Mathematical Sciences

Introduction: Cervical cancer is the third most prevalent cancer among w omen in Brunei Darussalam. This study aims to report the overall survival rates and associated factors of patients diagnosed with malignant cervical cancer in Brunei Darussalam.
Methods: A retrospective study of patients diagnosed with cervical cancer from 2007 to 2017 in Brunei Darussalam. The data were obtained from the population-based cancer registry in Brunei Darussalam. Kaplan-Meier survival analysis was used to estimate the overall survival rates at 1-, 3-and 5-year intervals while the log-rank test was used to assess differences in survival between groups. Cox Proportional Hazard (PH) regression analysis was used to examine the association of demographic and clinical factors on the survival of cervical cancer patients.
Results: A total of 329 registered malignant cervical cancer cases were analyzed. The mean age at diagnosis of patients with cervical cancer was 46.7 ± 12.2 years. There were 28.6% deaths and the overall survival rates at 1, 3 and 5 years were 85.4%, 72.6% and 68.6% respectively. Age at diagnosis, cancer stage and histology types were significant predictive factors for overall survival of the patients diagnosed with cervical cancers when analysed on both log rank tests and Cox PH model.
Conclusion: Age at diagnosis , cancer stage and histology types were significantly associated with the overall survival rates of cervical cancer patients in Brunei Darussalam. Early detection and management of cervical cancer at early stages should be prioritized to improve the survival rate and quality of cancer care.

'Middle censoring' is a very general censoring scheme where the actual value of an observation in the data becomes unobservable if it falls inside a random interval (L, R) and includes both left and right censoring. In this paper, we consider discrete lifetime data that follow a geometric distribution that is subject to middle censoring. Two major innovations in this paper, compared to the earlier work of Davarzani and Parsian [3], include (i) an extension and generalization to the case where covariates are present along with the data and (ii) an alternate approach and proofs which exploit the simple relationship between the geometric and the exponential distributions, so that the theory is more in line with the work of Iyer et al. [6]. It is also demonstrated that this kind of discretization of life times gives results that are close to the original data involving exponential life times. Maximum likelihood estimation of the parameters is studied for this middle-censoring scheme with covariates and their large sample distributions discussed. Simulation results indicate how well the proposed estimation methods work and an illustrative example using time-to-pregnancy data from Baird and Wilcox [1] is included.

Introduction: Breast cancer is the most common cancer and leading cause of cancer deaths among women worldwide. In Brunei Darussalam, breast cancer has the highest incidence rate among women. This study presents the survival rate of women diagnosed with breast cancer in Brunei Darussalam and explores the association between survival and demographic or clinical characteristics. Methods: This is a retrospective study of breast cancer diagnosed from 2007 to 2017 among women in Brunei Darussalam. Cancer data was retrieved from population based cancer registry. Kaplan-Meier survival analysis and Log rank test were applied to estimate the survival rates and the association between survival and important patients’ characteristics. Hazard ratios were derived using Cox Proportional Hazard model. Results: The survival rates of breast cancer patients at 1, 3 and 5 years were 89.5%, 79.2% and 72.0% respectively. The 5-year survival rates for cancer stages were 92.2% for localized, 76.9% for regional, and 21.4% for distant metastasis. Ethnicity, cancer stages and cancer stages-morphology interaction were significant independent predictors for breast cancer survival in Brunei Darussalam. Conclusion: The survival rate of women diagnosed with breast cancer in Brunei Darussalam and its significant predictors are similar to those reported from other developed countries. Further studies on predictors such as health seeking behaviours and impact of different cancer treatment will provide further insight in improving survival rates of breast cancer through early cancer detection programmes and strengthening of the healthcare service delivery.

It is widely known that students normally struggle in the mathematics topic of algebra. They tend to steer away from algebraic problems such as solving linear equation with one variable, let alone simultaneous equations, which require them to determine the values of two variables. This action research study investigates the effect of replacing the common symbolic representations with pictorial (static visual) representations in simultaneous equations lessons of 38 low-performing Year 10 students. The data for the study was collected by means of pre-and post-tests and facilitated by three worksheets as the intervention instruments. During the lessons, pictorial representations were used in solving simultaneous equations questions. These entailed drawing several pictorials that were given in the equations. In particular, drawings of burgers, fries, cheese slices, gift boxes and sweets were used as these were generally relatable to the students in real-life. The students were then provided with fresh worksheets and subsequently translated their workings from the pictorial part to x and y. And thus forms the symbolic part of the intervention. From the students" pre-test and post-test scores, it was evident that the pictorial representations helped the students in making significant improvements in the topic.

