# Presentation: 853329

## Conducting Multilevel Modeling for Informing Maternal and Child Health Outcomes 

**Jessica Griffin Burke, PhD, MHS **
- Assistant Professor
- Department of Behavioral and Community Health Sciences
- University of Pittsburgh Graduate School of Public Health
**Jay S. Kaufman, PhD**
- Associate Professor
- Department of Epidemiology
- University of North Carolina School of Public Health

## MODE-PTD (Multi-level modeling of Disparities and the Environment in Preterm Delivery) 

- Funded by the MCHB, HRSA
- On-going, multi-site collaborative of university researchers and state MCH officials
- Maryland
- Patricia O’Campo, Jessica Burke
- North Carolina
- Barbara Laria, Jay Kaufman, Lynne Messer, Paul
- Pennsylvania
- Jennifer Culhane, Irma Elo
- Michigan
- Claudia Holzman, Janet Eyster

## Training Session 

- Part I: Background - incorporating neighborhood context into the study of health outcomes
- Part II: Methods - interpretation of multilevel and contextual analysis

## Part I: Background incorporating neighborhood context into the study of health outcomes

## outline

- history of ecological analysis
- how neighborhoods are defined
- how to characterize neighborhoods and sources of data
- theories
- evidence
- the case of preterm birth
- challenges

## John Snow (1813-1858)public health epidemiologist

- 1854* On the Mode of Communication of Cholera* - Broad Street Pump Outbreak

## “The City”, 1925Park & Burgess

- _Theory:_ Via competition urban areas become divided into niches or “natural areas” where residents share common social characteristics

- I Loop

- II Transition zone

- III Working men’s homes

- IV Residential zone

- V Commuter zone

## social science research base map of Chicago1923-1924 Ernest Burgess

## Hull-House maps and papers, 1895Nina Brown

- undertook extensive primary data collection in Chicago neighborhoods
- recorded nationality, wages, and employment history through door to door surveys
- did not attempt to explain the distribution of poverty
- intent to prompt humanitarian response- public policy

## Hull-House maps and papers, 1895

## declining interest in neighborhoods

- during the mid-1970s interest in the connection between spatial location, social position and health began to wane.
- both socioeconomic and health outcomes were conceptualized as individual-level processes constrained only by family circumstances – “status attainment model”

- Douglas S. Massey, Contemporary Sociology, Vol. 27, No6 (Nov., 1998), 570-572

## why the study of neighborhoods lost its appeal?

- wariness of ecological data- “*ecological fallacy”*
- advances in statistical methods kept researchers busy with complex modeling of individual-level data – rise of social surveys with detailed information on individuals, families and households but little, if any information on neighborhood.
- methodological, conceptual and political individualism dominated since 1950’s

## back to the future:the rediscovery of neighborhood context

- by the mid-1980’s more and more complex statistical models were developed to “push around a fixed amount of variance in ever more trivial ways” with very few gains
- key event that  brought back ecology forcefully was the publication of William Julius Wilson’s , *The Truly Disadvantaged.*

- Douglas S. Massey, Contemporary Sociology, Vol. 27, No6 (Nov., 1998), 570-572.

## “The truly disadvantaged”William Julius Wilson

- argued that black urban poverty was perpetuated not only through individual and family-level mechanisms but also through structural mechanisms functioning at the ***neighborhood-level***

## the reemergence of neighborhood

-  Since the 1990’s “the new public health”
- calls to examine the *upstream* causes of disease
- calls to simultaneously examine both the distal and proximal causes of disease

## Trends in Neighborhood research: articles with “neighborhood” in the title

- Trends in Neighborhood research: articles with “neighborhood” in the title

- Social Science numbers from Sampson et al., 2002

## Individual and Neighborhood Effects

**Neighborhood A**

**Neighborhood B**

## Individual and Neighborhood Effects

**Neighborhood A**

**Neighborhood B**

**Individual Attribute Protection**

## Individual and Neighborhood Effects

**Neighborhood A**

**Neighborhood B**

**Individual Attribute Protection**

**Neighborhood Characteristic Protection**

## what is a neighborhood?

- geographic boundary around a residential setting.  Census boundaries are often used as proxy measures for residential neighborhoods
- neighborhoods are usually thought of as smaller than communities.  Communities can also be defined by unit of identity, i.e., church, school, work, social circle

