PHEindicatormethods: Common Public Health Statistics and their Confidence Intervals

Description

Functions to calculate commonly used public health statistics and their confidence intervals using methods approved for use in the production of Public Health England indicators such as those presented via Fingertips (https://fingertips.phe.org.uk/). It provides functions for the generation of proportions, crude rates, means, directly standardised rates, indirectly standardised rates, standardised mortality ratios, slope and relative index of inequality and life expectancy. Statistical methods are referenced in the following publications. Breslow NE, Day NE (1987) doi:10.1002/sim.4780080614. Dobson et al (1991) doi:10.1002/sim.4780100317. Armitage P, Berry G (2002) doi:10.1002/9780470773666. Wilson EB. (1927) doi:10.1080/01621459.1927.10502953. Altman DG et al (2000, ISBN: 978-0-727-91375-3). Chiang CL. (1968, ISBN: 978-0-882-75200-6). Newell C. (1994, ISBN: 978-0-898-62451-9). Eayres DP, Williams ES (2004) doi:10.1136/jech.2003.009654. Silcocks PBS et al (2001) doi:10.1136/jech.55.1.38. Low and Low (2004) doi:10.1093/pubmed/fdh175. Fingertips Public Health Technical Guide: https://fingertips.phe.org.uk/static-reports/public-health-technical-guidance/.

Author(s)

Maintainer: Georgina Anderson georgina.anderson@dhsc.gov.uk

Other contributors:

• Sebastian Fox [contributor]

• Matthew Francis [contributor]

• Paul Fryers paul.fryers@dhsc.gov.uk [contributor]

• Emma Clegg [contributor]

• Annabel Westermann [contributor]

• Joshua Woolner [contributor]

• Charlotte Fellows charlotte.fellows@dhsc.gov.uk [contributor]

• Olivia Box Power Olivia.BoxPower@dhsc.gov.uk [contributor]

See Also

Useful links:

• Report bugs at https://github.com/ukhsa-collaboration/PHEindicatormethods/issues

SII test datasets - DSR

Description

A data table of dummy Directly Standardised Rates by deprivation quintiles

Usage

data(DSR_data)

Format

A data table

Examples

DSR_data

SII test datasets - Life Expectancy

Description

A data table of life expectancy data by area and deprivation decile

Usage

data(LE_data)

Format

A data table

Examples

LE_data

Identifies whether each value in a dataset falls outside of 95 and/or 99.8 percent control limits based on the aggregated average value across the whole dataset as an indicator of statistically significant difference.

Description

This follows the funnel plot methodology published on the PHE Fingertips Technical Guidance page: https://fingertips.phe.org.uk/profile/guidance/supporting-information/PH-methods

Usage

assign_funnel_significance(
  data,
  numerator,
  denominator,
  rate,
  statistic = NULL,
  rate_type = NULL,
  multiplier = NULL
)

Arguments

Value

returns the original data.frame with the significance level appended

Author(s)

Matthew Francis

See Also

Other PHEindicatormethods package functions: calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(
  Area = c("A", "B", "C", "D"),
  numerator = c(10232, 12321, 15123, 13213),
  denominator = c(15232, 16123, 17932, 18475)
)
df %>%
  assign_funnel_significance(numerator, denominator,
                             statistic = "proportion", multiplier = 100)

Calculate Indirectly Standardised Rates using calculate_ISRate

Description

Calculates indirectly standardised rates with confidence limits using Byar's (1) or exact (2) CI method.

Usage

calculate_ISRate(
  data,
  x,
  n,
  x_ref,
  n_ref,
  refpoptype = "vector",
  type = "full",
  confidence = 0.95,
  multiplier = 1e+05,
  observed_totals = NULL
)

Arguments

Value

When type = "full", returns a tibble of observed events, expected events, indirectly standardised rate, lower confidence limit, upper confidence limit, confidence level, statistic and method for each grouping set

Notes

User MUST ensure that x, n, x_ref and n_ref vectors are all ordered by the same standardisation category values as records will be matched by position.

For numerators >= 10 Byar's method (1) is applied using the internal byars_lower and byars_upper functions. For small numerators Byar's method is less accurate and so an exact method (2) based on the Poisson distribution is used.

This function directly replaced phe_isr which was fully deprecated in package version 2.0.0 due to ambiguous naming

References

(1) Breslow NE, Day NE. Statistical methods in cancer research, volume II: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer, World Health Organisation; 1987.

