Life expectancy

What is Life Expectancy? Life expectancy at birth of a girl in the England now is 80.9 years. This means that a baby born now will live 80.9 years if………….. that baby experiences the same age-specific mortality rates as are currently operating in the England. Life expectancy is a shorthand way of describing the current age-specific mortality rates.

How is it calculated?

Population in age intervalNumber of deaths in the age interval.Age-specific death rate.Conditional probability that an individual who has survived to start of the age interval will die in the age interval. Conditional probability that an individual entering the age interval will survive the age interval Life table cohort population. The hypothetical population of newborn babies on which the life table is based. Number of life table deaths in the age intervalNumber of years lived during the age interval.Cumulative number of years lived by the cohort population in the age interval and all subsequent age intervals. Life expectancy at the beginning of the age interval.Width of the 19 age intervals used in this abridged life table.Fraction of the age interval lived by those in the cohort population who die in the interval. Because deaths in year 1 are not evenly distributed during the year (they are closer to birth), infants deaths contribute less than ½ a year.

Issues with Life Expectancy Advantages Single figure easily understood Directly comparable between populations Easy to calculate with available calculators Life tables are flexible tools allow modelling ‘what if’ scenarios Disadvantages More complex to calculate than standardised rates Confidence intervals more difficult to construct than standardised rates To understand why differences exist between populations need to look at age-specific rates

Monitoring trends over time Are we going to reach the target?

To answer this we need to be able to forecast/predict what the likely rate will be in However.. Forecasts are rarely perfect. Forecasts are more accurate for grouped data than for individual items Forecast are more accurate for shorter than longer time periods Are we going to reach the target?

Time series Assumes the future will follow same patterns as the past Forecasting using linear regression

Trend analysis forecasting First There should be a sufficient correlation between the time parameter and the values of the time-series data This can be checked be looking at the correlation coefficient.

Trend analysis method Trend analysis uses a technique called least squares to fit a trend line to a set of time series data and then project the line into the future for a forecast. Trend analysis is a special case of regression analysis where the dependent variable is the variable to be forecasted and the independent variable is time.

The general equation for a trend line F=a+bt Where: F – forecast, t – time value, a – y intercept, b – slope of the line. Least square method determines the values for a and b so that the resulting line is the best-fit line through a set of the historical data. After a and b have been determined, the equation can be used to forecast future values.

The trend line is the “best-fit” line Line fitted using add trend line Excel provides the equation So are we going to reach the target?

Trend analysis forecasting method Advantages: Simple to use, Excel function Trend( ) gives the predicted values at each time point, adding trendline to graph plots the trend Disadvantages: not always applicable for the long-term time series (because there exist several trends in such cases)

Forecasting using exponential growth curve Another method which produces linear forecasts using an exponential growth curve. It fits the best exponential curve to the data In this case produce very similar results However if predicting further into the future this method gives more conservative estimates in which the yearly drop decreases over time.

Very little difference between linear black line and exponential blue line

Non-linear trends Logarythmic Polynomial Power Exponential Excel provides easy calculation of the following trends

Using values from National Surveys

Body mass index (BMI), by survey year, age and sex Adults aged 16 and over with a valid height and weight measurement BMI (kg/m2)AgeTotal Men %%%% 2004 (unweighted) c 20 or under Over Over Over 30 a Over Mean Standard error of the mean (weighted) c 20 or under Over Over Over 30 a Over Mean Standard error of the mean Bases (Men) Why are there two sets of estimates? What does weighted mean? Which should we use?

Why should we weight? 1.Adjust for non response 2.Adjust for unequal selection probabilities 3.Adjust our sample to match known population totals

Adjust for unequal selection probabilities EG. in surveys where only one adult per household is interviewed, those living in households with more than one adult will have a less of a chance of being selected than those adults living on their own. A sample design weight is 1 divided by the probability of selection due to the survey design. However, these are usually scaled, so we define the weight as proportional to this number. If there are 3 adults in a given household the resulting sample design weight for the single interviewed adult will be proportional to 1/(1/3), i.e. proportional to 3. The influence of the respondent is being increased threefold to compensate for the fact the respondent was three times less likely to be included in the sample.

Nonresponse weights

Adjust for non response Non-response weights compensate for when someone refuses to take part in the survey. Weighting for total nonresponse involves giving each respondent a weight so that they represent the non-respondents who are similar to them in terms of survey characteristics. The non-response rate weight is proportional to 1 divided by the response rate for the weighting class Example: General Household Survey Work was conducted to match Census addresses with the sampled addresses of the GHS. It was possible to match the address details of the GHS respondents as well as the non-respondents with corresponding information gathered from the Census for the same address. It was then possible to identify any types of household that were being under-represented in the survey.

Adjust our sample to match known population totals Applied to make the data more representative of the population. Information on the population is usually derived from the decennial Census of Population. These weights allow for more accurate population totals of estimates. Whereas sample design (probability) and non-response weights result from a very simple computation (1/selection probability), post-stratification weights are mathematically complex.

