Reading Response Discussions

 Effect of Mass Distribution of Azithromycin for Trachoma Control on Overall Mortality in Ethiopian Children

Travis C. Porco, PhD, MPH; Teshome Gebre, MBA; Berhan Ayele, MSc; Jenafir House, MPH; Jeremy Keenan, MD; Zhaoxia Zhou, BS; Kevin Cyrus Hong, BS; Nicole Stoller, MPH; Kathryn J. Ray, MA; Paul Emerson, PhD; Bruce D. Gaynor, MD; Thomas M. Lietman, MD

JAMA. 2009;302(9):962-968. doi:10.1001/jama.2009.1266

http://jama.jamanetwork.com/article.aspx?articleid=184506

The unit of clustering was “communities”, which are also called subkebeles in the Amhara region of Ethiopia. These communities are in rural areas and consist of approximately 1500 individuals per community.

Mass oral azithromycin distribution as part of the WHO’s trachoma elimination program may also be efficacious against respiratory disease, diarrhea, and malaria— frequent causes of childhood mortality in trachoma-endemic areas. The hypothesized effect was reduced mortality rates of participants aged 1 to 9 years in treated communities compared to those in untreated communities.

The level of exposure which was measured was at the community (cluster) level in three different arms: 1) Annual azithromycin distribution to all individuals aged 1 year and older 2) quarterly treatment of thosedaged 1 to 10 years, and 3) delayed treatment (control group) where tx was given at 12 months. The level of the outcome was measured at the individual level.

The authors modeled mortality risk using clustered logistic regression at the individual level for the primary comparison, taking into account the possible statistical dependence of individuals in the same subkebele (i.e. cluster effects)

To ensure that the results were not dependent on the particular choice of statistical model, they also constructed other regression models to fit subkebele-specific estimated mortality rates, taking clustering at the level of the randomization unit into account. By estimating an additional aggregation parameter, negative binomial regression allowed them to model possible overdispersion of the mortality counts; as the aggregation parameter becomes very large, the negative binomial distribution approaches the Poisson distribution. I don’t think other models would be preferable to these methods.

Home-based versus clinic-based care for patients starting antiretroviral therapy  with low CD4⁺ cell counts: findings from a cluster-randomized trial (2014) Woodd SL, Grosskurth H,  Levin J, Amuron B, Namara G, Birunghi J, Coutinho A, Jaffar S

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3921227/pdf/aids-28-569.pdf

• Unit of clustering:
  • Similar estimated number of HIV-infected patients --> 1,453 participants into 22 clusters 859 participants home-based and 22 clusters 594 participants clinic-based care
• Hypothesized effects:
  • not mentioned but could have been --> home-based care reduced mortality rate among people living with HIV/AIDS
• Level of measured exposure:
  • Mortality ratio
  • age
  • sex
  • education
  • marital status
  • WHO stage
  • CD4 cell count
  • HIV-1 plasma viral load
  • ARV
    • stavudine, lamivudine, nevirapine
    • stavudine, lamivudine, efavirenz
    • zidovudin, lamivudine, nevirapine,
    • zidovudine, lamivudine, efavirenz
    • other
• Statistical model used to estimate effect:
  • mortality rate ratios were calculated using a Poisson regression random effects model with gamma distribution to account for clustering
  • Cox proportional hazards model using robust standard errors
• Other statistical models:
  • Hierarchical linear model
    • Two-level school effect models
      • Individuals nested within those clusters or
      • Using individual growth models
        • Exploring longitudinal data over time

Tanser F, Bärnighausen T, Grapsa E, Zaidi J, Newell M-L. High coverage of ART associated with decline in risk of HIV acquisition in rural KwaZulu-Natal, South Africa. Science 2013; 330:966-71.

The goal of this study was to determine whether being in a high-ART coverage area reduces the risk of HIV-acquisition. However, risk of HIV-acquisition for neighbors is highly correlated because 1) they are both living in an area with a certain HIV prevalence and 2) they are both living in an area with a certain ART coverage. Other factors may also cause data to be clustered: e.g. age and sex distributions in the local community may impact behavioral factors that lead to HIV transmission, community condom access, etc.

