Modeling the efficacy of hepatitis B vaccination in infants and post-vaccination survival analysis

Abstract

The need for the accurate prediction of the effectiveness of vaccines in infants to prevent Hepatitis B virus (HBV) infection and accurately analyze post-vaccination survival in case of infection calls for the adoption of a robust machine learning model. This study aimed to investigate an effective HBV vaccine for infants and predict the post-vaccination survival rate for infants at risk. A clinical study was carried out on the medical records of 609 cases of vaccinated infants, focusing on variables such as age, weight, gender, diagnosed symptoms and HBV vaccines administered on them. Four machine learning models were evaluated for the performances of the vaccines while Chi-square crosstab was employed to evaluate dependency of status pre- and post-vaccination. Aside from descriptive analyses of demographic variables, Kaplan-Meier method was also employed to predict the post-vaccination survival rate. Our findings indicate that Logistic Regression and Support Vector Machine models have moderate accuracy (77%) and high precision for positive cases but struggle with negative cases, similar to Decision Tree. The Random Forest model performs better overall (81% accuracy), with balanced precision and recall, excelling in positive case predictions. Feature importance analysis shows age and weight as key predictors of HBV status, with the Penta1 + Pneumo1 + Vpo1 + Rota1 vaccine as the most dependable for HBV. Findings suggest that higher vaccine doses may correlate with lower infection rates, and Kaplan-Meier analysis estimated a 0.05 chance of post-vaccination survival from HBV infection after 100 days.

Keywords

clinical survey hepatitis B virus hepatitis B vaccine infants machine learning post-vaccination survival

1 Introduction

The Hepatitis B virus (HBV) is a significant global health concern, responsible for a range of liver diseases from acute hepatitis to chronic conditions that can lead to liver failure, cirrhosis, or even hepatocellular carcinoma.¹ HBV is transmitted through contact with infectious blood or other bodily fluids, and vertical transmission from an infected mother to her infant during childbirth.^2–4 Given its severe impact on liver health, HBV poses a substantial burden on global healthcare systems, particularly in regions with high prevalence rates such as Sub-Saharan Africa and East Asia. This increased susceptibility highlights the need for integrated care approaches that address all associated infections simultaneously. Recent epidemiological data also indicate that HBV remains a significant public health issue globally, with over 290 million people living with chronic HBV infection.5 In regions like sub-Saharan Africa, where HBV prevalence is particularly high, effective vaccination programs and screening strategies are vital in controlling the spread of the virus. Studies such as those by6 demonstrate that targeted vaccination and education programs can significantly reduce HBV incidence in high-risk populations, reinforcing the importance of predictive models that incorporate demographic, clinical, and epidemiological factors to identify and manage at-risk groups more effectively.

Most individuals with HBV do not exhibit symptoms in the early stages of the infection, making it difficult to diagnose without laboratory tests.⁷ When symptoms do manifest, they may include jaundice, dark urine, fatigue, nausea, and abdominal pain, which can persist for several weeks. Diagnosing HBV involves a range of blood tests to differentiate it from other viral hepatitis infections and to determine whether the infection is acute or chronic.⁸ Additionally, co-infection with HIV is a significant concern, with approximately 1% of HBV-infected individuals also being HIV positive, and conversely, around 7.4% of those with HIV globally are also infected with HBV.⁹ Currently, there is no specific treatment for acute HBV infection; management focuses on supportive care, including fluid replacement and symptomatic relief.¹⁰

Hepatitis B Virus (HBV) poses a significant global health issue, with early detection in infants being crucial to prevent long-term complications and transmission. Despite advancements in HBV management, predicting HBV status in infants remains challenging due to the complexity of factors influencing infection, such as demographic information, clinical symptoms, and vaccination history. Existing methods for HBV screening often rely on conventional diagnostic approaches that may not fully utilize the available data or account for the interactions among multiple risk factors.¹¹ More so, this risk factors can be prevented in infants with effective dosage of vaccination.

Thus, the introduction of effective and safe vaccines in 1981 has been a major advancement in preventing HBV. The vaccine, which has demonstrated substantial economic benefits, is a critical component in reducing the incidence of chronic HBV infections and their severe long-term consequences.¹² The HBV vaccine, administered in a series of three doses—at birth, at one month, and at six months—has proven highly effective in providing long-lasting immunity, typically lasting for at least 20 years.¹³

In Nigeria, the prevalence of HBV among children is notably high, ranging from 11.5% to 13.6%. Vaccination at birth is crucial in preventing chronic HBV infection, with post-exposure prophylaxis showing an efficacy of 85%–95% when administered within 12 h of birth for infants born to chronically infected mothers.¹⁴ The effectiveness of vaccination programs is often assessed by vaccination coverage rates, which serve as indicators of program success and adherence to preventive medicine guidelines.¹⁵

While vaccinations are a cornerstone of public health strategies against HBV, the effectiveness and reach of these programs can be further enhanced by integrating them with other vaccines, such as those for Hepatitis A, diphtheria, tetanus, pertussis (DTaP), and human papillomavirus (HPV).¹⁶ This approach not only simplifies the immunization process but also improves adherence rates. To evaluate and enhance the efficacy of HBV vaccination programs and other interventions, it is essential to utilize advanced statistical and machine learning techniques.^17,18 Traditional methods such as survival analysis, which measure the time until an event occurs (such as disease progression or treatment failure), are valuable for understanding the progression of HBV and the impact of interventions.^19–22 However, survival analysis requires specific event data, such as mortality or disease occurrence, which may not always be available in the dataset. In the absence of such data, predictive modeling using supervised machine learning techniques, such as Logistic Regression, Random Forest, Support Vector Machine and Decision Tree provides an alternative approach. These methods can help identify key factors influencing HBV status and predict outcomes based on demographic and clinical features.^14,19 By integrating vaccination status into predictive models, researchers can enhance the accuracy of predicting HBV status, particularly among high-risk groups like infants born to HBV-positive mothers. This is corroborated by the work of,²³ which highlighted determinants of childhood immunization in sub-Saharan Africa.

