Coronavirus Cases in Australia
Project 1
Jiayu Sun 510098700 jzha7127:480362427 Tian Chen 500182596 Yanlin Zhu 510230687
University of Sydney | Math 1005 | May 2021
1 Executive Summary
The report aimed initially to investigate the inter-relationship between mortality rate with ICU and Ventilation cases. The interactions between these variables were explored graphically and numerically through RStudio using Australia’s Covid-19 data. It then investigated differences within the patterns of confirmed cases on a monthly scale, in order to extrapolate upon if their subsequent relationship affected mortality rates. Similarly, the second research question was explored graphically and numerically through RStudio using Australia’s Covid-19 data. The data itself was aggregated from covid19data.com.au, which subsequently has been verified with federal, state and territory health departments. Within the data set there are 13 variables present, consisting of 11 quantitative discrete variables and 2 qualitative ordinal variables. The first research question would be analysed using multiple linear regression models, where concluding statements will be based upon qualitative interpretations of the correlation between the variables within the models. The second research question required the use of histograms and boxplots to compare the number of confirmed cases on a monthly basis. Linear regression models would then be used to detect if the patterns of confirmed cases on mortality rate was statistically significant.
2 Initial Data Analysis (IDA)
COVID_during_20200125_20210418 <- read.csv("COVID_during_20200125_20210418.csv")
# Quick look at top 6 rows of data1
head(COVID_during_20200125_20210418)## date confirmed deaths tests positives recovered hosp icu vent vaccines
## 1 2020/1/25 4 0 0 0 0 0 0 0 0
## 2 2020/1/26 4 0 0 0 0 0 0 0 0
## 3 2020/1/27 5 0 0 0 0 0 0 0 0
## 4 2020/1/28 5 0 0 0 0 0 0 0 0
## 5 2020/1/29 9 0 0 0 0 0 0 0 0
## 6 2020/1/30 9 0 0 0 0 0 0 0 0## Size of data1
dim(COVID_during_20200125_20210418)## [1] 450 10## R's classification of data1
class(COVID_during_20200125_20210418)## [1] "data.frame"## R's classification of variables for data1
str(COVID_during_20200125_20210418)## 'data.frame': 450 obs. of 10 variables:
## $ date : chr "2020/1/25" "2020/1/26" "2020/1/27" "2020/1/28" ...
## $ confirmed: int 4 4 5 5 9 9 9 10 12 12 ...
## $ deaths : int 0 0 0 0 0 0 0 0 0 0 ...
## $ tests : int 0 0 0 0 0 0 0 0 0 0 ...
## $ positives: int 0 0 0 0 0 0 0 0 0 0 ...
## $ recovered: int 0 0 0 0 0 0 0 0 0 0 ...
## $ hosp : num 0 0 0 0 0 0 0 0 0 0 ...
## $ icu : int 0 0 0 0 0 0 0 0 0 0 ...
## $ vent : int 0 0 0 0 0 0 0 0 0 0 ...
## $ vaccines : int 0 0 0 0 0 0 0 0 0 0 ...2.0.1 IDA complexity:
The data contained 10 variables which all displayed the related data of COVID-19 in Australia. However, the variable of the total population in Australia is less related in this data set. Therefore, we changed to 9 variables to be used in Rstudio. These variables included confirmed cases, deaths, tests, positive cases, hospitalization, people who lived in ICU and used ventilation to breathe. The raw data began from 2020-01-25 to 2020-08-13. The data would be extremely complex if input all the data given in the source. Additionally, it’s accumulated for confirmed cases. The correlation will in ascending order only if the confirmed cases are accumulated. Thus, we clean the data set in to daily. Besides, we changed the variables from qualitative to quantitative. In other words, we changed the data into ordinal vector. This method would clarify graphs shown with these data. The main challenge was to clean the data, to code easier in Rstudio.