(2) Armitage P, Berry G. Statistical methods in medical research (4th edn). Oxford: Blackwell; 2002.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(indicatorid = rep(c(1234, 5678, 91011, 121314), each = 19 * 2 * 5),
                 year = rep(2006:2010, each = 19 * 2),
                 sex = rep(rep(c("Male", "Female"), each = 19), 5),
                 ageband = rep(c(0,5,10,15,20,25,30,35,40,45,
                                 50,55,60,65,70,75,80,85,90), times = 10),
                 obs = sample(200, 19 * 2 * 5 * 4, replace = TRUE),
                 pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE))

refdf <- data.frame(refcount = sample(200, 19, replace = TRUE),
                    refpop = sample(10000:20000, 19, replace = TRUE))

## calculate multiple ISRs in single execution
df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRate(obs, pop, refdf$refcount, refdf$refpop)

## execute without outputting metadata fields
df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRate(obs, pop, refdf$refcount, refdf$refpop, type="standard", confidence=99.8)

## calculate 95% and 99.8% CIs in single execution
df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRate(obs, pop, refdf$refcount, refdf$refpop, confidence = c(0.95, 0.998))

## Calculate ISR when observed totals aren't available with age-breakdowns
observed_totals <- data.frame(indicatorid = rep(c(1234, 5678, 91011, 121314), each = 10),
                       year = rep(rep(2006:2010, each = 2),4),
                       sex = rep(rep(c("Male", "Female"), each = 1),20),
                       observed = sample(1500:2500, 40))

df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRate(observed, pop, refdf$refcount, refdf$refpop,
    observed_totals = observed_totals)

Calculate Indirectly standardised ratios using calculate_ISRatio

Description

Calculates standard mortality ratios (or indirectly standardised ratios) with confidence limits using Byar's (1) or exact (2) CI method.

Usage

calculate_ISRatio(
  data,
  x,
  n,
  x_ref,
  n_ref,
  refpoptype = "vector",
  type = "full",
  confidence = 0.95,
  refvalue = 1,
  observed_totals = NULL
)

Arguments

Value

When type = "full", returns a tibble of observed events, expected events, standardised mortality ratios, lower confidence limits, upper confidence limits, confidence level, statistic and method for each grouping set

Notes

User MUST ensure that x, n, x_ref and n_ref vectors are all ordered by the same standardisation category values as records will be matched by position.

For numerators >= 10 Byar's method (1) is applied using the internal byars_lower and byars_upper functions. For small numerators Byar's method is less accurate and so an exact method (2) based on the Poisson distribution is used.

This function directly replaced phe_smr which was fully deprecated in package version 2.0.0 due to ambiguous naming

References

(1) Breslow NE, Day NE. Statistical methods in cancer research, volume II: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer, World Health Organisation; 1987.

(2) Armitage P, Berry G. Statistical methods in medical research (4th edn). Oxford: Blackwell; 2002.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(indicatorid = rep(c(1234, 5678, 91011, 121314), each = 19 * 2 * 5),
                 year = rep(2006:2010, each = 19 * 2),
                 sex = rep(rep(c("Male", "Female"), each = 19), 5),
                 ageband = rep(c(0,5,10,15,20,25,30,35,40,45,
                                 50,55,60,65,70,75,80,85,90), times = 10),
                 obs = sample(200, 19 * 2 * 5 * 4, replace = TRUE),
                 pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE))

refdf <- data.frame(refcount = sample(200, 19, replace = TRUE),
                    refpop = sample(10000:20000, 19, replace = TRUE))

df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRatio(obs, pop, refdf$refcount, refdf$refpop, type="standard")

## OR

df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRatio(obs, pop, refdf$refcount, refdf$refpop, confidence=99.8, refvalue=100)

## Calculate ISR when observed totals aren't available with age-breakdowns
observed_totals <- data.frame(indicatorid = rep(c(1234, 5678, 91011, 121314), each = 10),
                       year = rep(rep(2006:2010, each = 2),4),
                       sex = rep(rep(c("Male", "Female"), each = 1),20),
                       observed = sample(1500:2500, 40))

df %>%
    group_by(indicatorid, year, sex) %>%
    calculate_ISRatio(observed, pop, refdf$refcount, refdf$refpop,
    observed_totals = observed_totals)

Calculate Directly Standardised Rates using calculate_dsr

Description

Calculates directly standardised rates with confidence limits using Byar's method (1) with Dobson method adjustment (2) including option to further adjust confidence limits for non-independent events (3).

Usage

calculate_dsr(
  data,
  x,
  n,
  stdpop = NULL,
  type = "full",
  confidence = 0.95,
  multiplier = 1e+05,
  independent_events = TRUE,
  eventfreq = NULL,
  ageband = NULL
)

Arguments

Value

When type = "full", returns a tibble of total counts, total populations, directly standardised rates, lower confidence limits, upper confidence limits, confidence level, statistic and method for each grouping set. Use the type argument to limit the columns output.

