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 to investigate the inter-relationship between mortality rate with ICU and Ventilation cases. Interactions between these variables were explored graphically and numerically through RStudio using Australia’s Covid-19 data. Differences within patterns of daily confirmed cases were then investigated and extrapolated upon to evaluate their effect mortality rates. Similarly, the second research question was explored graphically and numerically through RStudio using Australia’s Covid-19 data. The main insight derived from question 1 alluded to enhanced healthcare in Australia as daily confirmed case couldn’t project mortality rates. Question 2 highlighted weak linear relations of ventilator and ICU cases from daily confirmed cases. Conversely, a strong relationship predicting ventilator-usage from ICU cases was noted and further explored to understand how the robust relationship was achieved and the impacts of raw data upon analysis. Hence, it signifies the increased availability of medical instruments, further augmenting Australia’s enhanced healthcare.
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:
Within the raw dataset there were 16 variables presents, consisting of 10 quantitative discrete variables and 6 qualitative ordinal variables. The data was cleaned to omit qualitative variables within the raw dataset, leaving behind 10 quantitative discrete variables. The remaining quantitative variables were presented on a cumulative basis but was subsequently manipulated into daily data with the exception of date. Further cleaning was required for the categorical variable date, where it was transformed into an ordinal vector. Consequently, it enabled enhanced clarity during coding and formulating numerical and graphical summaries graphs.
2.0.2 IDA classification:
4 variables were used in this project, i.e., confirmed cases, deaths, ICU incidence and ventilator usage. The qualitative variables exist in the raw data was omitted, resulting in only quantitative variables left. Among them confirmed cases and deaths were ordinal classified as cumulative qualitative cases. The logic delineating this change was due to the unidirectional flux of cumulative data for confirmed cases and deaths. Furthermore, date is an ordinal continuous variable, which was then categorized into an ordinal vector. Hence, it was inappropriate as it heavily impacts the results Therefore, summarizing and obtaining reliable results, required manipulation of the respective variables into daily quantitative daily data.
2.0.3 IDA data quality:
The data pertained from the dates 25/1/20 - 18/4/21 and was aggregated from covid19data.com.au, which subsequently has been verified with federal, state and territory health departments. Within the data set there are 16 variables presents, consisting of 10 quantitative discrete variables and 6 qualitative ordinal variables. 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, a strong correlation data between ICU and ventilator was observed, where it will be further explored in within research question 2.
2.1 Domain Knowledge
Coronavirus disease 19 (Covid-19) was first identified during December 2019 in Wuhan China and was formerly 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
options(max.print=1000000)
project_1 <- read.csv("project_1.csv")
project_1[c(1:450),c(2,3,4)]## confirmed icu vent
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## 450 14 3 0 data2= project_1[c(1:450),c(2,3,4)]
data2 [] <- lapply(data2, function(x) diff(c(0, x)))
confirmed=project_1$confirmed
icu=project_1$icu
vent=project_1$vent
class(confirmed)## [1] "integer" class(icu)## [1] "integer" class(vent)## [1] "integer" plot(confirmed, icu, main="Scatterplot")
cor(confirmed, icu)## [1] 0.5330952 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
## -47.750 -6.823 -5.913 1.390 80.304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.098493 0.932355 6.541 1.67e-10 ***
## confirmed 0.090547 0.006789 13.337 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.38 on 448 degrees of freedom
## Multiple R-squared: 0.2842, Adjusted R-squared: 0.2826
## F-statistic: 177.9 on 1 and 448 DF, p-value: < 2.2e-16 confint(mod.1, level=0.99)## 0.5 % 99.5 %
## (Intercept) 3.6866315 8.5103541
## confirmed 0.0729838 0.1081098 anova(mod.1)## Analysis of Variance Table
##
## Response: icu
## Df Sum Sq Mean Sq F value Pr(>F)
## confirmed 1 53727 53727 177.86 < 2.2e-16 ***
## Residuals 448 135326 302
## ---
## 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 = 0.71024, p-value < 2.2e-16 plot(confirmed, vent, main="Scatterplot")
cor(icu, vent)## [1] 0.9331518 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
