Formulas

Every formula the Countdown methodology states, in one place, in the order of the analysis. Each one has what its symbols mean and a link to the section that explains it; the section is the reference if the wording here and there differ. For the default values and thresholds themselves, see Defaults and thresholds.

Data quality

Reporting completeness (1a, 1b, 1c)

$\text{1a} = \frac{\text{monthly facility reports received}}{12 \times \text{number of facilities}}$

$\text{1b} = \frac{\text{districts with reporting completeness} \ge 90\%}{\text{total districts}} \qquad \text{1c} = \frac{\text{districts with no missing values across all forms}}{\text{total districts}}$

• 1a and 1b are the mean over the analysis’s reporting forms: ANC, delivery, immunization and OPD in RMNCAH analyses; ANC, delivery and immunization in vaccine analyses.
• 1c counts a district with no missing monthly value in the year for any reporting form.

Explained in: Reporting completeness.

Extreme outliers (2a, 2b)

A monthly value $x$ is an extreme outlier when it lies outside

$\tilde{x} \pm 5 \times MAD$

$\text{2a} = \frac{\text{monthly values not classified as outliers}}{\text{total monthly values}} \qquad \text{2b} = \frac{\text{districts with no outliers}}{\text{total districts}}$

• $\tilde{x}$: the median monthly value of the same series (the district’s, or the national or admin-1 series being assessed).
• $MAD$: the median absolute deviation of that series.
• Baseline: $\tilde{x}$ and $MAD$ are computed from all years except the most recent one, so the latest year is judged against the earlier years.

Explained in: Outlier detection.

Internal consistency: national ratios (3a, 3b, 3c)

$\text{3a} = \frac{\text{ANC1 reported}}{\text{Penta1 reported}}, \quad E_{3a} = 1.07 \times \frac{\text{ANC1}_{s}}{\text{Penta1}_{s}}$

$\text{3b} = \frac{\text{Penta1 reported}}{\text{Penta3 reported}}, \quad E_{3b} = \frac{\text{Penta1}_{s}}{\text{Penta3}_{s}} \qquad \text{3c} = \frac{\text{OPV1 reported}}{\text{OPV3 reported}}, \quad E_{3c} = \frac{\text{OPV1}_{s}}{\text{OPV3}_{s}}$

A national ratio $r$ is acceptable when

$\lvert r - E \rvert \le 0.05$

• $E$: the expected ratio; $\text{ANC1}_{s}$, $\text{Penta1}_{s}$, …: coverage in the most recent survey.
• 1.07: the expected ANC1 to Penta1 ratio with the same survey coverage for both, from 3% pregnancy loss, 2% stillbirths, 1.5% twins and 3% neonatal mortality before Penta1.
• 3c (OPV1 / OPV3) is for vaccine analyses.

Explained in: Internal consistency and Ratio calculations.

Internal consistency: district ratios

$\text{district check} = \frac{\text{districts with } 1.0 \le r_d \le 1.5}{\text{total districts}}$

• $r_d$: the district’s ratio — ANC1 / Penta1 (3c in RMNCAH analyses, 3f in vaccine analyses), Penta1 / Penta3 (3d; 3g), OPV1 / OPV3 (vaccine analyses, 3h).

Explained in: Internal consistency.

Overall data quality score

$\text{Score}_{\text{RMNCAH}} = \operatorname{mean}(\text{1a}, \text{1b}, \text{1c}, \text{2a}, \text{2b}, \text{3c}, \text{3d})$

$\text{Score}_{\text{vaccine}} = \operatorname{mean}(\text{1a}, \text{1b}, \text{1c}, \text{2a}, \text{2b}, \text{3f}, \text{3g}, \text{3h})$

• The components are the metrics above; the district ratio checks are 3c, 3d (RMNCAH) or 3f, 3g, 3h (vaccine). The 2024 guidebook left 1c out of the score; the apps include it.

Explained in: Overall quality score.

Data adjustment

Adjustment for incomplete reporting

$N_{\text{adj}} = N_{\text{rep}} + N_{\text{rep}} \times \left( \frac{1}{C} - 1 \right) \times k$

• $N_{\text{adj}}$: the number of events adjusted for incomplete reporting.
• $N_{\text{rep}}$: the raw number of events reported.
• $C$: reporting completeness, the proportion of expected facility reports received.
• $k$: the ratio of the volume of services in non-reporting facilities to that in reporting facilities (set by the analyst per service: the app starts at 0; the guidebook’s default is 0.25).