Notes

For total counts >= 10 Byar's method (1) is applied using the internal byars_lower and byars_upper functions. When the total count is < 10 DSRs are not reliable and will therefore be suppressed in the output.

References

(1) Breslow NE, Day NE. Statistical methods in cancer research, volume II: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer, World Health Organisation; 1987.

(2) Dobson A et al. Confidence intervals for weighted sums of Poisson parameters. Stat Med 1991;10:457-62.

(3) See the DSR chapter of the Fingertips Public Health Technical Guidance

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(
  indicatorid = rep(c(1234, 5678, 91011, 121314), each = 19 * 2 * 5),
  year = rep(2006:2010, each = 19 * 2),
  sex = rep(rep(c("Male", "Female"), each = 19), 5),
  ageband = rep(c(0,5,10,15,20,25,30,35,40,45,
                  50,55,60,65,70,75,80,85,90), times = 10),
  obs = sample(200, 19 * 2 * 5 * 4, replace = TRUE),
  pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE),
  esp2013 = rep(esp2013, 40)
)

## Example 1 - Default execution
df %>%
  group_by(indicatorid, year, sex) %>%
  calculate_dsr(obs, pop, stdpop = esp2013)

## Example 2 - Calculate both 95% and 99.8% CIs in single execution
df %>%
  group_by(indicatorid, year, sex) %>%
  calculate_dsr(obs, pop, stdpop = esp2013, confidence = c(0.95, 0.998))

## Example 3 - Drop metadata columns from the output
df %>%
  group_by(indicatorid, year, sex) %>%
  calculate_dsr(obs, pop, stdpop = esp2013, type = "standard")

## Example 4 - Calculate DSRs for non-independent events

library(tidyr)

# For non-independent events the input data frame must breakdown events into
# counts of unique individuals by event frequency. The code chunk below
# creates a dummy data frame in this required format. Note that assignment of
# 10%, 20% and 70% of events to each event frequency is purely to create a
# data frame in the required format whilst retaining the same total event and
# population distributions by group and age band as example 1 to allow
# comparison of the outputs.

df_freq <- df %>%
  mutate(
    f3 = floor((obs * 0.1)/3),         # 10 % of events in individuals with 3 events
    f2 = floor((obs * 0.2)/2),         # 20 % of events in individuals with 2 events
    f1 = (obs - (3 * f3) - (2 * f2))   # 70% of events in individuals with 1 event
  ) %>%
  select(!"obs") %>%
  pivot_longer(
    cols = c("f1", "f2", "f3"),
    names_to = "eventfrequency",
    values_to = "uniqueindividuals",
    names_prefix = "f"
  ) %>%
  mutate(eventfrequency = as.integer(eventfrequency))

# Calculate the dsrs - notice that output DSR values match those in
# example 1 but the confidence intervals are wider

df_freq %>%
  group_by(indicatorid, year, sex) %>%
  calculate_dsr(
    x = uniqueindividuals,
    n = pop,
    stdpop = esp2013,
    independent_events = FALSE,
    eventfreq = eventfrequency,
    ageband = ageband
  )

Calculate control limits for funnel plots

Description

Calculates control limits adopting a consistent method as per the PHE Fingertips Technical Guidance: https://fingertips.phe.org.uk/profile/guidance/supporting-information/PH-methods

Usage

calculate_funnel_limits(
  data,
  numerator,
  denominator,
  rate,
  type = "full",
  multiplier = NULL,
  statistic = NULL,
  ratio_type = NULL,
  rate_type = NULL,
  years_of_data = NULL
)

Arguments

Value

returns the original data.frame with the following appended: lower 0.025 limit, upper 0.025 limit, lower 0.001 limit, upper 0.001 limit and baseline average

Author(s)

Matthew Francis

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
set.seed(123)
df <- data.frame(obs = sample(200, 19 * 2 * 5 * 4, replace = TRUE),
                 pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE))
df %>%
    calculate_funnel_limits(obs, pop, statistic = "proportion", multiplier = 100)

For rate-based funnels: Derive rate and annual population values for charting based. Process removes rates where the rate type is dsr and the number of observed events are below 10.

Description

For rate-based funnels: Derive rate and annual population values for charting based. Process removes rates where the rate type is dsr and the number of observed events are below 10.