## neighborhood definitions

- administrative units
- blocks
- block groups		- counties
- census tracts		- states
- political units
- - wards
- - city council districts
- service districts
- 	- health districts		- fire battalion boundaries
- 	- police districts		- school boundaries
- 	- recreation districts		- postal zip codes
- self-defined neighborhood boundaries** **
- 	- shared environment
- 	- natural boundaries

## Wake neighborhoods

- block groups – 263
- census tracts – 105
- zip codes – 44 in Raleigh
- neighborhood groups
- police jurisdictions
- voting districts

## how do you measure neighborhood?

- administrative units in Wake County, NC

- within same census tract?

- within same block group?

## characterizing neighborhoods

*What types of data can we use?*
- compositional effects
- properties of individuals
- a.k.a., derived variables; aggregation of individual-level variables
- contextual effects
- properties of places
- a.k.a., integral variables; no individual-level analogs
- direct measures:
- measure of the built environment like “walkability”

## sources of neighborhood-level data

- administrative and public health data at the address level
- census data at the block, block group, and census tract level
- proprietary data
- primary data collection

## Geocode

***Match/Merge***

-  **Birth Records**

**DHS Records**

**Hospital Discharge        Data**

**City Health Center & FQHC Encounters**

-  **Shelter Episodes**

**Lead Test Results**

**Immunization Registry**

**Medicaid **
**Enrollment**

**School  Data**

**Cancer Registry**

**Fetal Death Records**

**Air Quality Census and Property Data**

**Death Records**

**Reportable   Diseases**

**Medical Claims Data**

**Licensing and Inspection**

**Crime Data**

**Utility Cut-off**
** ****Rate**

**Tax Delinquency**

**Business **
**Registry**

## theories of how neighborhoods influence health

- Social contagion or social diffusion theory
- imitating behavior / peer pressure, close proximity has spillover effect
- Socialization
- internalization of social norms and learning the boundaries of acceptable behavior
- Social comparison
- processes governed by levels of relative deprivation and status organizing processes
- Collective efficacy = social cohesion + informal social control
- Institutionalization
- behavioral regularities through structured and semi-structured organizations and actors, including employers, schools, enforcement agencies, and other social institutions
- Community resources
- Psychosocial stress pathways
- fear of crime and violence influences behavior change

## neighborhood effects: evidence

- Neighborhood context consistently has a “modest association” with numerous health outcomes:
- 25 studies reviewed
- Developed countries
- Individual-level attributes controlled for
- 23/25 had significant neighborhood effects
- Reviewed in Pickett & Pearl,* J. Epidemiol Community Health*, 2001; 55

## neighborhood effects associated with...

- all cause mortality
- chronic disease among adults
- self-rated health
- long-term disability
- cardiovascular symptoms or disease
- respiratory function
- health behaviors (i.e.,-smoking, sexual practices)
- domestic violence
- low birth weight and preterm birth

- To review recently published (1999-2004) multilevel research addressing neighborhood context and maternal and child health outcomes
- 31 selected and reviewed in detail and neighborhood characteristics classified into like categories
- Maternal and child health topics ranged across the life course from infant birth weight to parenting practices
- Majority of studies were from the United States, a few from Canada (6%), UK (10%) and the Netherlands (13%)

- neighborhood context and MCH outcomes

- Rajaratnam JK, Burke JG, O’Campo P. (2006). Maternal and child health and neighborhood context: The selection and construction of area-level variables. *Health and Place.*

## Categories of Neighborhood Characteristics (% of the 31 studies)*

- Income/Wealth (100%)
- Employment (74%)
- Family Structure (55%)
- Population Composition (52%)
- Housing (39%)
- Mobility (39%)
- Education (26%)
- Occupation (16%)
- Social Resources (36%)
- Violence and Crime (26%)
- Deviant Behavior (13%)
- Physical Conditions (19%)

## challenges

- what is the theory linking contextual variable and outcome of interest?
- what is the context?
- Geographic? Work,  Religious affiliations, Clubs, Social Networks ?
- what contextual-level variables should be measured?
- what is the spatial range of a contextual variable?
- what statistical techniques should be employed?
- limitations of a cross-sectional design-when to measure context?
- what individual-level characteristics need to be controlled for?

