Student paper on the ongoing research in Brazil

1. 1
Are age and week of first symptoms significant predictors of the number of days from admission
to discharge?
Name:
Institution Affiliation:
Date:

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Table of Contents
Study design.......................................................................................................................................3
Variables............................................................................................................................................3
Hypotheses........................................................................................................................................3
Univariate Analysis .............................................................................................................................4
Bivariate Analysis................................................................................................................................7
Statistical Test and Assumptions........................................................................................................10
Assumptions.................................................................................................................................10
Statistical test...............................................................................................................................10
Summary .........................................................................................................................................12

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Study design
In this study, the experimental research design was used. This is because patient age data
collected through a randomised online survey contained both the dependent and independent
variables. Ideally, data collection methods here included other methods such as observational
study—the observational study as the kind of study that is carried out over a more extended period.
For instance, the week first symptoms appeared, and the time of admission to discharge were
collected over a long period.
Variables
The dependent variables in the study are age (interval scale, integer) of the patients and the
week the first symptom was reported (continuous, integer), while the independent is the time from
admission to discharge. All three variables are continuous. There were no many changes made to
the data; only that was to set the minimum values for all ages to be greater than zero. This is also
critical as it filters values that were erroneously captured during the survey.
Hypotheses
Null (H0) hypothesis
There is no association between the week of first symptoms and the number of days from
admission to discharge.
Alternative (H1) hypothesis
There is an association between the week of first symptoms and the number of days from admission
to discharge.

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Univariate Analysis
Descriptives
Age_years Week_first_symptoms Time_admitted_discharge
N 4644 4644 4644
Mean 57.3 32.2 10.8
Median 61.0 31.0 8.00
Mode 64.0 28.0 7.00
Standard deviation 22.5 11.8 12.3
IQR 30.0 19.0 8.00
Minimum 1 1 1
Maximum 102 53 202
25th percentile 44.0 23.0 4.00
50th percentile 61.0 31.0 8.00
75th percentile 74.0 42.0 12.0
Table 1: Descriptive statistics
The average age of patients admitted to various hospitals is 57.3 years (SD=22.5)
(IQR=30). The median age is 61 years. The minimum period of the patient is one year, while the
maximum age is 102 years. The age distribution for the patients admitted is reasonably expected,
as shown in the graph below.

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Figure 1: Histogram showing the age distribution
The distribution of patients age admitted in various hospitals is reasonably standard.
On the Week_first_symptoms variable, the minimum week for the first week of breakout
is one, while the full week is 52 weeks. The average time for the Epidemiological week of first
symptoms is 32.2 weeks, and the median week is 31 weeks. The distribution of the time for the
Epidemiological week of first symptoms is skewed to the right.

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Figure 2: Histogram for Week_first_symptom.
From the figure above, we can see that most diseases take between 10 weeks to 50 weeks
to show the first symptom. The distribution of the week_frist sign is slight to the left.
On-time admitted to discharge; the average days' patients take from admission to release is 10.8
days, the standard deviation is (SD=12.3). The median is eight days; the minimum number of days
that patients take is one day. The maximum number of days that a patient has taken in the hospital
is 202 days.
Figure 3: Histogram for Time_admitted_dsicharge
The distribution of time from admission to discharge is skewed to the left. Most of the patients
who get admitted are released between day one and the 50th day.

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Bivariate Analysis
Data related to age, time of admission to discharge, and weeks of first symptoms were
analysed by jamovi software. Of 5000 participants who participated in the survey, only 4644
provided valid information. Age data showed a normal distribution, while week_first_symptoms
data were not normally distributed. The time_admitted _discharge data was skewed to the right.
The median age of the patients admitted is 61 years (IQR=30), (SD=22.5), the median
Epidemiological week of first symptoms is 32 days (IQR=19), (SD=11.8), and the median day for
the time of admission to discharge is eight days (IQR=8) and (SD=12.3). Generally, diseases take
a longer time for the symptoms to be first reported.
Figure 4: Scatter plot for age vs time of admission to discharge
There is a positive correlation between the age of the patient and the time the patients takes
from the time of admission to discharge. A straight rising line indicates this.

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Figure 5: Scatterplot for the time of admission to discharge vs a week of the first symptom
There is a negative assertion between the time of admission to discharge and the week of first
symptoms. This is indicated by a straight line running from left to right.

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Figure 6: Scatterplot for patients’ age vs a week of the first symptom
There is a weak positive correlation between the age of the patient and the week of the first
symptom. However, we can see disease tends to take longer in older people before the first
symptom than younger people.
Ideally, it was projected that there is an association between weeks of the first symptom to
time of admission to discharge and the relationship between age and time of access to discharge.
These are consistent with the earlier projections; however, a more robust statistical analysis is
required to prove this. It is interesting to note that the error term in figure 5 becomes magnified
and significantly reduced at places where there are data.