Usage

calculate_funnel_points(
  data,
  numerator,
  denominator,
  rate,
  rate_type = NULL,
  years_of_data = NULL,
  multiplier = NULL
)

Arguments

Value

returns the same table as provided with two additional fields. First will have the same name as the rate field, with the suffix "_chart", the second will be called denominator_derived

Author(s)

Sebastian Fox, sebastian.fox@phe.gov.uk

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

European Standard Population 2013

Description

A numeric vector containing nineteen 5-year age band populations making up the 2013 European Standard Population ordered from age 0-4, 5-9, 10-14 ... to ... 85-89, 90+. Sorted by increasing age band.

Usage

esp2013

Format

A numeric vector with 19 elements

Value

5000 5500 5500 5500 6000 6000 6500 7000 7000 7000 7000 6500 6000 5500 5000 4000 2500 1500 1000

Notes

The 2013 European Standard Population is modelled and published by Eurostat (1) for use in the production of age-standardised rates. It uses the unweighted average 2010-based population projections of the European Union (x27) and European Free Trade Association (x4) countries for the period 2011-2030 broken down into 5-year age bands from age 0 - age 95+ with the 0-5 age band separated into age 0 and age 1-4. The version provided with this package combines the age 0 and age 1-4 populations into a single 0-4 age band and combines the 90-94 and 95+ populations into a single 90+ age band, giving 19 age bands in total.

References

(1) Eurostat Methodologies and Working Papers. Revision of the European Standard Population: Report of Eurostat's Taskforce, 2013.
https://ec.europa.eu/eurostat/documents/3859598/5926869/KS-RA-13-028-EN.PDF/e713fa79-1add-44e8-b23d-5e8fa09b3f8f

Examples

esp2013

Calculate Directly Standardised Rates using phe_dsr

Description

Calculates directly standardised rates with confidence limits using Byar's method (1) with Dobson method adjustment (2). This function is soft-deprecated, please use calculate_dsr() instead.

Usage

phe_dsr(
  data,
  x,
  n,
  stdpop = esp2013,
  stdpoptype = "vector",
  type = "full",
  confidence = 0.95,
  multiplier = 1e+05
)

Arguments

Value

When type = "full", returns a tibble of total counts, total populations, directly standardised rates, lower confidence limits, upper confidence limits, confidence level, statistic and method for each grouping set

Notes

User MUST ensure that x, n and stdpop vectors are all ordered by the same standardisation category values as records will be matched by position.

For total counts >= 10 Byar's method (1) is applied using the internal byars_lower and byars_upper functions. When the total count is < 10 DSRs are not reliable and will therefore not be calculated.

References

(1) Breslow NE, Day NE. Statistical methods in cancer research, volume II: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer, World Health Organisation; 1987.

(2) Dobson A et al. Confidence intervals for weighted sums of Poisson parameters. Stat Med 1991;10:457-62.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(indicatorid = rep(c(1234, 5678, 91011, 121314),
                 each = 19 * 2 * 5),
                 year = rep(2006:2010, each = 19 * 2),
                 sex = rep(rep(c("Male", "Female"), each = 19), 5),
                 ageband = rep(c(0,5,10,15,20,25,30,35,40,45,
                                 50,55,60,65,70,75,80,85,90), times = 10),
                 obs = sample(200, 19 * 2 * 5 * 4, replace = TRUE),
                 pop = sample(10000:20000, 19 * 2 * 5 * 4, replace = TRUE))

## default execution
df %>%
  group_by(indicatorid, year, sex) %>%
  phe_dsr(obs, pop)
# ->
df %>%
  group_by(indicatorid, year, sex) %>%
  mutate(esp2013 = esp2013) %>%
  calculate_dsr(obs, pop, stdpop = esp2013)


## calculate both 95% and 99.8% CIs in single execution
df %>%
  group_by(indicatorid, year, sex) %>%
  phe_dsr(obs, pop, confidence = c(0.95, 0.998))
# ->
df %>%
  group_by(indicatorid, year, sex) %>%
  mutate(esp2013 = esp2013) %>%
  calculate_dsr(obs, pop, stdpop = esp2013, confidence = c(0.95, 0.998))

## alternatively, append the standard populations to your input dataframe
df %>%
  group_by(indicatorid, year, sex) %>%
  mutate(esp2013 = esp2013) %>%
  phe_dsr(obs, pop, stdpoptype = "field")
# ->
df %>%
  group_by(indicatorid, year, sex) %>%
  mutate(esp2013 = esp2013) %>%
  calculate_dsr(obs, pop, stdpop = esp2013)

Calculate Life Expectancy using phe_life_expectancy

Description

Compute life expectancy for a given age, and its standard error

Usage

phe_life_expectancy(
  data,
  deaths,
  population,
  startage,
  age_contents = c(0L, 1L, 5L, 10L, 15L, 20L, 25L, 30L, 35L, 40L, 45L, 50L, 55L, 60L,
    65L, 70L, 75L, 80L, 85L, 90L),
  le_age = "all",
  type = "full",
  confidence = 0.95
)

Arguments

Details

This function aligns with the methodology in Public Health England's Life Expectancy Calculator available on the Fingertips Technical Guidance web page.