-  Part II: interpretation of multilevel and contextual analysis

## overview

- why context matters
- multilevel models - synonyms
- what are we trying to explain?
- issues specific to nested data
- different types of multilevel models
- interpreting the different types of multilevel models
- fallacies

## why context matters

- empirically, individual outcomes can’t be explained exclusively by individual-level exposures
- persistent contextual effects are observed in outcomes across populations
- exposures are structured; distributions are differential

## methodological vs. conceptual issues

- recent methodological advancements have improved the estimation of neighborhood effects through fixed and random effects modeling; however, this often relegates the neighborhood to a covariate, or the black box of influences on health
- conceptual issues, or mechanisms through which neighborhoods influence health are still needed

## definition and synonyms

- ml modeling: a method that allows researchers to investigate the effect of group or place characteristics on individual outcomes while accounting for non-independence of observations
- synonyms:	different models:
- multilevel models	- fixed effects
- contextual models	- random effects
- hierarchical analysis	- generalized estimating equations
- panel data, repeated measures designs use ml methods as well

## why use multilevel models?

- outcomes may be clustered by some unit of aggregation (contextual unit)
- individuals within contexts may be similar in ways that are unmeasured
- to take into account clustering / non-independence of observations
- to partition the observed variability into within-context and between- context variables

## when are observations not independent?

- when data are collected by cluster / aggregating unit
- children within schools
- patients within hospitals
- drug users within neighborhoods
- cholesterol levels within a patient
- why care about clustered data?
- two children / observations within one school are probably more alike than two children / observations drawn from different schools
- does knowing one outcome inform your understanding about another outcome?

## why partition variance?

- ml models allow you to decompose the total variance in individual-level outcomes into within group and between group components
- empirically useful
- conceptually important (non-individualistic)
- allows for different types of policy or interventions to change population values / distributions

## linear and logistic regression – review

- linear model review:
- logistic model review:

- Y = β0 + β1X1 + β2X2...+ ε

- β0 = intercept	β1X1 = beta associated with exposure
- β2X2 = beta associated with first covariate + ...
- ε = error term

- ln P(X) / [1-P(X)] = α + β1X1 + β2X2...

- α = constant	β1 = beta associated with exposure
- β2 = beta associated with first covariate + ...

## model assumptions

- baseline outcome means (mean values when exposure = 0) differs only due to variability between subjects
- individuals, and their errors are, independent and identically distributed
- all non-specified variables (e.g., area-level variables; those confounders you did not measure) assumed = 0

## adding group-level variables

- problem: making cross-level inferences [drawing inferences regarding factors associated with variability in outcome at one level based on data collected at another level]
- e.g., making individual inferences based on group-level associations

- Yij = β0 + β1ijX1 + β2ijX2...+ jGj + εij

- Yij = outcome for individual i in context j
- β1ijX1 = beta associated with exposure for individual i in context j
- βj Gj = observed community variable 	εij = error term

## maybe group variables just interact with individual variables?

- interacting group- and individual-level variables will get you close to the right answer
- problem: error structure is multilevel, but errors only specified at the individual-level
- individuals within contexts are correlated with each other
- errors not independent and identically distributed

- ln P(Xij) / [1-P(Xij)] = αi + β1ijX1ij + β2ijX2ij +
- β3jGj + β2ijX2*β3jGj

## what’s the problem with a multilevel error structure?

- standard methods produce unbiased point estimates
- your betas or ORs will be ~correct
- standard errors too small
- confidence intervals will be wrong (too precise)
- unless you can demonstrate there are no correlations between the following:
- individual-level predictors
- group-level predictors
- unobserved characteristics

