1 Executive Summary

The aim of this report is to establish whether rates per 100 000 of the population of hospital admissions concluding in a primary or secondary diagnosis of obesity could act as a predictor for rates of bariatric surgical interventions in England in context of the demography of such episodes and interventions. However, the data does not support the application of a linear model to these observations. Using only rates of episodes concluding in a primary diagnosis of obesity does yield a more predictive model. However, chance and/or extraneous factors complicate the application of a linear model to this data.


2 Report

2.1 Initial Data Analysis (IDA)

Data for this report was gathered from the British National Health Service’s annual compendium of data concerning hospital admissions and prescriptions with obesity as a factor and/or bariatric surgery as an outcome from 2005/2006 to 2015/2016 (NHS, 2019). However, it does not include data from private healthcare services. As it concerns only inpatient hospital admissions, it does not fully reflect the extent to which obesity levels in the population impacts the NHS.

The source dataset had a number of tables with the relevant values and variables distributed amongst them. The relevant data was extracted into three spreadsheets.

Two contain numbers of admissions to hospital concluding in a primary or secondary diagnosis of obesity alongside numbers of admissions concluding in bariatric surgery in England for 2005/2006 and 2015/2016, one divided into age groups, and the other into patient gender.

The third contains rates per 100 000 of the population of hospital admissions concluding in a primary or secondary diagnosis of obesity, rates of admissions concluding only in a primary diagnosis of obesity, and rates of bariatric surgery, categorised by Commissioning Authority Regions. Some regions were omitted due to the absence of one or more values.

age <- read.csv("~/Downloads/age_bar_ad - Sheet1.csv")
gender <- read.csv("~/Downloads/gender_bar_ad - Sheet1.csv")
rates <- read.csv("~/Downloads/pri_sec_bar_100000 - Sheet1.csv")

dim(age)
## [1] 32  4
str(age)
## 'data.frame':    32 obs. of  4 variables:
##  $ Year             : Factor w/ 2 levels "2005/2006","2015/2016": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Age_Group        : Factor w/ 8 levels "<16","16-24",..: 1 2 3 4 5 6 7 8 1 2 ...
##  $ Diagnosis_Outcome: Factor w/ 2 levels "bariatric_outcome",..: 1 1 1 1 1 1 1 1 2 2 ...
##  $ Count            : int  2 21 189 375 319 123 6 0 1727 1717 ...
sapply(age, class)
##              Year         Age_Group Diagnosis_Outcome             Count 
##          "factor"          "factor"          "factor"         "integer"
dim(gender)
## [1] 8 4
str(gender)
## 'data.frame':    8 obs. of  4 variables:
##  $ Year             : Factor w/ 2 levels "2005/2006","2015/2016": 1 1 1 1 2 2 2 2
##  $ Gender           : Factor w/ 2 levels "female","male": 2 2 1 1 2 2 1 1
##  $ Count            : int  200 21432 808 30552 1418 175401 5020 349279
##  $ Diagnosis_Outcome: Factor w/ 2 levels "bariatric_outcome",..: 1 2 1 2 1 2 1 2
sapply(gender, class)
##              Year            Gender             Count Diagnosis_Outcome 
##          "factor"          "factor"         "integer"          "factor"
dim(rates)
## [1] 192   4
str(rates)
## 'data.frame':    192 obs. of  4 variables:
##  $ Comm_Reg         : Factor w/ 192 levels "NHS Airedale, Wharfedale and Craven",..: 1 5 7 17 22 40 48 58 63 67 ...
##  $ Pri_Sec_Ad_100000: int  2256 520 793 1773 793 1007 659 727 320 1451 ...
##  $ Pri_Ad_100000    : int  11 14 7 21 25 14 9 10 18 15 ...
##  $ Bar_Ad_100000    : int  6 11 7 12 11 11 7 5 14 6 ...
sapply(rates, class)
##          Comm_Reg Pri_Sec_Ad_100000     Pri_Ad_100000     Bar_Ad_100000 
##          "factor"         "integer"         "integer"         "integer"


2.2 Attempting to Predict Rates of Bariatric Interventions on the Basis of Inpatient Hospital Admissions With Primary or Secondary Diagnoses of Obesity