2.0.2 IDA classification:
9 variables used in this project were divided into two sets of data. One set is classified as cumulative qualitative cases, whereas another set is for daily quantitative cases. Date is an ordinal continuous variable, it could be recorded as both qualitative and quantitative. It reports the order of the day and reveals the period length. However, it is optimal to record it as quantitative data, as one may be willing to give a date category. On the other side, the other 8 variables, such as confirmed cases, tested positives cases, recovered cases, ICU cases, deaths, hospitalized cases, and vaccines are categorised as numerical discrete, quantitative variables. Only whole integers are involved in these data sets , as the number of testings cannot have decimals. To summarize and obtain results, mean and median were used for calculation.
2.0.3 IDA data quality:
Our data has originated from statistics provided by Australian governments at federal, state and territory levels, aggregated from www.covid19data.com.au, with data from 25/1/20 - 18/4/21 being utilized for this project. The data was voluntarily collated by Bolton (2021) with collaborators to provide statistics of COVID-19 in Australia summarized as a whole. We noticed that the data was not directly retrieved from the official platform, thus we have checked the accuracy by sampling survey on several random days and confirmed the collated data is accurate and authentic. However, there are still some limitations within the data. Firstly, the data was collected by summing the statistics from each state and territories from Australia, so there may be an error value in the final data statistic because of the different statistical criteria in each district. Moreover, after analysing the data of ICU and ventilator, it shows that the ventilator was not adequate for each ICU patient, which will be explored in more detail within research question 2.
2.1 Domain Knowledge
Coronavirus disease 19 (Covid-19) was first identified during December 2019 in Wuhan China and was formally declared a global pandemic by the World Health Organisation (WHO) on March 11,2020. Covid-19’s impact has not only effected public health, as its drastic influence has reached many other sectors of the economy, resulting in global turmoil. This is elucidated by its pathology, where it is transmitted through physical contact and airborne mechanisms. Hence, Covid-19 is depicted as highly contagious and hard to detect, augmenting its prevalence in society. Universally, the symptoms of covid-19 included cough, sore throat, fatigue, runny nose, and fever, where most individuals who contracted the virus recovered without severe medical intervention. However, it was estimated that 20% of global cases resulted in severe medical implication, leading to shortness of breath and pneumonia. These cases were most prominent in immunocompromised individuals, requiring the need for hospitalization, ICUs, and ventilators. The increased demand for medical interventions and equipment resulted in a shortage of supplies, adversely influencing its incidence of mortality in many countries. Fortunately, Australia imposed strict health and border policies throughout the earlier stages of Covid-19, effectively mitigating the transmission rate. This resulted in reduced cases, mortality, and hospitalisation for Covid-19, relative to other nations. Hence, exploring the corresponding results induced by the mechanisms underpinning Australia’s success to Covid-19, serves as an exemplar response model for other nations, and should be further investigated.
