Application of Instrumental Variable Analysis in Pediatric End-Of-Life Research: A Case Study

Abstract

Instrumental variable analysis (IVA) has been widely used in many fields, including health care to determine the comparative effectiveness of a treatment, intervention, or policy. However, its application in pediatric end-of-life care research has been limited. This article provided a brief overview of IVA and its assumptions. It illustrated the use of IVA by investigating the comparative effectiveness of concurrent versus standard hospice care for reducing 1-day hospice enrollments. Concurrent hospice care is a relatively recent type of care enabled by the Affordable Care Act in 2010 for children enrolled in the Medicaid program and allows for receiving life-prolonging medical treatment concurrently with hospice care. The IVA was conducted using observational data from 18,152 pediatric patients enrolled in hospice between 2011 and 2013. The results indicated that enrollment in concurrent hospice care reduced 1-day enrollment by 19.3%.

The Institute of Medicine¹ emphasizes a need for more research on the effectiveness of interventions to improve pediatric end-of-life outcomes. While many advancements have been made, there have been tremendous methodological challenges to overcome. Randomized Controlled Trials (RCT) are the gold standard for evaluating the effectiveness;² however, there are concerns when approaching children and families at the end of life due to rapid disease progression and clinical instability.³ This raises ethical concerns about the harm-to-benefit ratio of RCT participation and makes it challenging for researchers to identify the proper time for enrollment based on inclusion criteria while also ensuring retention.^4,5 Further, if treatment provides any potential health benefits, patients and their families may not be willing to be randomized because of the potential to end up within the control group that does not receive treatment, thus making it difficult for researchers to obtain consent.⁶ Challenges in the recruitment and retention of patients at the end of life who participate in RCTs may result in a cohort of atypical patients with unique health circumstances rendering results ungeneralizable to a population beyond a specific research study.^6–8 Instrumental Variable Analysis (IVA) is a statistical methodology that offers a viable alternative for drawing inferences about the effectiveness of treatment using existing observational data when the conditions mentioned above make conducting an RCT difficult.^2,9 A growing number of publications are applying IVA to examine the comparative effectiveness of interventions for adults at the end of life. However, applications to pediatric research are still scarce.¹⁰ This paper aims to introduce IVA and demonstrate its suitability for pediatric end-of-life research.

Background

Instrumental variable analysis (IVA) can be considered a reasonable alternative to an RCT when circumstances render it infeasible or cost-prohibitive. IVA can identify causal relationships between exposure and outcome when the existing data meet certain necessary assumptions.⁶ IVA and RCTs are similar in their need to identify the exposure variable, treatment, and control (i.e., comparison, in the case of IVA) groups. However, a critical difference is the mechanism that determines how patients are assigned to treatment and comparison groups. In the RCT, assignment is done using randomization, which ensures that receiving treatment is independent of patients’ known and unknown characteristics and that the treatment and comparison group are well-balanced across such characteristics, thus assuring the study’s results are unbiased.

In IVA, treatment and comparison groups are determined through an instrumental variable (i.e., instrument), which on the theoretical level, controls for observed and unobserved patient characteristics affecting the study outcomes.¹¹ In application, any sociodemographic, health-related, and unknown differences between patients in treatment and comparison groups are controlled using a first-stage regression equation, which estimates the amount of variation in the instrument due to the exposure. Then, the second-stage regression estimates the variation in the exposure variable induced by the instrument.⁷

Examples of Instrumental Variables in End-of-Life Research

Because IVA requires identifying instrumental variables that can predict receiving the exposure, the most common instrumental variables that are used in end-of-life and palliative literature measure access to end-of-life care. In pediatric end-of-life research, the use of IVA is still rare. Only one study applied the methodology identified.¹⁰ The authors hypothesized that the availability of transportation services for families with medically fragile children with intellectual disabilities affects access to specialized end-of-life care. Therefore, the availability of transportation services was used as an instrumental variable to compare the effectiveness of care provided by the primary care provider and a combination of primary care providers with targeted case management to improve end-of-life outcomes for the child.

