## 2 Materials and Methods  
The datasets for this study were obtained from a malaria vaccine pilot evaluation project (MVPE) conducted within 66 districts across three administrative regions in Ghana between April 2019 and April 2024 [27; 28]. Records of children aged 4 to 48 months were extracted from a baseline and an endline cross-sectional survey. Both surveys employed identical instruments, eligibility criteria, and field data collection procedures. Moreover, there were no major changes in vaccination policy or service delivery context in Ghana, supporting their homogeneity and suitability for combined analysis. Several features were extracted from the survey datasets, which included both child and caregiver demographics, household asset ownership data, and vaccination data. In this study, considerable time and effort was spent on data preprocessing, which is often the case for studies involving the use of machine learning models [29; 30; 31; 32]. Preprocessing tasks involved the resolution of missing values, data anomalies, and outliers due to transcription problems. Another important task performed was to standardise categorical data into binary vectors of 0 and 1. To achieve this, the one-hot encoding technique [33] was mainly used. As a result, multi-categorical features such as the mother's education level and the mother's occupation increased data dimensionality. To reduce data dimensionality [34], we applied the principal component analysis (PCA) technique [35]. The top 9 components, capturing 53% of the total variance, were retained. These components were then used to derive a single-point wealth index feature. New features, including the child's birth and timing of vaccination, were systematically engineered for modelling. With respect to vaccination timing windows, our assumptions were guided by principles used by [PERSON] and colleagues [19]. We defined timelines of a vaccine schedule within the threshold of one month, with an offset of two weeks before and after the target week of schedule (Figure 1). Table 1 showing the vaccination window computation for each schedule used in this study is presented in Appendix A. The computational logic used implies that the birth dose of the Oral Polio Vaccine (OPV0) administered beyond two weeks after birth is considered out of the timely window, while the first dose (OPV1) administered 4 to 8 weeks after birth is considered on time. Due to possible variations in the antigen-specific dates within a given schedule, the overall vaccination date for the schedule was estimated as the mean of the recorded antigen-specific dates. This derived date was then used to compute the number of days the child deviated from the recommended on-time window for that vaccination schedule. Denoting a vaccination schedule \((s)\) consisting of \((n)\) antigens, each with an associated actual vaccination date \(\{d_{1},\ d_{2},\ \ldots,\ d_{n}\}\), we modelled the derived actual vaccination date for the schedule \(A_{s}\) as follows:  
\[A_{s}=\frac{1}{n}\sum_{i=1}^{n}d_{i}\]  
where the actual date of vaccination for the schedule is computed as the average of the recorded antigen dates. Using the abovementioned time definitions and assumptions, two concepts were introduced to capture the timeliness of vaccine delivery at each schedule: on-time vaccination (OV) and vaccination deviation (VD). OV basically indicates whether the child received timely vaccination, while DV indicates early and late deviations from OV. The feature OV was represented as a binary vector (1 = within window, 0 = out of window) based on the upper and lower bound of each vaccination schedule. Mathematically, a given schedule \((i)\) was modelled as follows:  
\[OV_{i}=\left\{ \begin{array}{ll}1,&\quad if\ L_{i}\ \leq\ A_{i}\ \leq\ U_{i}\\ 0,&\quad otherwise\end{array} \right.\]  
where \(A_{i}\) represents the actual date of vaccination for schedule \((i)\), \(L_{i}\) represents the lower bound, and \(U_{i}\) represents the upper bound of the recommended on-time window.