## -22.8259 -0.6306 -0.1152 0.3694 10.5968
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.115188 0.222980 0.517 0.606
## icu 0.515451 0.009382 54.943 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.079 on 448 degrees of freedom
## Multiple R-squared: 0.8708, Adjusted R-squared: 0.8705
## F-statistic: 3019 on 1 and 448 DF, p-value: < 2.2e-16 confint(mod.2, level=0.99)## 0.5 % 99.5 %
## (Intercept) -0.4616276 0.6920043
## icu 0.4911821 0.5397192 anova(mod.2)## Analysis of Variance Table
##
## Response: vent
## Df Sum Sq Mean Sq F value Pr(>F)
## icu 1 50229 50229 3018.7 < 2.2e-16 ***
## Residuals 448 7454 17
## ---
## 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 = 0.72339, p-value < 2.2e-16 plot(confirmed, vent, main="Scatterplot")
cor(confirmed, vent)## [1] 0.4721358 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
## -34.175 -4.023 -3.636 0.949 40.769
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.414384 0.536602 6.363 4.9e-10 ***
## confirmed 0.044297 0.003908 11.336 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10 on 448 degrees of freedom
## Multiple R-squared: 0.2229, Adjusted R-squared: 0.2212
## F-statistic: 128.5 on 1 and 448 DF, p-value: < 2.2e-16 confint(mod.3, level=0.99)## 0.5 % 99.5 %
## (Intercept) 2.02627491 4.80249216
## confirmed 0.03418846 0.05440469 anova(mod.3)## Analysis of Variance Table
##
## Response: vent
## Df Sum Sq Mean Sq F value Pr(>F)
## confirmed 1 12858 12858.4 128.51 < 2.2e-16 ***
## Residuals 448 44825 100.1
## ---
## 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 = 0.78364, p-value < 2.2e-16 options(max.print=1000000)
DATA1 = read.csv("data_for_project_1.csv")
DATA1[c(1:450),c(1,2,3)]## \u9518\u7e1eonfirmed icu vent
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## 450 14 3 0 DATA3= DATA1[c(1:450),c(1,2,3)]
DATA3 [] <- lapply(DATA3, function(x) diff(c(0, x)))
class(confirmed)## [1] "integer" class(icu)## [1] "integer" class(vent)## [1] "integer" plot(confirmed, icu, main="Scatterplot")
cor(confirmed, icu)## [1] 0.5330952 mod <- lm(icu ~ confirmed)
summary(mod)##
## Call:
## lm(formula = icu ~ confirmed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -47.750 -6.823 -5.913 1.390 80.304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.098493 0.932355 6.541 1.67e-10 ***
## confirmed 0.090547 0.006789 13.337 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 17.38 on 448 degrees of freedom
## Multiple R-squared: 0.2842, Adjusted R-squared: 0.2826
## F-statistic: 177.9 on 1 and 448 DF, p-value: < 2.2e-16
## Summary investigated the extent to which the inter-relationship between daily confirmed cases, ICU incidence, and ventilator-usage can serve as a predictive model. Data.1, and DATA1 displayed weak linear relationships for residuals, with respective R^2 values of 0.2824 and 0.2232. Hence, the power for drawing conclusive statements for predicted ICU incidence and ventilator-usage from daily cases were limited, challenging initial assumptions which projected strong positive correlations between the respective variables. Furthermore, residual plots for both regression models highlighted ununiform distributions that were right skewed. Hence, indicating the presence of exceptionally high outliers, where distribution is biased towards higher values. Therefore, the regression models serve as a poor predictor for ICU incidence and ventilator-usage when considering the quantity of daily cases. The residual discrepancy for both models is explained by the asynchronous reporting of ICU incidence and ventilator-usage during initial stages of Covid-19. It’s elucidated through reports indicating zero cases in ICU and ventilator-usage within the first 66 days of the outbreak, whilst daily confirmed cases progressively increased. Furthermore, it’s augmented by drastic increases in ICU incidence and ventilator-usage between the 67th and 68th day of the outbreak, 70 and 33, respectively. Hence, prior data were accumulated retroactively within the 68th day, explaining the greater degree of heteroscedasticity and absence of zero conditional mean within the models. Furthermore, as daily confirmed cases decreased, similar patterns were not observed for ICU incidence and ventilator-usage, indicating that disease progression occurs past a daily scale. However, conflicting results presented new insights for uncovering differences within these regression models throughout varying time intervals.
