A method for estimating mortality rates using previous birth history

By Mark Myatt, Anna Taylor and W. Courtland Robinson

Mark Myatt is a consultant epidemiologist and senior fellow at University College London. His areas of expertise include infectious diseases, nutrition, and survey design. He is currently working on a rapid assessment procedure for trachoma prevalence.

Anna Taylor is Nutrition Adviser for Save the Children UK, supporting emergency nutrition operations.

W. Courtland Robinson is a Research Associate at the Centre for International Emergency, Disaster, and Refugee Studies, School of Hygiene and Public Health, Johns Hopkins University. The contributions of Afaf Mohammed and the rest of the Save the Children Sudan Programme are gratefully acknowledged.

This article proposes a practical method for estimating mortality in emergencies which includes a stepby- step guide to calculations and summarises the outcome of a field test carried out by Save the Children UK in Sudan early this year.

Traditionally, prevalence (e.g. the prevalence of undernutrition) and incidence (e.g. mortality) have been measured using two quite different epidemiological methods. These are:

**Prevalence.** Cross-sectional surveys such as the modified EPI 30 cluster survey commonly used to estimate the prevalence of undernutrition.

**Incidence.** Surveillance (monitoring) systems such as monitoring of burial places; routine reports from, for example, street leaders in refugee camps; routine reports of deaths in hospital from curative services. Surveillance systems usually require a reasonably stable situation and reliable population estimates. They also take a considerable time to establish and need to run for some time before data can be meaningfully analysed. These factors make them unsuitable for estimating mortality in emergency assessments. It is possible to estimate cumulative incidence retrospectively using a cross-sectional survey. This is currently the recommended method for estimating mortality in emergencies. There are, however, problems in this approach with regard to estimating mortality rates:

**Manipulation.** Any emergency assessment is prone to manipulation by an aid-savvy population or regime. Such manipulation will, generally, lead to an overestimation of incidence but in situations where households are in receipt of a general ration there may be a reluctance to report deaths and this may lead to an underestimation of incidence.

**Taboo.** In some cultures death is a taboo subject. This makes asking questions about deaths problematic and will lead to an underestimation of mortality.

**Unreliability.** Many handbooks on emergency assessment mention the importance of estimating mortality rates but provide scant details on exactly how this should be done. Whilst reviewing reports of emergency assessments we found that a variety of methods were used. Many of these assessments committed one or more gross methodological blunders. The most common of these was nesting of the mortality survey within a nutrition survey thereby excluding households in which all children under five years of age had died leading to underestimation of mortality. In general, the methods used lacked standardised procedures for defining households, enumerating household members, selecting the principal informant, ascertaining whether identified household members were living at home during the survey period, failing to define live-births, and not having a standardised question set. This lack of standardisation is likely to lead to large within and between observer variation within a single survey and, perhaps more importantly, large variations between surveys due to methodological problems and inconsistencies rather than to differences in underlying mortality rates.

**Difficulties in estimating the size of the denominator. **Household census methods require the tracking of a potentially large number of individuals over time, some of whom may move in and out of the household during the recall period (e.g. for work, military service, or to care for a relative in another community). Such individuals contribute a complicated sum of person days to the denominator. Individuals entering and leaving the household during the recall period may also be missed in a household census and contribute nothing to the estimated denominator. This leads to considerable difficulty in obtaining an accurate estimate of the denominator. This difficulty increases with increasing length of the recall period.

**Lack of guidance on sample size calculations and data-analysis procedures.** Current editions of handbooks on emergency assessment do not provide details on how sample sizes should be calculated. They offer conflicting advice on minimum sample sizes which are couched in terms of a minimum number of individuals or households rather than units of person-time-at-risk (i.e. the product of the number of individuals followed-up and the duration of the follow-up period). Key analytical procedures such as the calculation of a confidence interval on an estimated rate are also not covered in these handbooks.

Given these problems with the way mortality is currently estimated in emergency assessments, Save the Children UK (SC UK) decided to design and undertake preliminary testing of a method that might overcome these problems.

