Net effects of correlated determinants of health among U.S. older adults

Abstract

Background

The health effect produced by a contributing factor alone may be different from the effect when other interacting factors are present. The effects of a set of contributors, estimated by regression coefficients, may be invalid or inappropriate if some of the predictors are correlated or the model has interaction and nonlinear terms. The net effect (NE) of a given contributing factor is the effect produced by the factor alone, not by other factors due to their correlations with the factor of interest. This study estimated NE of selected determinants of health for U.S. older adults.

Methods

Participants, aged ≥ 65 years, were from the baseline 2020 Medicare Health Outcome Survey (N = 196,641). We examined the NE of each explanatory variable from five specified categories on four health outcomes: physical component summary scores (PCS), mental component summary scores (MCS), health utilities (SF-6D), and 2-year mortality. The five categories of explanatory variables included: six difficulties in activities of daily living (ADLs), three difficulties in instrumental activities of daily living (IADLs), five geriatric syndromes, five demographics, and fifteen chronic conditions. The NE for a given factor was calculated as the average of the factor’s marginal effect over all possible values of other factors.

Results

After adjusting for age, race, and sex, difficulty in walking contributed the greatest decrement in PCS (NE= -7.4) among the 6 ADLs. Other ADL decrements were 4.5-points for bathing, 4.4-points for getting in/out of chairs, 2.7-points for dressing, 1.5-points for using the toilet, and 1.3-points for eating. For MCS, difficulty in eating contributed the greatest decrement (-4.9), followed by bathing (-3.9) and walking (-3.2). For the SF-6D, difficulty in walking had a NE of -0.078 while difficulty in bathing had the greatest increment for 2-year mortality (8.1%). The NEs for the explanatory variables in the other categories are presented.

Conclusions

This study introduced NE as a measure of effect produced by each determinant of health and demonstrated how to estimate the net effect for various types of data. Our results highlight how the net effect varies within a given category, and differs according to physical and mental health and mortality.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12877-025-06814-8.

Introduction

Multiple factors can influence health, and these contributing factors may not affect health equally [1, 2]. These factors also may impact health through different mechanisms. In the realms of clinical practice, public health planning, and policy making, determining the effect of these contributing factors on a health outcome, such as decreases in health-related quality of life (HRQOL) and increases in incidence of a disease and/or mortality, would be of great value [3, 4]. Of note, the effect produced by a contributing factor alone may be different from the effect when other interacting factors, which can be confounders, moderators, or mediators, are present [5]. As an example, certain combinations of chronic conditions may be synergistically or antagonistically associated with lower HRQOL [6].

Researchers often have tried comparing different determinants of health that interact with one another with regard to their effects on health outcomes [7–9]. For example, based on common underlying causes or mechanisms, persons with hypertension have an increased risk of other cardiovascular conditions such as angina, myocardial infarction, stroke, or congestive heart failure, and lead to an adverse effect on HRQOL and mortlaity [8, 9]. When multiple interacting contributing factors are present, the part of the health effect that is produced by each factor alone should be estimated. In this study, we used the term “net effect” to represent the effect that is attributable to the factor, not by other factors due to their correlations with the factor of interest.

The effects of a set of explanatory variables are commonly assessed by regression coefficients in a multiple regression model [10–13]. The regression coefficient of a given explanatory variable is the expected change in the outcome, following a one-unit change in the predictor, with all other explanatory variables held constant. However, multiple regression has some limitations. First, if the model includes interaction terms between this variable and other covariates or polynomial terms of this variable, its regression coefficient cannot be interpreted in this manner. Second, for bounded outcomes such as health expenditures and health-related quality of life scores, two-part models are often used for better prediction and more intuitive interpretation [14–16]. However, regression coefficients in a two-part model cannot be interpreted as effects of corresponding predictors. Third, the estimated regression coefficient can be unreliable or misleading if some of predictors are highly correlated (i.e., multicollinearity) [17]. Common methods to deal with the multicollinearity include removing correlated predictors from the model, combining some highly correlated predictors into one predictor, and using ridge regression [17].