IVA in the adult population is quite common. For example, in several publications on cancer research, geographic variation in the application of specific cancer therapy has been used as an instrumental variable.^12,13 The authors of these studies hypothesized that because the geographic distribution of cancer therapies provided by healthcare centers is not random, some patients may have better access to certain therapies than others. The introduction of geographic variation in access to cancer therapies as an instrumental variable allows accounting for this inequality. As a result, the researchers determined the effects of receiving chemotherapy and cancer survival overall¹³ and lung cancer, specifically.¹²

In hospice studies, a commonly used instrumental variable is the geographic availability of hospice care.^14–16 It is hypothesized that hospices are distributed non-randomly in geographic regions, introducing additional bias in access to care. In one study, the geographic availability of hospices was operationalized as the number of hospice care providers within a specific geographic region.¹⁵ Doing so allowed evaluating the effect of hospice-provided care on survival near death. In two other studies,^14,16 geographic availability was operationalized as a travel distance to hospice care. Distance between nursing homes and hospices has also been used as an instrumental variable to evaluate the effects of hospice enrollment on the risks of hospitalizations.¹⁶ Distance between patients’ homes and hospice providers has also been used as an instrumental variable to determine the association between end-of-life care resources and patient outcomes in Pennsylvania’s ICUs.¹⁴

Another type of variable that has been widely used in health care literature but, to our knowledge, not in end-of-life care is a personal preference for care. The major assumption of the traditional RCT is that clinicians randomizing patients do not know which treatment is better for that patient to ensure that the treatment is assigned randomly. However, in observational studies, the clinicians’ preferences may affect the choice of treatments, introducing bias in the estimation of their effects.^17,18 Utilizing these preferences as instrumental variables may improve the assessment of the effects of different treatments. Pediatric end-of-life care research may also benefit from using parental preferences for care as instrumental variables. Because of the lack of specific standards for end-of-life care, parents set the goals of care, making decisions about who should provide care to their children.¹⁹ For some parents, the goal of end-of-life care may be limited to pain relief which a single hospice nurse can provide. Other parents may seek additional care from specialists in palliative care, mental health, dentistry, and so forth.²⁰ Thus, theoretically, the utilization of parental preference for care as instrumental variable may account for variation in treatments that children receive during hospice enrollment while not directly affecting the child’s health outcomes. Additional information on some of the nuances and limitations of using preference-based instruments in healthcare research may be found elsewhere.^17,21,22

A brief review of publications in end-of-life research shows that variability in geographic access to healthcare services can be considered an instrumental variable for the IVA. However, considering the large variability in pediatric end-of-life care and the lack of common standards in providing care, future research may also consider using other instrumental variables that affect the receipt of specialized care, such as healthcare providers’ treatment preferences in providing end-of-life care, pediatric end-of-life policies, and normative guidelines that are used in a specific region.

Assumptions of the IVA

There are three requirements that a well-defined instrumental variable must meet (Figure 1):

Figure 1. Assumptions of IVA and Variables of the Case Study.

Notes. Bold lines indicate holding assumptions of IVA, dotted lines indicate their violations. Variables from the case study are reported in parentheses.

1. Must be associated with the exposure variable (path a).

2. Must be exogenous (independent) from confounders (paths e and d; path c indicates a violation of this assumption).

3. Must be associated with the outcome variable only through its relation to the exposure (paths a and b) and not directly (path f)

The first assumption may be evaluated by reviewing estimates of first- and second-stage equations of IVA. The first-stage equation estimates the effect of the instrument on the exposure variable, while the second-stage equation estimates the effect of the exposure variable on the outcome variable. In a correctly specified model, the instrument would have a statistically significant effect on the exposure variable and exposure on the outcome.