## Desirable attributes of a method

The first step in designing the new method was to decide on a set of desirable attributes. After some deliberation, the following list was arrived at:

**Familiar sampling method. **The new method must be able to use proximity sampling of households as is used in most variants of the EPI 30 cluster method because most workers in the field are already familiar with this method (e.g. it is a commonly used method for assessing the nutritional status of a population in emergency situations). Other methods (e.g. simple random sampling, systematic sampling, stratified sampling, and adaptations of the EPI method) may also be used.

**Reliable.** The new method must use a standard validated question set applied to a single informant with a single relationship to the deceased.

**Low overheads.** The new method must have low resource overheads. It must be possible for data to be collected by a single enumerator. The data must also be simple to collect. The method should not require entry of large volumes of data onto computer. The data must be simple to analyse and not require the use of specialist computer software.

**Resistance to manipulation and taboo.** The intent of a mortality survey using the new method must not be obvious (i.e. it must not be obvious that data is being collected on recent deaths). The question set used must avoid any mention of death.

**Robust to denominator estimation problems. **The new method must simplify the estimation of the size of the denominator population and should also be robust to denominator changes caused by migration, displacement, or household members working or living away from home.

In addition, it was decided that simple tools for sample-size calculation and the calculation of a confidence interval on an estimated rate should be developed and placed in the public domain. It was decided that these tools should be general to the problem of estimating a single rate rather than being tied to the new method.

## Which mortality rate to estimate?

These considerations led to the decision to estimate under five years mortality rather than all-age mortality (crude mortality, CMR). Estimating under five years mortality has the following advantages:

- A single informant with a single relationship to the deceased may be used (i.e. mothers). Restricting the collection of data to mothers and their children simplifies the estimation of the size of the denominator population.
- A standard validated question set (the UNICEF 'previous birth history' (PBH) method) is already available. This question set makes no mention of death and has low data collection and analysis overheads. The PBH question set is shown in box 1. The flow of questions in the PBH question set is illustrated in figure 1.

An additional rationale for estimating under five years mortality rather than all-age mortality is that the under five years population is an early warning population (i.e. mortality is likely to rise in this population before it rises in the general population). Also, under five years mortality is less influenced than CMR by the age structure of the population. Different age structures can make comparisons between different populations meaningless without standardising for age (e.g. developed countries may have higher CMRs than developing countries because they have a higher proportion of elderly persons in their population). Standardisation is likely to require the collection of additional demographic data in emergency situations.

One disadvantage with the proposed method is that *maternal orphans* are excluded by the requirement that only living mothers are interviewed. It might be expected that the survival probabilities of maternal orphans are considerably lower than children whose mothers are still alive. This will cause any method based on the PBH question set to underestimate mortality. The degree to which this underestimates mortality will depend upon the maternal mortality rate. Underestimation may be a particular problem in situations of exceptionally high maternal mortality coupled with high under five years mortality due to (e.g.) HIV / AIDS or malaria epidemics in areas of unstable malaria endemicity. This problem was not considered in the development and testing of the method reported here. The method is, however, robust to denominator changes caused by migration, displacement, or household members living or working away from home during recall period. Such changes cause problems for CMR estimations methods, which rely on household census methods to estimate the size of the denominator. This robustness is not affected by the length of the survey recall period.

Most emergency handbooks concentrate on collecting data to estimate both crude mortality and under five years mortality. This approach is superficially attractive but is subject to the problems of manipulation, taboo, and unreliability mentioned earlier. Estimates of under-five mortality from such surveys are likely to lack precision due to inadequate sample sizes.

It should be noted that under five years mortality is** not **an appropriate indicator for initial assessments undertaken where considerable under five years mortality has occurred prior to the start of the followup period (e.g initial assessments undertaken very late in an unameliorated nutritional emergency), or in situations where mortality is likely to be highest in the adult or elderly population.

