Descriptive Statistics and Probabiity 1. Probability There are a total of 38 participating countries in the study ( ), Appendix D- country li

Maternal mortality ratio – one of the most widely used measures to quantify the risk of maternal deaths relative to the number of live births, has become a key performance indicator of t

Table of Information

Assignment Assignment 2: Individual Case Study

Student

Huynh Nhat Dang s3817974

s3817974@rmit.edu.vn

Table of Contents

Abbreviation 4

I Introduction 5

II Descriptive Statistics and Probabiity 6

1 Probability 6

a Test of statistical dependence 6

b Country category identification 7

2 Descriptive Statistics 7

a Measure of Central Tendency 7

b Measure of Variation 8

c Measure of Shape 8

III Confidence Intervals 9

1 Calculation 9

2 Assumption for calculation 9

3 Discussion on confidence intervals result 9

IV Hypothesis Testing 10

1 Trend of world maternal mortality ratio 10

2 Hypothesis testing procedure 10

3 Discussion on hypothesis testing result 11

V Conclusion 12

References 13

Appendice 14

Appendix A Sustainable Development 17 Goals 14

Appendix B Maternal Mortality Ratio Trends by region 15

Appendix C Life time risk of maternal deaths by income group: 1 in X 15

Appendix D Country list of the data set 15

(Notice: Some acronyms are also included with their explanation in the report.)

CPD – United Nations Population Division

CRVS - Civil Registration and Vital Statistics (CRVS) systems

GNI – Gross National Income

MMR – Maternal mortality ratio MMRate – Maternal mortality rate SDGs- Sustainable Development Goals

UN – United Nations UNFPA – United Nations Population Fund

UNICEF – United Nations Children Fund

WBG – World Bank Group WHO – World Health Organization

I Introduction

Sustainable development over decades has become a globally heated topic, with an utmost concern of ensuring human well-being by balancing social, economic and environmental aspects, allowing prosperity for current and future generations (Anbu 2020) Among a wide range of components in sustainability, maternal health, well-being and survival remain primary goals and an investment priority in the post-2015 framework for sustainable development strategy, at which social and health experts have adapted many statistical methods to examine

performance of healthcare system and global health status for further improvement (WHO 2015) Maternal mortality ratio – one of the most widely used measures to quantify the risk of maternal deaths relative to the

number of live births, has become a key performance indicator of the overall health population, of social status

of women in the society, and of the functioning of national healthcare system (WHO 2006) In fact, MMR measures the number of maternal deaths during a specific time period per 100,000 births during the same time period, different from a concept of maternal mortality rate (MMRate) – number of maternal deaths divided by women’s personal years ( WHO et al 2015) According to the report of WHO in 2015, a 45% reduction has been witnessed in maternal mortality ratio over the past 25 years, (from 380 deaths/ 100,000 live births in 1990

to 210 deaths/ 100,000 live births in 2015), yet it is far falling short of a global goal Of the global maternal deaths in 2015, developing regions account for approximately 99% (UNICEF 2019); yet, it is targeted that no country should have an MMR greater than 140/100,000 live births as an expectation by 2030 (WHO 2015) Targeting for maternal mortality ratio is vital, but accurate measurement of maternal mortality ratio remains an immense challenge for many reasons: numbers of deaths still go unnoticed and uncounted, a reluctance to report abortion-related health and even a lack of medical atribution and CRVS system (WHO et al 2019) Therefore, it

is observed that there has been a signficant progress in maternal deaths reduction; however, there is a plenty of room to improve as well as challenges to tackle in a global world

With its aim to promote sustainable development in health service, the United Nations has build up the 2030

Agenda for Sustainable Development with a total of 17 goals (Appendix A – UN 17 goals), at which the goal

number 3 aiming at “ensuring healthy lifes and promoting well-being at all ages” with monitoring maternal mortality ratio as one of important elements (UN 2017) The significance of reducing maternal mortality ratio links to an accomplishment of the goal in multiple ways: when reproductive health – a beginning stage of human life is adequately addressed, it quantifies that quality care for women and children is ensured before, during and after childbirth, laying a foundation for future children well-being development (WHO 2018) Also, the majority of death causes are preventable in the case that healthcare systems can ensure equitable equipment and treatment to women, where they can be treated with effective and timely clinical interventions for prenatal care (Jolivet et al 2018) Hence, if nations have successfully developed sustainable development for the aspects

of clinical care, they are highly capable of minimizing these maternal risks involved, thus lowering maternal mortality ratio significantly (Child E.W.E 2018) Although maternal mortality is considered a global challenge,

a disparity in maternal mortailtiy ratio exists between different nations, according to the World Health Statistics (WHO 2018) The conduct of Girum and Wasie (2017) points out that countries with low and middle income are facing a much higher MMR, pointing out that along with adult literacy rate, GNI per capital are signficantly negatively correlated with MMR In reality, almost of the deaths (99%) occurred in low-and middle income countries, with almost two-thirds (64%) occuring in African Region, followed by Southern Asia (Appendix B,