This action research focused on the use of concrete models in the teaching and learning of factorisation by participants from Year 10 low ability classes in Brunei. The study attempts to assist students" difficulties in learning algebra, specifically on factorising quadratic expressions with all positive coefficients by using simplified algebraic tile as a form of concrete manipulative to aid teaching and learning. These tiles act as the remedial approach to improve students" conceptual knowledge. Result analysis of 22 students indicated significant difference between the means of pre and post-tests students" results using t-test, suggesting that the implementation of concrete model does have an effect on students" achievements, and could possibly be used as an alternative approach to teaching this topic. There were also some positive feedback and concerns raised by students on the use of concrete models in their factorisation learning based on the interview of selected students in the study.

Students have been applied great pressure from global expectations and challenges of the 21 st century. Brunei Darussalam, with its new education system (SPN21) aims to prepare the students in facing the challenges and globalized world. This study investigated the effects of flipped classroom on students" academic performance. At the same time, this study helps to provide the students to improve on their 21 st century skills, provide a student-centered learning environment and allow students to be responsible in their own learning. This study, involving 16 Year 7 participants from an all-girls high school in Brunei, was an action research study and uses quantitative methods for data collection. Pre-test, post-test and delayed post-test were given to the students to measure their learning of mathematics in three teaching cycles involving the topicsWhole Number and Operations, Integers, and Fractions and Decimals. Analysis of the results from the pre-test, post-test and delayed post-test indicated an improvement in the overall students" performance.

The purpose of this action research paper was to investigate the use of manipulatives in the teaching of addition and subtraction of integers. This research also looked at the impact of technology integration in the Mathematics classroom towards students' academic performance, students' motivation in learning integers, and students' attitude towards technology in Mathematics. The intervention lessons, which included the use of hands-on coloured counters and virtual manipulatives in the Gizmos application webpage, were carried out in two classes comprising 51 students in a secondary school in Brunei. This research adopted a quantitative approach of analysing participants' assessment scores, in addition to individual responses to questionnaires, and observational data collected during the interventions. Analysis of the result indicates that there is improvement in students' academic performance, which carries positive impact towards students' motivation, and students' attitude from both intervention methods. Another important finding of the study was, students that achieved higher assessment scores were more motivated and had a more positive attitude after taking part in the technology-enhanced lessons.

As students progressed from primary to secondary school, they are exposed to the constant use of calculators in Mathematics. Due to this reason, some of them are becoming too comfortable and too dependent on calculator even for simple arithmetic. Hence, this study was conducted to promote mental computational skills amongst secondary students by using the Bubble Method. A total of 44 mathematics students from two different schools were selected to be the participants of this study and were involved in intervention lessons using the Bubble Method. Based on the analysis result of pre-test and post-test, administered before and after the intervention respectively, 11 students were selected for further interview. Based on the findings, the effect of the students" performance in calculating percentage has been found to be not statistically significant using the Bubble method, however, all the students who were interviewed agreed that the Bubble Method improved their mental computational skill.

Geometry has always been regarded as one of the most important area in Mathematics. The van Hiele model is one of the renowned theories focusing on the teaching and learning of geometry. While GeoGebra is a free, open-source dynamic geometry software developed to assist the teaching and learning of Mathematics in general. This study investigated the effectiveness of van Hiele phases with GeoGebra in geometric transformations, particularly for the topic of rotation in geometry. Some of the Year 11 students who participated in this study were interviewed. The focus of the interview was directed at exploring the students" views on van Hiele phase-based learning, the use of GeoGebra and the thought processes on the topic. The development of the interview analyses yielded two emerging themes namely, the impact of van Hiele phases and the impact of GeoGebra as an instructional tool. Although the combination was mainly perceived as positive, there were also reluctance in accepting due to the readjustment needs of the concepts and applications of the tool itself.

