







































Highlights in Bioscience;


 
Highlights in BioScience             

ISSN: 2682-4043 

DOI:10.36462/H.BioSci.20208                                                                                                          
 

 

Highlights in BioScience                                                                                                                                                                           July 2020| Volume 3 

http://bioscience.highlightsin.org/ 

Page 1 of 8 

                                           

 

Research Article 

 

 

Open Access 

 
 

 

 

 

 

1 National Center for Radiation Research and 

Technology, Cairo, Egypt 
2 Independent PhD researcher and Candidate, 

Faculty of Pharmacy, Cairo University, Egypt 
 

 

Contacts of Authors  

 

 

* To whom correspondence should be 

addressed: Mostafa Essam Eissa 

 

Citation: Rashed ER, Eissa ME (2020).  Long-

Term Quantitative Assessment of Women 

Survivability from Cancer: A Unique 

Descriptive Analysis. Highlights in BioScience 

Volume 3. Article ID 20208. dio:10.36462/ 

H.BioSci.20208 

 

Received:  June 4, 2020 

 

Accepted:  July 3, 2020 

 

Published: July 5, 2020 

 
 

Copyright: © 2020 Rashed  and Eissa. This is 

an open access article distributed under the 

terms of the Creative Commons Attribution 

License, which permits unrestricted use, 

distribution, and reproduction in any medium, 

provided the original author and source are 

credited. 

 

 

Data Availability Statement: All relevant data 

are within the paper and supplementary 

materials 

 

 

 

Funding: The authors have no support or 

funding to report. 

 

 

Competing interests: The authors declare that 

they have no competing interests. 

 

 

Long-Term Quantitative Assessment of Women 

Survivability from Cancer: A Unique Descriptive Analysis 

 
Engy Refaat Rashed

1
, Mostafa Essam Eissa*

2
 

 

Abstract 

      Statistical Process Control (SPC) methodologies are a set of 

statistical methods and techniques that were initially designed for 

industrial processes but could be adopted for non-industrial applications. 

The current prospective study aimed to provide a unique quantitative 

investigation of an epidemiological disease using the SPC program 

platform. The selected case herein was a long-term monitoring record of 

the yearly cancer mortality rates in women worldwide. Multidimensional 

segregation of the dataset into subgroups was conducted to visualize the 

clustering pattern based on nations (42 countries as boxplot), time and 

the Gaussian Mixture Model (two-interfering bell-shaped distributions 

approach). The trend of death rates versus the elapsed years would 

demonstrate a moderately negative correlation with the time following 

the theory of splines. Construction of control chart based on the fitted 

Weibull distribution showed a gradual steady improvement in 

survivability rates from malignancy. The greatest variations in the 

mortality ratios existed within the European countries.  

 

Keywords: Cancer, Gaussian mixture model, Mortality rate, Weibull. 

 

 

Introduction  

Malignancy is one of the most devastating diseases that affect humanity in 

the modern era of civilization. It threatens human lifestyle quality, productivity, 

financial and economic status of society and country, in addition to morbidity, 

disability and mortality [1]. Notably, women's health and well-being are severely 

impacted by the rising challenge of cancer disease in the community, which 

hinders them from serving their crucial role in any rising and developed nations. 

The burden of cancer among women is high in both High Income Countries 

(HICs) and Low Middle Income Countries (LMICs), although the distribution of 

most common cancers differs. This burden is predicted to extend as populations 

grow and age and because the prevalence of cancer risk factors increases in some 

countries, especially in LMICs. The costs of cancer are considerable and even 

catastrophic in HICs and LMICs alike. However, this burden of disease, loss of 

life, and economic hardship is not inevitable [2]. All of the foremost common 

cancers among women worldwide, including lung, breast, cervix, liver, and 

colorectum, have known means of prevention and/or early detection, which may 

be used to cut back incidence and mortality. Furthermore, carcinoma and cervical 

cancer, two of the highest four cancers in women worldwide have several proven 

prevention measures [3]. These two cancers combined represent about 20% of all 

cancer deaths among women [4]. 



 

 

Rashed and Eissa 2020                                                                                           Long-Term Quantitative Assessment of Women Survivability from Cancer 

 

 

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Many of those deaths may be prevented through 

effective tobacco control, vaccination, and screening 

activities. There are varieties of effective cancer control 

measures available to countries of all resource levels [4]. 