Logistic Regression, a method used for binary classification, can predict the likelihood of HBV positivity or negativity based on variables such as age, sex, symptoms, and vaccination status.^24,25 Random Forest, an ensemble learning method, enhances predictive performance by aggregating results from multiple decision trees, thereby improving accuracy and robustness. Analyzing the importance of various features using Random Forest can provide insights into which variables most significantly affect HBV outcomes. Thus, understanding the role of vaccination status, symptoms, or demographic factors in predicting HBV status can inform targeted interventions and public health strategies^26–28 highlights its robustness and versatility in various applications, as in the case of,²⁹ where the technique was used to assess effective intervention strategies for HBV transmission dynamics. Support Vector Machine (SVM) is gaining popularity because of its excellent properties of high generalization performance and global optimal solutions. Not only is its structure simple, but also its various technical capabilities is obviously boosted, especially the generalization ability.³⁰ Decision Tree is a non-parametric supervised machine learning technique of which its goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features.²⁸

The integration of these machine learning models into public health research enables a more nuanced understanding of HBV dynamics and intervention effectiveness. Using machine learning (ML) for analysing HBV data is a smart choice because these models can manage complex data relationships and handle situations where one class of data is much larger than others. They are also very accurate in predictions and help identify key factors influencing health outcomes. Moreover, machine learning can work well with big datasets and supports quick clinical decisions. Overall, ML strengthens HBV vaccination studies and improves public health efforts. By applying these techniques, researchers can identify high-risk groups, evaluate the impact of vaccination programs, and make data-driven decisions to improve health outcomes. This study's findings would provide more effective public health policies and interventions, contributing to the global effort to control and eventually eliminate HBV, some of the evidenced based policy has been highlighted in this study.

2 Materials and methods

2.1 Data preparation

This clinical study was conducted on the health records of 609 children who were immunized against Hepatitis B, with a special focus on their HBV outcome, post-immunization, between the year 2021 and 2023 at a government Hospital, Isale-Agbara, Osogbo, Osun State, Nigeria. Of the 609 children, 315 are female and 294 are male. Key indicators in the study include patient demographics information (such as age, sex, date of birth, and geographical location), clinical features (such as data on symptoms, previous HBV infections, and vaccination history), and vaccination status (such as records of HBV vaccination, including dates and types of vaccines administered). The study was approved by the ethics committee of the health ministry, Osun state government, Nigeria.

The ages of the infants were recorded in days and weight in kg. The clinical survey revealed the administration of six (6) different vaccines based on thirty-five (35) diagnosed symptoms among children of ages ranging between 0 to 726 days. The vaccines are BCG + VPO zero, Penta 1 + Pneumo1 + VPO1 + Rota1, Penta 2 + Pneumo2 + VPO2 + Rota2, Penta 3 + Pneumo3 + VPO3 + Rota3, MR1 + VAA, and MR2. The survey revealed that where there are no identified symptoms, BCG + VPO zero is mostly applicable to vaccinate the diagnosed infants. The post-vaccination clinical reports of the infants diagnosed with the surveyed symptoms were also investigated to elicit information for the estimated survival rate after vaccination.

After data cleaning and validation, the dataset was split into a training set and a testing set using a 70:30 ratio to ensure robust model performance. This split allowed for training the model on 70% of the data while reserving 30% for testing purposes. The training set facilitated the model's learning process, while the testing set provided an unbiased evaluation of the model's predictive capabilities. This approach helped to mitigate overfitting and enhance the generalizability of the model to unseen data.

For the implementation of the predictive models, Python codes were employed as the primary programming language. Its rich ecosystem of libraries, including Scikit-learn, Pandas, and NumPy, offers comprehensive support for data manipulation, model building, and evaluation, making it an ideal choice for this research. In this paper, four different machine learning models were employed while five evaluation metrics, Accuracy, Precision + Recall, F1, Confusion matrix, and Area under curve were used to compare the model for optimal performance. To identify the most suitable, four machine learning models would be evaluated namely, Logistics Regression, Random Forest, Support Vector Machine, and Decision Tree based on the stated metrics.

2.2 Logistic regression (LR) model

It is used as a foundational model for predicting binary outcomes in this study, specifically for determining the presence or absence of Hepatitis B Virus (HBV) infection (positive or negative).

