In Depth Analysis

Investigation into COVID-19’s Mortality Between the General and Nursing Home Population: Part One — Bayesian Probability Model for Time-Series Forecasting.

A look at COVID-19's effects on the Probability of Death given one’s Age and Residence.

Summary : In the following Part One of Three, a time-series is analyzed utilizing Bayesian Probabilities in an effort to build models to quantify the probability of death between the nursing home and general populations. It is found that the probabilities were not independent, and were calculated appropriately. Furthermore, several distinct differences were noted between the nursing home and general public in terms of probability of death, probability of belonging to a certain age group. Following the calculations of the final probability of condition given one’s location and age, the direct comparison at a yearly-, and age-level could finally be performed to describe the relative safety or harm associated with one’s residential location which demonstrate distinct probability differences at both the mean and time-series level. In part two, the data analysis performed in this part will be modeled into a time-series forecast analysis.

Table of Contents

Introduction of Part One: Investigation and Modeling

COVID-19 presented novel challenges from which Nursing Homes were not spared. In particular, there was raising concern on the proper management of Nursing Home residents who tested positive for COVID-19, or those who were transported to a hospital with subsequent nursing home re-admision. The ultimate police crafted was to re-admit and keep residents in their rooms if no other accommodations were available.The rationale in the Department of Health’s police was to prevent cross-contamination of residents as “roommates of symptomatic individuals may already be exposed” it was deemed unwise to move them to another room as a means to keep infection rates down(1).

Pennsylvania has an average of twelve million inhabitants with approximately 80,000 nursing home residents. Yet despite this large disparity in numbers, over 60% of novel COVID-19 infections and deaths occur within nursing homes in Pennsylvania, drawing criticism from the public (2). Scrutiny deepend when the Philadelphia Inquirer found that the Pennsylvania Department of Health had previous constructed a comprehensive and impactful plan to mitigate the risks associated with COVID-19 for nursing home residents; yet this plan failed to materialized (2). Although the raw numbers tell a harrowing tale, it is not clear if it is a truthful one. Is the disproportionate amount of infections and deaths observed from nursing homes due to a lack of leadership and appropriate actions, or is it due to the nature of nursing homes: older and sicker individuals than the population at-large.

Thus, it is of principle interest to the researcher to investigate and analyze the data in a meaningful manner so as to identify the true nature of COVID-19 and its respective behavior towards those living in nursing homes and those not.

Motivation

To guide and aid in understanding the proper mechanisms for protecting the residents of nursing homes in states during times of pandemics.

Goal

To determine if any significant differences in mortality existed between populations of COVID-19 patients for those who live in nursing homes versus those who live in the general population by utilizing a comprehensive, multi-faceted approach.

Methods

There will be three main parts to this investigation.

Methods — Part One : Characterization, and Probabilities

In the first part, two main sets of data will be collected: demographics on the living and the dead in both the general population and the nursing home population. These data were obtained from two main sources: the CDC WONDER portal provided the demographics for the living populations within the general population cohort while the demographics for the living were obtained from the Pennsylvania Health Statistics Website (3).

For the general population, there were several factors from which to pull the general demographics information by place of residence, as such, the CDC WONDER portal was utilized to pull all-demographics from 2010–2018 by age, and gender. From these data, the gender-, and date-matched hospice population was removed. The information provided from the state for nursing home demographics provided age-stratified but it did not provide gender-stratified. Thus the Pennsylvania data were utilized to ensure efficacy of the WONDER data, after which the WONDER data for Nursing Home demographics was directly utilized.

This process was repeated for the demographics of those that have died in Pennsylvania from 2010–2018; stratified by place of death, age, sex, and date (year and month). Again, the Pennsylvania Department of Health data provided a basis to ensure consistency of the CDC WONDER data, after which the CDC WONDER data was directly utilized. To ensure adequacy, the stratifications for age-cohorts had to be modified between the two sources (Pennsylvania and CDC); the modified age-cohorts are reported as: <18, 18–44, 45–59, 60–64, 65–69, 70–74, 75–79, 80–84, 85+, unless otherwise stated. This is due to the Pennsylvania data for reporting the demographics of death for nursing home residents extending the later age cohorts and compacting the former-age cohorts. This process was then retroactively applied to the living demographics as well to ensure ease of interpretation.