The net effect of a contributing factor can be interpreted as the part of the total effect collectively produced by a set of interacting factors that is attributed to the factor [18]. Thus, the research question is how to allocate the total effect produced by a set of factors to each individual factor. Cox proposed a set of axioms for the solution to the contribution allocation problems in the risk analysis [18]. In particular, the contribution allocation should satisfy the additive property, i.e., the net effects of presenting each factor in a set of binary factors should be summarized to the total effect when all factors in the set are presented.

In this study, we proposed to measure the net effect of a given contributing factor among a set of interacting contributing factors as the average of this factor’s marginal effect over all possible combinations of values of other factors in the set. This method was based on the concept solution to the contribution allocation in the risk analysis and the Shapley value, the shared cost problem of assigning the value of each player in a cooperative game [18, 19]. The NE is an extension of the Shapley value for various types of data. Using a large nationwide survey of U.S. older adults, we demonstrated the method through estimating the net effects of selected contributing factors on HRQOL scores and 2-year mortality.

Methods

Study sample

This study used data from the Medicare Health Outcome Survey (HOS) [20]. Initiated by the Centers for Medicare & Medicaid Services (CMS), the Medicare HOS is a nationwide annual survey of Medicare beneficiaries who voluntarily enrolled in Medicare Advantage private health plans that include persons aged 65 years and older and persons younger than 65 years with disabilities [20]. Each year, the survey randomly selects a cohort of continuously enrolled members from each Medicare Advantage plan. The selected individuals who complete a baseline survey are resurveyed two years later. This study used the Medicare HOS Public Use Data Files (PUFs) from the 2020 baseline survey of the Cohort 23 [21]. We included participants aged ≥ 65 years at the baseline. After excluding persons with a missing value of race and sex, the total sample size in this analysis was 196,643.

Measures

We examined four health outcomes: three HRQOL measures and 2-year mortality. Participants’ physical component summary (PCS) scores and mental component summary (MCS) scores were based on the Veterans RAND 12-Item Health Survey (VR-12) [22], and participants’ health utility (SF-6D) scores were derived from the VR-12 responses [23]. Participants who had died within two-years of the follow-up period were identified from the National Death Index, and the participants’ two-year mortality status was in the HOS data file [24].

The Medicare HOS also included three questions on recent number of unhealthy days: physically unhealthy days (PUD), mentally unhealthy days (MUD), and activity limitations days (ALD). These questions were intended to measure the participants’ perceived physical health, mental and emotional distress, and disability due to poor physical or mental health, respectively [25]. Unlike the PCS, MCS, and SF-6D measures, these measures did not mention a specific problem, symptom, or limitation. We examined these variables as an evaluation for the NE as well as a demonstration of the NE for count outcomes.

We examined selected explanatory variables in each of the following five categories: (1) Five demographics: age, race, gender, marital status, and education, which were binary or 3-category variables; (2) Six variables on difficulty in activities of daily living (ADLs): bathing, dressing, eating, getting in/out of chairs, walking, and using the toilet. These variables were binary (have difficulty or unable to do this activity vs. no difficulty); (3) Three variables on difficulty in instrumental activities of daily living (IADLs): preparing meals, managing money, and taking medication as prescribed. These variables were 3-category (no difficulty, have difficulty, and don’t do this activity); (4) Five geriatric syndromes: memory problems, pain interfered with activities, pain interfered with socializing, pain ratings, and sleep quality. These variables were 4–10 level ordinal categories and were treated as continuous variables; and (5) Fifteen chronic conditions that were based on if a doctor had ever told the respondent that they had a given condition (Table 1); all conditions were binary.

Table 1.