## Data arising from the PBH question set

The PBH question set yields three variables per mother. These are:

- The number of
**children**at risk - The number of
**new births**in the survey period - The number of
**new deaths**in the survey period

Such a small number of variables allows data collected from each mother to be summed by hand. Cluster or community level tallies can also be summed by hand. It is even possible to sum the cluster level tallies and calculate mortality rates directly, although calculation of confidence intervals is complicated if a multi-stage sample (e.g. cluster) sample is used. Hand calculation of mother and cluster tallies reduces the data-entry overhead to just three items per cluster (i.e. 90 data items for a 30 cluster survey).

## Analysing the PBH data

Survey level totals plug directly into the standard mortality estimation formula:

The rate multiplier is the reference population (e.g. per 1,000, per 10,000) divided by the number of periods of follow-up (e.g. 90 days).

Calculation of confidence intervals relies on:

being a proportion or period prevalence. Confidence intervals for a proportion from a two-stage cluster sampled survey may be calculated using the standard formula:

Where:

p = proportion observed in whole sample

pi = proportion observed in cluster i

k = number of clusters

Use of this formula accounts for variance loss (i.e. the design effect) due to the use of a two-stage sampling method. The format of the data and the equations required to calculate rates and confidence intervals are simple enough for all calculations to be performed using standard spreadsheet packages. Figure 2 shows an example spreadsheet created using Microsoft Excel. This spreadsheet is available (in Microsoft Excel '95 format) from: http://www.myatt.demon.co.uk/samplerate.htm

This is a general tool and may be used to calculate rates and confidence intervals on count data collected using a two-stage cluster sampled survey.

## Sample size calculation

Required sample sizes can be calculated using the standard formula:

Where:

? = rate

e = required size of standard error

For example, the sample size required to estimate a mortality rate of 2/10,000 persons/day with a 95% confidence interval of Â±1/10,000 persons/day using simple random sampling is:

This person-days-at-risk (PDAR) figure may be expressed as the number of children for which survival data should be collected by dividing the PDAR by the length of the follow-up period:

For example, with a follow-up period is 90 days, data on the survival of 854 children is required:

This may be expressed as the number of mothers that should be interviewed, by dividing this figure by an estimate of the average number of children under-five per mother alive at any time during the follow-up period:

More complex sampling strategies (e.g. the EPI 30 cluster method) can be accommodated by multiplying the calculated sample size by the expected design effect (usually estimated to be 2.0).

A sample-size calculator that implements the PDAR calculation has been developed and placed in the public domain. The sample size calculator is available from:

http://www.myatt.demon.co.uk/samplerate.htm

The sample-size calculator is a general tool for use with any survey that estimates a single rate.

Table 1: Results of for retrospective mortality surveys in North Darfur, February 2002 | |||||

FEZ | Child days at risk | Percentage of sample size met | Rate / 10,000 / day (95% CI) | Design effect | Interpretation |

Goz | 162,891 | 106% | 0.92 (0.40, 1.44) | 1.11 | Normal |

Tombac | 166,536 | 108% | 3.78 (3.07, 4.49) | 0.77 | Elevated - possibly serious situation |

Pastoral | 178,432 | 116% | 0.23 (0.02, 0.43) | 0.91 | Normal |

Non-wadi | 139,435 | 91% | 0.65 (0.25, 1.05) | 0.95 | Normal |

Table 2: Benchmarks for the interpretation of mortality rates | ||

CMR deaths / 10,000 / day | U5MR / 10,000 / day | Interpretation |

0.5 | 1 | Normal rate |

< 1 | < 2 | Elevated, cause for concern |

1-2 | 2-4 | Elevated, serious situation |

> 2 | >4 | Elevated, very serious situation |

>5 | >10 | Elevated, major catastrophe |

## Experiences in the field

A preliminary test of the proposed method was undertaken in four food economy zones (FEZ) in Northern Darfur, Sudan in January and February 2002. The beginning of Ramadan was used as the start of the recall period. Data was collected using a two stage cluster sample. Sample size requirements were calculated as follows:

