## Introduction

COVID-19 has traumatized the world. While virtually all Americans have felt the economic scourge of the pandemic, the actual risk of death is heavily biased against senior citizens.¹

Some of the most vulnerable individuals reside in nursing homes.² Nursing home administrators need to understand what risks put their patients in danger.³ Government executives and legislators also need to understand how these risks and vulnerabilities interact in order to formulate effective policy. For example, New York Governor Andrew Cuomo was criticized for his state directive, which ordered nursing homes to accept COVID-positive patients from hospitals.° The intention of the policy was to free up inpatient hospital capacity during the initial surge of COVID-19 patients.° By late July, more than 6,400 nursing home patients had died in New York.° Whether or not Governor Cuomo’s decision was unwise would be a difficult question to answer if politics weren’t a variable. However, the political controversy surrounding this question makes it near impossible to answer.

Regardless of the answer to the Cuomo question, it is critical that we understand how COVID-19 spreads and behaves in nursing homes.

This post analyzes how three major risk factors impact the probability that a nursing home will experience ** at least one** confirmed COVID-19 residential death. These factors are (i) new COVID positive admissions into a nursing home, (ii) COVID positive staff members and (iii) nursing home staffing shortages. That is, we seek to answer the following questions:

“As you get older, your risk for severe illness from COVID-19 increases. For example, people in their 50s are at higher risk for severe illness than people in their 40s. Similarly, people in their 60s or 70s are, in general, at higher risk for severe illness than people in their 50s. The greatest risk for severe illness from COVID-19 is among those aged 85 or older.”¹

“Given their congregate nature and resident population served (e.g., older adults often with underlying chronic medical conditions), nursing home populations are at high risk of being affected by respiratory pathogens like COVID-19 and other pathogens, including multidrug-resistant organisms (e.g., Carbapenemase-producing organisms, Candida auris ). As demonstrated by the COVID-19 pandemic, a strong infection prevention and control (IPC) program is critical to protect both residents and healthcare personnel (HCP).”³

**– Centers for Disease Control and Prevention**

#### 1. How do COVID-positive admissions into a nursing home affect the likelihood of at least one resident COVID-death occurring in a nursing home?

#### 2. How do COVID-positive nursing home staff members affect the likelihood of at least one resident COVID-death occurring in a nursing home?

#### 3. Do staffing shortages in nursing homes have an impact on the likelihood of at least one resident COVID-death occurring in a nursing home?

## Data

The cross-sectional dataset for this analysis is the **CDC’s Nursing Home COVID-19 Public File**, which contains 13,643 observations.¨ Definitions for each variables, and summary statistics are shown to the right.

The binary dependent variable, *+COVIDNursingHomeResidentDeaths*, equals 1 if a nursing home had at least one confirmed COVID residential death between the start of the outbreak and the end of May. **It should be noted that all variables adhere to this time horizon. **

To render a more intuitive regression interpretation, a logarithmic transformation was conducted on the independent variable that measures the number of new COVID positive admissions into a nursing home (*TOTCovidNursingHomeResidentDeaths*), which yielded the *LnCOVIDAdmission *variable. The same operation was also conducted on the independent variable that measures the number of staff members who were confirmed to have COVID (*TOTCovidAdmissions*), which yielded the *LnCOVIDStaff *variable.

Binary independent variables (equaling one for a positive value and zero for a value of 0) were also created from the two previously mentioned variables (yielding *AnyCOVIDAdmissions *& *AnyCOVIDStaffCases*, respectively).

The remaining covariates are binary. *QualityAssuranceCheck *equals 1 if a nursing home passed a quality assurance check while the remaining variables equal 1 if the nursing home faced a shortage of staff (each one refers to the type of shortage).

##### DEFINITIONS

## Methodology

This analysis employs three different regressions to estimate how the independent covariates impact the probability of at least one residential COVID-death in a nursing home. Both linear and non-linear techniques are utilized to estimate the model shown to the right in Figure 1.

The first two regressions are standard ordinary least squares (OLS) regressions, which result in the linear probability model (LPM). The first of these does not have state fixed effects but the second does employ them as controls.

As shown in Figure 2, the LPM offers an intuitive interpretation of the marginal effects of the covariates, both individually and as a whole, on the dependent variable: a one unit increase in an independent covariate increases the probability of the dependent variable equaling one (i.e. the probability that a nursing home has at least one residential COVID-death) by the covariate’s estimated coefficient.

However, the range of the model is not restricted to values between 0 and 1 (which is the support of any probability density function). As a result, the LPM can generate nonsensical fitted probabilities, including negative values and values greater than 1.

A solution to this issue is to employ a non-linear alternative: the logistic regression (aka *Logit – *shown in Figure 4.), which makes the predicted probabilities a function of the logistic cumulative distribution function (shown in Fig. 3). This preserves the *xβ *index and forces the predicted probabilities to lie between 0 and 1.

## Results

##### LPM

The first two regressions, found in columns (1) and (2) of Table 2 are the LPM regressions; the latter features state fixed effects. All of the variables that are statistically significant in the first LPM are also significant in the second. Because the second is likely a more accurate estimation of the population model, only those results will be discussed.