Sample characteristics, 2020 Medicare Health Outcome Survey (HOS) cohort 15, baseline

Variable	N	%	Variable	N	%
Total	196,643	100.0%	ADL1: Have any difficulty doing
Age			Bathing	29,681	15.1%
65–74	117,382	59.7%	Dressing	23,117	11.8%
75+	79,261	40.3%	Eating	10,031	5.1%
Race			Getting in/out of chairs	43,964	22.4%
White	156,356	79.5%	Walking	65,960	33.5%
Black	24,270	12.3%	Using toilet	16,916	8.6%
Other	16,017	8.1%	IADL2 Have any difficulty doing
Sex			Preparing Meals:
Male	81,540	41.5%	No, don’t have difficulty	157,496	80.4%
Female	115,103	58.5%	Yes, I have difficulty	20,662	10.6%
Education			Don’t do this activity	17,678	9.0%
Less than high school	32,839	17.0%	Managing Money:
High school	59,676	30.9%	No, don’t have difficulty	175,622	89.7%
Greater than high school	100,439	52.1%	Yes, I have difficulty	9,345	4.8%
Marital Status			Don’t do this activity	10,901	5.6%
Married	93,767	48.9%	Taking Medication as prescribed:
Non-married	97,952	51.1%	No, don’t have difficulty	178,221	91.3%
Chronic conditions			Yes, I have difficulty	9,590	4.9%
Hypertension	112,786	65.5%	Don’t do this activity	7,434	3.8%
Coronary artery disease	20,654	12.0%	Geriatric symptoms3	Mean	SD
Congestive heart failure	13,872	8.1%	Memory problems (1–5)	1.82	0.234
Heart attack	13,753	8.0%	Pain interfered w activities (1–5)	1.71	0.302
Other heart conditions	36,401	21.2%	Pain interfered w socializing (1–5)	1.82	0.271
Stroke	12,858	7.5%	Pain rating (1–10)	1.73	0.277
Diabetes	46,919	27.3%	Sleep quality (1–4)	1.67	0.234
Arthritis of hip or knee	75,582	43.9%	Outcomes	Mean	SD
Arthritis of hand or wrist	62,867	36.5%	PCS	41.8	12.3
Osteoporosis	35,424	20.6%	MCS	53.2	9.9
Sciatica	44,911	26.1%	SF-6D	0.737	0.157
COPD	32,376	18.8%		N	%
Inflammatory bowel disease	8,541	5.0%	Mortality	15,607	7.9%
Depression	33,988	19.7%
Cancer	26,373	15.3%

¹ADL: Difficulty in Activities of Daily Living

²IADL: Difficulty in Instrumental Activities of Daily Living

³Geriatric symptoms: all are based on original values

Statistical analysis

The net effect (NE) of a given factor in a set of binary contributing factors was based on the Shapley value and calculated as the average of the factor’s marginal effect over permutations of other factors in the set [18, 19, 26].

Let be a set of binary variables for presence or absence of a factor. Suppose notation is number of factors that do not include factor and is number of factors that include and . Let and be the mean outcome scores for those with factors, and , respectively. Thus, the marginal effect of factor for is . For each there are possible’s. Thus, the NE of is calculated as [18]:

1

satisfies the additivity property [18], i.e. the total effect of all factors, -, equals the sum of all individual NEs: . An illustration of NE for three binary contributing factors and a numerical example are in Appendix A.

All mean scores (and ) in formula (1) can be estimated directly from the data. However, when is relatively large, obtaining reliable direct estimates for all mean scores may not be possible even when the sample size is large. These mean scores can be estimated from a linear regression model that includes all interaction terms. For binary outcomes (e.g., mortality), the NE can be estimated from a logistic model. Similarly, for count outcomes (e.g., PUD), the NE can be estimated from a Poisson model. Because there were a large number of zero unhealthy days, the NE for these outcomes were estimated from a zero-inflated Poisson model, a type of two-part model.

The NE formula (1) can be extended to categorical explanatory variables with more than two categories. For a categorical predictor, its sub-categories are mutually exclusive states. Therefore, the NE for categorical predictors is averaged over combinations of all possible values of other predictors. To illustrate this method, let’s use following example that all explanatory variables were categorical variables of same number of categories (). Suppose category is the reference for all variables. Notation is for those with number of factors at categories and not including factor (i.e., is at the reference or ), the number of possible is . Similarly, notation is for those with factor at a given level and . Suppose and are the mean scores for and , respectively. The marginal effect of at level compared to the reference () for is . Therefore, the NE for variable at levels () vs. the reference (=) is:

2

The general form of the NE for mixed categorical predictors is:

3

where AM(.) is arithmetic mean over all possible combinations of .