Meeting the second assumption is difficult because there is always some correlation between the instrument and confounders because observational data are never allocated randomly.^7(p20) In some cases, this correlation can be negligible. In other cases, the effect of the instrumental variable on the exposure may be more substantial through the confounders (Figure 1, paths c and e) than directly (path a), resulting in an underestimation of the effectiveness of exposure. There is no specific test for testing the exogeneity of the instruments. Instead, two contingency tables are used. In the first table, the characteristics of the patients are tabulated across levels of the instrument, and in the second table - across treatment and comparison groups.²¹ Variables that are highly correlated within each table must be excluded from further analysis.

The third assumption can also be challenging to meet because the instrument may directly affect the outcome (path f) and is stronger than its effect through the exposure variable (paths a and b). This indicates the overall weakness of the instrument, which can be assessed using four approaches. First, by examining R², adjusted R², and partial R² estimates in the first-stage equation. The R² coefficient shows the overall correlation between the instrument, covariates, and exposure variable. The adjusted R² is adjusted to the number of predictors in the model. The value of the partial R² indicates the exogenous variation imposed by the instrumental variable after partialling out the effect of covariates.

Second, the effect of the instrument on the exposure can be examined using the F statistic, which indicates the significance of the instrument. If the value of the F statistic were not statistically significant, then the instrument variable would not have any additional explanatory power for the exposure variable after controlling for covariates. The value of the F statistic itself is also important; it is recommended to be above the critical value of 10 points.²³

The third approach includes using the Cragg and Donald’s test with Stock and Yogo’s critical values.²³ If the eigenvalue statistic of the Cragg-Donald’s test is smaller than the critical value of a 10% rejection rate, then the instrument is weak.

The fourth approach is to investigate the endogeneity of the exposure variable and whether a conventional regression analysis should be used instead of IVA. The endogeneity of the exposure may be tested by using Durbin and Wu–Hausman tests.^21(p543),24

Additionally, the validity of the IVA analysis can be estimated by comparing it with the results of a simple regression model (for example, OLS). Generally, if the instrumental variable is identified correctly, the effect of the treatment on the outcome variable estimated by IVA would be larger than the one estimated by a simple regression model.

For the proper specification of the IVA analysis, three major factors must be considered: the type of exposure variable, dependent variables, and the number of instrumental variables. Based on that, one of the four models may be selected, including two-stage Least Square (2SLS or TSLS), Limited Information Maximum Likelihood (LIML), Generalized Method of Moments (GMM), and probit (see Table 1). Structural Equation Models (ESM) that also can be used for IVA are beyond the scope of this review and extensively covered elsewhere.^{see 25–28} When choosing between 2SLS and LIML, it is necessary to consider that the LIML estimator may produce less bias in estimates and confidence intervals with better coverage rates than the 2SLS estimator.^29,30 The major advantage of GMM is that it can be used for modeling the effects of multiple instrumental variables.³¹ However, in models with one instrumental variable, all three estimators produce almost indistinguishable results.³⁰ Models that include binary dependent variables should be estimated using a probit model. However, when the exposure variable is binary as well, the 2SLS model may produce results very similar to probit.^32(p144) In this case, the advantage of the 2SLS model is that it produces estimates that can be easily interpreted and has more post-estimation commands that can check the assumptions of instruments in IVA.

Table 1.

IVA Model Specification in Stata

#	Dependent variable	Exposure variable	Number of instrumental variables	Model
1.	Continuous	Binary/Continuous	One	2SLS/LIML
2.	Continuous	Binary/Continuous	Multiple	GMM
3.	Binary	Binary	One	Probit/2SLS
4.	Binary	Continuous	One	Probit

Case Study: Impact of Pediatric End-of-Life Care Models on 1-day Hospice Admission