According to the LPM fitted values, none of the staffing shortage variables are significant and some are nonsensical. For example, according to the LPM results, a shortage of clinical (non-nursing) staff in a nursing home decreases the probability of at least one COVID-residential death. Thus, the LPM indicates that staffing shortages are not a significant risk factor for nursing homes.

The variable *AnyCovidAdmissions* is highly significant and indicates that a nursing home’s decision to admit at least one new COVID-positive resident is associated with a 18.6 percentage point (pp) increase in the probability of at least one residential COVID-death. This variable is an intercept term that is contrasted with the *LnCovidStaffCases *variable, which allows for a marginal slope change in the fitted regression line. This covariate is also significant at the .1% level and indicates that a 1% increase in COVID-positive new residents admitted into a nursing home is associated with a .0617 pp increase in the probability of at least one residential COVID-death, which means that doubling the number of COVID-positive residents increases the same chance of death by 6.17 pp.

The staff counterpart covariate to the *AnyCovidAdmissions *variable is *AnyCovidStaffCases*. The results show that this variable is not significant. However, the *LnStaffCases* covariate is highly significant and the results indicate that a 1% increase in COVID-positive staff increases the probability of at least one residential COVID-death by .173 percent, while a 100% increase in the covariate leads to a 17.3 pp increase in the dependent variable.

**Taken as a whole, and when using the mean values of each covariate as inputs, the LPM regression model in column (2) produces a fitted probability of .220941. This indicates that the average probability for a nursing home in the United States to experience at least one residential COVID-death is about 22%**

While highly significant, the *QualityAssuranceCheck* variable’s results are counterintuitive and will be discussed in the *Logit* analysis below.

##### LOGIT

The main regression of interest, the *Logit*, is found in column (3) of Table 2, while the marginal effects of that regression can be seen in column (4). State fixed effects are included in the *Logit* regression.

The *QualityAssuranceCheck *marginal effect coefficient was significant but curiously positive: according to the regression results, a passing grade is associated with a 28.3 percentage point (pp) increase in the probability of at least one residential COVID-death.

This is probably due to spurious correlation: nursing homes that are required to be audited likely have characteristics that put patients at higher risk, although this cannot be confirmed from the available data. All staff shortage variables are not found to be significant, except for *NursingShortage *(which is significant at the 5% level) unlike the LPM. The results indicate that if a nursing home experiences a nursing shortage, the probability of at least one COVID death is expected to increase by 2.5 pp. **Thus, like the LPM, the Logit results do not indicate that staffing shortages are large COVID risk factors for nursing home residents.**

Administrators must keep residents safe and be able to care for new patients. The results show that a nursing home’s decision to admit at least one new COVID-positive resident is associated with a 12.8 pp increase in the probability of at least one COVID residential death. The results also indicate that a 1% increase in COVID-positive new residents admitted into a nursing home is associated with a .0428 pp increase in the probability of at least one residential COVID-death. Put another way, if a nursing home experiences a 100% increase in COVID-positive new residents, we’d expect to see a 4.28 pp increase in the probability of at least one residential COVID-death. Both coefficient estimates are significant at the .1% level. **This suggests that new COVID admissions pose a significant risk to nursing home residents.**

New patients are not the only vectors of infection in nursing homes. According to the logit regression, if a nursing home had at least one staff member with COVID, we’d expect to see the probability of at least one residential COVID-death increase by 2.33 pp. Additionally, a 1% increase in the number of COVID-positive staff members is associated with a .11 pp increase in the probability of at least one residential COVID-death (or a 100% increase is expected to lead to a 11 pp increase in probability). These results are significant at the 5% level and .1% level, respectively.

**Both the LPM and the Logit suggest that COVID-positive staff have a greater marginal effect (per infected individual) on the probability of at least one residential COVID-death than new COVID-positive residents. However, both are significant risk factors that nursing home administrators should monitor.**

Sources Referenced

- Centers for Disease Control and Prevention. (2020). “Older Adults.” U.S. Department of Health and Human Services. (https://www.cdc.gov/coronavirus/2019-ncov/need-extra-precautions/older-adults.html
- Centers for Disease Control and Prevention. (2020). “People Who Live in a Nursing Home or Long-Term Care Facility.” U.S. Department of Health and Human Services. https://www.cdc.gov/coronavirus/2019-ncov/need-extra-precautions/people-in-nursing-homes.htm
- Centers for Disease Control and Prevention. (2020). “Preparing for COVID-19 in Nursing Homes.” U.S. Department of Health and Human Services. https://www.cdc.gov/coronavirus/2019-ncov/hcp/long-term-care.html

º Ferré-Sadurní, Luis., Harris, Amy Julia. (2020). “Does Cuomo Share Blame for 6,200 Virus Deaths in N.Y. Nursing Homes?” The New York Times.

¨Centers for Disease Control and Prevention. (2020). “COVID-19 Nursing Home Dataset.” https://healthdata.gov/dataset/covid-19-nursing-home-dataset