Length of Stay in Hospitals

Introduction:

The problem focuses on the statistics of large and medium hospitals available with Australian Institute of Health and Welfare (AIHW). The dataset is about the average length of stay of people in the hospitals. The data can be used to derive a focussed analysis based on what relation the hospitals’ peer group has on the basis average length of stay in the hospital in terms of number of days.

View(alos_data)

library(dplyr)

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Attaching package: 㤼㸱dplyr㤼㸲

The following objects are masked from 㤼㸱package:stats㤼㸲:

    filter, lag

The following objects are masked from 㤼㸱package:base㤼㸲:

    intersect, setdiff, setequal, union

colnames(alos_data)

 [1] "Reporting unit"                   "Reporting unit type"              "State"                           
 [4] "Local Hospital Network (LHN)"     "Peer group"                       "Time period"                     
 [7] "Category"                         "Total number of stays"            "Number of overnight stays"       
[10] "Percentage of overnight stays"    "Average length of stay (days)"    "Peer group average (days)"       
[13] "Total overnight patient bed days"

#Renaming Columns
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Reporting unit"] <- "reporting_unit"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Reporting unit type"] <- "reporting_unit_type"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "state"] <- "state"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Local Hospital Network (LHN)"] <- "local_hospital_network"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Peer group"] <- "peer_group"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Time period"] <- "time_period"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Category"] <- "category"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Total number of stays"] <- "total_number_of_stays"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Number of overnight stays"] <- "number_of_overnight_stays"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Percentage of overnight stays"] <- "percentage_of_overnight_stays"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Average length of stay (days)"] <- "alos_days"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Peer group average (days)"] <- "peer_group_average_days"
names(average_length_of_stay_multilevel_data)[names(average_length_of_stay_multilevel_data) == "Total overnight patient bed days"] <- "Total_overnight_patient_bed_days"

View(average_length_of_stay_multilevel_data)

alos_data_filtered <- select(average_length_of_stay_multilevel_data,State,local_hospital_network,peer_group,time_period,category,alos_days)

View(alos_data_filtered)

#Deleting alos values with np and -

alos_data_filtered<-alos_data_filtered[!(alos_data_filtered$alos_days=="NP"),]
alos_data_filtered<-alos_data_filtered[!(alos_data_filtered$alos_days=="-"),]
View(alos_data_filtered)

alos_data_filtered %>% boxplot(as.numeric(alos_days) ~ peer_group, data = .,col = "yellowgreen", ylab="Average length of stay (days)",xlab="Peer Group") #Side-by-side boxplot

NA

alos_data_filtered2 <- alos_data_filtered[(alos_data_filtered$peer_group=="Large hospitals") | (alos_data_filtered$peer_group=="Medium hospitals"),]

alos_data_filtered2 %>% boxplot(as.numeric(alos_days) ~ peer_group, data = .,col = "yellowgreen", ylab="Average length of stay (days)",xlab="Peer Group") #Side-by-side boxplot

#alos_data_filtered2 <- transform(alos_data_filtered2, alos_days = as.numeric(alos_days))
View(alos_data_filtered2)

alos_data_filtered2 %>% group_by(peer_group) %>% summarise(Min = min(alos_days,na.rm = TRUE),
Q1 = quantile(alos_days,probs = .25,na.rm = TRUE),
Median = median(alos_days, na.rm = TRUE),
Q3 = quantile(alos_days,probs = .75,na.rm = TRUE),
Max = max(alos_days,na.rm = TRUE),
Mean = mean(alos_days, na.rm = TRUE),
SD = sd(alos_days, na.rm = TRUE),
n = n(),
Missing = sum(is.na(alos_days)))

3.986874 - 3.706049

[1] 0.280825

install.packages("car")

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library(car)

Loading required package: carData
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Attaching package: 㤼㸱car㤼㸲

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alos_data_lh <- alos_data_filtered2[alos_data_filtered2$peer_group %in% "Large hospitals",]
View(alos_data_lh)

alos_data_mh <- alos_data_filtered2[alos_data_filtered2$peer_group %in% "Medium hospitals",]
View(alos_data_mh)

alos_data_lh$alos_days %>% hist(xlab = "Average Length of Stay (days) - Large Hospitals",col = "cornflowerblue" , main = "")

alos_data_mh$alos_days %>% hist(xlab = "Average Length of Stay (days) - Medium Hospitals",col = "cornflowerblue" , main = "")

Start hypothesis test

alos_data_lh$alos_days %>% qqPlot(dist="norm")

[1] 3734  226

alos_data_mh$alos_days %>% qqPlot(dist="norm")

[1] 692 693

As many observations lie outside the 95% CI level, we move to Levene’s Test

leveneTest(alos_days ~ peer_group, data = alos_data_filtered2)

group coerced to factor.

Levene's Test for Homogeneity of Variance (center = median)
        Df F value    Pr(>F)    
group    1  16.585 4.707e-05 ***
      6591                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The equal variance cannot be assumed as the probability value is < 0.05

Now we perform the Welch two-sample test

t.test(alos_days ~ peer_group,
      data = alos_data_filtered2,
      var.equal = FALSE,
      alternative = "two.sided")

    Welch Two Sample t-test

data:  alos_days by peer_group
t = 5.6615, df = 4611, p-value = 1.592e-08
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.1835797 0.3780687
sample estimates:
 mean in group Large hospitals mean in group Medium hospitals 
                      3.986874                       3.706049 

Two-sample -test result summary:

We assumed normality as no of samples in both peer groups > 30 Levene Test, p<0.05 variances are not homogeneous Diff bet means 0.280825 95% CI[0.1835797 0.3780687] p value = 1.592e-08, p < alpha

Decision Reject H0 (H0 was that the means are equal)

Conclusion The results of the study found a statistically significant mean difference between large and medium hospitals, t(df=4611) = 5.6615, p=1.592e-08, 95% CI for the difference in means [0.1835797 0.3780687].