Rationale for cross-verification between Pennsylvania and the Department of Health data stemmed from the main concern that the the definition of “Place of Death” as recorded is literally the place of death — regardless of where the person lived. As such, there was concern that those who resided in nursing homes but were transported out of the nursing home via emergency medical services and either died prior to or after arriving at a hospital would not be recorded as a “Nursing Home” death. These fears were eased due to year-wide data being found from the Pennsylvania Department of Health which counted death not as its place but as a count of residents per nursing home (a subset of discharges). These data were then verified with yearly-produced data from CDC Wonder and the state-provided place of death demographics data, with subsequent retrieval of the monthly data therefrom.

Once the characteristics were described, and the nature of the environment adequately summed, the next step will be to utilize classical Bayesian probabilities to model the death between the geographical cohorts. There were several reasons behind choosing a probabilistic model to quantify the differences in death between the two geographical cohorts:

1- The testing capabilities country-wide have been too variable to be reliable and do not come with demographic information.

2- There may be an increase in associated-mortality secondary to COVID-19 infection that may not be identifiable via standard testing.

3- Capturing the behavior of death prior to COVID-19, and forecasting into 2020 will help determine the deviance of death secondary to COVID-19 without respect to cause of death but with respect to demographics of geographical, age, and gender cohorts.

The bayesian forecast model is contingent on the assumption that any significant deviation from the model’s predictions is based entirely on the effects of COVID-19. It is not equipped to parse out any reasoning behind any significant deviation. It is the researchers belief that by simultaneously remaining broad-scoped in terms of COVID-19’s effects (both direct deaths and indirect), while specifying the cohorts under investigation (place of death cohorts) with confounding variables (gender, age) via a probability model will yield significant and appropriate insight for the question at-hand.

Once the appropriate characterizations of the individual cohorts are performed, and the probability models mapped out, part two will incorporate COVID-19 data and map it onto the models predictions to determine any significant deviation between the nursing home population’s response and the general populations response to COVID-19 in terms of relative safety. From there, party three will look more closely with more rigorous data, if indicated, to analyze the relative affects of geographical location versus age on COVID-19 death rates.

Statistical Definitions

The production of the probabilities were employed using classical bayesian probability models. The goal is to compute:

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That is, the probability of either being dead or alive P(C) given the location P(L) of either nursing home or general public and given one’s age P(Age).

Several probabilities were utilized in both the acquisition of the end-point probability, and as bench-marks for time-series analysis that will be utilized for model selection.

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the probability of condition will show the change in the probability of dying in Pennsylvania through 2010–2020 without respect to age, location, or gender. It is important to visualize this in terms of probability so that its affects of seasonality, if any, or any affects noted on a larger time scale (year-to-year) can be taken into affect during model formation.

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probability of location will show us the probability of living within either the nursing home cohort or the general population cohort. It may be that this changes, or, it may be dependent on the sex or age of the population, thus it is important to analyze and model.

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will show the relative probabilities of condition (dying or living), depending on the particular geographical residence without respect to demographics of the dead. This will be important to observe on a time-dependent manner for two main reasons: the first is to identify trends associated with each individual cohort, but as well to identify any intra-cohort trends; that is: is there an association between the probability of dying in one geographical location as compared to the other? This will be interesting to look at with the COVID-19 data to see if any pre-established trends intra-geographical cohort alter in response to COVID-19.

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will show the relative probabilities of condition, dependent on the age cohort, without respect to geographical location. It is established that COVID-19 disproportionately affects the elderly, and as such, it is principle concern to the research to quantify the probability of dying per age-cohort and model it since one the nursing home cohort will have a greater density of elderly cohorts and thus an inherent increase in mortality associated with COVID-19 (5).

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will show the probability of either belonging to the nursing home cohort or the general population cohort given one’s age. This will be modeled due to an age-related dependency on location: the older one is, the more likely they are to be included in the nursing home cohort. Thus, the older one is, and the more likely they are to be included in the nursing home cohort, the more likely they are to die from COVID-19. This affect needs to be modeled so as to remove the non-COVID-19 related affects.