Considering a data set, where the response falls into one of two categories, Yes or No. Rather than modeling this response Y directly, logistic regression was use to model the relationship between $p (X) = P r (Y = 1 | X)$ and X. For convenience we are using the generic 0/1 coding for the response using a linear regression model to represent these probabilities as stated below:

\begin{aligned} p (X) = β_{0} + β_{i} X_{i} \end{aligned}

(1)

In logistic regression, we use the logistic function,

\begin{aligned} p (X) = \frac{e^{β_{0} + β_{i} X_{i}}}{1 + e^{β_{0} + β_{i} X_{i}}} \end{aligned}

(2)

After a bit of manipulation of (2), we find that odd to be

\begin{aligned} \frac{p (X)}{1 - p (X)} = e^{β_{0} + β_{i} X_{i}} \end{aligned}

(3)

The logistic function for a response variable Y is defined based on the log-odds (logarithm of the odds) of the probability p of the outcome occurring, with $β_{i}$ representing the parameters of the model

\begin{aligned} P (Y = 1 | X) = \frac{1}{1 + e^{- (b_{0} + b_{1} x_{1} + \dots + b_{p} x_{p)}}} \end{aligned}

(4)

where,

P (Y = 1 | X)

is the probability that the response variable Y equals 1 (HBV positive) given predictors X which include key demographic factors such as age, gender, socioeconomic status, vaccination history, and clinical symptoms associated with HBV infection.

2.3 Random forest (RF)

It is employed to enhance the predictive accuracy of HBV status by capturing complex interactions among predictor variables. This method constructs multiple decision trees during training and aggregates their predictions to make a final decision. Each decision tree is built by randomly selecting subsets of features and data points, which helps in addressing overfitting and improving model robustness. These processes were summarized with three major algorithms of bootstrapping, decision tree, and aggregation which allows for a better understanding of the variables that most influence HBV infection status. The importance for each feature on the constructed decision tree is then calculated as:

\begin{aligned} f i_{i} = \frac{Σ_{J : n o d e J s p l i t s o n f e a t u r e i^{n i_{J}}}}{Σ_{k \in a l l n o d e s^{n i_{k}}}} \end{aligned}

(5)

where

f i_{i}

is the importance of feature i and

n i_{J}

is the importance of node j.

This is then normalized to a value $0 a n d 1$ by dividing Equation (6) with the sum of all features’ importance values given as:

\begin{aligned} n o r m f i_{i} = \frac{f i_{i}}{Σ_{J \in a l l f e a t u r e s^{f i_{J}}}} \end{aligned}

(6)

Thus, the final feature importance at the Random Forest level, is its average over all the trees given as:

\begin{aligned} R F f i_{i} = \frac{\sum_{j \in a l l t r e e s} n o r m f i_{i j}}{T} \end{aligned}

(7)

where, RF

f i_{i}

is the importance of feature i calculated from all trees in the random forest model;

n o r m f i_{i j}

is the normalized feature importance for i in tree j and T is the total number of trees.

2.4 Support vector machines (SVMs)

The support vector machine (SVM) is an extension of the support classifier to include non-linear class boundary. Support vector classifier (SVC) suitable if the boundary between two classes is linear and not suitable in the case of non-linear boundaries. The support vector machine uses kernels to enlarge the feature space to give room for a non-linear boundary between the classes. If we have two observations $x_{i}, a n d x_{i}^{'}$ then their inner products can be expressed as

\begin{aligned} (x_{i}, x_{i}^{'}) = \sum_{j = 1}^{p} x_{i j} x_{i j}^{'} \end{aligned}

(8)

The linear SVC can be expressed as

\begin{aligned} f (x) = β_{0} + \sum_{i = 1}^{p} α_{i} (x, x_{i}) \end{aligned}

(9)

\begin{aligned} K (x_{i}, x_{i}^{'}) = {(1 + \sum_{j = 1}^{p} x_{i j} x_{i j}^{'})}^{d} \end{aligned}

(10)

where

(x_{i}, x_{i}^{'})

is the inner product of two observation

x_{i}, x_{i}^{'}

and K is known as the kernel. The function of K is to compare the similarity of two observations. The combination of support vector classifier with a non-linear kernel such as that of (10) results in a support vector machine.

\begin{aligned} f (x) = β_{0} + \sum_{i = 1}^{n} α_{i} K (x, x_{i}) \end{aligned}

(11)

The output of the support vector regression follows the Equation (11), just as we have in the general linear model, and there are n parameters $α_{i}$ , $i = 1, 2, \dots ., n,$ one for each training observation. It follows that $α_{i} ϵ R ∖ 0$ apply only to support vectors in the solution. That is, $α_{i}$ would only zero if a training observation is not a support vector.

The SVM is employed based on a regularization parameter tunning and the tolerance parameter of 0.01 each with a nonlinear mathematical function (Kernel) specified as:

\begin{aligned} [\frac{1}{n} \sum_{i}^{n} = 1 \; \; max (0,1 - (y_{i} - (w^{T} x_{i} - b))] + λ ‖ w ‖^{2} \end{aligned}

(12)

2.5 Decision tree (DT)

DT algorithm works by dividing the 609 observations into two homogeneous sets in view of the highly important variables making the study distinct. The mathematical expression adopted is in relation to the one used by Adeboye et al. (2023) given as;

\begin{aligned} P = \frac{n_{A}}{n_{A} + n_{B}} \end{aligned}

(13)

Chi-square crosstab was employed to evaluate dependency of status pre- and post-vaccination. Aside from descriptive analyses of demographic variables, Kaplan-Meier was also employed to predict the post-vaccination survival rate. Kaplan-Meier offers useful graphs and estimates that show survival rates over time. This information is important for sharing and understanding survival patterns in both medical and research, particularly in clinical trials and epidemiological studies. The compelling attraction to Kaplan-Meier method is that it is easy to understand and dependable for determining the survival rates. It works well in studies with missing data and without needing to assume the data's distribution. The results are presented in the next section.

