Table 1 The outcome and covariates based on Malaria Indicator Survey in Kenya (2020), Tanzania (2017) and Uganda (2018/19). Travel time was modelled while nighttime lights were derived from satellite imagery. Geographical coordinates were available at the cluster level, and all data were resolved at this level

Outcome

ANC4+

At least four antenatal care visits by a skilled provider (doctors, nurses, midwives, medical assistants, clinical officers, assistant clinical officers, assistant nurses, maternal and child health aides collapsed to either 0 (< 4 ANC visits, including no visits) or 1 (ANC4+ visits).

Aggregation unit

District

Health planning subnational units for each country, 47 counties in Kenya, 135 districts in Uganda, and 184 districts in mainland Tanzania (S1 Fig. 1) which were used as the aggregation unit across the equity stratifiers.

Equity stratifiers

Maternal education

The highest level of education attained by the woman at the time of the survey re-classified as no education (0) or some education (primary, secondary, or higher, whether complete or incomplete) (1)

Household wealth

Relative household wealth classified into quintiles based on principal component analysis of household assets and other characteristics [50]. The poorest and poor quintiles were collapsed to poor (0), while middle, rich and richest collapsed to non-poor category (1).

Travel time to nearest health facility

Travel time in minutes to the nearest health facility analytically modelled (continuous variable) and extracted for each survey cluster. It was categorized as having good access (≤1 hour) or being marginalized (> 1 hour) [51].

Other covariates

Nighttime light lights (NTL)

Remotely sensed nighttime light emissions based on satellite observations expressed using radiance (watt per steradian per square meter). Mean NTL was extracted per cluster as a continuous variable.

ANC initiation for women with at ≥1 visit

Initiation of first ANC visit for women with at least 1 visit during pregnancy classified as timely (1) (visit within first trimester) or late (0) (visit during the second or third trimester). Those 0 visits were treated as missing

Health media exposure

Any form of exposure to health information (from radio, internet, magazines, social media, newspapers, social mobilization campaigns by the government, billboards, television, or community events) (1) or no access at all (0). We considered any form of access to health information (exposure) instead of frequency of access to general information from media that is not health nuanced. The sources of health-related messages in Kenya were 14 while Uganda and Tanzania had eight sources.

Decision to seek ANC services

Woman’s participation in decision-making to seek ANC services for herself classified as involved (made the decision independently, or joint decision with spouse) or never involved (decision made by either the spouse or someone else). This is based on the household structure and who was living with the woman at the time of the survey.

Birth order

The ordinal position of the index live birth during the survey classified as first birth or higher order birth.