 1000)
SMR
Denby
15
125
Sandmoor
19.8
90
(a)Write down which district has the higher crude death rate.(1)
(b)Write down which district has the higher SMR.(1)
(c)Using both sets of figures, explain why the crude death rates alone give a misleading impression of which district truly has worse-than-expected mortality, and state what the SMR values reveal instead.(4)
(Total for Question 9 is 6 marks)
10
The bar chart shows the SMR for four hospital trusts, P, Q, R and S, in the same year. The dashed line shows the reference value of SMR = 100.
(a)Write down the SMR of Trust Q.(1)
(b)Write down which trust has the highest SMR.(1)
(c)Trust P has an SMR of 70. Interpret what this means for Trust P.(2)
(d)Explain why comparing the raw number of deaths at each trust, instead of their SMRs, could give a misleading picture of how well each trust is performing.(2)
(Total for Question 10 is 6 marks)
11
For each statement about crude rates and the SMR, write down whether it is True or False.
(i)An SMR of 100 means the observed number of deaths exactly matches the number expected from the standard population's age-specific rates.(1)
(ii)A crude rate always gives a fairer comparison between two areas than a standardised rate.(1)
(iii)The standard population's age-specific rates are applied to each area's own local population in each age band; the standard population's total size does not need to match the local area's total size.(1)
(Total for Question 11 is 3 marks)
12
A health analyst wants to investigate whether Health Trust Kelwood has an unusually high number of deaths, once the age of its patients is taken into account.
(a)(Plan) State what data the analyst needs to collect about Kelwood in order to calculate its SMR.(1)
(b)(Collect) Give one appropriate source the analyst could use to obtain reliable data on deaths and population numbers.(1)
(c)(Process) Kelwood has a population of 15,000, split by age band as shown.
Age band
Population
Standard age-specific death rate (per 1000)
Under 40
6,000
1
40-64
4,000
5
65 and over
5,000
50
Kelwood recorded 345 actual deaths that year. Calculate the expected number of deaths and the SMR for Kelwood.(4)
(d)(Interpret) Interpret Kelwood's SMR, and suggest one action the analyst might recommend as a result.(2)
(Total for Question 12 is 8 marks)
13
Trust Marlow has an SMR of 140. The expected number of deaths at Marlow, based on the standard population's age-specific rates, was 250.
(a)Calculate the actual (observed) number of deaths recorded at Trust Marlow.(3)
(b)Trust Nesbury has an SMR of 80 and recorded 240 observed deaths. Calculate the expected number of deaths for Trust Nesbury.(3)
(Total for Question 13 is 6 marks)
14
A local newspaper reports: 'Greenfield Hospital has an SMR of 130, while Riverside Hospital has an SMR of 95, so Greenfield must be a worse hospital than Riverside.' Greenfield specialises in treating complex, high-risk cases referred from other hospitals, while Riverside mainly treats routine, lower-risk cases.
(a)Evaluate the newspaper's claim, explaining one reason why comparing SMRs alone may still not give a completely fair comparison between the two hospitals.(3)
(b)Explain why, despite this limitation, the SMR is still generally a fairer way to compare hospitals' mortality than using crude death rates or raw numbers of deaths.(2)
(Total for Question 14 is 5 marks)
15
The line graph shows the SMR for Trust Oakhaven each year from 2021 to 2024. The dashed line shows the reference value of SMR = 100.
(a)Write down the SMR for Trust Oakhaven in 2023.(1)
(b)Describe the trend in Trust Oakhaven's SMR from 2021 to 2024.(1)
(c)By 2024, is Trust Oakhaven's mortality still higher than expected for its patients' age structure? Justify your answer using the graph.(2)
(d)Suggest one possible reason for the improving trend shown in the graph.(1)
(Total for Question 15 is 5 marks)
16
Millfield has a population of 40,000, split by age band as shown.
Age band
Population
Standard age-specific death rate (per 1000)
Under 40
10,000
1
40-64
18,000
5
65 and over
12,000
50
Millfield recorded 840 actual deaths that year.
(a)Calculate the crude death rate for Millfield.(2)
(b)Calculate the expected number of deaths for Millfield, using the standard population's age-specific rates.(3)
(c)Calculate the SMR for Millfield.(2)
(d)Evaluate what the crude rate and the SMR together suggest about mortality in Millfield, and explain why relying on the crude rate alone would give an incomplete picture.(3)
(Total for Question 16 is 10 marks)
Mark scheme · H14 Crude and Standardised Rates
Question 1
(a) B1 the number of deaths per 1000 people in the population, oe
(a) Answer: The number of deaths per 1000 people in the population.