The purpose of this paper is to show that short-ranged dependence prevailed for Singapore-Malaysia exchange. Although, it is perceived that there is some evidence of long-ranged dependence [1,2], it is still unclear whether Singapore-Malaysia exchange indeed exhibits long-ranged dependence. For this paper, we focus on the currency rate for a sixteen-year period ranging from September 2002 to September 2017. We estimate the Hurst parameter using the famous rescaled R/S statistics technique. From our analysis, we showed that the Hurst parameter is approximately 0.5 which indicates short-ranged dependence. This short memory property is further validated by performing a one-tailed z-test whose alternative hypothesis is that the Hurst parameter is not 0.5 at 1% significance level. We conclude that the alternative hypothesis is rejected. The existence of short memory proves that the behaviour of the exchange rate is unpredictable, supporting the efficient market hypothesis, which states that not only is price movement completely random but also tomorrow's prices are predicted by all the information in today's prices.

Background: Colorectal cancer (CRC) is the third most common cancer in both men and women. In most Asian
countries, both the incidence and mortality rates of CRC are gradually increasing. In Brunei Darussalam, CRC ranks
first and second in lifetime risk among men and women respectively. This study aims to report the overall survival
rates and associated factors of CRC in Brunei Darussalam. Methods: This is a retrospective study examining CRC
data for the period 2007 to 2017 retrieved from a population based cancer registry in Brunei Darussalam. A total of 728 patients were included in the analysis. Kaplan Meier method was used to estimate survival rates. Univariate analysis using log-rank test was used to examine the differences in survival between groups. Multivariate analysis using Cox PH regression was used to estimate hazard of death and obtain significant predictors that influence CRC patients’ survival. Results: The median survival time for colorectal, colon and rectal cancer patients were 57.0, 85.8 and 40.0 months respectively. The overall 1-, 3- and 5- year survival rates for CRC patients were 78.0%, 57.7% and 49.6% respectively. In univariate analysis, age at diagnosis, ethnicity, cancer stage, tumour location and histology were found to have significant difference in CRC patients’ survival. In the Cox PH analysis, older age (≥70 years), cancer stage, ethnicity and other histological type were determined as associated factors of CRC patients’ survival. Conclusion: This study found the overall 5-year survival rate of CRC in Brunei Darussalam is similar to that in some Asian countries such as Singapore and Malaysia. However, more efforts need to be carried out in order to raise awareness of CRC and improve the survival of CRC patients.

Background: This study aims to determine the survival rates for children and adolescents aged 0-19 years diagnosed with childhood cancer and to evaluate the associated factors for childhood cancer survival in Brunei Darussalam. Methods: The analysis was based on de-identified data of 263 childhood cancer for the period 2002 to 2017 retrieved from a population-based cancer registry. Overall survival was estimated using the Kaplan-Meier method. Univariate analysis, using the log-rank test, was used to examine the differences in survival between groups. Multivariate analysis, using the Cox Proportional Hazard (PH) regression model, was used to estimate the hazard ratios (HRs) and select the significant associated factors for childhood cancer patients’ survival. Results: The overall 1-, 5- and 10-year survival rates for all childhood cancers combined were 79.4%, 70.0% and 68.8% respectively. The most common types of cancer were leukemias, malignant epithelial neoplasms, lymphomas and tumours of the central nervous system (CNS). The 5-year survival estimates were highest for malignant epithelial neoplasms (84.2%) while the lowest was tumours of the CNS (44.1%). Log rank tests showed significant differences in childhood cancer patients’ survival between tumour types and period of diagnosis. In the Cox PH analysis, the presence of lymphomas, gonodal and germ cell neoplasms, and malignant epithelial neoplasms compared to leukemia; children aged 1-4 and 5-9 years compared to adolescents aged 15-19 years; and periods of diagnosis in 2002-2006 and 2007-2011 compared to 2012-2017 were significantly associated with lower hazard of death in this study. Conclusion: This study provides a baseline measurement of childhood cancer survival for monitoring and evaluation of cancer control programmes, to allow planning of cancer control program strategies such as surveillance, screening, and treatment to improve childhood survival rates in Brunei Darussalam.