3 Research queation 1
COVID_during_20200125_20210418 <- read.csv("COVID_during_20200125_20210418.csv")
COVID_during_20200125_20210418 <- read.csv("COVID_during_20200125_20210418.csv")
View(COVID_during_20200125_20210418)
COVID_during_20200125_20210418[c(1:450),c(2,3)]## confirmed deaths
## 1 4 0
## 2 4 0
## 3 5 0
## 4 5 0
## 5 9 0
## 6 9 0
## 7 9 0
## 8 10 0
## 9 12 0
## 10 12 0
## 11 13 0
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## 450 29519 910 data=COVID_during_20200125_20210418[c(1:450),c(2,3)]
data [] <- lapply(data, function(x) diff(c(0, x)))
confirmed=data$confirmed
deaths=data$deaths
plot(confirmed, deaths, main="Scatterplot")
pop.1 <- lm(deaths ~ confirmed)
abline(pop.1, col=2, lwd=3)
hist(residuals(pop.1))
plot(pop.1)
cor(confirmed, deaths)## [1] 0.4437132 shapiro.test(residuals(pop.1))##
## Shapiro-Wilk normality test
##
## data: residuals(pop.1)
## W = 0.4958, p-value < 2.2e-16 confint(pop.1, level=0.99)## 0.5 % 99.5 %
## (Intercept) 0.11280890 1.41392011
## confirmed 0.01445352 0.02392759The first research question investigated differences within the patterns of confirmed cases on a monthly scale, evaluating if the relationship of their subsequent difference on mortality rates was statistically relevant
4 Research Question 2
data2=read.csv("covid.txt")
options(max.print=1000000)
data2[c(1:450),c(2,8:9)]## confirmed icu vent
## 1 4 0 0
## 2 4 0 0
## 3 5 0 0
## 4 5 0 0
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## 450 29519 3 0data2= data2[c(1:450),c(2,8:9)]
data2 [] <- lapply(data2 , function(x) diff(c(0, x)))
confirmed=data2$confirmed
icu=data2$icu
vent=data2$vent
class(confirmed)## [1] "numeric" class(icu)## [1] "numeric" class(vent)## [1] "numeric" plot(confirmed, icu, main="Scatterplot")
cor(confirmed, icu)## [1] 0.159778 mod.1 <- lm(icu ~ confirmed)
plot(mod.1)
abline(mod.1, col=2, lwd=3)
par(mfrow=c(2,2))
summary(mod.1)##
## Call:
## lm(formula = icu ~ confirmed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.269 -0.611 0.267 0.313 68.781
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.328300 0.204700 -1.604 0.109461
## confirmed 0.005106 0.001491 3.426 0.000669 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.815 on 448 degrees of freedom
## Multiple R-squared: 0.02553, Adjusted R-squared: 0.02335
## F-statistic: 11.74 on 1 and 448 DF, p-value: 0.0006693 confint(mod.1, level=0.99)## 0.5 % 99.5 %
## (Intercept) -0.857827707 0.201228221
## confirmed 0.001250596 0.008962141 anova(mod.1)## Analysis of Variance Table
##
## Response: icu
## Df Sum Sq Mean Sq F value Pr(>F)
## confirmed 1 170.8 170.814 11.737 0.0006693 ***
## Residuals 448 6520.2 14.554
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1hist(residuals(mod.1))
boxplot(residuals(mod.1))
shapiro.test(residuals(mod.1))##
## Shapiro-Wilk normality test
##
## data: residuals(mod.1)
## W = 0.33473, p-value < 2.2e-16 plot(confirmed, vent, main="Scatterplot")
cor(icu, vent)## [1] 0.4510595 mod.2 <- lm(vent ~ icu)
plot(mod.2)
abline(mod.2, col=2, lwd=3)
par(mfrow=c(2,2))
summary(mod.2)##
## Call:
## lm(formula = vent ~ icu)
##
## Residuals:
## Min 1Q Median 3Q Max
## -26.4317 0.0029 0.0029 0.0029 27.9606
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.002897 0.156667 -0.018 0.985
## icu 0.434615 0.040629 10.697 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.323 on 448 degrees of freedom
## Multiple R-squared: 0.2035, Adjusted R-squared: 0.2017
## F-statistic: 114.4 on 1 and 448 DF, p-value: < 2.2e-16 confint(mod.2, level=0.99)## 0.5 % 99.5 %
## (Intercept) -0.4081700 0.4023752
## icu 0.3295137 0.5397162 anova(mod.2)## Analysis of Variance Table
##
## Response: vent
## Df Sum Sq Mean Sq F value Pr(>F)
## icu 1 1263.9 1263.86 114.43 < 2.2e-16 ***
## Residuals 448 4948.1 11.04
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 hist(residuals(mod.2))
boxplot(residuals(mod.2))
shapiro.test(residuals(mod.2))##
