## 3 Results
### Exploratory Data Analysis
#### 3.2.2 Timing of Vaccination and Birth  
In this section, descriptive summaries on vaccination timing and season of birth are presented. Table 7 presents the distribution of children who received vaccination within the on-time window for age. Figure 5: Child age distribution of defaulter and non-defaulter classes. From the results, a decreasing trend in on-time vaccination is observed for both classes. At birth, 62.75.3% of children within the defaulter class received their vaccine dose on time, compared to 84.52% of non-defaulters. At 6 weeks, 56.34% of defaulters received the dose on time versus 68.73% of non-defaulters. This decreased further at 10 weeks (42.68% vs. 56.22%) and at 14 weeks, where 32% of children within the defaulter class received the dose on time, compared to 43.78% of those in the non-defaulter group. Timely vaccination at the later schedule dates was extremely low, with inconsistent distributions between the defaulter and non-defaulter classes. We further examined off-time vaccination windows by early and delayed vaccination. Table 8 presents the results of vaccinations administered earlier than the expected window. Overall, early vaccination was an infrequent event across both classes, with proportions generally below 5% at all timepoints. At week 6, 1.14% of defaulters and 1.44% of non-defaulters received vaccines early (\(p\) = 0.152). Similar marginal differences were observed at week 10 (1.18% vs. 1.08%) and week 14 (1.25% vs. 1.17%). These findings suggest no significant difference in early vaccination uptake between the groups during the foundational stages of the immunization schedule. At month 6, however, a higher proportion of defaulters (1.02%) received early vaccines compared to non-defaulters (0.67%). The difference widened at month 9, with 2.63% of defaulters vaccinated early compared to 2.06% of non-defaulters. A reversed trend was observed for the last two schedule dates. At month 12, non-defaulters were significantly more likely to receive vaccines early (3.13%) compared to defaulters (1.03%). At month 18, a proportion of 4.47% of the non-defaulter class received early vaccination compared to 3.41% of the defaulter class. The results on delayed vaccination show significant differences in distributions, with a higher number from the defaulter class reporting delays in the first four schedules. The results for delayed vaccination are presented in Table 9.  
At birth, 29.75% of defaulters reported delayed vaccination compared to 13.95% of non-defaulters (\(p<0.001\)). At week 6, 40.49% of defaulters reported delayed vaccination compared to 29.35% of non-defaulters (\(p<0.001\)). Similar trends, with statistically significant differences (\(p<0.001\)), were observed at week 10 (53.49% of defaulters versus 42.03% of non-defaulters) and at week 14 (62.20% of defaulters versus 54.57% of non-defaulters). At month 6, however, a higher proportion of non-defaulters (86.77%) reported delayed vaccination compared to defaulters (78.30%), with a statistically significant difference observed (\(p<0.001\)). At month 9, the difference was marginal, with 76.73% of defaulters and 74.55% of non-defaulters reporting delays (\(p=0.006\)). Again, a reverse trend was observed at months 12 and 18. A significant proportion of non-defaulters reported delayed vaccinations at month 12, 60.72% compared to 33.07% of defaulters (\(p<0.001\)), and at month 18, 59.31% compared to 43.79% of defaulters (\(p<0.001\)). A heatmap for visualising delayed vaccination by age and vaccination timing is presented in Figure 6.  
From Figure 6, we can observed that delayed vaccination is marginal in frequency. The map shows an increased frequency of delayed vaccination, particularly for months 9 and 18. The results on birth seasonality (Table 10) reveal statistically significant associations (\(p<0.001\)) between season of birth and vaccination default.