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will show us the cumulative probability of dying given both your age and your geographic location. This will be the overall statistic modeled to determine COVId-19s affect and thus the relative safety associated with either residing in a nursing home or in the general population given one’s age.

Demographics

Demographics of the Living

General Population

Pennsylvania has an average of 12 million inhabitants from the years 2010 to present. Of these 12 million inhabitants, approximately 80,000 reside in nursing homes.

The average population within Pennsylvania is an almost equal distribution of sexes (51% woman, 49% men), with the top three relative age brackets being: 18–44 years of age (32% total population (2,495,000), equal proportions of men to woman), 45–59 years of age (22% of total population (2,730,000), with equal parts men and woman), and <18 years of age(21% of total population (2,495,000), with 51% men, and 49% female. The equal distribution of sex diminishes as age increases: over the age of 35 years of age, the female sex dominates with yearly increases with those 85 and older being 65% female. In fact, the age-cohorts: 60–64, 65–69, 70–74, 75–79, 80–84, and 85+ are all dominated by females.

Nursing Home Population

Within nursing homes, the average number of woman within nursing homes is 30,570 (68%) a year with men at 15,292 (31%) per year. Woman account for twice the population within nursing homes as men, and account for the older population with the most-common age group for woman being 90–94 years of age whereas the majority of men account for 80–84 age bracket.

Combined, woman over the age of 90–94 years account for 19% of the total nursing home population. The top three age brackets for woman are: 90–94 years old (average yearly population 5699; 18.6% of woman; 12.4% of both sexes ), 95+ years old (average yearly population 5327; 17.4% of woman, 11.6% both sexes), and 85–89 years old (average yearly population 5236; 17.1% of women, 11.4% both sexes). The least three female age groups for nursing homes are: less than 18 years old (zero), 18–44 (average yearly population 451; 1.5% of woman, 1% both sexes), and 60–64 years old (average yearly population 1130, 3.7% of woman; 2.5% both sexes).

Men, on the other hand are present in both fewer numbers and younger ages than females. The three largest age brackets for men were: 80–89 years old (average yearly population 2,146; 14% of men; 4.7% of both sexes), 85–89 years old (average yearly population 2,035; 13.3% of men; 4.4% of both sexes), and 75–79 (average yearly population 1,964; 12.9% of men; 4.2% of both sexes). The least three populated age-cohorts for men within nursing homes were: less than 18 (only one recorded), male 18–44 years old (average yearly population 564; 3.7% of men, 1.2% of both sexes), and 95+ years old (average yearly population 1,030; 6.7% of men, 2.3% of both sexes).

Combined, the three most-populated age brackets within nursing homes are: 85 years of age (average yearly population: 7,271; woman: 5,237 (72%), men: 2,035 (28%)), 80 years of age (average yearly population 6,589; woman: 4,443 (67%) , men: 2,146 (33%)), and 75 years of age (average yearly population: 5,152; woman: 3,187 (62%), men: 1,965 (38%)). In fact, the only age cohorts wherein men out numbered woman were in the 18–44 cohort (56% men), 45–59 age cohort (54% men), and the 60–64 age cohort (53% men).

Of particular note, it is interesting that the vast majority of 100+ years of age residents within nursing homes are female, from the years 2010–2018 (Females: 6703 (89.5%), Males: 783 (10.4%)).

Figure 1 is a visual demonstrating of the distribution of ages between the general population and the nursing home population:

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Figure 1: A look at the relative ratios of age and gender between the General Population and the Nursing Home Population.

Demographics of the Dead

General Population

In Pennsylvania’s general population, from the years 2010–2018, the three most popular age cohorts to experience death were: 85+ (326 per 10,000 residents for Female; 200 deaths per 10,000 residents for Male), 80–84 (141, and 128 deaths per 10,000 residents for female and males, respectively), and 75–79 (116, and 113 per 10,000 residents for female and males, respectively). It is unsurprising that the per-capita death rates have drastic differences between the sexes as there is an increase in female dominance with an increase in age-cohort. Concurrently, the ratio of deaths between male and females demonstrates that population-wide, females die less often, despite making up a larger population, than men (81 female deaths per 100 male deaths).