3 Results

Table 1 provides a descriptive summary of variables age and weight while Table 2 provides a summary of the study population's characteristics, including vaccine types and HBV status post-vaccination. The dataset includes 609 entries with an average age of 14.15 days and a standard deviation of 44.62 days. Ages range from 0 to 726 days, with 25th percentile at 2 days, the median at 5 days, and the 75th percentile at 11 days. Weights range from 0.34 to 18.85 kg, with mean weight as 4.27 kg, standard deviation at 2.13 kg with the 25th percentile at 3.3 kg, the median at 3.6 kg, and the 75th percentile at 4.3 kg. Among the 609 population, 294(48.3%) were males while the remaining 315(51.7%) were females. Of the 609 patients involved in the research clinical survey, 483 infants were found to HBV positive (213 Males and 270 Females) while 126 were negative (67 Males and 59 Females). 19 registered births did not seek for vaccine while 590 infants were vaccinated with 6 different types of vaccination. Of all the vaccine types, BCG + VPO zero was the most administered vaccine with 572 (93.9%) infants gotten vaccinated with different number of doses. 549 infants, constituting the majority got only one dose while two and three doses were administered to 33 and 8 infants respectively. Among the participants who received one dose, 121 tested negative, while 428 tested positives. For those who received two doses, only 2 tested negatives, while 31 were positive. Also, three 3 were negative and 5 were positive among those who received three doses. The clinical survey revealed the diagnoses of 35 different symptoms, of which fever is the most prevalent with 25 (4.1%) male and 28 (4.6%) female diagnosed with the symptom were all found to be positive.

Table 1.
Descriptive summary table.

Age (Days) Weight (kg)

Count 609 609

Mean 14.149425 4.27445

Std 44.62028 2.12762

Min 0 0.34

25% 2 3.3

50% 5 3.6

75% 11 4.3

Max 726 18.85

	Age (Days)	Weight (kg)
Count	609	609
Mean	14.149425	4.27445
Std	44.62028	2.12762
Min	0	0.34
25%	2	3.3
50%	5	3.6
75%	11	4.3
Max	726	18.85

Table 2.

Socio-demographic and clinical characteristics analysis (total = 609).

					HBV STATUS
Factors			Frequency	Percentage	+VE	-VE
Gender:	Male		294	48.3	213	67
	Female		315	51.7	270	59
Vaccines-	BCG + VPO zero		572	93.9
	Penta1 + Pneumo1 + VPO1 + Rota1		8	1.3	7	1
	Penta2 + Pneumo2 + VPO2 + Rota2		1	0.2	1	0
	Penta3 + Pneumo3 + VPO3 + Rota3		6	1.0	6	0
	MR1 + VAA		2	0.4	2	0
	MR2		1	0.2	1	0
Unvaccinated			19	3.1	-	-
Vaccines Dose-	One		549	92.6	428	121
	Two		33	6.4	31	2
	Three		8	1.0	5	3
Symptoms-	Jaundice	Male	6	1.0	6	0
		Female	17	2.8	17	0
	Dark Urine	Male	20	3.3	20	0
		Female	14	2.3	14	0
	Fatigue	Male	5	0.8	5	0
		Female	10	1.6	10	0
	Irritability	Male	1	0.2	1	0
		Female	1	0.2	1	0
	Abdominal Discomfort	Male	4	0.7	4	0
		Female	5	0.8	5	0
	Enlarged Liver	Male	13	2.1	13	0
		Female	5	0.8	5	0
	Spleen	Male	3	0.5	3	0
		Female	3	0.5	3	0
	Pale stool	Male	17	2.8	17	0
		Female	23	3.8	23	0
	Abdominal Swelling	Male	3	0.5	3	0
		Female	0	0.0	0	0
	Failure to Thrive	Male	25	4.1	25	0
		Female	4	0.7	4	0
	Fever	Male	25	4.1	25	0
		Female	28	4.6	28	0
	Inadequate Weight	Male	2	0.3	2	0
		Female	4	0.7	4	0
	Rash	Male	17	2.8	17	0
		Female	12	2.0	12	0
	Persistent Vomiting	Male	4	0.7	4	0
		Female	10	1.6	10	0
	Joint Pain	Male	5	0.8	5	0
		Female	7	1.1	7	0
	Stiffness	Male	7	1.1	7	0
		Female	10	1.6	10	0
	Poor Feeding	Male	6	1.0	6	0
	Female	6	1.0	6	0
	Weakness	Male	10	1.6	10	0
		Female	15	2.5	15	0
	Bleeding	Male	3	0.5	3	0
		Female	4	0.7	4	0
	Nutritional Deficiency	Male	10	1.6	10	0
		Female	7	1.1	7	0
	Respiratory Distress	Male	0	0.0	0	0
		Female	1	0.2	1	0
	Skin Changes	Male	10	1.6	10	0