For continuous explanatory variables, the NE was calculated by averaging over all possible values of all the other predictors as the continuous predictor increases from a reference point to  [18]. The NE is interpreted as the effect attributable to a one-point increase in the predictor. For a continuous variable with a lower bound and a upper bound, we can re-scale this variable so that the re-scaled variable ranges from 0 to 1. For example, the pain rating variable has a value from 1 for “no pain” to 10 for “worst imaginable pain”. The NE of the re-scaled pain rating is the effect attributable to having the “worst imaginable pain” vs. “no pain”.

The estimated NE can be adjusted for possible confounders by replacing mean scores in NE formulas with standardized mean scores using the direct standardization method. Standard errors of NE estimates were obtained from the bootstrap method. All analyses were performed using SAS, version 9.4 (SAS Institute Inc.).

Results

Approximately 60% of participants were between age 65 years and 74 years, and 40% were 75 years and older (Table 1). About 80% of participants were white, 12% were Black, and the remaining 8% were other races; about 59% were females. The mean PCS was 41.8 (SD = 12.3), mean MCS was 53.2 (9.9), and mean SF-6D was 0.737 (0.157). Among these participants, 15,607 (7.9%) died during the 2-year follow-up. Table 1 also includes the descriptive statistics of all explanatory variables.

We estimated the NE for each of the six ADLs, all of which were binary variables. The lower part of Table 2 presents standardized mean scores (by age, race, and sex) of the four outcomes for participants who had difficulty for none of the six ADLs and for all six ADLs, as well as the total effect of the six ADLs, which is the mean score difference between these two groups (difficulties for all vs. no difficulty). For example, the standardized mean PCS was 26.3 for those who had all six difficulties and 48.1 for participants who had none of the six difficulties. Thus, the total effect of the six ADLs on PCS contributed a 21.9-point decrement (26.3 vs. 48.1) in PCS.

Table 2.

Net effect (NE) for each of the 6 activities of daily living (ADLs)

Difficulty in Activities of Daily Living (ADLs)	PCS		MCS		SF-6D		Mortality
	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1,2	S.E.
Bathing	−4.5	0.33	−3.9	0.34	−0.060	0.0042	8.1%	0.82%
Dressing	−2.7	0.32	−2.0	0.34	−0.040	0.0041	6.6%	0.80%
Eating	−1.3	0.28	−4.9	0.30	−0.049	0.0035	4.3%	0.67%
Getting in/out of chairs	−4.4	0.32	−1.1	0.33	−0.042	0.0040	0.8%*	0.78%
Walking	−7.4	0.36	−3.2	0.38	−0.078	0.0047	5.0%	0.93%
Using toilet	−1.5	0.30	−2.0	0.31	−0.035	0.0037	3.6%	0.71%
Sum of NE	−21.9		−17.1		−0.304		28.4%
	Mean1	S.E.	Mean1	S.E.	Mean1	S.E.	Mean1	S.E.
None (of the 6 difficulties)	48.1	0.05	55.4	0.05	0.812	0.0007	4.1%	0.15%
All (of the 6 difficulties)	26.3	0.13	38.3	0.14	0.508	0.0017	32.5%	0.37%
Total effect2	−21.9		−17.1		−0.304		28.4%