## how to tell if you need multilevel models

- reality 1: anytime you have data collected from some aggregate unit / clusters, you will have to use ml models
- reality 2: calculating an intraclass correlation coefficient will quantify your clustering (in absence of running a ml model)
- reality 3: even if your ‘clustered data’ aren’t empirically clustered, article and grant reviewers may demand it

## intraclass correlation coefficient

- estimates the degree of clustering by unit of aggregation
- icc = between cluster variance / total variance*
- icc = 0 : people within the same context no more similar
- 	to each other than they are to any random person elsewhere
- icc > 0 : people in same context more similar to each other than to people in other contexts

- *total variance = between cluster + within cluster variances

## modeling clustered data

- Two main approaches:
- population average models with robust variance estimators
- marginal models that account for cross level correlation across all units of aggregation
- not conditional on being in a certain cluster; does not model clustering directly
- provides robust tests, corrected standard errors, corrects for heteroskedasticity*
- ml models
- random effects models (unit-specific models that condition on specific units of aggregation for inference)
- fixed effects models (area-level coefficients held constant across units of aggregation)
- mixed models (models that combine some fixed and random effects; not going into any more detail about mixed models in this lecture)

- * heteroskedasticity results from errors not having constant variance

## population average models

- Yij = preterm birth (1) versus term birth (0) for woman *i* in tract *j*
- Xij = low (1) or high (0) ses for woman *i * in tract *j*
- no locations specified, just averaged over all tracts
- allows you to compare ‘average low’ versus ‘average high’ ses women

- Pr (Y ij=1 | Xij) = *f* (Xij )

- note: no group / cluster mean

## population average models

- pros
- model response change as function of covariates ‘averaged’ over group to group heterogeneity
- economists, sociologists like these models
- cons
- do not explicitly account for heterogeneity across higher-level units / contexts
- do not allow examination of group to group variation

## multilevel models random and fixed

- random effects models
- random intercept	       random slope
- random slope and random intercept

- random intercept models: context specific mean realized from a random distribution

- random slope models: exposure effect realized from a random distribution

## random effects model

- model in its most general form
- random effects for some or all regression parameters (parameters don’t have single fixed values, but are modeled as realizations from distributions
- the estimated variance of the random effect allows us to partition variability into within context (i.e., between subject) and between context (i.e., context heterogeneity)

- Pr (Y ij=1 | Xij) = *f* (Xij , μj)

- note: conditioning on μj, the cluster-specific parameter

## fixed slope random intercept model

- level 1 equation: for preterm birth (logistic model)
-     ln [(P{Yij=1 | μj}) / (P{Yij=0 | μj })] = 0j  + Xij 1i + μj

- odds of preterm delivery for individual i in tract j, given random effects (μj)

- 2nd
- equation

- vector of covariates

-  level 2 equation: 0j = 00 + ... + μj

- mean of the distribution of
- random intercepts

- context-level
- random effects

## random effects models

- pros
- helps explain variance in area or context effects
- allows observation of group to group variation and interaction with individual-level variables
- cons
- don’t account for selection bias
- don’t account for omitted variable bias

## fixed effects models

- context-specific variables not allowed to vary; held fixed
- controls for time invariant observed and unobserved contextual variables
- usually accomplished by creating an indicator for each unit of analysis (i.e., block group)

## fixed effects models

- pros
- controls for neighborhood effects
- controls for selection bias
- controls for time invariant contextual omitted variable bias
- economists love these models
- cons
- doesn’t explain variance between contexts
- can’t identify independent contextual effects
- statistically inefficient

## how to decide which model to use

- depends on what you want to say...
- if you want to look at risk / odds for the average individual with some exposure compared with average individual with some other exposure, use a population averaged model
- if you want to talk about how changes in context specific exposures will change the risk / odds in that context, use the unit-specific model
- if you want to want to consider the effect of some variable holding all observed and unobserved variables contextual factors constant, use a context fixed effect model

## Highest quartile of neighborhood deprivation clusters in downtown Raleigh and in Northeast Wake county near Rolesville and Zebulon.