There is a difference in the distributions of death between men and female gender cohorts when compared to one another (p-value <0.05). Furthermore, even within the specific gender-cohort, there is a significant less death per capita in females than in males (p-value <0.05). This suggests two things: there is an overall difference between male and female death rates, and woman tend to experience less per-capita intra-cohort deaths.

A look at the time-dependent nature of death reveals strong seasonality: the years are flanked by increase in rates followed by a gradual decrease into the summer. This can be seen in Figure 2. Separating out the age cohorts demonstrates that the seasonality noted in deaths is due to the 85+ cohort rather than a population-whole phenomena.

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Figure 2: A: Demonstration of the general populations death pattern from years 2010–2018 by gender; B) A look at seasonality throughout the year for years 2010–2018 (legend not included); C) Look at contributing age cohorts to seasonality (age cohorts <18 years, and 18–44 removed due to insignificant quantities). Per-capita calculated at per 10,000 residents

Clearly there is a distinction between the age-cohorts and the amount of deaths throughout the year. This may be important to account for later as the age-cohort most affected by seasonality is the age-cohort most affected by COVID-19.

Nursing Homes
In the nursing home population, per capita death rates of age and sex are analyzed at death per 10,000 residents. The three most deadly age-cohorts within nursing homes are 85+ (for both men and woman; 180 deaths per 10,000 residents for females, 80 deaths per 10,000 residents for males), the 80–84 age group for females. In fact, not surprsingly, the per capita death rate increases as dependent on age in both cohorts, with females outnumbering men.

Since females outnumber men in nursing homes and seem to extend more into the later age groups, woman have a significantly more mortality per capita for overall population (p-value < 0.05); but in terms of gender-specific values, woman have a lower per-capita death value per female population count within nursing homes: 595 per 10,000 female residents for Females, and 743 deaths per 10,000 male residents for Men. Performing a student T-test on the per capita death rates of men versus woman in nursing homes demonstrated a p-value <0.05. This suggests two observations that seem evident from the description of the demographics from above: woman account for the majority of the population within nursing homes, which increases, significantly so, their per-capita death when compared to the nursing home population as a whole while simultaneously, the longevity associated with woman, as observed from their increase in relative abundance with an increase in age, suggests less intra-female death than intra-male death. This is supported by the per capita deaths when calculated at the gender-cohort level.

It is apparent that the deaths within nursing home age-cohorts follow similar trends to those of the general population, namely: seasonality. However, unlike the general cohort, there is not one-specific age-cohort that dominants the seasonality trend — there seems to be an age-dependent affect on the age cohorts’ response to seasonality: dominating in the 85+ cohort and diminishing until the 70–74 cohort.

These trends can be visualized in Figure 3:

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Figure 3: A: Death through the years separated by Gender, per capita values calculated at gender-cohort level; B: Gender-cohort decomposition into monthly death values, demonstrating the seasonality of death (legend excluded); C: Decomposition of age-cohorts throughout the years to look at seasonality per age cohort.

Demographics Summary

The general population and the nursing home population demonstrate noteworthy differences that will need to be taken into account when modeling the death of both in part two. Of note, although woman make up the majority of the population in nursing homes, they vastly under-perform men in terms of death. As well, there is a clear seasonality to death that persists in both the nursing home and general populations with the nursing home experiencing a greater involvement of age cohorts in the production of seasonality. Another difference was the overall ranking of deaths between nursing homes and the general public. Whereas in the nursing homes the per-capita death decreased in natural order (older to less old), that was not the case in the general population.

Creation and Characterization of Probabilities

Probability of Condition

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The probabilities of death versus living is not too particularly deviant from the ratios of death seen above in the demographics. Essentially, the two are the same: they are calculated as a proportion of dead to living, regardless of demographics and geographic location.