		Female	4	0.7	4	0
	Endocrine Disturbance	Male	6	1.0	6	0
		Female	6	1.0	6	0
	Development Delay	Male	5	0.8	5	0
		Female	3	0.5	3	0
	Growth Failure	Male	7	1.1	7	0
		Female	9	1.5	9	0
	Dark Urine and Fever	Male	1	0.2	1	0
		Female	0	0.0	0	0
	Itching	Male	2	0.3	2	0
		Female	3	0.5	3	0
	Swelling of Leg	Male	6	1.0	6	0
		Female	4	0.7	4	0
	Bone Abnormalities	Male	1	0.2	1	0
		Female	0	0.0	0	0
	Tiredness	Male	11	1.8	11	0
		Female	13	2.1	13	0
	Irritability	Male	2	0.3	2	0
		Female	3	0.5	3	0
	Stomach Pain	Male	2	0.3	2	0
		Female	0	0.0	0	0
	Immunodeficiency	Male	0	0.0	0	0
		Female	1	0.2	1	0
	Trouble Sleeping	Male	0	0.0	0	0
		Female	2	0.3	2	0
	Difficulty Growing	Male	1	0.2	1	0
		Female	2	0.3	2	0
	Absence of Symptoms	Male	75	12.3	75	0
		Female	58	9.5	58	0

Table 3 presents the results for the test of association between HBV status and vaccine dose. There is need to determine if significant association exist between HBV Vaccine dose and HBV status (-ve and +ve) by employing the Pearson Chi-square statistic of 5.991 with p-value of 0.05 suggests a marginally significant association between HBV status and vaccine dose while the Likelihood Ratio value of 7.213 with a P-value of 0.027 confirms the existence of the significant association.

Table 3.

Cross tabulation and chi-square value for HBV vaccine (dose) and HBV status.

	HBV vaccine(dose)			Chi-Square Values	P-value
HBV status(positive/negative)	1	2	3	Pearson – 5.991	0.05
Negative	121	2	3	Likelihood Ratio – 7.213	0.027
Positive	428	31	5	Likelihood Ratio – 7.213	0.027

The histograms in Figures 1 and 2 present the distribution of age and weight respectively. Both figures show concentration of data points around the lower age and weight ranges. The distribution is right-skewed, with a long tail towards older ages and heavier weights. There is a prominent peak near the beginning of the x-axes, indicating a significant number of individuals within a specific younger age group and lighter weight group.

Figure 1.

Age in days showing the distribution of the ages of the diagnosed and immunized children.

Figure 2.

Weight in kg showing the distribution of the weight of the diagnosed and immunized children.

Figure 3 presents the correlation matrix of the relationships among key variables of age, weight, sex, symptoms, HBV vaccine doses, HBV status (positive/negative), and vaccine types. The strongest correlations are observed between age and weight (0.83) and weight and HBV vaccine doses (0.88), indicating that heavier children tend to be older and receive more vaccine doses. The correlation between age and the vaccine doses is also significant (0.78), suggesting that older children may have received more doses. Sex shows weak negative correlations with age, weight, and vaccine doses, indicating minimal impact on these variables. Symptoms have a very weak correlation with HBV status (−0.11), suggesting that symptoms may not be significantly predictive of infection status in this dataset. The correlation between vaccine type and HBV vaccine doses (0.68) indicates that certain vaccine types are associated with specific dosage patterns. The understanding provided by these relationships informed clinical decision-making as observed in the examined clinical records, and targeted public health strategies.

Figure 3.

Correlation heatmap showing the correlation matrix of the relationships among key variables of age, weight, sex, symptoms, HBV vaccine doses, HBV status (positive/negative), and vaccine types.

3.1 Machine learning (ML) model results

In evaluating the four ML models adopted for predicting the HBV status, several performance metrics and characteristics were considered. Table 4 presents the comparative results based on the adopted metrics which showed that LR and SVM exhibited mixed performances. While they correctly predict positive HBV cases with a precision of 0.77 and a recall of 0.87, they failed to identify any negative cases, resulting in a precision of 0.00 for class 0 as illustrated in Figures 4 and 5. The overall accuracy of the models stand at 77%, indicating that they both correctly classify 77% of instances, but this is primarily due to their successes in predicting positives rather than accurately distinguishing between the two classes. The macro and weighted averages reflect significant imbalances in performance across classes, with a macro F1-score of 0.44 and a weighted F1-score of 0.67, highlighting its inability to generalize well for class 0.

Figure 4.

The confusion matrix for the logistic regression model shows the performance in classifying instances into two classes: negative and positive.

Figure 5.

Confusion matrix for support vector machine provides the classification report for a support vector machine model assessing HBV status.

Table 4.

Model evaluation and comparison.

Metrics	Precision	Recall	F1-Score	Support
Logistics Regression
0(Negative)	0	0	0	42
1(Positive)	0.77	1	0.87	141
Accuracy			0.77	183
Macro average	0.39	0.5	0.44	183
Weighted average	0.59	0.77	0.67	183
Random Forest
0(Negative)	0.65	0.4	0.5	42
1(Positive)	0.84	0.94	0.89	141
Accuracy			0.81	183
Macro average	0.75	0.67	0.69	183
Weighted average	0.8	0.81	0.8	183
Support Vector Machine
0(Negative)	0	0	0	42
1(Positive)	0.77	1	0.87	141
Accuracy			0.77	183
Macro average	0.39	0.5	0.44	183
Weighted average	0.59	0.77	0.67	183
Decision Tree
0(Negative)	0.47	0.45	0.46	42
1(Positive)	0.84	0.85	0.85	141
Accuracy			0.76	183
Macro average	0.66	0.65	0.65	183
Weighted average	0.76	0.76	0.76	183

RF and DT on the other hand, demonstrates more balanced performance across both classes. With 0.65 and 0.47 precisions, 0.40 and 0.45 recalls respectively for RF and DT for negative cases; impressive precisions of 0.84, recalls of 0.94 and 0.85 respectively for positive cases, both models effectively identify positives while also recognizing a portion of the negatives. The overall accuracy of 81% and 76% respectively for both models indicate they both correctly classify higher percentages of instances than both LR and SVM. Additionally, the macro average metrics (precision: 0.75, 0.66; recall: 0.67, 0.65; F1-score: 0.69, 0.65) and weighted averages (precision: 0.80, 0.76; recall: 0.81, 0.76; F1-score: 0.80, 0.76) respectively for the two models suggest a more reliable and balanced predictive capability. The predictive abilities of these two models were equally illustrated in the confusion matrices of Figures 6 and 7. Thus, while all models provide insights into HBV status prediction, the RF model emerges the better choice due to its superior overall accuracy, balanced performance across all classes, and robustness against class imbalances. Its ability to predict both positive and negative cases more effectively makes it the preferred model for practical applications in HBV status prediction.