## neighborhood deprivation and odds of preterm birth

*	*White women	Black women*	*
- 	_OR__	__95% CI__	__OR__	__95% CI__	_
- 4th quartile	**1.28 (1.01, 1.61)** 	**1.48 (1.00, 2.18)**
- 3rd quartile	1.10 (0.94, 1.29)	1.37 (0.93, 2.04)
- 2nd quartile	1.05 (0.90, 1.22)	1.39 (0.93, 2.08)
- 1st quartile	1.00 (referent)	1.00 (referent)
- Age 35+	1.13 (0.89, 1.44)	**2.07 (1.57, 2.72)**
- Age 30-34	1.00 (0.80, 1.44)	**1.66 (1.30, 2.11)**
- Age 25-29	1.19 (0.95, 1.48)	**1.30 (1.04, 1.61)**
- Age 20-24	1.00 (referent)	1.00 (referent)
- Age <20	1.09 (0.75, 1.59)	**0.69 (0.52, 0.92)**
- < High school	1.31 (0.96, 1.78)	**1.87 (1.46, 2.39)**
- High school	**1.31 (1.10, 1.56)**	**1.36 (1.12, 1.64)**
- > High school	1.00 (referent)	1.00 (referent)
- Not married	1.19 (0.95, 1.49)	**1.46 (1.21, 1.76)**
- Married	1.00 (referent)	1.00 (referent)

- Messer LC, Buescher PA, Laraia BA. Kaufman JS. SCHS study No. 148. Nov 2005.

## tract high unemployment is associated with preterm birth for Black women

*	**	*_*Logistic*_*	*_*Logistic (robust)*_*	*_*Random Effects*_
- 		_OR__	__  95% CI__	__OR__	__  95% CI__	__OR__	__  95% CI_
- >5% unemployment	1.29	(1.08, 1.55) 	1.29	(1.04, 1.61) 	1.31	(1.04, 1.64)
- Age 25-29	1.31 (1.05, 1.64)	1.31 (1.04, 1.61)	1.31	(1.05, 1.64)
- Age 30-34	1.69 (1.33, 2.15)	1.70 (1.35, 2.10)	1.68	(1.32, 2.14)
- Age 35+	2.10 (1.60, 2.76)	2.10 (1.60, 2.77)	2.10	(1.60, 2.75)
- High school	1.37 (1.13, 1.66)	1.37 (1.10, 1.70)	1.38	(1.14, 1.67)
- < High school	1.74 (1.36, 2.26)	1.74 (1.33, 2.27)	1.76	(1.34, 2.29)
- Not married	1.49 (1.23, 1.80)	1.49 (1.25, 1.77)	1.49	(1.23, 1.80)

## example causal interpretations

- standard logistic model (>5% unemployment versus 5% unemployment)
- 		OR = 1.29	(95% CI: 1.08, 1.55)
- assuming that women are evenly distributed across neighborhoods with regard to preterm birth, the odds of preterm delivery will increase by 29% for a randomly selected woman living in a high unemployment tract compared with a randomly selected woman living in a low unemployment tract

## example causal interpretations

- population average logistic model (>5% unemployment versus 5% unemployment)
- 		OR = 1.29	(95% CI: 1.04, 1.61)
- the odds of preterm delivery will increase by 29% for a randomly selected woman (read: average woman) in a census tract with low unemployment who is relocated to a tract high unemployment

## example causal interpretations

- random effects logistic model (>5% unemployment versus 5% unemployment)
- 		OR = 1.31	(95% CI: 1.04, 1.64)
- the odds of preterm delivery will increase by 31% for a randomly selected woman in a specific census tract with low unemployment if that tract is somehow manipulated to have a high unemployment

## conclusion

- standard regression models assume that data is not clustered by a higher level grouping
- one can model clustered data by either using methods robust to this violation of assumptions, or else by modeling this clustering directly
- random effects models estimate *conditional *parameters (i.e., the effect of exposure *given *a particular cluster)