UNICEF), which could be explained by a lack of proper medical care among these nations (WHO 2014) By

contrast, high- income countries witness an opposite pattern with rare maternal death occasion - 1 over 5400

lifetime risks (Appendix C, UNICEF) Therefore, the evidence shows that there exists an inverse relationship between two variables - MMR and GNI

This following report covers a number of aspects, including an analysis of the maternal mortality ratio among

38 studied countries and thorough investigation into the relationship between MMR and Gross National Income (GNI) Its aim is to figure out what is behind this trend of maternal mortality ratio, at which three methods of descriptitve statistics and a conduct of confidence intervals and hypothesis testing would be respectively applied, interpreted and evaluated in a systematic manner

II Descriptive Statistics and Probabiity

1 Probability

There are a total of 38 participating countries in the study (Appendix D- country list), which is divided into three categories based on their Gross Domesitc Income:

Low-income countries (LI) GNI less than$1000 per capita

Middle-income countries (MI ) GNI between $1000 and $12500 per capita

High-income countries (HI) GNI higher than $12500 per capita

Additionally, they are also grouped into two different categories according to their maternal mortality ratio The country would be regarded as having high maternal mortality ratio (H), provided that it happens to have more than 50 death cases per 100,000 live births By contrast, those having equal or fewer than 50 deaths per 100,000 live births are classified as “low maternal mortality ratio” countries (L) Below is a contigency table that has put countries into these multiple categories:

High Maternal Mortality Ratio (H)

Low Maternal Mortality Ratio (L)

Total

Table II.1: Contigency Table of each country category on Maternal Mortality Ratio (2015)

a Test of statistical dependence

With the purpose of determining whether income and maternal mortality ratio are statistically dependent or independent, we use a mathematical evidence by comparing a probability of all countries with a high maternal mortality ratio (H), regarded as P (H), and a conditional probability of countries having high maternal mortality ratio (H) given that they are high-income countries (HI), which is P (H | HI) Here is the result:

P (H | HI) = = = 0

P (H) = = = 0.605

From the above calculation, the probablity of countries having high maternal mortality ratio P (H) is not

equal to the probablity of countries having high maternal mortality ratio given that they are high-income

P (H | HI) P (H); (0

ones, leading to a conclusion that income and maternal mortality ratio are statistically dependent events.

It also means that the level of country income has an impact on the occurrence of maternal mortality

b Country category identification

To identify which country category most likely to have a high maternal mortality ratio, we calculate a conditional probability of countries having high maternal mortality ratio given that they belong to each category (low-income, middle-income or high-income):

P (H HI) = ǀ = 0 = 0%

P (H MI) = ǀ = 0.85 = 85%

P (H LI) = ǀ = 1 = 100%

From the above calculation, low-income country is the category with the greatest likelihood of having high maternal mortality ratio, with the probability of 100% - clearly explained, all countries (6 over 6) in the category have high maternal mortality ratio This indicates that low-income countries are more likely to have high maternal mortality ratio than other country categories

2 Descriptive Statistics Min >,<,= Lower

Bound

Max >,<,= Upper

Bound

Result

Table II.2: Test of outliers in three country categories (unit: deaths per 100,000 live births)

With a view to guarantee an accurate analysis of three measurements in descriptive statistics, a test of outliers is conducted From an above test table, it is confirmed that there are two existing upper outliers in the middle-income category, which have extremely high maternal mortality ratio compared to others in the same category

a Measure of Central Tendency

-Table II.3: Central Tendency of each country category on Maternal Mortality Ratio (2015) (unit : deaths per 100,000 live births)

Since we have calculated that two outliers exist in the data set, the only measure in central tendency not affected

by extreme values is Median Therefore, Median is the most suitable tool to be applied in this case As can be seen from Table II.3, the median of low-income countries is the highest with 544.2 deaths per 100,000 births To

be more detailed, 50% of low-income countries would have a maternal mortality ratio greater than 544.2 deaths per 100,000 births, which is also the highest number of all categories This is followed by middle-income countries with 184.3 deaths per 100,000 births, and high-income countries appear to have the lowest median with only 9.75 deaths per 100,000 births, nearly sixty-six times smaller than Median of low-income countries Hence, the comparison of Median shows that low-income countries witness a much higher maternal mortality ratio than those with higher income level; and the higher the income level is, the smaller Median and lower maternal mortality ratio

P (H | LI) > P (H | MI) > P (H | HI)

b Measure of Variation

Table II.4: Measure of variation of each country category on Maternal Mortality Ratio (2015) (unit : deaths per 100,000 live births)

Because Means of all three categories are drastically different from one another, the best measure to compare a degree of variation is Coefficient of Variation (CV), which is specifically designed for comparing multiple data sets with distinctive Means From a Table II.4, high-income countries have the lowest CV with 41.29%, meaning that their maternal mortality would concentrate more on an average value 9.75 and less disperse At the same time, Middle-income and low-income countries have higher CVs, especially middle-income category with about 120% These values suggest that two country categories witness a signficant spread of maternal mortality ratio from average values This higher level of variation might become an obstacle to draw an accurate conclusion of statistical patterns in specific category

c Measure of Shape

Figure II.5: Measure of Shape of each country category on Maternal Mortality Ratio (2015) (unit : deaths)