1. the unit of clustering;

local community, which we can loosely think of as the people within 3km (really measured using a standard Gaussian kernel of radius 3 km, i.e. people are weighted higher the closer they are to you and people more than say 2*3km=6km away are unlikely to have much impact on you)

2. the hypothesized effects and the level at which the exposure is measured (is it a characteristic of the cluster or the observation within the cluster); and

Outcome: HIV acquisition of individuals Hypothesis: Individuals are less likely to contract HIV the higher the local community-level ART coverage is Exposure: local community-level ART coverage

3. the statistical model used to estimate the effect

some sort of hazard model (they don’t say if it’s a cox proportional hazards model or some other hazard model, but given how they present results, I would suspect that it is) 4. whether there are any other statistical models that might be appropriate and whether they would be preferable (e.g., GEE vs mixed).

I picked this paper because I found it confusing in the context of clustered data analysis and as I am reading it more I am realizing it is probably not exactly what was in mind for this assignment...

They didn’t seem to account for clustering aside from including group-level predictors that could account for clustering (e.g. prevalence and ART-coverage). They did a sensitivity analysis by including community-level condom use as an additional predictor. Here, it seems like they ignored clustering due to the unknown (behavioral) factors that might give rise to differences in the effect of ART coverage on HIV acquisition. They refer to “noise” at various points, which I would describe as unmeasured community level factors that might give rise to different (i.e. mixed) effects of ART coverage on HIV acquisition. We might be interested in this heterogeneity in response to ART-coverage. How one would do this is unclear to me:

1) how does one account for clustering in hazard models? E.g. a mixed-effects hazard model. I’m sure this is done, but is not straightforward.

2) how would one do this on the continuous scale for community-level that they use?

Neighborhood socioeconomic context and cognitive decline among older Mexican Americans: Results from the Sacramento Area Latino Study on Aging

 Adina Zeki Al Hazzouri et al. 2011

1) Unit of clustering

Three levels: seven measurements of cognitive decline over time (level 1) within 1789 individuals (level 2) who lived in 259 neighborhoods (level 3).

2) The hypothesized effects and the level at which the exposure is measured (is it a characteristic of the cluster or the observation within the cluster)

The purpose of this study was to determine the association between neighborhood socioeconomic position (SEP) and cognitive decline trajectories, and how this is impacted by individual level characteristics. Older people and their cognitive decline may be sensitive to the socioeconomic conditions of their neighborhoods independent of their individual level SEP, but it is likely that individual level characteristics also influence cognitive outcomes as well.

Several exposures of interest: Time (operationalized as age), individual SEP variables (education, income, occupation), and neighborhood SEP. Neighborhoods were operationalized as census tracts, and the SEP score was constructed based on census on: percent with no high school diploma, percent living below poverty, percent unemployed, percent who owned their home, percent vacant housing units, median rooms in household.   

Outcome: Participants’ cognitive scores based on the Mini-Mental State Exam (logged transformed errors).

3) The statistical model used to estimate the effect. Describe whether there are any other statistical models that might be appropriate and whether they would be preferable (e.g., GEE vs mixed).

Hierarchical linear models were used.

Level 1: Cognitive scores as a function of time (i.e. age)

Level 2: Individual SEP variables and baseline risk factors

Level 3: Neighborhood SEP

Random effects: initial cognitive function and linear rate of cognitive decline at levels 2 and 3.

Mixed models appear to be the best model (that I know of) for this study question because there are multiple levels of clustering that were addressed. Furthermore, using a mixed model allowed the authors to account for random slopes (cognitive decline) within individuals and within neighborhoods. 

Nau C, Schwartz BS, Bandeen-Roche K, Liu A, Pollak J, et al. 2015. Community socioeconomic deprivation and obesity trajectories in children using electronic health records. Obesity (Silver Spring) 23:207-12.