The function is for an abridged life table using 5 year age intervals with a final age interval of 90+. The table has been completed using the methods described by Chiang.(1, 2) This age structure and methodology is used by The Office for National Statistics to produce life expectancy at national and local authority level.(3)

This function includes an adjustment to the method for calculating the variance of the life expectancy estimate to include a term for the variance associated with the final age interval. In the Chiang method the variance of the life expectancy is the weighted sum of the variance of the probability of survival across all the age intervals. For the final age interval the probability of survival is, Chiang argues, zero and has zero variance. However, Silcocks et al argue(4) that in the case of the final age interval the life expectancy is dependent not on the probability of survival but on the mean length of survival (1/M<sub>omega</sub>). Therefore the variance associated with the final age interval depends on the age-specific mortality rate M<sub>omega</sub>.

Life expectancy cannot be calculated if the person-years in any given age interval is zero. It will also not be calculated if the total person-years is less than 5,000 as this is considered to be the minimum size for robust calculation of life expectancy.(5) Zero death counts are not a problem, except for the final age interval - there must be at least one death in the 90+ interval for the calculations to be possible.

Individual Life Expectancy values will be suppressed (although confidence intervals will be shown) when the 95% confidence interval is greater than 20 years.

The methodology used in this function, along with discussion of alternative options for life expectancy calculation for small areas, were described Eayres and Williams.(6)

Value

returns a data frame containing the life expectancies and confidence intervals for each le_age requested. When type = 'full' additionally returns the cumulative populations and deaths used in each LE calculation and metadata indicating parameters passed.

Author(s)

Sebastian Fox, sebastian.fox@phe.gov.uk

References

(1) Chiang CL. The Life Table and its Construction. In: Introduction to Stochastic Processes in Biostatistics. New York, John Wiley & Sons, 1968:189-214.

(2) Newell C. Methods and Models in Demography. Chichester, John Wiley & Sons, 1994:63-81

(3) Office for National Statistics Report. Life expectancy at birth by health and local authorities in the United Kingdom, 1998 to 2000 (3-year aggregate figures.) Health Statistics Quarterly 2002;13:83-90

(4) Silcocks PBS, Jenner DA, Reza R. Life expectancy as a summary of mortality in a population: statistical considerations and suitability for use by health authorities. J Epidemiol Community Health 2001;55:38-43

(5) Toson B, Baker A. Life expectancy at birth: methodological options for small populations. National Statistics Methodological Series No 33. HMSO 2003.

(6) Eayres DP, Williams ES. Evaluation of methodologies for small area life expectancy estimation. J Epidemiol Community Health 2004;58:243-249

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)

## A simple example
df <- data.frame(startage = c(0L, 1L, 5L, 10L, 15L, 20L, 25L, 30L, 35L, 40L, 45L, 50L, 55L,
                              60L, 65L, 70L, 75L, 80L, 85L, 90L),
                 pops = c(7060L, 35059L, 46974L, 48489L, 43219L, 38561L, 46009L, 57208L,
                          61435L, 55601L, 50209L, 56416L, 46411L, 39820L, 37978L,
                          37039L, 33288L, 23306L, 11936L, 11936L),
                 deaths = c(17L, 9L, 4L, 8L, 20L, 15L, 24L, 33L, 50L, 71L, 100L, 163L,
                            263L, 304L, 536L, 872L, 1390L, 1605L, 1936L, 1937L))
phe_life_expectancy(df, deaths, pops, startage)

## or with multiple confidence limits
phe_life_expectancy(df, deaths, pops, startage, confidence = c(95, 99.8))

## OR

phe_life_expectancy(df, deaths, pops, startage, le_age = c(5, 25), type = "standard")