Explained in: Numerator adjustment formulas and parameters and Configuring the k-factor.

Low reporting rates

$C = \begin{cases} C_{\text{reported}} & \text{if } 75\% \le C_{\text{reported}} \le 100\% \\ \operatorname{median}\{\, C_{\text{district}} : 75\% \le C_{\text{district}} \le 100\% \,\} & \text{if } C_{\text{reported}} < 75\% \text{ or missing} \end{cases}$

• $C_{\text{reported}}$: a district’s reporting rate for a service in a month.
• $C_{\text{district}}$: the district’s reporting rates for that service. The month’s count is then adjusted with $k$ as usual; the count itself is kept.

Explained in: Critical data threshold rules.

Replacing outliers and missing values

$x_{\text{outlier}} \rightarrow \operatorname{median}(\text{the district's non-outlier months in the same year})$

$x_{\text{missing}} \rightarrow \operatorname{median}(\text{the district's monthly values in the same year})$

• An outlier is a monthly value outside $\tilde{x} \pm 5 \times MAD$ of the district’s series (see Extreme outliers).

Explained in: Summary of data adjustment business rules.

Denominators

Coverage

$\text{Coverage} = \frac{\text{population who received the service}}{\text{population who need the service}}$

• The numerator is the adjusted number from the facility data; the denominator is the target population, estimated with the selected denominator option.

Explained in: Denominator assessment and selection.

Denominators derived from ANC-1

• NMR, PNMR: neonatal and post-neonatal mortality rates; infants: the infants eligible for Penta (under 1).
• Each indicator uses the population that matches it: pregnancies for ANC, deliveries for institutional deliveries, live births for institutional live births and BCG, infants for Penta, the measles targets for measles.

Explained in: Computing the derived denominators.

Denominators derived from Penta-1

• The measles targets are computed from infants as for ANC-1.
• The population-growth versions of the ANC-1 and Penta-1 options adjust these for annual population growth, using the population indicator chosen in the population trend comparison; the methodology page gives no formula for that adjustment.

Explained in: Computing the derived denominators.

Implied crude death rate (DHIS2 projection check)

$\text{CDR} = \text{CBR} - \text{growth rate}$

• CDR, CBR: crude death and birth rates (per 1,000). A DHIS2 projection is flagged when the implied CDR is negative or below 5 per 1,000.

Explained in: Population trend comparison.

Survey comparison

$\text{best option} = \arg\min_{\text{option}} \; \lvert \text{coverage}_{\text{routine, option}} - \text{coverage}_{\text{survey}} \rvert$

• Compared for institutional live births and Penta-3 against the most recent survey (the gold standard), at national and subnational level.

Explained in: Denominator selection examination.

Coverage

Immunization denominators

$\text{Denominator} = \text{Live births} - \text{Neonatal deaths}$

$\text{Measles 1 denominator} = \text{Live births} - \text{Neonatal deaths} - \text{Postneonatal deaths}$

$\text{Measles 2 denominator} = \text{Live births} - \text{Neonatal deaths} - (2 \times \text{Postneonatal deaths})$

• The first is the denominator for BCG and the Penta doses (children eligible for vaccination); measles 1 uses the children who survive the first year; measles 2 the children aged 24-35 months.

Explained in: Immunization.

Family planning demand satisfied

$\text{Demand satisfied} = \frac{\text{Use of modern contraceptives}}{\text{Unmet need} + \text{Use of modern contraceptives}}$

Explained in: Family planning.

Subnational

Composite coverage index

$\text{CCI} = \frac{\text{ANC4} + \text{institutional live births} + \text{SBA} + \text{IPT2} + \text{PNC} + \text{Penta3} + \text{Measles 1}}{7}$

• Coverage of each indicator, with equal weight.

Explained in: Subnational statistical summaries (one-pager).

Units meeting a target

$\text{Units meeting the target} = \frac{\text{regions or districts meeting the target}}{\text{total regions or districts}} \times 100$

• A target such as “Penta-3 at least 80% in every district” is met when this reaches 100%.

Explained in: Target values.