Unit: Child (repeated BMI measures within child over time from 2001-2012), n = 163,473 with 3.2 observations per child (range = 1-13)

Level of exposure: community (defined as minor civil division in Pennsylvania). Exposure was community socioeconomic deprivation (CSD) of the community that the child lived in.

Hypothesis: higher community socioeconomic deprivation will lead to steeper BMI trajectories and there will be critical periods where BMI is especially vulnerable to community deprivation.

Model: Mixed effects linear model

Fixed: age, age², age­³, quartiles of CSD, medical assistance, cross-products of age, age², age³ with CSD and medical assistance.

Random: random intercept for child and random slopes for age and age² to allow trajectories to vary across children.

Could they have used GEE?: Yes, they had a large number of individual units (163,473 children) and did not interpret the random effects in their mixed-model. They could still look at trajectories over time by including age, age², and age³ interactions as fixed effects. Even though they used a community-level exposure they did not seem to account for children nested in communities in their models. There is no report of residual autocorrelation that might remain after using the mixed-model.

Betts KS, Williams GM, Najman JM, Alati R. Generational changes in tobacco use by young women: a cross-generational analysis of mother-daughter dyads. Drug Alcohol Rev. 2014 Sep;33(5):540-7. PMID: 25091802.

1. Unit of clustering – Mother-Daughter dyad
2. Hypothesized effects – change in young female smoking prevalence and intensity using cross-generational and equivalent measures of smoking across a generation of mothers and daughters; whether or not the associations between smoking with education and depressive symptoms are higher in the daughters’ generation
3. Level at which exposure is measured – Individual level, as both the mothers and the daughters were assessed for the outcomes (# of cigarettes) and covariates (education [dichotomous], Delusions-States-Symptoms Inventory, 20-item version of the Centre for Epidemiological Studies Depression (CES-D))
4. Statistical model used to estimate the effect – multinomial logistic regression for correlated responses main predictor is the generation, outcome is the change in smoking levels; Confidence intervals for the parameter estimates were obtained from 1000 bootstrapped samples; marginal model (random effects model) treats mothers’ and daughters’ smoking, as well as education and depressive symptoms, as repeated measures of the same unit of observation (same dyad).
5. Other statistical models that might be appropriate and whether they would be preferable – conditional random effects model?

Article: Characteristics of Latrines in Central Tanzania and Their Relation to Fly Catches Irish S, Aiemjoy K, Torondel B, Abdelahi F, Ensink JHJ (2013) Characteristics of Latrines in Central Tanzania and Their Relation to Fly Catches. PLoS ONE 8(7): e67951. doi: 10.1371/journal.pone.0067951

Unit of clustering: Village/town

Exposure level: Latrine characteristics are observed within the cluster

 Statistical Model: The original analysis (conducted me in my naïve days before biostats 209) did not account for any clustering by village. This is of concern because we would expect the outcome (number of flies) to be highly dependent on study site (village or town).  I reanalyzed the data to account for the correlation studcture using 4 different models investigated to best fit the data: 1) a linear regression model without accounting for village, 2) a linear regression model accounting for clustering by village by including it as a variable in the model, 3) a generalized estimating equation with village as the group variable and 4) a random effects model (allowing random intercepts for village). All four models were then used with different distributions of the outcome variable total fly count (normal/untransformed, log +1 transformed, and a gamma distribution). 

Table 1: Final models with coefficients (standard errors) and p-values 

The mixed effect model is the most appropriate model for the data as it allows for random intercepts for village, the residuals are normally distributed it preserves the measure of effect of interest.  The results of this model are as follows: Latrines with roofs produced on average 14.78% (95% CI: 4.33% - 50.41%) of the flies produced in latrines without roofs (p=0.002), accounting for any clustering by village.  