The implementation of the Affordable Care Act in 2010 made it possible for children enrolled in Medicaid to receive symptom-oriented hospice care together with disease-oriented medical treatment (i.e., concurrent hospice care). It is still relatively novel and may not be available through hospices in certain areas. Previous studies done with adult populations have shown that implementation of concurrent hospice care results in an increase in the length of hospice stay. Indeed, many patients enroll in hospice when treatment fails and death is inevitable. They may use hospice just for one day, and it can be extremely burdensome for hospices to perform work related to admission and death in a single day, which must conduct double the amount of work. For example, hospices must do all the paperwork required for enrolling patients in hospice, which takes hours, while also providing intense end-of-life care, which may take hours as well, and all of it must be done in one day. In contrast, enrollment in concurrent hospice care may be done in the earlier stages of disease progression, with a smoother transition from disease-oriented treatment to care focused on symptom management. The purpose of this study was to investigate the comparative effectiveness of concurrent hospice care versus standard hospice care in reducing the number of pediatric hospice patients with 1-day hospice enrollment.

Methods

Design and Sample

Data for this study came from the Centers for Medicare and Medicaid services that manage Medicaid health care plans, which is the largest pediatric insurer in the US. The data represented 18,152 pediatric patients under 21 years of age who were enrolled in hospice between January 1, 2011, and December 31, 2013. This study was reviewed and approved by the Institutional Review Board at the University of Tennessee, Knoxville (UTK IRB-18–04361-XP).

Measures

The end-of-life outcome of interest was the 1-day hospice enrollment. Children were differentiated by those who were enrolled in hospice for one day from those enrolled for two or more days. The treatment group included children who were enrolled in concurrent hospice care; the comparison group—included children in standard hospice care. The latter was the reference category in the analysis.

Covariates in the model included demographic, health, hospice, and community characteristics. Demographic characteristics included age, gender, race, and Hispanic ethnicity. Health status was measured using indicators of having a single complex chronic condition,³³ multiple complex chronic conditions, mental or behavioral health conditions, and technology dependence. Hospice characteristics included the size of the hospice: whether it had less than 50 employees (small hospice) or more than 50 employees (large hospice); ownership type: private or non-profit/government-owned; years of operation; and whether the hospice had a pediatric program. Community characteristics included the proportion of households with and without a high school diploma and with low income. The region of residence was categorized using the U.S. Census Bureau distinction and included: Northeast, Midwest, South, and West. Rurality was measured using the definition of the Health Resources and Services Administration.³⁴

Analytical approach

Hospice episodes (N = 42, 754) were created to accommodate for the fact that the same patient could be enrolled in hospice multiple times, each time receiving a different model of care.³⁵ These episodes were created using consecutive days of hospice admission, an approach that is commonly used in the literature.^36,37 The overall descriptive statistics are presented in Table 2.

Table 2.

Descriptive Statistics (N = 42,754)

	Statistic
1-day hospice enrollment, %	50.4%
Number of health care providers, M (SD)	1.29 (1.49)
Concurrent Hospice Care, %	34.4%
Demographic Characteristics
Age, M (SD)	7.45 (6.3)
Female, %	48.8%
non-Hispanic whites, %	53.8%
Black, %	27.2%
Hispanic, %	22.0%
Complex Chronic Condition, %	48.4%
Multiple Complex Chronic Conditions, %	28.0%
Mental/Behavioral Conditions, %	34.1%
Technology Dependence, %	22.9%
Hospice Characteristics
>50 employees, %	35.6%
Non-profit/Government, %	38.7%
Years of Operation, M(SD)	18.30 (9.8)
Pediatric Program, %	33.7%
Community Characteristics
No High School Education, M (SD)	14.00 (4.09)
High School Education, M (SD)	24.17 (9.93)
≤ $50,000/yr Household Income, %	35.6%
Northeast, %	57.5%
Midwest, %	24.3%
South, %	11.8%
West, %	6.5%
Rural, %	33.4%

IVA was conducted in several steps.^31,38 First, an instrumental variable that measures parental preference for care was identified, the number of providers seen during a hospice episode (see Figure 1). The hypothesis was that the preference for the number of providers seen during hospice enrollment affects the choice of model of hospice care, concurrent versus standard, but does not affect the duration of hospice stay.