Figure 6.

The confusion matrix for the random forest model evaluates the model's performance in classifying instances into two classes: negative and positive.

Figure 7.

Confusion matrix for decision tree model evaluates the model's performance in classifying instances into two classes: negative and positive.

Feature importance chart is presented in Figure 8 for RF model, being the best. The bar chart illustrates the relative importance of different features in predicting the outcome variable. Age and weight emerge as the most influential factors, with significantly higher importance compared to other features while Penta1 + Pneumo1 + Vpo1 + Rota1 vaccine appears to be the best. This suggests that Penta1 + Pneumo1 + Vpo1 + Rota1 vaccine, age and weight play a crucial role in determining the status outcome of infants.

Figure 8.

Feature importance from random forest illustrates the relative importance of different features in predicting the outcome variable.

The ROC curve illustrated in Figure 9 visualizes the performance of LR and RF models, being the identified classification models. It plots the True Positive Rate (TPR) against the False Positive Rate (FPR) for different classification thresholds. The closer a curve is to the top-left corner, the better the model's performance, and both models show a clear distinction from the random baseline. LR (AUC = 0.74) slightly outperforms RF (AUC = 0.73), indicating a marginally better ability to discriminate between positive and negative classes. However, both models demonstrate reasonable discriminative power.

Figure 9.

ROC curve and area under the curve (AUC) visualizes the performance of two classification models, random forest and logistic regression (i.e., the best two models). It plots the True Positive Rate (TPR) against the False Positive Rate (FPR) for different classification thresholds.

The Kaplan-Meier (KM) curve illustrates the proportion of individuals surviving past a specific point in time following the onset of HBV infection. Initially, there's a rapid decline in survival probability, indicating a high risk of adverse events shortly after infection. According to Figure 10, this signifies that the chance of an infant surviving HBV infection when they are not vaccinated is estimated at 0.05 after 100 days. There was a steep decline in the early days (0 −50 days), indicating that many children subjected to clinical trials became infected with HBV immediately they are born before vaccination was administered. However, the curve flattens out over time, suggesting an increased likelihood of long-term survival for those who survive the initial critical period, due to the positive impacts of timely and adequate vaccination. The shaded area represents the confidence interval, indicating the uncertainty around the survival estimates, especially when many individuals are no longer under the protection of vaccines.

Figure 10.

Kaplan-Meier survival curve for HBV infection illustrates the proportion of individuals surviving past a specific point in time following the onset of HBV infection.

The research discussion focused on the analyses of the correlation between HBV vaccine doses and HBV status, and evaluate the effectiveness of predictive models in diagnosing HBV infection. Initially, descriptive statistics were employed to summarize key variables, such as age and weight, across a sample of 609 individuals. The correlation matrix identified relationships among variables, highlighting significant relationships between age, weight, and vaccine doses. To assess the effectiveness of HBV vaccination, cross-tabulation and Chi-square tests were used to analyze the relationship between vaccine doses and HBV status. This was followed by the application of ML models to predict HBV status. Each model's performance was evaluated based on metrics such as precision, recall, F1-score, and overall accuracy. The ROC curve and AUC provided additional insights into the models’ discriminative power.

The descriptive statistics revealed that the sample had a wide range of ages (0 to 726 days) and weights (0.34 to 18.85 kg), with a notable concentration of younger and lighter individuals. The gender distribution was slightly with more females were present. The HBV status distribution showed a high prevalence of positive cases (464) compared to negative cases (126). The correlations highlight key relationships among age, weight, and vaccination, providing insights into the factors influencing HBV status and the effectiveness of vaccination in preventing infection among children while Chi-square results suggest a marginally significant association between HBV status and vaccine.

Regarding model performance, RF and DT demonstrates more balanced performance across both classes compared to LR and SVM. Finally, the KM curve showed the proportion of individuals surviving past a specific point in time following the onset of HBV infection and this was estimated at 0.05 within 100 days. However, the curve flattens out over time, suggesting an increased likelihood of long-term survival for those who survive the initial critical period of 100 days, after being vaccinated.

4 Conclusion

Hepatitis B is a significant global health issue, with substantial implications for individual and public health. Effective vaccination is crucial in controlling the spread of HBV, yet understanding the impact of vaccination doses on infection rates remains a critical area of investigation. By employing statistical and ML methodologies, the study provides insights into vaccination effectiveness and model performance. The presence of a significant association between vaccine doses and HBV status suggests the need for more improved vaccination strategy with much credence given to Penta1 + Pneumo1 + Vpo1 + Rota1 vaccine, age and weight of registered infants. Though Penta1 + Pneumo1 + Vpo1 + Rota1 vaccine appears to be scarce or not frequently in used like the BCG + VPO zero, the research results confirmed the former to be the most effective in terms of post-vaccination survival. The Random Forest model's superior performance in predicting both positive and negative HBV cases suggests it as a more robust tool for clinical applications. Its ability to handle class imbalances and provide balanced performance makes it a valuable asset in diagnostic settings. The estimated post-vaccination survival rate is also an indication of the effectiveness of the vaccine regime investigated during the clinical survey. Thus, this research provides valuable insights into the effectiveness of HBV vaccination and the capabilities of different predictive models.