Article: Wang J, Yu R, Shete S. Comparison of multilevel modeling and the family-based association test for identifying genetic variants associated with systolic and diastolic blood pressure using Genetic Analysis Workshop 18 simulated data. BMC Proc. 2014 Jun 17;8(Suppl 1 Genetic Analysis Workshop 18Vanessa Olmo):S30. doi: 10.1186/1753-6561-8-S1-S30. eCollection 2014.

http://www.biomedcentral.com/1753-6561/8/S1/S30

(1) Unit of clustering 

There were actually two levels of clustering in this article. The data were simulated but based on real data and evaluated an outcome of systolic and diastolic blood pressure measurements taken for each individual at 3 different time points and for 741 individuals belonging to 310 sibships. Therefore the two clustering levels were at the individual level (since there were 3 bp measurements for each individual) and at the sibship level (since there were multiple siblings within each sibship). 

(2) Hypothesized effects 

The hypothesized effect was that there are certain variants in the genome that cause systolic or diastolic blood pressure to be higher or lower for each individual. But since this is simulated data, this effect was not just hypothesized it was actually created in the data by selecting certain variants that have been shown in previous literature to be causal, they selected 105 SNPs that are causal for systolic blood pressure and 117 SNPs that are causal for diastolic blood pressure. 

(3) Level at which the exposure is measured 

The exposure was measured at the individual level since each person’s genotype does not change across the three time points, and each person’s genotype would only affect that person’s blood pressure measurements. 

(4) Statistical model used to estimate the effect

A three-level multi-level mixed effects model is used in which the equation is described by both fixed and random effects parameters: Yijk = B0 + B1(SNPij) + B2(SEXij) + B3(AGEijk) + A1(PC1ij)+…+A10(PC10ij) + Mi + Tij + Eijk

where Yijk is the systolic or diastolic blood pressure value at time point, k (= 1,2,3), for an individual, j (=1,…,741), within each sibship, i (=1,…310). And the following coefficients are the fixed effects for each covariate = B0, B1, B2, B3, A1…A10; and the following coefficients are the random effects for the sibships = Mi, the individuals = Tij, and the blood pressure values = Eijk. 

(5) Other statistical models

The family-based association test (FBAT), which is typically used for genetic studies that utilize family data, employs a conditional linear regression in which each family is considered as a separate stratum and effects on blood pressure are estimated within each family. In the paper they compared the multi-level model to this FBAT test where they only used the first data point since FBAT are not able to use more than one clustering level. The concept of the FBAT test is that each individual’s genotype is compared to the un-transmitted genotypes from their parents. For example if the mother was AT and the father was CG, and the individual’s genotype was AC, then the transmitted genotype (AC) is compared to the three un-transmitted genotypes (TC, AG, and TG). Alternatively the paper also mentions an approach where both models are combined, not sure how though? I am assuming they might be referring to an averaging method or a Bayesian method?

Cluster-Randomized Controlled Trial of an HIV/Sexually Transmitted Infection Risk-Reduction Intervention for South African Men

Jemmott, J.B., Jemmott, L.S., O’Leary, A., Ngwane, Z., Icard, L.D., Heeren, G.A., Mtose, X., and Carty, C. 

The objective of this study was to test the efficacy of a risk-reduction intervention in a setting where heterosexual transmission of HIV is the dominant mode of transmission.

The unit of clustering was the neighborhood level in Eastern Cape Province, South Africa. Randomization was done on matched-pairs of neighborhoods to either HIV/STI risk-reduction intervention or a control intervention regarding health issues not related to sexual risk. There were 22 neighborhoods randomized to each arm.

Exposures and outcomes of interest were measured at the individual level. The primary outcome of interest was report of consistent condom use during vaginal intercourse in the past 3 months.

GEE was used for analysis of results. Particularly for the non-linear GEE models (any of the binary outcomes), a mixed-effect model may make more sense, as the outcome of interest here is focusing on individual level effects of the intervention rather than population average effects. The GEE gives a better approximate of the population average effect, but the mixed model would give a better approximation of the individual level effect. The relatively few number of clusters may be a problem for GEE.