The plateauing and declining trends seen in some of the developed nations have been attributed to the CRC screening programs either regional or nationally that have been implemented for many years. As CRC takes between five to ten years to develop,

Background: Colorectal cancer (CRC) is a major cause of cancer-related mortality worldwide. It is the second leading cause of cancer death in men and women in Brunei Darussalam in 2017, posing a major burden on society. Methods: This retrospective cohort study (n = 1035 patients diagnosed with CRC in Brunei Darussalam from 1st January 2002 until 31st December 2017) aims to compare the overall survival rates of CRC patients (2002-2017), to compare survival rates between two study periods (2002-2009 and 2010-2017) and to identify prognostic factors of CRC. Kaplan-Meier estimator and log-rank tests were performed to analyse the overall survival rates of CRC patients. Multiple Cox regression was performed to determine the prognostic factors of CRC with adjusted hazard ratios (Adj. HRs) reported.

Background: Prevention, control, and treatment of respiratory tract cancers are important steps towards achieving target 3.4 of the UN Sustainable Development Goals (SDGs) - a one-third reduction in premature mortality due to non-communicable diseases by 2030. We aimed to provide global, regional, and national estimates of the burden of tracheal, bronchus, and lung cancer and larynx cancer and their attributable risks from 1990 to 2019.
Methods: Based on the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 methodology, we evaluated the incidence, mortality, years lived with disability, years of life lost, and disability-adjusted life-years (DALYs) of respiratory tract cancers (ie, tracheal, bronchus, and lung cancer and larynx cancer). Deaths from tracheal, bronchus, and lung cancer and larynx cancer attributable to each risk factor were estimated on the basis of risk exposure, relative risks, and the theoretical minimum risk exposure level input from 204 countries and territories, stratified by sex and Socio-demographic Index (SDI). Trends were estimated from 1990 to 2019, with an emphasis on the 2010-19 period.
Findings: Globally, there were 2.26 million (95% uncertainty interval 2.07 to 2.45) new cases of tracheal, bronchus, and lung cancer, and 2.04 million (1.88 to 2.19) deaths and 45.9 million (42.3 to 49.3) DALYs due to tracheal, bronchus, and lung cancer in 2019. There were 209 000 (194 000 to 225 000) new cases of larynx cancer, and 123 000 (115 000 to 133 000) deaths and 3.26 million (3.03 to 3.51) DALYs due to larynx cancer globally in 2019. From 2010 to 2019, the number of new tracheal, bronchus, and lung cancer cases increased by 23.3% (12.9 to 33.6) globally and the number of larynx cancer cases increased by 24.7% (16.0 to 34.1) globally. Global age-standardised incidence rates of tracheal, bronchus, and lung cancer decreased by 7.4% (-16.8 to 1.6) and age-standardised incidence rates of larynx cancer decreased by 3.0% (-10.5 to 5.0) in males over the past decade; however, during the same period, age-standardised incidence rates in females increased by 0.9% (-8.2 to 10.2) for tracheal, bronchus, and lung cancer and decreased by 0.5% (-8.4 to 8.1) for larynx cancer. Furthermore, although age-standardised incidence and death rates declined in both sexes combined from 2010 to 2019 at the global level for tracheal, bronchus, lung and larynx cancers, some locations had rising rates, particularly those on the lower end of the SDI range. Smoking contributed to an estimated 64.2% (61.9-66.4) of all deaths from tracheal, bronchus, and lung cancer and 63.4% (56.3-69.3) of all deaths from larynx cancer in 2019. For males and for both sexes combined, smoking was the leading specific risk factor for age-standardised deaths from tracheal, bronchus, and lung cancer per 100 000 in all SDI quintiles and GBD regions in 2019. However, among females, household air pollution from solid fuels was the leading specific risk factor in the low SDI quintile and in three GBD regions (central, eastern, and western sub-Saharan Africa) in 2019.
Interpretation The numbers of incident cases and deaths from tracheal, bronchus, and lung cancer and larynx cancer increased globally during the past decade. Even more concerning, age-standardised incidence and death rates due to tracheal, bronchus, lung cancer and larynx cancer increased in some populations-namely, in the lower SDI quintiles and among females. Preventive measures such as smoking control interventions, air quality management programmes focused on major air pollution sources, and widespread access to clean energy should be prioritised in these settings.