These findings underscore the need for continued research and development in both vaccination strategies and predictive modeling to improve HBV management and public health outcomes. The study setting may have been confined to one geographical area, but the findings are very much generalizable. The model performance studied in this work could be suitable also for use beyond the study location and, eventually, be extended to other regions.

While the current study pays attention to HBV-containing vaccines, which distinguish this case from the studies of non-HBV vaccines, where only DTP-Hib or DTP alone is given without any component of hepatitis B, efforts have been garnered towards recommending the most effective vaccine for the survival of susceptible HBV patients.

5 Policy implication

The effective management and eventual elimination of HBV significantly rely on well-structured vaccination policies that can be executed through Evidence-Based Policymaking. Such policies, however, hinge on the availability of quality comprehensive data analyses, reliable information, and evaluations on what combinations and methods of vaccines provide optimal health results which in this case the current study has provided.

Official statistics have a significant impact in enabling evidence-based policymaking concerning the public health response to HBV. These statistics capture population-based information such as the prevalence of HBV infection, vaccination uptake including coverage rates, and cases of post-vaccination infections or breakthroughs. With official statistics, health authorities and policymakers are equipped to calculate the at-risk populations with low vaccination coverage and gaps within existing immunization policies. Such information helps guide strategic health interventions which result in maximum benefit from implemented health policies and appropriate usage of funds. For example, this study supports claims that though the BCG + VPO zero vaccine is widely utilized in practice, Penta1 + Pneumo1 + VPO1 + Rota1 vaccine combination certainly provides better control against HBV infection while improving post-vaccination survival rates greatly over other available options.

The findings from this study highlight how important it is for policymakers to have access to large, official datasets. When such data backs up the research, it can influence how health policies are shaped in no small measure. A major role of these official statistics is to help monitor and evaluate vaccination programs. By continuously collecting data on vaccination trends and the rate of hepatitis B virus (HBV) cases, policymakers can see how well their strategies are working. This ongoing monitoring is crucial because it can quickly reveal if vaccination rates are dropping or if there are new outbreaks or access issues. This swift feedback allows for timely changes in policies, ultimately leading to better health outcomes.

Furthermore, having these official statistics available promotes accountability and transparency. They provide everyone—from the public to healthcare professionals and global organizations—with valuable insights into how vaccines are performing. Regular updates ensure that those in charge are held accountable for health outcomes. In summary, the evidence from this study makes a strong case for revamping HBV vaccination strategies to focus on more effective combinations, allowing health authorities to create targeted, data-informed initiatives that can significantly improve public health and help eliminate HBV risks worldwide.

Supplemental Material

sj-xlsx-1-sji-10.1177_18747655251363659 - Supplemental material for Modeling the efficacy of hepatitis B vaccination in infants and post-vaccination survival analysis

Supplemental material, sj-xlsx-1-sji-10.1177_18747655251363659 for Modeling the efficacy of hepatitis B vaccination in infants and post-vaccination survival analysis by Nureni O Adeboye, Olumide S Adesina, Timothy A Ogunleye and Lawrence O Obokoh in Statistical Journal of the IAOS

Footnotes

Acknowledgements

There is no funding or external source directly responsible for this research. All the relevant internet sources utilized have been duly acknowledged. The authors however, wish to appreciate the management of Health Planning Research and Statistics Department of Osun State government, Osogbo, Nigeria.

ORCID iDs

Nureni O Adeboye

Olumide S Adesina

Timothy A Ogunleye

Lawrence O Obokoh

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Supplemental material

Supplemental material for this article is available online.

References

Schillie

Murphy

Sawyer

. A comprehensive immunization strategy to eliminate hepatitis B virus transmission in the United States. Morb Mortal Wkly Rep 2018; 67: 1–20.

Pattyn

Hendrickx

Vorsters

, et al. Hepatitis B vaccines. J Infect Dis 2021; 224(Suppl 4): S343–S351.

Medvedev

Brotherton

Gai

, et al. Development and validation of a simplified score to predict neonatal mortality risk among neonates weighing 2000 g or less (NMR-2000): an analysis using data from the UK and The Gambia. The Lancet. Child & Adolescent Health 2020; 4: 299–311.

Adeboye

Adesina

Afolabi

, et al. Advanced principal component analysis of Various risk factors of hepatitis B prevalence in Nigeria. Tanzania Journal of Science 2024; 50: 676–691.

WHO 2023 In Nigeria, boosting viral hepatitis awareness and treatment. Retrieved on 5th August 2023 from https://www.afro.who.int/countries/nigeria/news/nigeria.

Ortiz

Scanlon

Mullens

, et al. Effectiveness of interventions for hepatitis B and C: a systematic review of vaccination, screening, health promotion and linkage to care within higher income countries. J Community Health 2020; 45: 201–218.

Morakinyo

Fagbamigbe

. Neonatal, infant and under-five mortalities in Nigeria: an examination of trends and drivers (2003–2013). PloS One 2017; 12: e0182990.