Many of those measures are extremely cost-effective given 

the lives saved for the cost of the intervention, especially 

within the case of vaccination. To stop cancer within the 

future, countries must prioritize policies to cut back known 

cancer risk factors and make prevention accessible to any or 

all. For those that have cancer today, effective treatments 

and palliative care are also needed. Additionally, to those 

needs, cancer surveillance and research for the prevention 

and treatment are indispensable for the setting of cancer 

control priorities and for determining the foremost effective 

interventions and coverings in an exceedingly given context 

[4]. For LMICs, all of those activities may require support 

and commitment from the worldwide community. 

While malignant diseases are holding and exhaustive 

and comprehensive databases that were collected from 

extensive surveys and gathering centers from national and 

international organizations, it is the interpretation of the 

results that would derive useful conclusions and insight 

through record’s pattern [5, 6]. The application of Statistical 

Process Control (SPC) methodologies was historically 

started at the end of the first quarter of the 20
th

 century in the 

industrial field the monitoring, control and improvement of 

the manufacturing processes as well as product quality 

by Walter A. Shewhart at Bell Laboratories [7, 8]. In 

addition to the wide industrial applications, SPC techniques 

have been applied even in the improvement of service fields. 

Moreover, SPC techniques were found to be useful in 

other non-industrial fields for assessment, evaluation and 

investigation of specific inspection properties or events [9, 

10]. Some interesting fields of implementation include - but 

not limited to - environmental monitoring (EM), 

microbiological water quality, surgical site infection, 

epidemiological diseases and outbreaks [11-15]. The 

previous studies embraced control charts, Pareto diagrams, 

Box-and-Whisker plots, distribution identification, 

correlation analysis and fitted line curves, in addition to 

other conventional analysis tools such as descriptive 

statistics. While epidemiological diseases constitute a 

continuous threat that strike humanity, it would be useful to 

develop a quantitative descriptive tool that describes the 

progression and behavior of these diseases.  

One of the important indicators that could provide 

insight into cancer progression is the mortality ratio of the 

patients that could be found in the database of national and 

international health organizations. The application of 

statistical tools and process control methodologies was 

sought as a unique metric means in the evaluation and 

comparison of the epidemiological status that could support 

in the decision-making and cancer management and control. 

Accordingly, the present analysis might reveal new horizons 

for researchers to a simple, fast and useful way to study 

other diseases, outbreaks and pandemics. 

Materials and Methods 

SPC Perspective of Long-Term Global Trend of Cancer 

in Women  

Cancer mortality rates records of different countries 

were obtained as a downloadable database file from the 

websites: https://www.cancer.gov/ and https://www.who.int/ 

[16, 17] and women data were extracted from the Excel file 

by filtering and arranged chronologically (Table S1). Three 

different computer programs were used in data processing 

combined as statistical software platform viz Prism - 

GraphPad v6.01, Minitab v17.1.0 and Excel built-in 

XLSTAT v2014.05.03 [18-21]. The Prism - GraphPad 

v6.01 commercial scientific software was used for the 

preliminary data description followed by defining the 

significance estimation of the change of the yearly mortality 

rates with time. The Excel built-in XLSTAT v2014.05.03, 

which is a statistical suite add-in, was used for drawing of 

Gaussian Mixture Model (GMM), which is a probabilistic 

model to spot typically disseminated subpopulations inside a 

general populace. Blend models, as a rule, do not require 

prior knowledge of datasets subordination to the subgroup, 

permitting the model to become familiar with the 

subpopulations spontaneously [22]. Thus, it will be 

important in this case for viewing the overall data-clustering 

pattern for the record from 1960 to 2017.  

On the other hand, Minitab as a statistical tool package 

was assigned for fitting line modeling, box plot creation, 

histogram drawing and data trending using process behavior 

chart [23]. Two-dimensional data segregation was done 

based on GMM and individual countries found in the record 

to identify clustering pattern of data. Construction of the 

mean (X-bar)-variation (  -S) trending chart was executed 

according to the distribution identification scheme in 

Minitab. Shewhart charts show mean of the death rate and 

the standard deviation along with the event window i.e. 

Upper Control Limit (UCL) and Lower Control Limit 

(LCL). 