Data.2, which depicted the inter-relationship between residuals for variables ICU, and Vent displayed a strong linear relationship. This is evidenced by the R^2 value of 0.873, indicating that 87.3% of variance for cumulative ventilator-usage is explained by the predicator variable, where its closely aggregated around the fitted regression line, and no significant patterns of distribution were noticed within the Residual vs Fitted model. It’s elucidated through the proximity and immediate use of ventilators when required by patients in ICU. Furthermore, domain knowledge has indicated that sufficient quantities of ventilators were available when necessary. Consequently, residuals were relatively less prone to the temporal effects of delayed reporting. The predictive model is further augmented by a 0.93 correlation coefficient between the two variables, establishing their inter-relationship. However, residuals discrepancy between the quantiles poses a limitation as it indicates ununiform distribution of residuals. This was largely influenced by the presence of exceptionally high outliers which skewed the distribution of residuals to the right, observed in the graphical and numerical summaries. However, they were not influential upon the regression line, observed within the Residuals vs Leverage diagnostic plot.
Ultimately, only data.2, predicting ventilator-usage from ICU incidence, presents a viable fit inside the regression model due to the reduced influence of temporal factors during reporting and their proximity within the clinical context.
4 Research Question 2
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(2:450),c(2,3)]## confirmed deaths
## 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
## 12 14 0
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## 450 29519 910 data=COVID_during_20200125_20210418[c(2:450),c(2,3)]
data [] <- lapply(data, function(x) diff(c(0, x)))
View(data)
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] 0.4434641 shapiro.test(residuals(pop.1))##
## Shapiro-Wilk normality test
##
## data: residuals(pop.1)
## W = 0.49626, p-value < 2.2e-16 confint(pop.1, level=0.99)## 0.5 % 99.5 %
## (Intercept) 0.11335931 1.41777799
## confirmed 0.01443909 0.023926694.1 Summary
The first 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 statistic the scatter plot between the response variable was, daily deaths, and the predictor variable, daily confirmed cases, displayed a weak regression relationship, evidenced by the R^2 value of 0.4437. Hence, only 44.37% of variance for daily deaths is explained by the predictor variable. Furthermore, residuals plots indicated ununiform distribution of data, suggesting a strong right-skewed data. Hence, within the regression model, heteroskedasticity and non-constant variance was observed. This was visualised graphically through the residual histogram, indicating that residuals were biased towards higher value. Residual diagnostic plot for scale-location further augmented the uniform distribution of residuals, suggesting a positive correlation between residual variance with the x-axis. Hence, the OLS assumptions were violated within the linear model, depicted by the strongly right-skewed residuals which were not closely aggregated around the fitted regression line. Furthermore, within the Residuals vs Fitted diagnostic plot, a noticeable portion of the residuals were aggregated around the lower fitted values. Consequently, this alluded to an inadequate linear relationship between both variables. Hence, the linear model serves as a poor predictor for projecting mortality rates through daily confirmed cases. Furthermore, the regression line was largely influenced by the presence of exceptionally high outliers, skewing the distribution of residuals to the right as observed in the Residuals vs leverage diagnostic plot. Hence, further signifying patterns heteroskedasticity and non-linearity within the regression model
The discrepancy between residuals within the linear model is elucidated through the domain knowledge. Domain knowledge has indicated that Australia rapidly enacted border and health policies, which limited the transmission of Covid-19 within the population. Furthermore, the mortality rate was dampened as availability of medical instruments were enhanced. Thus, the mortality rate shows a weaker correlation with confirmed cases as time passed. However, it must be noted that mortality progression occurs past a daily scale, varying between individuals. Hence, lag within the recorded data between the respective variable is evident, impacting their correlation. In conclusion, the predicting capacities of the linear model predicting mortality through daily confirmed cases is poor due to advancements within the clinical environment as Covid-19 progressed.
5 Referfencing List
References Australian Financial Review. (2020). Has Australia been too successful in combating COVID-19?. Retrieved from https://www.afr.com/policy/health-and-education/has-australia-been-too-successful-in-combating-covid-19-20201022-p567n7
Bolton, M. (2021). COVID-19 Data Update 2021-4-18. Retrieved from: https://github.com/M3IT/COVID-19_Data/blob/master/Data/COVID19_Data_Hub.csv
Verity, R., Okell, L.O.,Dorigatti ,I., Winskill, P., Whittaker, C., Imai, N. (2020) Estimates of the severity of coronavirus disease 2019: a model-based analysis. THE LANCET Infectious Diseases, 20(6), 669-677. doi 10.1016/S1473-3099(20)30243-7
World Health Organisation. (2020). Archived: WHO Timeline - COVID-19. Retrieved from https://www.who.int/news/item/27-04-2020-who-timeline---covid-19