2.2.1 Attempting to Fit a Linear Model to Rates of Primary and Secondary Obesity Admissions Compared with Rates of Bariatric Intervention

pri_or_sec_adm <- rates$Pri_Sec_Ad_100000
pri_adm <- rates$Pri_Ad_100000
bar_adm <- rates$Bar_Ad_100000
plot(pri_or_sec_adm, bar_adm, pch = 16, cex = 0.8, col = "chartreuse4", main = "Rates per 100 000 of Hospital Admissions Concluding in \n Bariatric Interventions Plotted Against Rates of Hospital Admissions \n With a Primary or Secondary Diagnosis of Obesity", xlab = "Rates of Primary or Secondary Obesity Diagnoses", ylab = "Rates of Bariatric Interventions")

regr = lm(bar_adm ~ pri_or_sec_adm)
abline(regr, col = "coral2", lwd = 2)

regr$coeff
##    (Intercept) pri_or_sec_adm 
##   14.411962481   -0.001280454
res = lm(pri_or_sec_adm ~ bar_adm)$residuals
plot(pri_or_sec_adm, res, pch = 16, col = "cyan4", main = "Residual Plot Showing Marked Linearity", xlab = "Rates of Primary or Secondary Obesity Diagnoses", ylab = "Residuals")
abline(h = 0, col = "red1")

In spite of the apparent plausibility of a predictive link existing between rates of hospital inpatient admissions concluding in a primary or secondary diagnosis of obesity and rates of bariatric surgical interventions, there seems to be no meaningful correlation between the two, at least for the period of 2015-2016 - fitting a regression line, if anything, actually shows a very slight negative correlation. Examining the pattern of residuals indicates that whatever relationship exists between the two variables is not best modelled by a linear regression.

This can be taken to indicate that, whatever determinants of rates of bariatric interventions may exist, they are independent of (or only mediately dependent on) rates of admission concluding in obesity diagnoses broadly.


2.2.2 Attempting to Fit a Linear Model to Rates of Primary Obesity Admissions Compared with Rates of Bariatric Intervention

Given the independence of primary and secondary obesity diagnoses from bariatric surgical interventions, perhaps narrowing down to rates of only primary diagnoses of obesity provides a better candidate for a predictor of rates of bariatric intervention.

This seems to be so plausible as to be almost trivial. While secondary diagnoses of obesity occur for patient admissions where it is possible that the more immediate medical concern requires non-bariatric interventions, primary diagnoses of obesity occur for patient admissions where bariatric interventions (whether surgical or not) are necessarily immediately required. It therefore might be expected that rates of bariatric surgical interventions and rates of primary diagnoses of obesity can be captured well by a linear model.

plot(pri_adm, bar_adm, pch = 16, cex = 0.8, col = "chartreuse4", main = "Rates per 100 000 of Hospital Admissions Concluding in \n Bariatric Interventions Plotted Against Rates of Hospital Admissions \n With a Primary Diagnosis of Obesity", xlab = "Rates of Primary Obesity Diagnoses", ylab = "Rates of Bariatric Interventions")

regr_2 = lm(bar_adm ~ pri_adm)
abline(regr_2, col = "coral2", lwd = 2)

regr_2$coeff
## (Intercept)     pri_adm 
##   2.4670944   0.5326179
res_2 = lm(bar_adm ~ pri_adm)$residuals
plot(pri_adm, res_2, pch = 16, col = "cyan4", main = "Residual Plot Showing Increasing Variance", xlab = "Rates of Primary Obesity Diagnoses", ylab = "Residuals")
abline(h = 0, col = "red1")

Plotting the data, the initial expectation does seem to be the case. However, some regions exhibit ratios of the two variables that are not completely consistent with a linear model. While these represent a small subset of the overall data sample, the pattern of residuals shows a potentially meaningful increase in variance as rates of primary diagnoses increase. While the explanation of this pattern likely depends on determinants not captured by the data used for this report, the Section 2.4 briefly discusses some possible factors that might complicate the application of a linear model to the relationship between these two variables, including some features of the demography of the phenomena visualised in the following section


2.3 The Demography Over Time of Hospital Inpatients With Primary or Secondary Diagnoses of Obesity and Those Who Receive Bariatric Interventions

2.3.1 Comparing Admissions and Interventions in 2005/2006 and 2015/2016 by Age Group

library(ggplot2)
ggplot(age, aes(x = age$Diagnosis_Outcome, y = age$Count, color = age$Diagnosis_Outcome)) + geom_point(size = 3) + facet_grid(age$Year ~ age$Age_Group) + scale_y_continuous(trans='log2') + theme(axis.text.x=element_blank(), legend.title=element_blank()) + labs(y = "Numbers of Patients", x = "") + scale_color_manual(name="Admission Type", labels = c("Bariatric Surgery Outcome", "Primary or Secondary Obesity"), values = c("bariatric_outcome"="coral4", "obesity_diagnosis"="cyan2"))
## Warning: Transformation introduced infinite values in continuous y-axis

###Infinite values on the y-axis have been introduced by a zero-value data-point for the over 74 bariatric outcomes group in 2005/2006.