## Unordered age bands example
df <- data.frame(startage = c("0", "1-4", "5-9", "10 - 14", "15 - 19", "20 - 24", "25 - 29",
                              "30 - 34", "35 - 39", "40 - 44", "45 - 49", "50 - 54",
                              "55 - 59", "60 - 64", "65 - 69", "75 - 79", "80 - 84",
                              "85 - 89", "90 +", "70 - 74"),
                 pops = c(7060L, 35059L, 46974L, 48489L, 43219L, 38561L, 46009L, 57208L,
                          61435L, 55601L, 50209L, 56416L, 46411L, 39820L, 37039L,
                          23306L, 11936L, 11936L, 37978L, 33288L),
                 deaths = c(17L, 9L, 4L, 8L, 20L, 15L, 24L, 33L, 50L, 71L, 100L, 163L,
                            263L, 304L, 872L, 1605L, 1936L, 1937L, 536L, 1390L))
phe_life_expectancy(df, deaths, pops, startage,
                    age_contents = c("0", "1-4", "5-9",
                                     "10 - 14", "15 - 19",
                                     "20 - 24", "25 - 29",
                                     "30 - 34", "35 - 39",
                                     "40 - 44", "45 - 49",
                                     "50 - 54", "55 - 59",
                                     "60 - 64", "65 - 69",
                                     "70 - 74", "75 - 79",
                                     "80 - 84", "85 - 89",
                                     "90 +"))

df <- data.frame(area = c(rep("Area 1", 20), rep("Area 2", 20)),
                 startage = rep(c(0L, 1L, 5L, 10L, 15L, 20L, 25L, 30L, 35L, 40L, 45L, 50L, 55L,
                                  60L, 65L, 70L, 75L, 80L, 85L, 90L), 2),
                 pops = rep(c(7060L, 35059L, 46974L, 48489L, 43219L, 38561L, 46009L, 57208L,
                              61435L, 55601L, 50209L, 56416L, 46411L, 39820L, 37978L,
                              37039L, 33288L, 23306L, 11936L, 11936L), 2),
                 deaths = rep(c(17L, 9L, 4L, 8L, 20L, 15L, 24L, 33L, 50L, 71L, 100L, 163L,
                                263L, 304L, 536L, 872L, 1390L, 1605L, 1936L, 1937L), 2))
df %>%
       group_by(area) %>%
       phe_life_expectancy(deaths, pops, startage)

Calculate Means using phe_mean

Description

Calculates means with confidence limits using Student's t-distribution method.

Usage

phe_mean(data, x, type = "full", confidence = 0.95)

Arguments

Value

When type = "full", returns a data.frame of value_sum, value_count, stdev, value, lowercl, uppercl, confidence, statistic and method for each grouping set

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_proportion(), phe_quantile(), phe_rate(), phe_sii()

Examples

library(dplyr)
df <- data.frame(values = c(30,40,50,60))

## default execution
phe_mean(df, values)

## calculate 95% and 99.8% CIs in single execution
phe_mean(df, values, confidence = c(0.95, 0.998))

## calculate multiple means in a single execution

df2 <- data.frame(area = rep(c("Area1", "Area2"),each=3),
                  values = c(20,30,40,200,300,400)) %>%
                  group_by(area)
phe_mean(df2,values)
phe_mean(df2,values,type="standard", confidence=0.998)

Calculate Proportions using phe_proportion

Description

Calculates proportions with confidence limits using Wilson Score method (1,2).

Usage

phe_proportion(data, x, n, type = "full", confidence = 0.95, multiplier = 1)

Arguments

Value

When type = "full", returns the original data.frame with the following appended: proportion, lower confidence limit, upper confidence limit, confidence level, statistic and method

Notes

Wilson Score method (2) is applied using the internal wilson_lower and wilson_upper functions.

The percentage argument was deprecated in v1_1_0, please use multiplier argument instead

References

(1) Wilson EB. Probable inference, the law of succession, and statistical inference. J Am Stat Assoc; 1927; 22. Pg 209 to 212.
(2) Newcombe RG, Altman DG. Proportions and their differences. In Altman DG et al. (eds). Statistics with confidence (2nd edn). London: BMJ Books; 2000. Pg 46 to 48.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_quantile(), phe_rate(), phe_sii()

Examples

# ungrouped data frame
df <- data.frame(area = rep(c("Area1","Area2","Area3","Area4"), each=3),
                 numerator = c(NA,82,9,48, 6500,8200,10000,10000,8,7,750,900),
                 denominator = rep(c(100,10000,10000,10000), each=3))

phe_proportion(df, numerator, denominator)
phe_proportion(df, numerator, denominator, confidence=99.8)
phe_proportion(df, numerator, denominator, type="standard")
phe_proportion(df, numerator, denominator, confidence = c(0.95, 0.998))

# grouped data frame
library(dplyr)
dfg <- df |> group_by(area)
phe_proportion(dfg, numerator, denominator, multiplier=100)

Assign Quantiles using phe_quantile

Description

Assigns data to quantiles based on numeric data rankings.