(b) M1 200 / 25000, oe
(b) A1 8 cao
(b) Answer: 8 per 1000
(c) M1 150 / 10000, oe
(c) A1 15 cao
(c) Answer: 15 per 1000
Question 2
(a) B1 Pinehurst cao
(a) Answer: Pinehurst
(b) B1 recognises that Pinehurst has an older population, and older people are naturally more likely to die in a given year, oe
(b) B1 explains that the higher crude rate in Pinehurst could simply be due to its age structure rather than poorer health or care, so the comparison is not fair unless age is taken into account, oe
(b) Answer: Pinehurst's higher crude rate may simply reflect its older population, since older people are more likely to die each year regardless of how healthy the town's population is overall; the crude rates do not account for this difference in age structure.
Question 3
(a) B1 identifies that crude rates are affected by age structure, e.g. an area with more older people will tend to have a higher crude rate even with the same underlying health, oe
(a) B1 states that standardisation is designed to adjust for/remove this effect of differing age structures, allowing a fairer comparison of underlying mortality between areas, oe
(a) Answer: Crude rates can be misleading because they are affected by an area's age structure, not just its underlying health, so an older population will tend to show a higher crude rate anyway. Standardisation is designed to adjust for these age differences so that areas can be compared fairly.
(b) B1 the standard population's age-specific death rates cao
(b) Answer: The standard population's age-specific death rates, applied to the local area's population in each age band.
Question 4
(a) B1 B cao
(a) Answer: B) (Observed deaths / Expected deaths) x 100
(b) B1 100 cao
(b) Answer: 100
Question 5
(a) B1 10 cao
(a) Answer: 10
(b) B1 30 cao
(b) Answer: 30
(c) B1 200 cao
(c) Answer: 200
(d) M1 10 + 30 + 200, oe (ft their (a) to (c))
(d) A1 240 cao
(d) Answer: 240
Question 6
(a) M1 300 / 240 x 100, oe (ft their total from Question 5)
(a) A1 125 cao
(a) Answer: 125
(b) B1 identifies that Denby had more deaths than would be expected, given its age structure, oe
(b) B1 quantifies this as 25% more deaths than expected (or a quarter more), oe
(b) Answer: Denby recorded 25% more deaths than would be expected, given its age structure, based on the standard population's rates.
(c) B1 more cao
(c) Answer: More deaths than expected.
Question 7
B1 Hollow Green = 122 cao
B1 Marsh End = 224 cao
B1 Top Fenwick = 312 cao
Answer: Hollow Green 122; Marsh End 224; Top Fenwick 312
Question 8
(a) M1 5x1 + 7x5 + 8x50, oe
(a) M1 5 + 35 + 400, oe
(a) A1 440 cao
(a) Answer: 440
(b) M1 396 / 440 x 100, oe (ft their (a))
(b) A1 90 cao
(b) Answer: 90
(c) B1 Sandmoor had 10% fewer deaths than expected, given its age structure, oe
(c) Answer: Sandmoor recorded 10% fewer deaths than would be expected, given its age structure.
Question 9
(a) B1 Sandmoor cao
(a) Answer: Sandmoor
(b) B1 Denby cao
(b) Answer: Denby
(c) B1 recognises that Sandmoor's higher crude rate (19.8 vs 15) might suggest Sandmoor has worse mortality, oe
(c) B1 but Sandmoor also has an older population, so a higher crude rate is expected anyway, oe
(c) B1 the SMR values show the opposite once age structure is accounted for: Denby's SMR (125) is higher than Sandmoor's (90), meaning Denby has more deaths than expected for its own age structure while Sandmoor has fewer, oe
(c) B1 concludes that Denby, not Sandmoor, is the district with the worse-than-expected mortality outcomes, oe
(c) Answer: The crude rates alone suggest Sandmoor (19.8) has worse mortality than Denby (15), but this is misleading because Sandmoor has an older population, which naturally raises its crude rate. Once age structure is accounted for, the SMR values show the opposite: Denby's SMR of 125 is higher than Sandmoor's 90, meaning Denby actually has more deaths than expected for its own age structure, while Sandmoor has fewer. So Denby, not Sandmoor, is the district with worse-than-expected mortality.
Question 10
(a) B1 100 cao
(a) Answer: 100
(b) B1 Trust S cao
(b) Answer: Trust S
(c) B1 identifies that Trust P had fewer deaths than expected, given its patients' age structure, oe
(c) B1 quantifies this as 30% fewer deaths than expected, oe
(c) Answer: Trust P recorded 30% fewer deaths than would be expected, given the age structure of its patients.
(d) B1 raw death counts depend on how many patients each trust treats and their age/case mix, so a trust treating more patients or older/sicker patients would have more deaths anyway, oe
(d) B1 the SMR adjusts for these differences by comparing observed deaths with the number expected for that trust's own patient population, allowing a fairer like-for-like comparison, oe
(d) Answer: Raw death counts depend on how many patients a trust treats and their age or case mix, so a trust with more or older patients would naturally record more deaths, even with equally good care. The SMR adjusts for this by comparing observed deaths with the number expected for that trust's own patients, giving a fairer comparison.