The probability of dying shows the characteristic seasonality. Furthermore, there has been a recent trend since 2014 of increasing probability of death throughout the state. These can be visualized in Figure 4 . The minor loss of stationarity within the time-series data will be addressed during model selection. For now, only the probability of death has been shown, but the probability of the living is just: P(C) = 1 — P(C).

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Figure 4: A: A look at the yearly change in probability of death with the probability normalized to a normal distribution, blue line represents LOESS regressions; B) Look at seasonality within the normalized probability of death.

Probability of Location

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The probability of location, whether living in a nursing home or living in the general population regardless of gender, or age, is performed a the year-level due to the data-reporting of demographics. Yet there is a clear decrease in the probability of living in a nursing home with a range of 0.57% — 0.63% throughout the years. Figure 5 demonstrates this trend.

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Figure 5: A look at the change in probability for living in a nursing home from years 2010–2018.

Probability of Condition, given Location

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The probability of condition, depending on one’s location will help elucidate any underlying trends that may account for an increase or decrease in death throughout time. This is a conditional probability, and as such, test of independence should be performed to determine how to calculate the conditional probabilities.

Test of Independence

A simple test of independence of: P(C|L)=P(C) was performed and it was not satisfied. As such, P(C|L) = P(L|C)P(C) is computed.

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The probability of dying, given residence in a nursing home, along with

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the probability of dying, given residence in the general public, are analyzed in this section.

The probability of dying in a nursing home from the years 2010–2013 experienced a drastic decrease, which rebounded slightly and has remained mostly steady since 2016. Furthermore, the probability of dying in the general public remained steady from 2010–2015, after which it experienced a slight increase. Graph 6 shows the trends of the probability of dying throughout the two cohorts. The small percentage of death within the nursing home population is mainly due to the relatively small percentage of nursing home residents in comparison to the general population. Normalizing for population is not apart of this section.
In reference to the preceding section on the probability of living in a nursing home, it was noted that there has been a steady decrease in the probability thereof; this may account for the decrease in an other-wise stable metric.

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Figure 6: A) Look at the change in probability of death given residence in nursing home through time; B) Change in probability of death given residence in general public through time.

More interesting, however, is the seasonal decomposition of the two cohorts. In the investigation of demographics of death between the general population and the nursing home population, it was noted that there appeared to be a diminished seasonality within the demographics of the dead of the nursing home cohort. This is not supported with Figure 7 which shows the flux of seasonality difference between the two cohorts remains stable throughout the year. The normalized percent difference shows us that there is, on average, a 2.5% greater z-score for the probability of death within nursing homes than in the general public, with flaring towards the beginning and end of the years.

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Figure 7: A) Seasonality decomposition between: A) The nursing home population and B) the general population, and C) The normalized percent difference between the nursing home and general public as calculated by General Probability — Nursing Home Probability.

Probability of Condition, given one’s Age

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Mapping the time-dependent nature of the probability of dying given the probability of belonging to a specific age-group is necessary due to the disproportionate nature of COVID-19’s lethality. As well, it will be an important building block in the construction of the gamma probability.

Furthermore, P(pi) is an interesting metric as the probability of dying given a certain age-cohort is dependent on both the relative amounts of that age-cohort and the relative amounts of death within that age-cohort nor for controlling for relative population counts.
Looking at just the probability of death given one’s age throughout the entire population of Pennsylvania reveals some interesting trends (Figure 8). Firstly, the highest probability resides at the 18–44 age cohort; that is, if we selected a random person and randomly put them into an age-cohort and then the person died, the most likely event at ~10% would be 18–44. Although this is not entirely surprising as the 18–44 cohort makes up the greatest demographic cohort population-wide, and these statistics are not meant for nursing home versus general public comparisons.

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Figure 8: Look at the probability of death given a specific age-cohort through the years 2010–2018.