Usage

phe_quantile(
  data,
  values,
  nquantiles = 10L,
  invert = TRUE,
  inverttype = "logical",
  type = "full"
)

Arguments

Value

When type = "full", returns the original data.frame with quantile (quantile value), nquantiles (number of quantiles requested), groupvars (grouping sets quantiles assigned within) and invert (indicating direction of quantile assignment) fields appended.

Notes

See OHID Technical Guide - Assigning Deprivation Categories for methodology. In particular, note that this function strictly applies the algorithm defined but some manual review, and potentially adjustment, is advised in some cases where multiple small areas with equal rank fall across a natural quantile boundary.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_rate(), phe_sii()

Examples

df <- data.frame(
  region    = as.character(rep(c("Region1","Region2","Region3","Region4"),
                               each=250)),
  smallarea = as.character(paste0("Area",seq_along(1:1000))),
  vals      = as.numeric(sample(200, 1000, replace = TRUE)),
  stringsAsFactors = FALSE)

# assign small areas to deciles across whole data frame
phe_quantile(df, vals)

# assign small areas to deciles within regions by pre-grouping the data frame
library(dplyr)
df_grp <- df %>% group_by(region)
phe_quantile(df_grp, vals)

# assign small areas to quintiles, where highest value = highest quantile
phe_quantile(df, vals, nquantiles = 5L, invert=FALSE)

Calculate Rates using phe_rate

Description

Calculates rates with confidence limits using Byar's (1) or exact (2) CI method.

Usage

phe_rate(data, x, n, type = "full", confidence = 0.95, multiplier = 1e+05)

Arguments

Value

When type = "full", returns the original data.frame with the following appended: rate, lower confidence limit, upper confidence limit, confidence level, statistic and method

Notes

For numerators >= 10 Byar's method (1) is applied using the internal byars_lower and byars_upper functions. For small numerators Byar's method is less accurate and so an exact method (2) based on the Poisson distribution is used.

References

(1) Breslow NE, Day NE. Statistical methods in cancer research, volume II: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer, World Health Organisation; 1987.
(2) Armitage P, Berry G. Statistical methods in medical research (4th edn). Oxford: Blackwell; 2002.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_sii()

Examples

# ungrouped data frame
df <- data.frame(area = rep(c("Area1","Area2","Area3","Area4"), each=3),
                 obs = c(NA,82,9,48, 6500,8200,10000,10000,8,7,750,900),
                 pop = rep(c(100,10000,10000,10000), each=3))

phe_rate(df, obs, pop)
phe_rate(df, obs, pop, type="standard")
phe_rate(df, obs, pop, confidence=99.8, multiplier=100)

# grouped data frame
library(dplyr)
dfg <- df %>% group_by(area)
phe_rate(dfg, obs, pop)

Calculate Slope Index of Inequality using phe_sii

Description

phe_sii()returns the slope index of inequality (SII) statistic for each subgroup of the inputted dataframe, with lower and upper confidence limits based on the specified confidence.

Usage

phe_sii(
  data,
  quantile,
  population,
  x = NULL,
  value = NULL,
  value_type = 0,
  transform = FALSE,
  lower_cl = NULL,
  upper_cl = NULL,
  se = NULL,
  multiplier = 1,
  repetitions = 1e+05,
  confidence = 0.95,
  rii = FALSE,
  intercept = FALSE,
  reliability_stat = FALSE,
  type = "full"
)

Arguments

Details

The Relative Index of Inequality (RII) can also be returned via an optional argument.

The SII and RII are two measures of health inequality. They show the relation between the level of health or frequency of a health problem in different population groups and the ranking of these groups on the social scale.

The input dataframe should be grouped before passing to the function if an SII/RII for each subgroup is required, and quantiles ordered from least to most advantaged.

Value

The SII with lower and upper confidence limits for each subgroup of the inputted data.frame.

Calculation

The SII is calculated using linear regression (1). To allow for differences in population size between quantiles (e.g. deprivation deciles), each is given a rank score (or relative rank) based on the midpoint of its range in the cumulative distribution of the total area population. The quantiles are first ordered (e.g from 1 most deprived to 10 least deprived for deprivation deciles). If quantile 1 then contains 12 percent of the total population, its relative rank is 0.12/2=0.6. If quantile 2 includes 10 percent of the population, its relative rank is 0.12+(0.10/2)=0.17. A square root transformation is applied to the regression to account for heteroskedasticity (the tendancy for the variances of the quantile values to be related to the size of the values, ie larger values will tend to have larger variances). A regression model is fitted to the transformed data: Y * \sqrt a = \sqrt a + b * \sqrt a, where Y is the value of the indicator for the quantile, a is the proportion of the total population in the quantile and b is the relative rank. The SII is the gradient of the resulting fitted line, and could be positive or negative according to the indicator polarity. Since the relative ranks, by definition, range from 0 to 1, the SII is the difference between the fitted value at x=1 and x=0. The RII is the ratio of the fitted value at x=1,Y1 and the fitted value at x=0,Y0. which can be calculated as: RII = (Y0 + SII)/Y0

Transformations

The indicator type can be specified as 1 (rate), 2 (proportion) or 0 (other), using the value_type parameter. This setting determines the data transformations that will be applied in the following two parts of the method.