¹All scores were age-race-gender standardized

²Total effect was difference in mean score between All and None

^*p value > 0.05 for testing NE = 0

The upper part of Table 2 presents the NE of each of the six ADLs. For example, difficulty in walking had the greatest negative NE (−7.4) on PCS among the six ADLs, indicating that this difficulty contributed a 7.4-point decrement in PCS. Moreover, difficulty in bathing directly contributed a 4.5-point decrement; getting in/out of chairs, 4.4-point decrement; dressing, 2.7-point decrement; using the toilet, 1.5-point decrement; and eating, 1.3-point decrement. Of note, the sum of all NEs equals the total effect of the six difficulties, i.e., (−4.5) + (-2.7) + (-1.3) + (-4.4) + (-7.4) + (-1.5) = -21.9 = (26.3 - 48.1). For MCS, difficulty in eating contributed the greatest negative effect among the six ADLs (NE= −4.9), followed by bathing (NE= −3.9) and walking (NE= −3.2). For the health utility (SF-6D), difficulty in walking contributed the greatest negative effect (NE= −0.078) while difficulty in using the toilet contributed the least negative effect (NE= −0.035). For 2-year mortality, difficulty in bathing had the greatest NE, contributing an 8.1% increase while difficulty in getting in/out of chairs had a non-significant NE of 0.8%.

Table 3 presents the results for the three IADLs, which were all 3-level categorical variables. Because a participant cannot be in both the “had difficulty” category and “don’t do this activity” category for a given difficulty, the total effect as well as the sum of NE is impossible to define. Regarding the NE, using the PCS outcome as an example, for preparing meals, having difficulty (vs. not having difficulty) contributed a 14.0-point decline while not doing this activity contributed a 12.3-point decline. For managing money, having difficulty contributed a 3.1-point decline while not doing this activity contributed a 2.7-point decline. For taking medication as prescribed, having difficulty contributed a 4.1-point decline while not doing this activity contributed a 3.1-point increase.

Table 3.

Net effect (NE) for each of the 3 instrumental activities of daily living (IADLs)

Difficulty in Instrumental Activities of Daily Living (IADL)	PCS		MCS		SF-6D		Mortality
	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.
Preparing Meals2
Have difficulty	−14.0	0.61	−6.3	0.53	−0.164	0.0075	9.8%	1.44%
Don’t do this activity	−12.3	0.55	−4.7	0.48	−0.130	0.0068	13.9%	1.28%
Managing Money2
Have difficulty	−3.1	0.59	−7.5	0.51	−0.092	0.0073	1.9%*	1.39%
Don’t do this activity	−2.7	0.55	−3.4	0.48	−0.045	0.0068	5.0%	1.28%
Taking Medication as prescribed2
Have difficulty	−4.1	0.43	−6.4	0.37	−0.082	0.0054	5.0%	1.02%
Don’t do this activity	3.1	0.64	−1.1	0.55	0.021	0.0078	3.2%	1.48%

¹All scores were age-race-gender standardized

²reference category is “don’t have difficulty”

^*p value > 0.05 for testing NE = 0

We estimated the NE of five demographic variables to demonstrate this method for some mixed types of categorical predictors: three predictors were binary variables (age, gender, and marital status) and two predictors were 3-category variables (race and education); the result is in Table 4.

Table 4.

Net effect (NE) for each of the 4 demographics

Demographics	PCS		MCS		SF-6D		Mortality
	NE	S.E.	NE	S.E.	NE	S.E.	NE	S.E.
Age (ref: 65–74)
75 or older	−2.4	0.38	0.1*	0.31	−0.018	0.0046	8.0%	0.77%
Race (ref: White)
Black	−1.2	0.52	−0.6*	0.36	−0.011*	0.0058	−0.8%*	0.72%
Other	−0.1*	0.52	−1.9	0.37	−0.019	0.0052	−1.8%	0.77%
Sex (ref: Male)
Female	−1.2	0.41	−0.4*	0.30	−0.018	0.0042	−3.3%	0.74%
Marital status (ref: Married)
Non-married	−2.0	0.32	−1.5	0.31	−0.032	0.0043	3.8%	0.60%
Education (ref: < High school)
High school	2.8	0.44	2.3	0.37	0.041	0.0059	−1.9%	0.74%
>high school	5.9	0.59	3.7	0.30	0.073	0.0059	−4.3%	0.86%

^*p value > 0.05 for testing NE = 0

Using PCS outcome as an example, being aged 75 years or older (vs. 65–74 years) was associated with a 2.4-point decrease; identifying as Black (vs. white), a 1.2-point decrease; identifying as another race, a non-significant 0.1-point decrease; being female (vs. male), a 1.2-point decrease; being non-married (vs. married), a 2.0-point decrease; having a high school education (vs. less than high school), a 2.8-point increase; and having more than a high school education, a 5.9-point increase.