Question 11
(i) B1 True cao
(i) Answer: True
(ii) B1 False cao
(ii) Answer: False
(iii) B1 True cao
(iii) Answer: True
Question 12
(a) B1 the observed number of deaths at Kelwood in a year, and Kelwood's local population split by age band, oe
(a) Answer: The number of observed deaths at Kelwood in a year, and Kelwood's population split by age band.
(b) B1 any valid source, e.g. official health service administrative records, or a national statistics agency's mortality data, oe
(b) Answer: Official health service records, or mortality data published by a national statistics agency.
(c) M1 6x1 + 4x5 + 5x50, oe
(c) A1 276 cao (expected deaths)
(c) M1 345 / 276 x 100, oe (ft their expected deaths)
(c) A1 125 cao (SMR)
(c) Answer: Expected deaths = 276; SMR = 125.
(d) B1 Kelwood recorded 25% more deaths than expected, given its patients' age structure, oe
(d) B1 suggests a sensible follow-up action, e.g. investigating Kelwood's care standards or other risk factors further, or comparing with other trusts to see if the pattern is unusual, oe
(d) Answer: Kelwood recorded 25% more deaths than expected for its age structure (SMR = 125). The analyst might recommend investigating Kelwood's care standards or other risk factors further to understand why.
Question 13
(a) M1 140 / 100, oe (finds the SMR as a decimal multiplier)
(a) M1 their multiplier x 250, oe (dep)
(a) A1 350 cao
(a) Answer: 350
(b) M1 240 / 80, oe
(b) M1 their value x 100, oe (dep)
(b) A1 300 cao
(b) Answer: 300
Question 14
(a) B1 identifies that SMR only adjusts for age (and sex) structure, not for other factors that affect mortality risk, oe
(a) B1 explains that Greenfield treats more complex/high-risk referred cases, which could raise its SMR even with equally good or better care, so the claim may be unfair, oe
(a) B1 concludes that the claim is not fully justified/cannot be confirmed from SMR alone, oe
(a) Answer: The claim is not fully justified. SMR only adjusts for age (and sex) structure, not for other factors like case complexity. Greenfield treats more complex, high-risk referred cases, which could raise its SMR even if its care is just as good as Riverside's, so comparing SMRs alone does not prove Greenfield is a worse hospital.
(b) B1 SMR at least adjusts for age (and sex) structure, which crude rates and raw counts do not, oe
(b) B1 so SMR removes one major source of unfair comparison (differing patient age profiles), even if other factors like case-mix still need to be considered, oe
(b) Answer: SMR still adjusts for the patients' age (and sex) structure, which crude death rates and raw counts do not. This removes one major source of unfair comparison, even though other factors like case complexity may still need to be considered separately.
Question 15
(a) B1 115 cao
(a) Answer: 115
(b) B1 the SMR has steadily decreased/fallen each year, moving closer to 100, oe
(b) Answer: Trust Oakhaven's SMR has steadily decreased from 2021 to 2024, moving closer to 100.
(c) B1 Yes cao
(c) B1 the 2024 SMR (108) is still above 100, meaning about 8% more deaths occurred than expected, even though the gap has narrowed considerably since 2021, oe
(c) Answer: Yes. The 2024 SMR of 108 is still above 100, meaning around 8% more deaths occurred than expected, although the gap has narrowed a lot since 2021 (SMR 132).
(d) B1 any sensible reason, e.g. improvements in patient care/treatment protocols, better staffing levels, or changes in the types of patients treated, oe
(d) Answer: Trust Oakhaven may have introduced improvements to patient care or treatment protocols over this period.
Question 16
(a) M1 840 / 40000, oe
(a) A1 21 cao
(a) Answer: 21 per 1000
(b) M1 10x1 + 18x5 + 12x50, oe
(b) M1 10 + 90 + 600, oe
(b) A1 700 cao
(b) Answer: 700
(c) M1 840 / 700 x 100, oe (ft their (b))
(c) A1 120 cao
(c) Answer: 120
(d) B1 recognises that the crude rate (21 per 1000) alone has no benchmark, so it is impossible to tell whether this is high or low without further information, oe
(d) B1 the SMR of 120 shows that, once Millfield's age structure is accounted for, it had 20% more deaths than expected, oe
(d) B1 concludes that standardisation reveals a genuine excess in mortality that the crude rate alone could not show, since age differences could otherwise mask or wrongly explain the raw figures, oe
(d) Answer: The crude rate of 21 per 1000 alone cannot be judged as high or low without a benchmark. The SMR of 120 shows that, once Millfield's age structure is taken into account, it actually had 20% more deaths than expected. This reveals a genuine excess in mortality that the crude rate alone could not show, since age differences could otherwise mask or wrongly explain the raw figures.