2.3.2 Comparing Admissions and Interventions in 2005/2006 and 2015/2016 by Gender

ggplot(gender, aes(x = gender$Diagnosis_Outcome, y = gender$Count, color = gender$Diagnosis_Outcome)) + geom_point(size = 3) + facet_grid(. ~ gender$Year + gender$Gender) + scale_y_continuous(trans='log2') + theme(axis.text.x=element_blank(), legend.title=element_blank()) + labs(y = "Numbers of Patients", x = "")+ scale_color_manual(name="Admission Type", labels = c("Bariatric Surgery Outcome", "Primary or Secondary Obesity"), values = c("bariatric_outcome"="coral4", "obesity_diagnosis"="cyan3"))


2.4 Summary and Discussion

Perhaps counterintuitively, combined rates of admissions to hospital with outcomes of primary and secondary diagnosis of obesity does not yield an even approxiamtedly predictive model for rates of bariatric intervention.

Narrowing the view to only primary diagnoses of obesity does seem to provide a more predictive model. However, a number of extreme results for some commissioning regions complicate the application of a linear model to this phenomenon. As rates of primary obesity diagnoses increase above 80 cases per 100 000 of the population, rates of bariatric interventions seem to level out below 50 cases per 100 000.

Referring to the demography of these phenomena in Section 2.3, it is possible that, in the aberrant Commissioning Authority Regions, the relevant subset of the population has a higher proportion of very young or very old patients, two subsets of the obese patient population that have historically disproportionately received less surgical interventions than other groups, and elsewhere it has been observed that they have are considered less suitable candidates for the procedure (Santry et al, 2007). Patient screening for the procedure generally involves taking into account other physical and mental health issues, so these could also be involved (Neff et al, 2013).

There are also gendered differences in the numbers of both obesity diagnoses and bariatric interventions, and elsewhere it has been noted that men tend to opt for bariatric interventions less than women (Santry et al, 2007). however, because both male and female patients seem to have roughly similar ratios of obesity diagnoses to bariatric interventions, it is not necessarily the case that gender differences in the population alone could account for the variation in overall rates.

Applying a linear model to this data might also be complicated by socio-economic factors beyond the scope of the data used for this report - it has been observed that children from lower income backgrounds are more at risk of obesity than peers from higher income backgrounds (NHS, 2018). While any surgical interventions would be state-subsidised, and so the cost of the intervention itself may not be a consideration for prospective patients as it may be elsewhere, other factors specific to some socio-economic groups may affect rates of surgery (Buchwald, 2005). Elsewhere it has been noted that higher income individuals, and individuals with more social support, tend more to opt for bariatric surgery (Santry et al, 2007).

Finally, while bariatric surgeries may potentially cost less for the NHS than other obesity-related interventions, the UK has generally lagged behind other countries in offering surgery as a treatment for obesity (Boseley, 2017). Thus, different institutional cultures in English hospitals, perhaps more pronounced in some regions than others, might affect the ratios of diagnoses to surgeries.


3 References

Primary Source:

National Health Service. (2019). NHS Statistics on Obesity, Physical Activity, and Diet, England. Retrieved 27 August 2019, from https://digital.nhs.uk/data-and-information/publications/statistical/statistics-on-obesity-physical-activity-and-diet/statistics-on-obesity-physical-activity-and-diet-england-2019

Secondary Sources:

Boseley, S. (2017). UK Needs to Perform Thousands More Obesity Operations, Say Surgeons. The Guardian. Retrived from https://www.theguardian.com/society/2017/sep/01/uk-needs-to-perform-thousands-more-obesity-operations-say-surgeons

Buchwald, H. (2005). Bariatric Surgery for Morbid Obesity: Health Implications for Patients, Health Professionals, and Third-Party Payers. Journal of the American College of Surgeons, 200 4, 593-604. doi: https://doi.org/10.1016/j.jamcollsurg.2004.10.039

National Health Service. (2018). Children From Poorer Backgrounds More Affected by Rise in Childhood Obesity. Retrieved 27th August 2019, from https://www.nhs.uk/news/obesity/children-poorer-backgrounds-more-affected-rise-childhood-obesity/

Neff, K. J., Olbers, T., & le Roux, C. W. (2013). Bariatric Surgery: The Challenges With Candidate Selection, Individualizing Treatment and Clinical Outcomes. BCM Medicine, 11 8. doi: 10.1186/1741-7015-11-8

Santry, H. P., Lauderdale, D. S., Cagney, K. A., Rathouz, P. J., Alverdy, J. C., & Chin, M. H. (2007). Predictors of Patient Selection in Bariatric Surgery. Annals of Surgery, 245 1, 59-67. doi: 10.1097/01.sla.0000232551.55712.b3

Source for Guidance with Visualisation Coding:

Kabacoff, Rob. (2018). Data Visualization With R. Retrived 5 September 2019, from https://rkabacoff.github.io/datavis/