Leumi

Bigna

Amougou

, et al. Global burden of hepatitis B infection in people living with human immunodeficiency virus: a systematic review and meta-analysis. Clin Infect Dis 2023; 71: 2799–2806.

Shen

Ong

, et al. Blueprint to hepatitis B elimination in China: a modelling analysis of clinical strategies. JHEP Reports 2023; 5: 100833.

10.

Lawal

Adeniyi

Akintan

, et al. Prevalence of and risk factors for hepatitis B and C viral co-infections in HIV infected children in Lagos, Nigeria. PloS One 2020; 15: e0243656.

11.

Atilola

Tomisin

Randle

, et al. Epidemiology of HBV in pregnant women, South West Nigeria. J Epidemiol Glob Health 2018; 8: 115–123.

12.

Oludoun

Adebimpe

Ndako

, et al. The impact of testing and treatment on the dynamics of hepatitis B virus. F1000Res 2021; 10: 936.

13.

Oladepo

Dipeolu

Oladunni

. Nigerian Rural mothers’ knowledge of routine childhood immunizations and attitudes about use of reminder text messages for promoting timely completion. J Public Health Policy 2019; 40: 459–477.

14.

Huang

, et al. Application of machine learning in predicting survival outcomes involving real-world data: a scoping review. BMC Med Res Methodol 2023; 23: 268.

15.

Adesina

Adedotun

Adeboye

, et al. On COVID-19 vaccination in Nigeria: an empirical study. Int J Des Nat Ecodyn 2023; 18: 219–224.

16.

Schurink-van't Klooster

De Melker

. The National Immunisation Programme in the Netherlands: Surveillance and developments in 2018–2019. 2019.

17.

Liang

Zhuang

. A literature review of mathematical models of hepatitis B virus transmission applied to immunization strategies from 1994 to 2015. J Epidemiol 2018a; 28: 221–229.

18.

Din

. Mathematical analysis of a new nonlinear stochastic hepatitis B epidemic model with vaccination effect and a case study. Eur Phys J Plus 2022a; 137: 558.

19.

Terrault

Lok

McMahon

, et al. Update on prevention, diagnosis, and treatment of chronic hepatitis B: AASLD 2018 hepatitis B guidance. Hepatology 2018; 67: 1560–1599.

20.

Adeboye

Ajibode

Aako

, et al. On the survival assessment of asthmatic patients using parametric and semi-parametric survival models. Occup Dis Environ Med 2020; 8: 50–63.

21.

Adeboye

Adesanya

. On the survival assessment of diabetic patients using machine learning techniques. Int J Res Innov Appl Sci (IJRIAS) 2022; 7: 69–75. https://www.rsisinternational.org/journals/ijrias/DigitalLibrary/volume-7-issue-1/69-75.pdf

22.

Deo

. Survival analysis—Part 2: Cox proportional hazards model. PMC. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7876211/ (2021).

23.

Fenta

Biresaw

Fentaw

, et al. Determinants of full childhood immunization among children aged 12–23 months in sub-Saharan Africa: a multilevel analysis using demographic and health survey data. Trop Med Health 2021; 49: 29.

24.

Cleves

Gould

Gutman

. An introduction to survival analysis using Stata. Stata Press, 2019.

25.

Huang

Chen

Wang

. Machine learning approaches for predicting HBV infection outcomes: a systematic review. J Viral Hepat 2020; 27: 823–834.

26.

Ishwaran

Kogalur

Blackstone

, et al. Random survival forests. Ann Appl Stat 2020; 2: 841–860.

27.

Beasley

Hwang

Lee

. Hepatitis B virus infection in children: a prospective study of the natural history of hepatitis B virus infection in children. J Infect Dis 2023; 147: 476–482.

28.

Boulesteix

Janitza

Kruppa

. Overview of random forest methodology and practical guidance with emphasis on clinical applications. Cancer Inform 2019; 12: 1–17.

29.

Wodajo

Gebru

Alemneh

. Mathematical model analysis of effective intervention strategies on transmission dynamics of hepatitis B virus. Sci Rep 2023a; 13: 8737.

30.

Qayyum

Qadir

Bilal

, et al. Secure and robust machine learning for healthcare: a survey. IEEE Rev Biomed Eng 2020; 14: 156–180.

Supplementary Material

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Modeling the efficacy of hepatitis B vaccination in infants and post-vaccination survival analysis

Abstract

Keywords

1 Introduction

2 Materials and methods

2.1 Data preparation

2.2 Logistic regression (LR) model

Table 1. Descriptive summary table. Age (Days) Weight (kg) Count 609 609 Mean 14.149425 4.27445 Std 44.62028 2.12762 Min 0 0.34 25% 2 3.3 50% 5 3.6 75% 11 4.3 Max 726 18.85

5 Policy implication

Supplemental Material

sj-xlsx-1-sji-10.1177_18747655251363659 - Supplemental material for Modeling the efficacy of hepatitis B vaccination in infants and post-vaccination survival analysis

Footnotes

Acknowledgements

ORCID iDs

Funding

Declaration of conflicting interests

Supplemental material

References

Supplementary Material

Table 1.
Descriptive summary table.

Age (Days) Weight (kg)

Count 609 609

Mean 14.149425 4.27445

Std 44.62028 2.12762

Min 0 0.34

25% 2 3.3

50% 5 3.6

75% 11 4.3

Max 726 18.85