The figure II.5 points out many noticeable differences between box-and-whisker plots of three country categories Firstly, data distribution of high and middle-income countries are left-skewed while that of low-income countries is opposite with right-skewness, even though both middle and low low-income countries have a higher Mean compared to the Median It could be explained by the existence of two upper-bound outliers in middle-income country category, making its Mean value become higher than it supposedly is In addition, we can see that middle-income countries has the longest right whisker since it contains extreme values and both middle and low-income countries witness greatly stretched box-and-whisker plots far to the right These skewness patterns indicate that maternal mortality ratio in 50% of low-income countries is likely to concentrate

on significant values of the right side while maternal mortality ratio of high and middle-income countries would

be more concentrated to the left, with middle-income being more variable

III Confidence Intervals

1 Calculation

This part aims to calculate confidence interval of the world average maternal mortality ratio (per 100,000 live births) It is supposed that the level of significance (α) is 0.05 Hence, its confidence level is calculated: 1- 0.05

= 0.95 A table of data for confidence interval calculation is attached below:

Confidence level (1 - )*100% 95%

Population standard deviation  unknown

As the population standard deviation is unknown, we will resort to sample standard deviation S; therefore,  Student’s t-table distribution is used instead of z-table:

Degree of freedom: d x f = n – 1 = 37 Significance level: = 0.05

So, we are 95% confident that the world average maternal mortality ratio in 2015 lies between 108.85 and 263.15 deaths per 100,000 live birth

2 Assumption for calculation

In the calculation, although a population standard deviation is unknown, a sample size of the data set is 38, which is higher than 30 – a requirement from the Central Limit Theorem Therefore, Central Limit Theorem is applicable and the simple size is sufficiently large to have an approximately normal distribution, hence no assumption is needed

3 Discussion on confidence intervals result

In the case that a population standard deviation is recognized, z-value table would come into use because of having both sufficient sample size and population standard deviation One advantage of utilizing a z-value table for confidence interval calculation is of its standardization from an actual population data ( Educba n.d.), and the mean and sample standard deviation S are likely to vary dramatically from one sample to another in

student-t disstudent-tribustudent-tion, which generastudent-tes a greal deal of uncerstudent-tainstudent-ty instudent-to sstudent-tastudent-tisstudent-tics work (Anderson 2014) Once a degree of uncertainty diminishes, a confidence interval is getting smaller, since confidence interval is a way to show what the uncertainy is with a certain statistic (Moore & McCabe 2002) At the same time, for any given level of confidence, critical z-values are smaller than critical t-values when the sample size is not considerable (McEnvoy 2018) And, when critical values are smaller, confidence intervals width will decrease, supporting our above idea that using a population standard deviation will cause narrower confidence intervals With this decrease in width of confidence intervals, a margin of error (e) – a factor to view a difference of a sample mean

 t =  1.6871

from a true population mean will get smaller, ensuring a precise result from the calculation (Bowerman, Duckworth & Froelich 2018)

In short, when a population standard deviation is known, confidence interval width gets narrower for higher certainty, leading to a more accurate confidence intervals result

IV Hypothesis Testing

1 Trend of world maternal mortality ratio

From a calculation in Part III, we are 95% confident that the world average maternal mortality ratio in 2015 is between 108.85 and 263.15 deaths per 100,000 live births According to the report of WHO, the world average maternal mortality ratio in 2014 is 221 deaths per 100,000 live births When comparing this value with a confidence interval calculated above, the average value in the year 2014 – 221 deaths falls between 108.85 and 263.15 deaths, making it unsure to state that whether the maternal mortality ratio will decrease, increase or remain unchanged in the long run Yet, a point estimate of the confidence interval (the sample mean) is 186 deaths, which is seen to be lower than 221 deaths in the 2014 data Therefore, we would make a speculation that the world maternal mortality ratio is expected to decrease in the future A hypothesis testing is conducted to examine our claim

2 Hypothesis testing procedure

Confidence level (1 - )*100% 95%

Population standard deviation  unknown

Step 1 Check the distribution: because the sample size n is 38 which is higher than 30, a Central Limit

Theorem (CLT) is applicable, satisfying that the sampling distribution of mean is normally distributed

Step 2 State null and alternative hypotheses:

Null hypothesis H ; < 221 (our claim)0 

Alternative hypothesis H ; 221 1  

Step 3 Choose table: The population standard deviation is unknown and a mean sampling distribution is

normally distributed, so we would use a t-table

Step 4 Choose rejection region: With the sign of H1 is “”, we would use an upper-tailed test

Step 5 Determine critical value (CV):

Degree of freedom: d x f = n – 1 = 37

Level of significance: = 0.05

 Since it is an upper-tailed test, t is +1.687