Use in conjunction with the transform parameter in calculation of the SII: It is recommended that rates and proportions are transformed prior to calculation of the SII by setting the transform parameter to TRUE for these indicator types. This will perform a log transformation for rates, or logit for proportions, and return outputs transformed back to the original units of the indicator. These transformations are recommended to improve the linearity between the indicator values and the quantile, which is an assumption of the method. A user-provided standard error will not be accepted when the transform parameter is set to TRUE as the confidence limits are required for this transformation.

Use in calculation of the standard error: Rates and proportions, and their confidence limits, are transformed prior to calculation of the standard error for each quantile. This is because it is assumed that the confidence interval around the indicator value is non-symmetric for these indicator types. Note that this transformation is not controlled by the transform parameter and is applied based on the value of the value_type parameter only. A user-provided standard error will not be accepted when the transform parameter is set to TRUE as the confidence limits are required for this transformation.

Warning

The SII calculation assumes a linear relationship between indicator value and quantile. Where this is not the case the transform option should be considered. Small populations within quantiles can make the SII unstable. This function does not include checks for linearity or stability; it is the user's responsibility to ensure the input data is suitable for the SII calculation.

References

(1) Low A & Low A. Measuring the gap: quantifying and comparing local health inequalities. Journal of Public Health; 2004;26:388-395.

See Also

Other PHEindicatormethods package functions: assign_funnel_significance(), calculate_ISRate(), calculate_ISRatio(), calculate_dsr(), calculate_funnel_limits(), calculate_funnel_points(), phe_dsr(), phe_life_expectancy(), phe_mean(), phe_proportion(), phe_quantile(), phe_rate()

Examples

library(dplyr)

data <- data.frame(area = c(rep("Area1", 10), rep("Area2", 10)),
                   decile = c(1:10, 1:10),
                   population = c(7291, 7997, 6105, 7666, 5790, 6934, 5918, 5974, 7147, 7534, 21675,
                                  20065, 19750, 24713, 20112, 19618, 22408, 19752, 18939, 19312),
                   value = c(75.9, 78.3, 83.8, 83.6, 80.5, 81.1, 81.7, 84.2, 80.6, 86.3, 70.5,
                              71.6, 72.5, 73.5, 73.1, 76.2, 78.7, 80.6, 80.9, 80),
                   lowerCL = c(72.7,75.3,80.9,80.2,77.1,78,79,81.4,75.8,83.2,
                               70.1,71.1,72,73.1, 72.7, 75.7, 78.2,80.1,80.4,79.5),
                   upperCL = c(79.1,81.4,86.8,87.1,83.8,84.2,84.4,86.9,85.4,
                                89.4,71,72.1,73.2,73.7,75.8,78.8,79.8,81.2,81.3,80.9),
                   StandardError = c(1.64,1.58,1.51,1.78,1.7,1.56,1.37,1.4,2.43,
                                     1.57,0.23,0.26,0.3,0.16,0.79,0.78,0.4,0.28,0.23,0.35)
                   )


# Run SII function on the two areas in the data
phe_sii(group_by(data, area),
        decile,
        population,
        value_type = 0, # default normal distribution
        value = value,
        lower_cl = lowerCL,
        upper_cl = upperCL,
        confidence = 0.95,
        rii = TRUE,
        type = "standard")

# Supplying the standard error instead of the indicator 95 percent confidence limits
# gives the same result
phe_sii(group_by(data, area),
        decile,
        population,
        value_type = 0,
        value = value,
        se = StandardError,
        confidence = 0.95,
        rii = TRUE,
        type = "standard")

# multiple confidence intervals, log transforming the data if they are rates
phe_sii(group_by(data, area),
        decile,
        population,
        value_type = 1,
        transform = TRUE,
        value = value,
        lower_cl = lowerCL,
        upper_cl = upperCL,
        confidence = c(0.95, 0.998),
        repetitions = 10000,
        rii = TRUE,
        type = "standard")

SII test datasets - Prevalence

Description

A data table of example prevalence data by area and deprivation decile

Usage

data(prevalence_data)

Format

A data table

Examples

prevalence_data