Rate to estimate | 2/10,000 persons/day |

95% CI (Â±) | 1/10,000 persons/day |

Expected design effect | 2.0 |

PDAR | 153,664 |

Average length of follow-up period (days) | 80 |

Sample size (children) | 1921 (i.e. 153,664 Ã· 80) |

Average number of children < 5 years per mother | 2.0 |

Sample size (mothers) | 961 (i.e. 1921 Ã· 2.0) |

Cluster size (mothers) | 26 |

Minimum number of clusters of size 26 required | 37 (i.e. 961 Ã· 26) |

For each test survey, data was collected using 38 clusters of 26 mothers (one extra cluster was sampled to ensure that the sample size requirement was met even if one or two clusters were located in communities with less than 26 mothers). The required sample size was met in three of the four food economy zones (table 1). The expected design effect of 2.0 that was used to calculate the required sample size proved to be an overestimate and the sample sizes collected were sufficient to estimate the expected rate with a precision better than the specified Â±1/10,000 persons / day.

The following procedures and definitions were used in the surveys:

- All women in the reproductive age range in a selected household were questioned.
- Births were defined as live births. A distinction was made between live births and still births or miscarriages. Live born children were defined as those born alive even if the child died immediately after birth. A baby who cried or breathed, if only for a few minutes, counted as a live birth.

The results of these surveys are summarised in table 1. It was not possible to validate these results by comparison with surveillance data. However the mortality rates reflect the findings of nutrition surveys undertaken at the same time in the same villages (i.e. the Tombac area was characterised by higher prevalence of undernutrition by MUAC than by weight-for-height z-scores, and a high prevalence of oedema).

Data proved both easy and rapid to collect with enumerators taking no longer than the teams measuring children for concurrent nutrition surveys. Data analysis was also straightforward.

## Further work

The results of the initial testing are promising but further work is required to:

### The PBH question set

Have you ever given birth?

If NO, then MOVE ON TO NEXT MOTHER

If YES, when was your most recent birth?

If more than 5 years ago, then STOP and MOVE ON TO NEXT MOTHER

If less than 5 years ago, was this before or after [START OF RECALL PERIOD]?

If after [START OF RECALL PERIOD], then ADD 1 TO NEW BIRTHS

Where is this child now?

If ALIVE, then ADD 1 TO KIDS AT RISK

If DEAD, then: Did this child die before or after [START OF RECALL PERIOD]?

If child died after [START OF RECALL PERIOD], then: ADD 1 TO NEW DEATHS and ADD 1 TO KIDS AT RISK

Did you have a birth before this child?

If NO, then MOVE ON TO NEXT MOTHER

If YES, then REPEAT for previous birth

**Validate the estimates arising from the proposed method. **This may be easiest to do in a refugee camp where routine monitoring of deaths is undertaken. Validation should be a relatively rapid process given that random or systematic samples may be used. Other overheads (e.g. travel costs) should also be low.

**Establish reasonable design effects for use in sample size calculations. **The pilot surveys used an expected design effect of 2.0 in order to calculate the required sample size for each survey. This produced estimates with a reasonable degree of precision. The test surveys presented here yielded negligible design effects. It is possible that, as experience with the method grows, the expected design effect may be revised down thus reducing costs.

**Establish benchmark values for the interpretation of under five years mortality.** The benchmarks that are currently used to interpret under five years mortality are derived by doubling those used to interpret crude mortality (table 2). Under five years mortality may be subject to higher regional variation than crude mortality and simple global benchmarks may prove inappropriate. This problem may be assessed by a desk review of mortality data and appropriate benchmarks developed.

**Use of the methods with alternative sampling methods.** The EPI survey method is limited to producing an overall estimate of mortality for a survey area. If estimates of mortality are required at village level then other sampling strategies (e.g. sequential sampling plans) could be used. At present there is no experience with using the proposed method with alternative sampling methods.

For further information contact: Mark Myatt, Consultant Epidemiologist & Senior Research Fellow, The Institute of Ophthalmology, University College London, Unit B, Station Building, Llanidloes, Powys SY18 6EB, UK or Anna Taylor, SC UK at email: a.taylor@scfuk.org.uk

Imported from FEX website