Another interesting trend has been the the decrease in both <18 and 45–59 age-cohort probabilities of death; although this may be due to either a decrease in the probability of belonging to that cohort or the probability of death truly decreasing; it is unsure. A quick look a the other probabilities show that there doesn’t seem to be an incremental decrease to explain the phenomena: that is, if it was expected that the decrease in the probability of death, for age cohorts 45–59 was decreasing due to a decrease in population count and a relatively steady probability of death, we would expect to see a decrease in the probability of death for age cohorts 60–64 due to an influx of individuals graduating to the next age-cohort. Yet this is not the case: although subtle, there is a clear increase in probability of death for age cohort 60–64, which would either be explained by 1) a decrease in the 60–64 population or an increase in the probability of death for that age cohort; this minimizes the chances that the decrease in probability of death for the 45 -59 age cohort is due to an efflux of populous but rather a true decrease in probability of death for that age-cohort (or due to a decrease in those graduating from the 18–44 cohort).

Probability of Location, given one’s Age

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For quick analysis in this section, only the probability of residing in a nursing home, given one’s age is analyzed. As expected, the probability of living in a nursing home increases with age. Surprisingly, however, is the age cohort 45–59 which seems within the same range as the 85+ age-cohort and the 80–84 year cohort has experienced a decrease in probability of living in a nursing home. This will be an important characteristic of the relationship between the general public and the nursing home public to keep in mind given COVID-19’s prevalence within nursing homes and its increased lethality towards those of higher age-cohorts. The trends can be visualized in Figure 9.

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Figure 9 : A look at the probability of living in a nursing home given one’s age.

Probability of Death, given one’s Age and Location

The final composite, dependent Bayesian probability was calculated as such:

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This is gives the definitive probabilities for Part One. In it, it describes the probability of dying, given one’s age and location. It will be this from which the models will be crafted. Two models will be explicitly analyzed here:

The Probability of Dying, given one’s Age and Nursing Home Residence

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The probability of dying, given ones location in a nursing home is demonstrated in Figure 10. A few characteristics that remained steady throughout the distillation process was the seasonality of the deaths. Surprisingly, there seems to be an inverse relationship between the probability of death given nursing home residence with age: the younger a person is within a nursing home, the higher their probability of death is. This makes sense considering the younger one is, the more sick they would have to be to be introduced into a nursing home. Historically, the 85+ year cohort has been experiencing an increase in the probability of death starting at around 2015.

It should be noted that for the graph, the age cohorts of <18 years of age and 18–44 were removed due to lack of a sufficient quantity of deaths to produce meaningful probabilities Thus, they will be removed during model selection as well. Another factor that may have to be taken into account during model selection is the drastic deviation noted from the normal in the years 2010–2011; for reasons unknown to the researcher, it seems that in years 2010–2011 the probability of death decreased drastically as an inverse relationship with age-cohort in nursing homes.

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Figure 10: A) A look at the probability of death per age-group within nursing homes throughout the years 2010–2018, ages less than 44 removed due to insufficient data. B) A look at the seasonality of the age cohorts.

Probability of Death given one’s Age and General Population Residence

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The probability of dying, given one’s location in the general public is demonstrated in Figure 11. A few things worth mentioning that differ from the probability of dying given one’s age and nursing home residence : the seasonality demonstrates that the years 2010–2011 in the general public did not experience a large probability of death throughout the year. Furthermore, the seasonality is still present, and much to the same degree as within the nursing home. There, however, does not seem to be any drastic changes in the probability of death throughout the years 2010–2018. Unlike the nursing home cohort, however, it appears the standard pattern of direct relationship between probability of death and age remain intact: the older one is in the general public the more likely they are to die.

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Figure 11: A) A look at the probability of death through the years within the general population; B) A look at the seasonality of the probability of death from years 2010–2018. Note Y-axis is log10, ages <18–18–44 removed due to insufficient data.

Comparing the two cohorts side by side, as in Figure 12 an interesting phenomena appears: within the older cohorts, when normalized, it is obvious that the probability of death is significantly less than the probability of death for the same age-cohorts for their respective location-cohort between the nursing home and the general pubic. This brings credence to the idea that nursing homes are safe environments for the elderly, when measured with the end-point of death.

However, there is much greater variation in the probability of death per age-group within the nursing home cohort than the general public cohort. At present, no theories come to mind as to why that is.

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Figure 12: A) Normalized probability of death per age group within the Nursing Home Cohort; B) Normalized probability of death pre age group within the General Cohort.

