Restricted dimensions of quality of health care and infrastructure The analysis is restricted to the relationship between health services quality and infrastructure dimensions for which we have data. As health care quality is a multidimensional concept, we are not able to explain all its variability with the proposed approach and the available data sets. However, our approach allows us to explore the associations between the variables of interest and provide suggestive evidence on the relevance of the access to infrastructure to the quality of health services in Kenya. We based our discussion and recommendations acknowledging these limitations of the methodology.

Longitudinal and cross-sectoral dimensions of SDI Despite SDI surveys being a rich source of information, these data did not allow us to pursue a causal analysis due to lack of an exogeneity source. Therefore, this study only presents correlations between access to infrastructure and health service quality. These are still useful benchmarks for illustrating the potential that investments in infrastructure might have for improving the quality of health service delivery.<sup>17</sup> Infrastructure is a cross-sectoral and typically long-term investment that might influence services simultaneously in multiple sectors over many years. Ideally, the education SDI data would also have been exploited in this paper, but the 2012 education data was several years more outdated and done at a smaller scale (i.e., only representative at the country level, not at the county level). Moreover, it was impossible to perform an intertemporal analysis using the 2012 and 2018 health SDI data sets due to several methodological changes that made data not fully comparable over the years (e.g., different sample methodologies, different facilities, and different levels of representativeness).

Finally, as mentioned before, the last SDI data set for Kenya is from 2018. Although it is not completely outdated, in the past years, Kenya has made important improvements both in infrastructure and health service delivery, which might not be captured by the present analysis. Nevertheless, for the purpose of the analysis, we use the most up-to-date data available.

Limitations of geospatial data The main limitation of geospatial data is that the information is not as granular as for the SDI data set. For example, the Master Facility List, although the most updated list of health centers in Kenya, contains very limited information about each facility (i.e., level of the facility and ownership). Additionally, the calculations for other geospatial data are often predictions for small areas based on multiple data sources, and in some cases the calculations based on sources like MAP might be challenging because of the geospatial coverage range capacity. This makes it less precise for the analysis as compared to SDI data collected directly from health facilities and more susceptible to capture other geographical aspects such as urban/rural status. Also, the information estimated with geospatial data is less specific than SDI data; for instance, it is only possible to study access to electricity (a dummy variable) instead of the quality of the connection at this stage.

> 17 Other dimensions of quality of health service delivery were also considered but not included in this paper. For instance, one attractive aspect of the 2018 SDI is that it included an exit interview for users, capturing the supply side of the services and the perceptions of the demand. Nevertheless, the sample of users is small (up to five patients per facility, with many facilities having only one patient interviewed), questions were only asked about family planning services, and there is no variation in the inpatients' perceptions of quality.

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