Second, the two-step regression equation of the IVA model was computed using the 2SLS estimator with episodes clustered by children to accommodate for correlations between episodes from the same child.³⁹ The 2SLS estimator was appropriate for estimating the effects of binary exposure variables on binary dependent variables.³² The first-step regression of the IVA model was used to investigate whether the instrument affected the exposure variable (see Model 1, Table 3). The second-step regression (Model 2, Table 3) was used to estimate the effect of the exposure variable on the outcome.

Table 3.

Instrumental Variable and Logistic Regression Analyses (N = 42,754)

Variables	Instrumental Variable Analysis				Logistic Regression
	Model 1. Concurrent hospice care		Model 2. 1-Day Hospice enrollment		Model 3. 1-Day Hospice enrollment
	β (SE)	p	β (SE)	p	OR [95% CI]	p
Instrument
Number of healthcare providers	.070(.003)	<.001
Independent Variable
Concurrent hospice care	-	-	−.193 (.012)	<.001	1.071 [1.000, 1.151]	.051
Demographic Characteristics
Age	.002 (.001)	<.001	.003 (.001)	<.001	1.019 [1.012, 1.025]	<.001
Female	−.009 (.008)	.251	−.002 (.006)	.709	0.972 [0.900, 1.050]	.470
Caucasian	.002 (.011)	.825	.049 (.008)	<.001	1.549 [1.396, 1.718]	<.001
Black	−.009 (.010)	.374	.034 (.010)	<.001	1.354 [1.209, 1.517]	<.001
Hispanic	.014 (.011)	.196	−.014 (.007)	.055	0.844 [0.764, 0.932]	.001
Complex Chronic Cond.	−.050 (.008)	<.001	−.166 (.010)	<.001	0.493 [0.444, 0.546]	<.001
Multiple Complex Chronic Cond.	.018 (.017)	.296	−.077 (.011)	<.001	0.505 [0.434, 0.588]	<.001
Mental/Behavioral Cond.	.012 (.010)	.899	−.040 (.007)	<.001	0.719 [0.655, 0.079]	<.001
Technology Dependence	.005 (.020)	.782	.003 (.009)	.729	0.908 [0.781, 1.056]	.212
Hospice Characteristics
>50 employees	−.015 (.011)	.210	−.010 (.007)	.161	1.031 [0.930, 1.142]	.566
Non-profit/Government	.048 (.011)	<.001	.004 (.001)	.675	0.826 [0.727, 0.939]	.004
Years of Operation	.001 (.001)	.635	−.003 (.001)	<.001	0.967 [0.960, 0.974]	<.001
Pediatric Program	.012 (.012)	.298	.036 (.009)	<.001	1.110 [0.968, 1.261]	.138
Community Characteristics
No High School Education	−.002 (.001)	.176	−.001 (.001)	.065	0.986 [0.972, 1.000]	.061
High School Education	−.001 (.001)	.312	−.003 (.001)	<.001	0.989 [0.981, 0.997]	.007
Low income	.061 (.001)	<.001	.048 (.010)	<.001	1.373 [1.218, 1.547]	<.001
Midwest	.075 (.020)	<.001	.144 (.015)	<.001	0.423 [0.341, 0.527]	<.001
South	.120 (.020)	<.001	.023 (.013)	.064	0.406 [0.338, 0.488]	<.001
West	.082 (.025)	<.001	−.030 (.012)	.015	0.184 [0.138, 0.246]	<.001
Rural	.013 (.013)	<.297	.037 (.010)	<.001	1.257 [1.101, 1.436]	.001
Model Statistics
R2	.068		.124		.180
Adj. R2	.067
Partial R2	.043
F			497.573	<.001
Cragg-Donald eigenvalue			1905.78
Stock and Yogo (10%)			16.38
Partial R2			.043
Durbin χ2			94.578	<.001
Wu-Hausman			94.732	<.001