## Shapiro-Wilk normality test
##
## data: residuals(mod.2)
## W = 0.39496, p-value < 2.2e-16 plot(confirmed, vent, main="Scatterplot")
cor(confirmed, vent)## [1] 0.2151266 mod.3 <- lm(vent ~ confirmed)
plot(mod.3)
abline(mod.3, col=2, lwd=3)
par(mfrow=c(2,2))
summary(mod.3)##
## Call:
## lm(formula = vent ~ confirmed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.2948 -0.2611 0.3484 0.3948 31.4273
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.434559 0.195126 -2.227 0.0264 *
## confirmed 0.006625 0.001421 4.663 4.13e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.637 on 448 degrees of freedom
## Multiple R-squared: 0.04628, Adjusted R-squared: 0.04415
## F-statistic: 21.74 on 1 and 448 DF, p-value: 4.127e-06 confint(mod.3, level=0.99)## 0.5 % 99.5 %
## (Intercept) -0.939320521 0.07020166
## confirmed 0.002949174 0.01030004 anova(mod.3)## Analysis of Variance Table
##
## Response: vent
## Df Sum Sq Mean Sq F value Pr(>F)
## confirmed 1 287.5 287.488 21.739 4.127e-06 ***
## Residuals 448 5924.5 13.224
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 hist(residuals(mod.3))
boxplot(residuals(mod.3))
shapiro.test(residuals(mod.3))##
## Shapiro-Wilk normality test
##
## data: residuals(mod.3)
## W = 0.40206, p-value < 2.2e-16 options(max.print=1000000)
DATA1 = read.csv("data_for_project_1.csv")
DATA1[c(2:450),c(1,2,3)]## \u9518\u7e1eonfirmed icu vent
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## 450 14 3 0 DATA3= DATA1[c(2:450),c(1,2,3)]
DATA3 [] <- lapply(DATA3, function(x) diff(c(0, x)))
class(confirmed)## [1] "numeric" class(icu)## [1] "numeric" class(vent)## [1] "numeric" plot(confirmed, icu, main="Scatterplot")
cor(confirmed, icu)## [1] 0.159778 mod <- lm(icu ~ confirmed)
summary(mod)##
## Call:
## lm(formula = icu ~ confirmed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.269 -0.611 0.267 0.313 68.781
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.328300 0.204700 -1.604 0.109461
## confirmed 0.005106 0.001491 3.426 0.000669 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.815 on 448 degrees of freedom
## Multiple R-squared: 0.02553, Adjusted R-squared: 0.02335
## F-statistic: 11.74 on 1 and 448 DF, p-value: 0.0006693
## Summary The second research question investigated differences within the patterns of confirmed cases on a daily scale, evaluating if the relationship of their subsequent difference on mortality rates was statistically relevant
- Both data.1, and data.3 displayed a weak linear regression relationship, with respective R^2 values of 0.2824 and 0.2232. Hence, the power for drawing conclusive statements for projected ICU incidence and ventilator-usage from daily confirmed cases is limited. This challenged the initial assumption, which projected a strong linear relationship between daily confirmed cases with ICU incidence and ventilator-usage. Furthermore, the residual plots for both linear regression models highlighted an ununiform distribution of the OLS residuals However, the conflicting results presented new insights to uncover if the linear association of confirmed cases with ICU incidence and ventilator-usage differed throughout varying time intervals.
- Data.2, which depicted the inter-relationship between the variables ICU, and Vent displayed a strong linear regression relationship. This is evidenced by the R^2 value of 0.873, indicating that 87.3% of the variance for cumulative ventilator-usage can be explained by the variance for cumulative ICU incidence within the regression model. Hence, 87.3% of the data points for predicted ventilator-usage are aggregated close to the fitted regression line, augmenting the predictive model for ventilator-usage and ICU incidence. Furthermore, the predictive model is further enhanced by a 0.93 correlation coefficient between the two respective variables, indicating a strong linear relationship. However, similarly to data.1 and data.3, the discrepancy between the minimum and maximum residuals from the median poses a limitation as it indicates ununiform distribution of residuals.