Table 5 presents results for the five symptoms, each of which is a continuous variable. For continuous predictors, the NE represents the effect contributed by having the worst score for the contributing factor in contrast to the best score. For example, having the worst (highest) pain interfered with daily activities score contributed a 13.5-point decline in PCS, a nonsignificant 1.0-point difference in MCS, a 0.111-point decline in SF-6D, and a 7.7% increase in 2-year morality, respectively, as compared to the best (lowest) pain score for this category. This table also includes the NEs of the five symptoms for PUD, MUD, and ALD. The results of the PUD, MUD, ALD were mostly consistent with the results of the PCS, MCS, and SF-6D. For example, having the worst (highest) pain interfered with daily activities score contributed a 9.3-point increase in physical health (PUD), a nonsignificant 0.6-point difference in mental health (MUD), and a 5.2-point increase in total physical and mental health (ALD) as compared to the best (lowest) score.

Table 5.

Net effect (NE) for each of the 5 symptoms

Geriatric Symptoms	PCS		MCS		SF-6D		Mortality		PUD		MUD		ALD
	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.
Memory problems	0.3*	0.37	−13.6	0.48	−0.083	0.0039	10.9%	1.59%	4.7	0.37	13.3	0.36	9.3	0.25
Pain: daily activities2	−13.5	1.07	1.0*	1.23	−0.111	0.0098	7.7%	1.97%	9.3	0.6	0.6*	0.58	5.2	0.41
Pain: socializing3	−4.9	0.72	−13.5	0.92	−0.128	0.0064	10.6%	1.85%	6.7	0.46	6.9	0.44	10.1	0.33
Pain rating	−4.1	0.8	−1.3*	1.03	−0.051	0.0095	−3.2%*	2.43%	5.3	0.52	2.4	0.51	2.7	0.35
Sleep quality	−0.2*	0.45	−7.3	0.52	−0.045	0.0046	−0.7%*	1.91%	2.9	0.4	4.8	0.39	3.1	0.25

¹All scores were age-race-gender standardized

²Pain interfered with daily activities

³Pain interfered with socializing

*p value >0.05 for testing NE=0

Finally, we estimated the NE for the 15 chronic conditions (Table 6). Arthritis of the hip or knee contributed the biggest decline in PCS (NE= −5.1), followed by COPD (NE= −3.6), sciatica (NE= −3.4), and congestive heart failure (NE= −3.3). Depression contributed a far greater decline in MCS (NE=−11.8) than any of the other conditions, and this amount was more than the other 14 conditions combined (−9.6). Congestive heart failure was the biggest driver for 2-year mortality with a NE of 9.4%, followed by stroke (NE = 5.6%), cancer (NE = 3.9%), COPD (NE = 3.5%), and depression (NE = 2.7%), while sciatica contributed a 1.0% decline in mortality.

Table 6.