Note. SE=Standard Error. All analyses were controlled for study years. OR= odds ratios. Reference categories: standard hospice care, male, non-Caucasian, non-Black, non-Hispanic, no complex chronic conditions, no multiple complex chronic conditions, no mental/behavioral conditions, no technology dependence, <50 employees, private, no pediatric program, high income (> $50,000), North-East, urban. Total sample 42,753 observations,

Third, a contingency table (Table 4) was created with means and frequencies of children’s demographic, health, and community characteristics for concurrent and standard hospice care and cross levels of the instrument—seeing one health provider versus two or more to estimate whether the model met the second assumption about the independence of the instrument from other confounders.^21,40 A standardized mean difference coefficient (d) was reported that measures the standard difference between means in two groups in units of pooled within-group standard deviation.⁴⁰ Values of coefficient below 0.20 indicated a small effect; between 0.20 and .49 – small to medium effect; between 0.50 and 0.79 – medium to large; between 0.80 and 1.3 – large, and 1.3 and more – very large effect.⁴¹

Table 4.

Distribution of Sample Characteristics by Instrumental and Treatment Variables (N = 42,754)

	Treatment Groups			Instrumental Variable Groups
	Standard hospice care (n = 33,029)	Concurrent hospice care (n = 9,725)	d	1 health care provider (n = 37,963)	2+ health care providers (n = 4,791)	d
Demographics
Age	7.4	7.8	0.06	7.5	7.1	0.06
Female	48.2	47.0	0.02	48.1	47.2	0.02
Caucasian	47.5	45.0	0.05	48.3	36.2	0.25
Black	22.7	19.7	0.07	22.9	14.7	0.20
Hispanic	28.3	28.2	0.00	28.9	22.8	0.15
Complex Chronic Cond.	63.6	66.4	0.06	60.3	95.7	0.91
Multiple Complex Chronic Cond.	43.8	51.2	0.16	41.0	81.3	0.97
Mental/Behavioral Cond.	46.5	50.4	0.08	45.5	62.0	0.34
Technology Dependence	36.9	43.4	0.15	34.8	66.8	0.73
Hospice Characteristics
>50 employees	41.0	42.3	0.03	38.7	62.2	0.49
Non-profit/Government	38.1	41.2	0.06	39.8	31.5	0.17
Years of Operation	18.2	18.6	0.04	17.8	22.1	0.49
Pediatric Program	34.3	38.2	0.08	33.1	51.3	0.38
Community Characteristics
No High School Education	13.9	14.5	0.14	13.8	15.7	0.38
High School Education	24.0	24.9	0.11	23.8	27.3	0.39
Low income	25.8	34.4	0.18	25.3	47.0	0.45
Northeast	55.0	41.7	0.27	57.1	11.1	1.16
Midwest	16.0	17.4	0.03	15.6	21.7	0.14
South	8.2	16.1	0.24	6.1	40.4	0.87
West	20.9	24.9	0.15	21.2	26.9	0.18
Rural	40.4	46.5	0.13	40.6	51.4	0.22

Note. d = Standardized difference is the difference in means between the two groups in units of the pooled standard deviation.^{see 40,41}

Fourth, the R² was reported, along with the adjusted R² and partial R² statistics from the first-stage equation, to evaluate whether the model met the third assumption (i.e., that the instrument must affect the dependent variable only its relationship with the exposure variable, Model 1, Table 3). The effect of the instrument on the exposure variable using the F statistic was also examined. The weakness of the instrument was assessed using Cragg-Donald’s eigenvalue statistic together with Stock and Yogo’s critical values.²³ The endogeneity of the exposure variable was assessed using the Durbin χ2 and Wu-Hausman test, which answers the question of whether a simple regression model should be used instead of IVA.