Should we use the weighted or unweighted estimates? Should we ever use the unweighted versions?

measuring inequalities

Inequality means: …differences between parts of a population …considering DISTRIBUTIONS …considering the way a “good” (e.g. life expectancy, income, educational attainment, access to public transport, etc.) is distributed throughout a population …may consider “fairness” (i.e. equity) [but don’t forget that being equitable sometimes means being unequal

Inequality and its measurement The existence of inequalities in health and death is rarely disputed, but there is contention over: –Causes of inequality –Methods to monitor and measure –Extent of inequality, increase or decrease –What can be done

Inequalities indicators incorporate a measure (e.g. mortality rate, low birthweight rate, unemployment rate) –Eg births < 2500 gms / 1000 live births an inequalities dimension (e.g. social class, ethnicity, geographical area) a comparison (e.g. rate, ratio, range, relative or absolute differences)

Inequalities indicators incorporate: Health gain indicator only –Change over time without reference to a comparitor population BUT Health inequalities indicator –Involves a comparison between: LAs, PCTs: eg compare Derby City PCT with East Midlands average Compare between different age and sex groups within a single PCT Compare between the most and least deprived wards within a LA etc

Different Health Gaps A CD X axis: health measure eg teenage conception rates by LA Y axis: frequency Range = difference between best and worst (B-A) B National target measure (eg for life expectancy) = D – C (difference between average and bottom 20%) Ratio between highest and lowest = B/A (eg relative mortality rate between Social Class V and Social Class I) Bottom 20%

Gini Coefficient The Gini coefficient is a measure of inequality of a distribution. It is defined as a ratio with values between 0 and 1: the numerator is the area between the Lorenz curve of the distribution and the uniform distribution line; the denominator is the area under the uniform distribution line.

A population where there is a perfectly equally and equitably distribution of a resource. Cumulative percentage of the population Cumulative percentage of a resource throughout the population % of the population own 20% of the resource 40% of the population own 40% of the resource 60% of the population own 60% of the resource 80% of the population own 80% of the resource 100% of the population own 100% of the resource

A population where there is an unequal and inequitable distribution of a resource. Cumulative percentage of the population Cumulative percentage of a resource throughout the population % of the population own 8% of the resource 40% of the population own 17% of the resource 60% of the population own 37% of the resource 80% of the population own 62% of the resource 100% of the population own 100% of the resource 8% A B 9% 20% 25% 38%

A population where there is an unequal and inequitable distribution of a resource. Cumulative percentage of the population Cumulative percentage of a resource throughout the population % A B ,620 3,480 = B = A + B 5,000 Gini coefficient = A / (A+B) = 1,520 / 5,000 = 0.3 1,520 = A

A real example Divide all the wards in the East of England into quintiles (5 groups) in order of educational deprivation (IMD2000 methodology) Calculate how many: –a) Teenage conceptions occur in each group –b) Live births occur in each group The numbers will not be evenly spread throughout the 5 groups This can both be displayed and quantified using Lorenz curves and Gini coefficients respectively.

a) Teenage conceptions

A population where there is an unequal and inequitable distribution of a resource (<18 yr conceptions) Cumulative percentage of the wards Cumulative percentage of a resource throughout the wards % of the wards experience 6% of the <18 yr conceptions 40% of the wards experience 15% of the <18 yr conceptions 60% of the wards experience 27% of the <18 yr conceptions 80% of the wards experience 53% of the <18 yr conceptions 100% of the wards experience 100% of the <18 yr conceptions 6% A B 9% 12% 26% 47% Wards – quintiles - by educational deprivation score Least……………………………………………. Most

A population where there is an unequal and inequitable distribution of a resource (<18 yr conceptions) Cumulative percentage of the wards Cumulative percentage of a resource throughout the wards % A B 9% 12% 26% 47% Wards – quintiles - by educational deprivation score Least……………………………………………. Most ,530 3,010 = B = A + B 5,000 Gini coefficient = A / (A+B) = 1,990 / 5,000 = 0.4 1,990 = A (Source: VS Conceptions; IMD 2000 DETR; erpho: 2001 Annual Profile) ,520

Measures of Spatial Inequalities in Health within PCTs The trend in premature mortality rates is examined for each City deprivation quintile. A regression line is fit through the data for each quintile. On X axis: plot time banded (3 year intervals) On Y axis: plot DSR < 75 all causes per City deprivation quintile Slope comparison across deprivation quintiles reveals progress in the most disadvantaged areas vs most affluent areas

Slope index of inequality A regression line is drawn through a health measure stratified by a measure of socio-economic status On X axis: plot average IMD2000 scores for ward deprivation quintiles in N&S On Y axis: plot DSR < 75 all causes for ward deprivation quintiles in N&S If slope reduces over time evidence of reduction in health inequalities

Funnel Plots can be used to demonstrate health inequality variation traffic lighting approach used in Regional Public Health Indicators 4 bands of performance: Red Alert = ‘investigate further’, Amber = ‘cause for concern’, Green = ‘doing well’ If within the 2  limits then the area is indistinguishable from the average those in favour of this approach argue that it discourages inappropriate ranking as per caterpillar charts emphasizes visually the increased variability expected of smaller PCTs, LADs