A direct comparison can be performed on the probabilities of death, given one’s location and one’s age, as is seen in Table 1. These probabilities are given in the %-probability format, and are calculated as the mean probability of death per age group within each cohort per month.

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Table 1: A look at the respective probabilities of death given one’s age and residence.

It is clear that for those 85+, the probability of dying, per year, is substantially lower in the nursing home cohort than in the general public. As seen above, the probability of dying in the 18–44 age-cohort is substantially higher in the nursing home population than the general (0.23% per year versus 0.01%). This coincides with the idea that the younger one is the sicker they are if they are in a nursing home. Furthermore, it seems that the highest probability of death for those in nursing homes occurs at the 45–59 age cohort whereas the highest probability of death per the general population is the 85+ year cohort.

To visualize these relationships, Figure 13 shows the probability of dying, given one’s age and residence in the general public, plotted against the probability of dying, given one’s age and residence in a nursing home. The relationship is clear: the direct relationship between age and probability of death given one’s age and residence in the general public versus the inverse relationship of the probability of death and age given one’s residence in a nursing home.

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Figure 13: Correlation Plot between the Probability of death given one’s age and location: y-axis is general public, x-axis is the nursing home; x-axis is log10.

These probabilities, or rather, their changes will be analyzed as end-points in Part Two as a method of quantifying the relative effects of COVID-19.

Conclusion

Here the Time-Series Bayesian Probability Models underwent their development for the construction of a predictive time-series analysis of COVID-19’s effects compared between those living in nursing homes and those living within the general population. Several probabilities were calculated, ultimately producing the probability of dying, given one’s age and residential location. Some trends were elucidated that will be controlled for in Part Two when developing the predictive models. Namely, the probability of death (P(C)) exhibited both seasonality and stationarity which persisted throughout the transformation process towards the gamma probability. It was also discovered that there has been an overall decrease in the probability of residing within nursing homes despite an increase in the probability of residing in a nursing home, given one’s age. This trend held true for all age-cohorts, except most notably the 80–84 cohort.

In finality, the gamma probability demonstrated the most noteworthy insights into the behavior of the nursing home versus the general population cohorts. Both the nursing home cohort and the general cohort experienced seasonality, with no stationarity noted within the general cohort, despite a slight stationarity noted in the nursing home, 85+ years cohort. Furthermore, an interesting reversal of risk was discovered between the two geographical cohorts: whereas the normal distributions of the nursing homes’ probability of deaths show an inverse relationship with age, the opposite is true in the general public. This phenomena makes intuitive sense when one considers the circumstances surround placing a younger individual in a nursing home which suggests a more-sick individual than their respective counterpart within the general population.

This is along-side an increase in variability associated with the probability of death within nursing homes, compared to the general public. It is not certain why this would be the case.

These data will be modeled appropriately in Part Two.

Next Steps

Now that the Bayesian Probability Models have been developed, the characteristics described above will be modeled utilizing time-series forecasting models in Part Two. From there, COVID-19-related data will be incorporated to assess the magnitude of change due to COVID-19. The conclusion of part two will allow a statement on the relative increase or decrease probability of death, given one’s location and one’s age.

Sources

[1] “Interim Guidance for Nursing Facilities during COVID-19 (03/18/20)”. March, 2020. Pennsylvania Department of Health

[2] “Pa. had an early plan to protect nursing home residents from the coronavirus, but never fully implemented it”. May, 2020. The Philadelphia Inquirer.

[3] “CDC WONDER”. Centers for Disease Control and Prevention <www.wonder.cdc.gov>

[4] “Nursing Home Reports”. Pennsylvania Department of Health Health Statistics. <www.health.pa.gov/topics/HealthStatistics/HealthFacilities/NursingHomeReports/Pages/nursing-home-reports.aspx>

[5] “Provisional Death Counts for Coronavirus (COVID-19). June, 2020. Center for Disease Control <www.cdc.gov>

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Hi! I’m a molecular biologist turned Paramedic turned aspiring data scientist. I like all things science, history, data, math, and medicine!

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