Net effect (NE) for each of the 15 chronic conditions

Chronic conditions	PCS		MCS		SF-6D		Mortality
	NE1	S.E.	NE1	S.E.	NE1	S.E.	NE1	S.E.
Hypertension	−1.8	0.17	0.1*	0.14	−0.012	0.0021	0.1%*	0.41%
Coronary artery disease	−1.2	0.20	−0.2*	0.17	−0.007	0.0025	0.0%*	0.48%
Congestive heart failure	−3.3	0.19	−1.6	0.16	−0.037	0.0024	9.4%	0.46%
Heart attack	−1.0	0.19	−0.2*	0.16	−0.008	0.0023	1.2%	0.46%
Other heart conditions	−1.1	0.21	−0.2*	0.17	−0.009	0.0025	1.4%	0.49%
Stroke	−2.8	0.17	−1.3	0.14	−0.030	0.0021	5.6%	0.40%
Diabetes	−3.2	0.17	−0.4*	0.14	−0.025	0.0021	1.2%	0.41%
Arthritis of hip or knee	−5.1	0.19	−0.3*	0.16	−0.047	0.0023	−0.2%*	0.44%
Arthritis of hand or wrist	−1.7	0.18	−0.7	0.15	−0.023	0.0022	0.0%*	0.42%
Osteoporosis	−2.4	0.17	−1.3	0.14	−0.032	0.0021	1.7%	0.41%
Sciatica	−3.4	0.18	−1.3	0.15	−0.045	0.0021	−1.0%	0.41%
COPD	−3.6	0.18	−0.5	0.15	−0.028	0.0021	3.5%	0.41%
Inflammatory bowel disease	−1.0	0.15	−1.6	0.13	−0.019	0.0018	−0.6%*	0.36%
Depression	−1.2	0.18	−11.8	0.15	−0.112	0.0022	2.7%	0.43%
Cancer	−1.6	0.15	−0.1*	0.13	−0.010	0.0019	3.9%	0.37%
Total NE	−34.3		−21.4		−0.445		28.9%
	Mean1	S.E.	Mean1	S.E.	Mean1	S.E.	Mean1	S.E.
None	51.6	0.14	56.4	0.12	0.851	0.0018	4.1%	0.34%
All conditions	17.2	1.74	35.0	1.44	0.406	0.0211	32.9%	1.61%
Total effect2	−34.3		−21.4		−0.445		28.9%

¹All scores were age-race-gender standardized

²Total effect was difference in mean score between All and None

^*p value > 0.05 for testing NE = 0

Discussion

This study estimated the net effect for selected explanatory variables in each of the following five categories: demographics, difficulties in ADLs, difficulties in IADLs, geriatric symptoms, and chronic conditions to respondents’ HRQOL and 2-year mortality among U.S. older adults. The NE quantifies determinants of health in each category with respect to their size and direction of influence. By doing so, the drivers of health outcomes, i.e., the most influential factors, can be identified [4]. Our results highlight how the NE varies according to and within a given category. Furthermore, the NE may differ according to physical and mental health and mortality.

For physical health, the top factors that had the greatest negative NE on PCS scores included difficulty in walking among the six ADLs, preparing meals (both difficulty and don’t do this) among the three IADLs, and pain interfered with daily activities among the five symptoms. Predictably, don’t need to take prescribed medication was found to have a positive NE on PCS. Viewing the other factors, arthritis of the hip or knee had the greatest negative NE among chronic conditions. By contrast, with regard to mental health, the top factors with the greatest negative NE on MCS scores included difficulty in eating among the six ADLs, difficulty managing money among the three IADLs, and memory problems among the five symptoms. Depression expectedly had the greatest negative NE among the 15 chronic conditions while, among demographic variables, education played the greatest role.

While the effects of age, chronic conditions, and ADLs on HRQOL and mortality are well-recognized [2, 7, 27], the effect of symptoms such as memory problems and certain IADLs on these outcomes may seem less evident. In a community-dwelling sample of older adults, Yu and colleagues revealed that mild cognitive impairment has a stronger relationship with disability than impairments in mobility [28]. Similarly, investigators have found that both impairments in executive function and cognition are associated with functional decline (as assessed by IADLs and ADLs) and an increase in mortality among community-dwelling elderly [29, 30]. Yet, in the health care context, monitoring chronic conditions tends to be more commonly performed as opposed to addressing the interaction between these conditions, ADLs, IADLs, and symptoms in order to address long-term health needs [31]. Emphasizing and encouraging healthy behaviors and assessing areas related to cognition, depression, and pain may have a positive effect on HRQOL as well as mortality [32]. Ultimately, these categories should be examined in an integrated and holistic manner, given that preserving physical functioning is associated with improved functional independence (as assessed by ADLs and IADLs) [33]. In this community-dwelling sample of elderly, monitoring respondents who report these difficulties might prove to be helpful with regard to administering resources needed to preserve functional capacity and prevent or delay institutional living.

The NE is an extension of the Shapley value [19], a solution for allocating contributions or shared costs among a group of players who have collaborated in a cooperative game. The Shapley value method bas been used in risk analysis to measure attributable risk [18] and in machine learning to measure contributions of inputs to an outcome [34]. The NE works for different types of data and for models with interaction and nonlinear terms, and allows for both positive and negative effects. Since the NE measures the effect contributed by each factor, it helps to understand causal pathways between explanatory variables and the outcome by examining NE for different sets of predictors [4].