Results and Discussion 

Descriptive Statistics and Correlation Output 

        A preliminary examination of the database for the basic 

statistical analysis yielded a result in Table 1 showing the 

coinciding countries with the annual values. Data are mildly 

positive or right-skewed [24]. Failure to comply with 

normality distribution was followed by the screening of the 

closest possible spreading pattern that might fit the record. 

A Weibull distribution hypothesis could not be rejected as a 

suitable fit for the raw dataset based on the Anderson-

Darling test (AD). 

https://en.wikipedia.org/wiki/Walter_A._Shewhart
https://en.wikipedia.org/wiki/Bell_Laboratories


 

 

Rashed and Eissa 2020                                                                                           Long-Term Quantitative Assessment of Women Survivability from Cancer 

 

 

Highlights in BioScience                                                                                                                                                                           July 2020| Volume 3 

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Table 1: Descriptive statistics of the cancer mortality rates showing the number of deaths per 100000 individuals at CI
*
 95% 

and the corresponding countries numerically to the parameters value using Prism - GraphPad v6.01 

Column Statistics Mortality Rates (per 100000) Concerned Department 

Minimum 93.30    TUR 2009  

25% Percentile 159.1    ZAF 2005  

Median 183.8    AUS 1963, FIN 1984, POL 1985  

75% Percentile 205.4  
  GBR 1962, FIN 1964, CHL 1991, 

NLD 1997  

Maximum 286.4    ISL 1960  

10% Percentile 140.9    GRC 1983  

90% Percentile 227.4    LUX 1984, CZE 1996  

Arithmetic Mean 183.2    SWE 1987  

Std. Deviation 32.85 NA 

Std. Error of Mean 0.7461 NA 

Lower 95% CI of mean 181.8    AUS 1975, FIN 1980, CRI 1990  

Upper 95% CI of mean 184.7  

  SWE 1984, SVN 1988, NOR 

2003, NZL 2010, CZE 2012, GBR 

2016  

Lower 95% CI of median 181.8    AUS 1975  

Upper 95% CI of median 185.4    SWE 1983 and 1988, ITA 1990  

Shapiro-Wilk normality test 

 W 0.9973 

 

P value 0.0017 NA 

Data passing normality test (alpha=0.05) No  

Coefficient of variation 17.93%  

Geometric mean 180.2    SVK 2006, ISL 2010  

Lower 95% CI of geo. mean 178.7    POL 2011  

Upper 95% CI of geo. mean 181.7    EST 1990  

Method of outlier detection: ROUT
ε
 (Q 

= 10.00%) 
No aberrant record  

NA 

Skewness 0.04484 NA 

Kurtosis -0.3441 NA 

*CI = Confidence Interval
 
;
 
NA = Not Applicable;  ε Robust regression and Outlier removal 

 

No aberrant values could be detected through the 

overall record. Thus, mortality rates showed apparent 

concatenation in the values with a range of 193.1 

deaths/100000 cases with half and four-fifths of data record 

resides within a range of 46.3 and 86.5 deaths/100000 cases, 

respectively, suggesting extensive tailing. The mean and the 

median were almost coincided with the geometric mean very 

close to the average confirming that there is no extreme 

value(s) distant from the group collectively [25]. However, 

the arithmetic mean is slightly greater than that of the 

geometric mean as expected for the basic rule in 

mathematics [26]. This gap is reflected similarly on the 

Confidence Intervals (CIs) which showed the corresponding 

shift too. The relative standard deviation (RSD) showed 

significant dispersion of data around the mean of about 

18%. In addition, Kurtosis value suggests data broadening 

with shoulders that is a variation from the normal bell-

shaped spreading if the normal distribution is expected, a 

sign of possible mixed intervening patterns [24]. This would 

probably be the result of the impact of annual and regional 

variations that was reflected in the total record of women 

cancer mortality. Table 2 demonstrates the moderately 

negative correlation between the women mortality rates and 

the time in years [27, 28]. Accordingly, there was an 

improvement of women survivability with time passing, 

which might be partially attributed to the development of 

effective detection and control measures for the containment 

of cancer epidemiology [29]. 

Dataset Clustering Approaches: A Multidimensional 

Analysis         

        Data stratification using GMM analysis estimated two 

possible mixed bell-shaped spreading, indicating a global 

overlapping distribution of mortality rates among the studied 

nations in Figure 1.  