Finally, to illustrate the third assumption of the IVA, the relationship between the type of hospice enrollment and 1-day enrollment was modeled using a logistic regression equation (Model 3, Table 3). Because children in the study may have had multiple hospice enrollment episodes, we modeled clustering of hospice episodes for the children. Then the effects of the exposure variable estimated by the logistic regression model and the second equation of the IVA were compared. If the effect of the exposure variable on outcome were stronger in the simple regression model than in the second step of IVA, that would indicate the presence of critical confounding variables unaccounted for in the simple model. It is also important to keep in mind that the logistic model (Model 3, Table 3) reports the odds of the occurrence of the 1-day hospice enrollment, whereas the linear regression model applied to a binary dependent variable (Model 2, Table 3) the probability of a such event.

Stata 15.0 software package was used for conducting IVA. Other packages, such as R and SAS, may also be used for this type of analysis and have been covered elsewhere.^42,43

Results

Sample Characteristics

Slightly more than half of all children (50.4%) were enrolled in hospice for just one day, and around one in three children were enrolled in concurrent hospice care (34.4%; see Table 2). The average age of children was around 7 years (SD = 6.3). Half of the children (48.8%) were female, of the non-Hispanic white race (53.8%), and had at least one complex chronic condition (48.4%). One in three children (28.0%) had multiple complex chronic conditions or mental/behavioral health conditions (34.1%), and fewer than one in four children (22.9%) had technology dependence. One in three hospices (35.6%) was large, had more than 50 employees, had non-profit or governmental ownership (38.7%), and had pediatric programs (33.7%). Most of the children (57.5%) resided in the Northeast, and around one in three children resided in rural communities.

Testing the First Assumption of IVA

The results of the first-stage equation (Model 1. Table 3) indicate that the number of providers seen in hospice was a statistically significant predictor of enrollment in concurrent hospice care. An increase of health care providers by 1 increased enrollment in concurrent hospice care by 7%. The results of the second-stage equation indicated that the type of hospice enrollment had a statistically significant effect on the proportion of children enrolled in hospice for one day. The enrollment in concurrent hospice care resulted in a 19.3% decrease in 1-day hospice enrollment.

Testing the Second Assumption of IVA

The distribution of sample characteristics by instrumental and treatment variables is presented in Table 4. As expected, there was a significant correlation between the severity of health conditions and the number of healthcare providers seen during hospice enrollment. In comparison to those children who saw only one healthcare provider, children who saw multiple healthcare providers were more likely to have complex chronic conditions (60.3% vs. 95.7%). They were also twice as likely to have multiple complex chronic conditions (41.0% vs. 81.3%) and have technological dependence (34.8% vs. 66.8%). There were also large differences in the place of residence: most of the children who resided in the Northeast (57.1%) saw one healthcare provider, whereas most of the children residing in the South (40.4%) saw 2 or more care providers. The overall imbalance in characteristics of children in two groups with one health care provider and 2+ health care providers indicates that the instrumental variable did not perform as a perfect randomizer. This result was expected and may indicate that the effect of the exposure variable on the dependent variable was slightly underestimated by the IVA. At the same time, small to medium differences in characteristics of children enrolled in standard versus concurrent hospice care may indicate that the bias in the relationship between the instrument and exposure variable is negligible.

Testing the Third Assumption of IVA

As shown in Table 3, both R² and adjusted R² were around 7%, which is a relatively small number, but this value can be inflated because we fitted the 2SLS model for estimating binary dependent variables. Partial R² was equal to .043 and only slightly smaller than the R², indicating that most of the variation between the predictors in the first model and the exposure variable could be explained by the variation in the instrument. The F statistic was statistically significant (p < .001), and its value was 497.573, much larger than the critical value of 10, indicating a strong correlation between the instrument and the exposure variable. The value of the Cragg-Donald eigenvalue statistic was equal to 1905.78, which is much larger than the critical value of 16.38 of Stock and Yogo’s test for the lowest rejection rate of 10% that could be tolerated. This indicates that the null hypotheses can be rejected and that the instrument was weak.²³

The results of the logistic regression analysis are presented in Model 3, Table 3. It showed that when controlling for demographic, hospice, and community characteristics, enrollment in concurrent hospice care increased the odds of receiving hospice care for 1 day by 7% (OR = 1.071, 95% CI [1.000, 1.151]). However, the effect was not statistically significant, with p = .051.