The NE has many advantages over the regression coefficients which may be invalid or inappropriate if some of predictors are correlated or the model has interaction or nonlinear terms [17]. The calculation of the NE includes interaction terms and allows polynomial terms in the model. The NE is particularly useful when examining the effects of predictors in a two-part model for outcomes with a ceiling effect [15]. For example, the EuroQol EQ-5D index is truncated at 1 which represents the best possible health state. Tsiachristas and colleagues found that a two-part model had a better performance than other models for modeling the EQ-5D [15]. We estimated the NE for number of unhealthy days using a zero-inflated Poisson model (a type of two-part model).

The net effects and regression coefficients quantify different characteristics. Specifically, the regression coefficient is the expected change in the outcome for a one-unit change in the independent variable, holding all other independent variables constant. The NE is the average marginal effect of an independent variable on the outcome over all possible scenarios. Thus, these two measures may not be comparable. For example, difficulties in walking had a larger negative value for the regression coefficient than for the NE (−12.3 vs. −7.4) (Appendix B). For difficulties in using the toilet and in eating, regression coefficients were positive and close to zero (0.3 and 0.4, respectively) while the NEs were both negative (−1.5 and − 1.3, respectively). Of note, this comparison does not indicate validity of a measure.

In addition to representativeness of the Medicare HOS data and accuracy of variable measurements, this study has several limitations. First, some of the explanatory variables, such as pain interference, may be part of the subconstructs of the three HRQOL measures based on the VR-12 questionnaire [22], and, therefore, had large a NEs on HRQOL. However, these variables also had a large NE on other HRQOL measures that did not contain any subconstructs of explanatory variables such as the three CDC Healthy Days Measures, each of which was based on a single question about perceived health [25]. These results demonstrated the validity of our findings on HRQOL. Second, this is a computationally intensive method. When the number of predictors is relatively large, obtaining accurate NE estimates may not be possible, even when the sample size is large. Therefore, the NE estimates for some of the 15 chronic conditions should be interpreted with caution, especially with regard to mortality. Third, if one or more explanatory variables were influenced by the outcome, the estimated NE might be subject to collider bias [35]. Thus, one should be careful when selecting explanatory variables for the calculation of NE. Fourth, the NE was computed separately within each category. Potential cross-category dependencies may have been ignored.

Conclusions

In summary, this study introduced net effect as a measure of how much each determinant of health influences the outcomes and demonstrated how to estimate net effect for continuous, binary, and count outcomes and for both continuous and categorical predictors. This method allows inclusion of interaction terms and polynomial terms if a nonlinear relationship exists and works for 2-part models. Calculation of NE is a useful supplement to the standard multiple regression analysis.

Abbreviations

HRQOL

Health-related quality-of-life

VR-12

The Veterans RAND 12-Item Health Survey

PCS

Physical component summary score

MCS

Mental component summary score

SF-6D

Short Form health utility

ADL

Activities of daily living

IADL

Instrumental activities of daily living

HOS

Medicare Health Outcome Survey

CMS

The Centers for Medicare & Medicaid Services

PUF

Public Use Data Files

NE

Net effect

Authors’ contributions

Both authors contributed to the study conception. Haomiao Jia was in charge of the design, methodology, software, data curation, and analysis. Both authors were involved in the writing, editing, and visualization. Both authors read and approved the final manuscript.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Data availability

The Public Use Data Files (PUF) are available at the Centers for Medicare & Medicaid Services (CMS) website: [https://hosonline.org/en/]. You can download the data file by choosing the “Select Analytic PUF DATA File” box.

Declarations

Ethics approval and consent to participate

This study was a secondary data analysis of the Medicare HOS data which were public access data. The PUF Medicare HOS data does not include personal identifiable information and does not meet the requirements of human subjects research as defined by the Department of Health and Human Services. Ethical approval was not required.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.