Inequality (MADM)

The median absolute deviation from the median (MADM) of district coverage within an admin-1 unit measures the spread between districts; the methodology page defines it in words and gives no formula.

Explained in: Inequality.

Mortality

Institutional mortality rates

$\text{iMMR} = \frac{\text{maternal deaths in health facilities}}{\text{live births in health facilities} / 100{,}000}$

$\text{iSBR} = \frac{\text{stillbirths in health facilities}}{\text{births in health facilities} / 1{,}000}$

$\text{Neonatal deaths before discharge} = \frac{\text{neonatal deaths before discharge}}{\text{live births in health facilities} / 1{,}000}$

• The population (MMR, SBR) and community (cMMR, cSBR) rates are the same with the deaths and births in the population or the community. They are computed from unadjusted data.

Explained in: Institutional mortality in the CD2030 analytical approach.

Stillbirths to maternal deaths

$\text{ratio} = \frac{\text{reported stillbirths}}{\text{reported maternal deaths}}$

• Usually for a year; a data quality flag is raised when the ratio is outside 5-25.

Explained in: Ratio of stillbirths to maternal deaths at national level.

Population, community and institutional MMR

$M_p = (M_i \times P_i) + (M_c \times (1 - P_i))$

$M_c = \frac{M_p - (M_i \times P_i)}{1 - P_i}$

• $M_p$: maternal mortality ratio in the population; $M_i$: institutional maternal mortality ratio; $M_c$: maternal mortality ratio in the community.
• $P_i$: the proportion of live births in health facilities.

Explained in: Mathematical modeling and formulations and Back-calculating community mortality.

Expected institutional MMR and completeness of reporting

$\text{Expected } M_i = \frac{M_p}{P_i + \left( \frac{M_c}{M_i} \times (1 - P_i) \right)}$

$\text{Completeness of facility reporting} = \frac{\text{Reported } M_i}{\text{Expected } M_i}$

• $\frac{M_c}{M_i}$: the assumed ratio of community to institutional maternal mortality.
• The same approach applies to stillbirths, with all births instead of live births.

Explained in: Calculating expected institutional mortality and Computing reporting completeness.

Neonatal deaths before discharge: rough completeness check

$\text{institutional neonatal mortality (before discharge)} \ge 0.5 \times \text{population neonatal mortality}$

Explained in: Considerations for iSBR.

Outliers in mortality data

$\lvert x_{\text{year}} - \bar{x} \rvert > 3\sigma \qquad \text{or} \qquad \lvert x_{\text{month}} - \tilde{x} \rvert > 5 \times MAD$

• $\bar{x}$, $\sigma$: the long-term annual mean and standard deviation; $\tilde{x}$, $MAD$: the baseline median and median absolute deviation of the monthly values.

Explained in: Outlier detection thresholds.

Service utilization and health system

Outpatient and inpatient utilization

$\text{OPD visits per child per year} = \frac{\text{adjusted under-5 OPD visits in the year}}{\text{under-5 population (DHIS2 projection)}}$

$\text{Admissions per 100 children under 5} = \frac{\text{under-5 admissions in the year}}{\text{under-5 population}} \times 100$

$\text{Discharges} = \text{Admissions} - \text{Deaths}$

• The shares of OPD visits and of admissions contributed by children under five are under-5 visits (admissions) divided by all visits (admissions).

Explained in: Outpatient service utilization and Inpatient service utilization.

Case fatality rate

$\text{Pediatric case fatality rate} = \frac{\text{Number of children who die in hospital}}{\text{Total number of admissions (Discharges + Deaths)}}$

• Computed from unadjusted data only.

Explained in: Case fatality rate.

Health system density

$\text{Health facility density} = \left( \frac{\text{Total number of health facilities}}{\text{Total population}} \right) \times 10{,}000$

$\text{Hospital density} = \left( \frac{\text{Total number of hospitals}}{\text{Total population}} \right) \times 100{,}000$

$\text{Inpatient bed density} = \left( \frac{\text{Total inpatient beds}}{\text{Total population}} \right) \times 10{,}000$

Explained in: Number of health facilities per 10,000 population, Number of hospitals per 100,000 population and Inpatient bed density per 10,000 population.

See also

• Defaults and thresholds: the values the formulas use
• Indicator definitions: the data elements behind each indicator
• Glossary: the terms the methodology uses