Discussion

The purpose of this study was to introduce the IVA and illustrate it using observational data of pediatric patients enrolled in hospice care. The result indicated that enrollment in concurrent care reduced receiving 1-day hospice care by 19.3%. The validity of the instrumental variable was assessed using the R², adjusted R², partial R², and F statistics, Cragg-Donald’s eigenvalue statistic together with Stock and Yogo’s critical values, Durbin χ2, and Wu-Hausman tests. It also showed that the results of IVA were superior to the results of the simple regression model. Among software packages for conducting the IVA, Stata provides a large variety of tools for computing the effects and comes as default or can be preinstalled. This software provides many estimators and can run tests to estimate whether the instrument meets all three assumptions of the IVA.

IVA has limitations. It can be difficult to identify a suitable instrument that meets the necessary assumptions required of a strong predictor of the exposure variable in addition to influencing the outcome variable and having no relationship with the characteristics of patients. In practice, these ideal requirements can be hard to achieve, leading to slightly biased estimates of the effect of the exposure on the outcome. However, IVA provides numerous tests and statistics that can be used to identify any issues in instrument selection and modeling.

Despite these limitations, utilization of IVA can be especially beneficial for future studies that aim to investigate the comparative effectiveness of treatments for vulnerable and hard-to-reach populations which historically have been excluded from RCTs, such as medically fragile children, children with medical complexity or complex chronic conditions. New knowledge generated from quasi-experimental studies would generate a higher level of evidence than from non-experimental studies. Additionally, it would facilitate the transition from simplistic single practices and treatment strategies that are based on anecdotal clinical experience to evidence-based systems,⁴⁴ which would assist in choosing treatment options for sick children.

One of the significant challenges in conducting IVA is the proper identification of the instrumental variable. It can be helpful to think of the instrument as a pseudo-randomizer that affects receiving treatment without directly affecting the outcome variable. Existing literature suggests that proximity to healthcare providers,^14–16 availability of transportation services¹⁰ and any other variables that determine preference for receiving care²¹ can be considered as reliable instrumental variables. Based on that, for researchers who are planning to use IVA in their prospective observational studies, it can be helpful to collect additional geospatial data on hospice locations, community needs in health care services,⁴⁵ or data on hospice length of stay, hospice disenrollment, emergency room transition, and inpatient transition.⁴⁶ Also, some researchers advise that instrumental variables must always and completely precede the exposure variable. Based on existing literature, we view this approach as restrictive and unnecessarily limiting options for instrumental variables. In particular, the instrument that was used in this study falls into the category of so-called personal preference-based instruments.²¹ Conceptually, within this framework, personal preferences, due to their subjective nature, are allowed to be time-variant, quickly change in time, and overlap with the exposure in time.²¹ For example, in several studies, clinician preference for treatment was used as an instrumental variable.^18,21 The limitations of the preference-based framework were further justified in the follow-up publications.^{see 21,22}

In summary, IVA provides numerous advantages when RCTs are infeasible or cost-prohibitive in end-of-life research. IVA’s application is less time-intensive in terms of data collection and potentially less invasive for patients. This methodology provides nursing researchers a unique opportunity to conclude the effectiveness of different healthcare approaches and strategies leveraging existing observational data and a quasi-experimental design. The main challenge of IVA is that it can be difficult to identify an instrumental variable that may explain why some patients receive a particular form of treatment while others don’t. Although the most common instrumental variables that are used in end-of-life research measure geographic access, other characteristics of health care services, including parental preferences for care, may also be suitable instruments.