 

 

Rashed and Eissa 2020                                                                                           Long-Term Quantitative Assessment of Women Survivability from Cancer 

 

 

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Table 2: Non-parametric correlation of the mortality rates 

from malignant diseases versus time (in years) at CI 95% 

with two-tailed P-value using Prism - GraphPad v6.01 

 

Spearman (r) 
Time versus Death Rate 

Interpretation 

 r  -0.4110 

 95% CI
*
  -0.4484 to -0.3721 

 P (two-tailed)  < 0.0001 

 P value summary  ****  

 True or asymptotic P value  

calculation
**

 
 Asymptotic 

 Significance  at α = 0.05  Yes 

 Number of paired XY   1938 
*CI = Confidence Interval; **Refer to the calculation method of p-

value using either the exact or approximation to the actual 

distribution;  ****P ≤ 0.0001 

 

Cumulative Distribution Function (CDF) and Q-Q 

plots showed the convenience of this assumption. The first 

and the second distributions were called (Φ Phi) and (Ψ Psi) 

with contribution proportions 0.57 and 0.43, respectively 

(Figure 1).  However, there was no clustering tendency that 

could show any heterogeneity according to the Normalized 

Entropy Criterion (NEC), which was greater than one with 

the selected the Integrated Completed Likelihood (ICL) 

criterion with the standard algorithm (EM) Expectation 

Maximization [30]. The means and covariances of Φ and Ψ 

for malignancy mortality rates in women were 222.7, 241.0 

and 1892.4, 909.9, respectively. 

 
Figure 1: Dataset segregation, based on Gaussian Mixture 

Model (GMM) approach, showing two mixed distribution 

pattern with low (green) and high (pink) rates of mortality 

from malignancy, generated using XLSTAT v2014.05.03. 

 

The geographically based data segregation shows that, 

ascendingly, Turkey, the Republic of Korea, Brazil, Mexico 

and Greece demonstrated the lowest average mortality rate 

values could be demonstrated in Figure 2. While countries 

with the ascending order from the lowest order of 

survivability to the highest means were Denmark, Hungary, 

Ireland, Czechia, GBR and Netherlands (Figure 2). 

 

Figure 2: Dataset segregation, based on WHO geographical distribution by countries shown as Box plot, indicating the means, 

data spreading and the aberrant annual mortality rates records generated using Minitab v17.1.0.



 

 

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The highest mortality rates from cancer occurred 

primarily in the EUR region with the domination of 

economically rich nations suggesting that the overall 

survivability of women from cancer depends on other 

factors that seemed to be important to be controlled in 

addition to the improvement of the healthcare quality. This 

assumption might be partially in agreement with previous 

analysis provided by some researchers that had linked the 

prevalence of some types of cancer in the high-income 

countries with some adverse lifestyles such as smoking, 

obesity and alcohol consumption [31, 32]. Nevertheless, it 

should be noted that beforehand rigorous control, awareness 

and actions taken about cancer detection and diagnosis 

associated with controlled monitoring might be one of the 

important reasons for the comprehensiveness of data records 

of high-income and developed nations if compared with 

those from the relatively lower income-countries. This 

hypothesis may be a factor that contributed to a possible 

underestimation of the actual overall estimation of the 

mortality rates in the developing and low-income countries. 

The time-based data segregation shows that, Europe 

WHO region was the most versatile with divergent mortality 

rates between nations, as it is rich with country data, in 

contrast to the African area that includes only South Africa. 

This could also be seen on the extend of the outlier figures 

(denoted by asterisks) above and below the box plot graphs 

in Figure 3. South Africa data record only started in 1993, 

which is later than the other three regions by 33 years and 

reaching its peak in 1999 (Figure 3). The annual spreading 

of death cases rates for AMR and WPR was less than that of 

EUR. However, the distribution of WPR values was 

generally more compact than that of AMR, where greater 

pervasion could be observed between annual records. The 

general profile can be seen in Figure 3 with the yearly 

steady and almost regular decline in death rates started with 

AMR in late 1980s, EUR and WPR at almost 1995. 

 

Figure 3: Dataset segregation based on WHO geographical distribution by time order shown as Box plot, indicating data 

spreading and the aberrant mortality rates records generated using Minitab v17.1.0.