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Statistical Test and Assumptions
Assumptions
It is assumed that the variables used in this case must be in ordinal or ratio scale. Age variables,
week of first symptom (time) and time of admission to discharge are all on inn ordinal scale. This
gives us enough evidence that the variables under study meet all the assumptions required for the
use of Spearman's rank correlation method.
Statistical test
Correlation Matrix
Age_years Week_first_symptoms
Age_years Pearson's r —
p-value —
Spearman's
rho
—
p-value —
Week_first_symptoms Pearson's r 0.044 —
p-value 0.003 —
Spearman's
rho
0.043 —
p-value 0.004 —
Note. * p < .05, ** p < .01, *** p < .001
Table 2: Correlation matrix between the week of first symptoms and age of the patients
Spearman's rank-order analysis run shows that there is a relationship between 4644
patients admitted. The jamovi output shows a positive relationship between the ages of the
week of the first symptom. The results(r(4642)=0.043, p=0.004) indicates that there is a
significant association. This shows that as the patient's age increases, the week of the first
symptom will also increase. In other words, older patients will take a longer time before the
first symptom seen in them. Therefore, we reject the null hypothesis and conclude that the data

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gives enough evidence at 0.05 significant level that there is an association between the age of
the patient and the week of the first symptom.
Correlation Matrix
Week_first_symptom
s
Time_admitted_discharg
e
Week_first_symptoms Pearson's r —
p-value —
Spearman'
s rho
—
p-value —
Time_admitted_discharg
e
Pearson's r -0.029 —
p-value 0.039 —
Spearman'
s rho
0.009 —
p-value 0.548 —
Note. * p < .05, ** p < .01, *** p < .001
Table 3: Correlation matrix between the week of first symptoms and time of admission to
discharge.
The Spearman's correlation conducted reveals a fragile positive association between
the time of admission to discharge and the week of the first symptom. This is indicated by
(Spearman's rho, r=0.09, p=0.09). We can see from the table that Pearson's coefficient gives is
negative, showing that there a negative linear association. However, when considering the
Speramn’s Rank correlation, there is a positive relationship between the week of first symptom
and time of admission to discharge. Since the p-value is more remarkable than the level of
significance, we fail to reject the null hypothesis and conclude that there is no association
between the weeks of the first symptom and the time of admission discharge at a 0.05 level of
significance.

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Correlation Matrix
Time_admitted_discharge Age_years
Time_admitted_discharge Pearson's r —
p-value —
Spearman's
rho
—
p-value —
Age_years Pearson's r 0.079 —
p-value < .001 —
Spearman's
rho
0.116 —
p-value < .001 —
Table 4: Correlation matrix between the age of the patient and time of admission to discharge.
The above table agreeable that the Spearman's' rank correlation run through the jamovi
software indicated that (rho=0.015, p=0.001), which is statistically significant. We therefore
reject the null hypotheses and conclude there is a positive association between the patients’
age and time of admission to discharge. This shows that older patients are likely to take longer
days in hospitals compared to younger patients.
Summary
Data were collected using a randomised online survey within Brazil. A sample of 5000
patients was enrolled for the study. In this case, only 4644/50000 (92.88%) participants had
completed their survey. Data were cleaned using jamovi to remove the inconsistency and errors
that occurred during collection. Each variable from the cleaned data was tested for normality using
the histogram. It was found that the age distribution among the patients was reasonably standard,
while the time of admission to discharge shows no normality in its distribution. The week of the
first symptom is skewed to the right. The average age of patients is 57.3 years (IQR=30). The

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youngest person admitted had one year, while the oldest patient admitted had 102 years. The
median age of the patient is 61 years, and a standard deviation is 22.5 years. Week of the first
symptom on the hand has a mean of 32.2 weeks (IQR=19), a standard deviation of 11.8 weeks.
According to analysis, the whole week of the sign is 53 weeks, while the minimum weeks of the
first symptom, according to research, is one week. The time of admission to discharge is averagely
10.8 days (IQR=8), SD=12.3 days. Also, the minimum days of admission time to release is one
day and 202 days maximum.
The Spearman's rank correlation analysis revealed a positive association between the age
of the patient and time of admission and discharge (rho=0.116, p=0.001), which is statistically
significant. This shows that older Brazilian patients are likely to stay longer in hospitals compared
to younger patients. Also, the analysis between the week of the first symptom and the time of
admission reveals that there is a fragile, nearly no association between them (rho=0.009, p=0.548),
which is not statistically significant at 0.05 significant level. Interesting, there is a positive
association between the age of the patient and the week of symptom (rho=0.043, p=0.004),
statistically significant at 0.05 significant level. However, the association between the dependent
variables was not the primary objective of the analysis. But it reveals that as the age of the patient
increases, the week of the first symptom also increases. Based on our research question, we reject
the null hypothesis and conclude that the data provide enough evidence to support an association
between the week of first symptoms and the number of days from admission to discharge.