 



 

 

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Fitted Line of Yearly Average Death Rates from Cancer 

for the Affected Women Populations versus Time 

Dataset pattern showed a steady decline in the global 

mortality rates from cancer after the initial high plateau that 

could be demonstrated by the quadratic relation with 

significant correlation (Figure 4). The regression equation 

was expressed through Polynomial Regression Analysis of 

average mortality rates from cancer for women versus the 

time (in years).  

Log10 (Y) = - 10245 + 6222 Log10 (T)- 944.5 Log10 (T)2…eq.(1) 

Where: Y and T are the years and death rates from cancer 

worldwide were recorded for women, respectively, with S = 

0.00577903, R-Sq and R-Sq(adj) = 97.0%. Figure 4 

illustrates this relation between death rates and years 

graphically. 

 

 

Figure 4: Polynomial regression analysis graph showing 

quadratic equation modeling, Confidence Interval (CI) and 

Prediction Interval (PI) along with R
2
 and the Standard 

Error of the Regression (S), generated using Minitab 

v17.1.0. 

Trending of Global Women Survivability from 

Malignancy Using Process-Behavior Chart 

In Figure 5, Histogram showed a pattern of dual hump 

that could be explained from GMM model. Boxplot graph is 

indicative of the pattern for the studied WHO regions 

(Figure 5). AFR demonstrated the lowest mean and 

spreading due to the inclusion of ZAF only for relatively a 

short period from the region, in contrast of EUR with upper 

and lower aberrant records from some countries in the 

European region from Island (1960) and Turkey (2009, 

2010 and 2011). The survivability rate in WPR is better that 

AMR. Analysis of the distribution fitting showed the 

convenience of the Weibull distribution based on the 

probability plot examination as could be observed in Figure 

5. Plots the method mean (Xbar chart) and method standard 

deviation (S chart) over time for variable information in 

subgroups (Figure 5). This dual type of control chart is 

extensively used to observe the steadiness of procedures in 

lots of fields. Both the Xbar and S charts are displayed 

together due to the need to interpret each chart to decide if 

the trend is stable [32]. The procedure variation in s chart 

was almost stable within the control limits and tendency 

toward lower annual variation since 1979. The Xbar chart in 

Figure 5 showed initially intermittent excursions in the first 

few years followed by a successive shift in the annual 

mortality means leading to a declining curve with the 

improvement of survivability over time until exceeding the 

lower bound, which is a desirable outcome [33]. The last 

record of 2017 was incomplete during data registration that 

may explain the apparently sudden rise in mortality ratio due 

to the inclusion of few countries with high values in the 

process-behavior chart of Figure 5.

Figure 5: SPC analysis tools, (control chart, histogram and box plot) of the global cancer mortality rates in women with 

Weibull probability fitting plot, showing the overall trend of the annual death rates as   -S control chart and the pattern of 

WHO regions as box and whisker plot, generated using Minitab v17.1.0.



 

 

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Conclusion 

SPC methodologies could provide a unique insight into 

the characteristics and patterns of epidemiological diseases. 

Quantitative assessment of mortality and/or morbidity levels 

may be a useful indispensable tool in management and 

future decision-making. Further studies are crucial to access 

the absolute number of deaths since using the ratio record 

alone may not reflect the real progression of the disease. For 

instance, the annual increase in the number of cancer 

patients may counterbalance the efforts to control deaths and 

the actual yearly mortality number could be a rising 

challenge to the efforts of cancer healthcare sector due to 

exacerbation of cancer epidemiology. In addition, the 

accuracy of the investigation and analysis is largely 

dependent on the Impartialness and comprehensiveness of 

the database. However, cancer researchers could adopt 

similar techniques to track different types of malignancies in 

their countries over time to access the changes in the 

epidemiological pattern and the effectiveness of the control 

measures. The application of SPC methodologies would be 

encouraged to be projected in future studies of other 

diseases such as Coronavirus disease (COVID-19) global 

cases. 

Supplementary Files 

The Supplementary Material for this article can be found 

online at: https://doi.org/10.36462/H.BioSci.20208   

 

Supplementary Table S1: List of countries whose data have 

been used in this study and their corresponding abbreviation. 

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