Assignments
- Week 1: -- article discussion Tuesday 03 Apr 2018
- Reading: Overview chapter from van Belle, Fisher, Heagerty
and Lumley (2004)
- Applications: please locate a journal article that uses longitudinal or multilevel data analysis methods (e.g. look for "change" analysis, or mixed models, or GEE) -- be prepared to discuss the following aspects:
- Population
- Scientific question(s)
- Analysis approaches
- Issues (missing data, model selection, time-dependent
covariate, etc.)
- Summary Form to complete:
CorrelatedData-PaperReview.doc (MS Word document)
- Week 2:
- Reading: DHLZ Chapters 3 and 4; or FLW Chapters 2 and 3
- Analysis: MACS CD4 and viral load data
- MACS-cd4-vload0.raw --- Multicenter AIDS Cohort Data
- MACS-cd4-vload0.txt --- documentation
- MACS-cd4-vload0-999.raw --- Multicenter AIDS Cohort Data with -999 rather than NA for missing values
- [1] Input the data and summarize the distribution of baseline viral load.
- [2] Summarize the distribution of CD4 in years 1, 2, 3, and 4.
- [3] Summarize the mean CD4 (and standard deviation) in years 1, 2, 3, and 4 separately
for groups based on baseline viral load (see Table 18.1 of VFHL; Table 1.1 of PDF above).
- [4] Plot individual series of longitudinal observations for a selection of subjects.
- [5] Characterize the correlation among CD4 measurements.
- [6] Compute a slope over time for each subject and summarize these slopes.
- [7] Plot slopes versus the log baseline viral load. Is there an apparent association
between the baseline viral load and the subsequent rate of decline? (see
Figure 18.5 in VFHL; Figure 1.5 of PDF above).
- [8] Use linear mixed models to evaluate whether the level of CD4 and/or the rate of
decline in CD4 is associated with the baseline viral load.
- [9] Provide an interpretation for the estimates of the variance for the random effects
(random intercepts, random slopes).
- [10] Use generalized estimating equations (GEE) to evaluate whether the level of CD4
and/or the rate of decline in CD4 is associated with the baseline viral load.
- Comments on Exercise:
- Week 3:
- Reading: Estimation and Inference for LMM -- DHLZ Chpts 4, 5; FLW Chpts 8 (and 7)
- Analysis: MACS CD4 and viral load data
- [Note] I needed to add the option "clear" to my use of "statsby".
- [Note] The chapter presents the cut-offs for L,M,H VIRAL0 as rounded values -- I used
slightly different values in analysis.
- [1] Do you think the regression analysis presented in VFHL (2004) should adjust
for CD8? Justify.
- [2] Do you think the regression analysis presented in VFHL (2004) should adjust
for AGE of the subject? Justify.
- [3] The analysis in VFHL (2004) used categories of viral load at baseline (VLOAD0).
However, the scatterplot presented on page 740 (handout p. 21) shows a solid
line fit to the points. What regression model would allow the CD4 slope to
decrease linearly with increasing logVLOAD0?
- [4] Note that an interpretation is given on page 750 (handout p. 37) for the coefficient
of MONTH. The estimate for this coefficient is shown as -5.398 using a
linear mixed model with random intercepts and slopes.
However, on page 740 (handout p. 20) the average slope for the
low viral load group is estimated as -5.715. These values are similar -- does
the coefficient in the linear mixed model also have an interpretation as an
average slope? Justify.
- Comments on Exercise:
- Discussion: review exercises for discussion on Tuesday 17 April 2018
- Week 4:
- Reading: Mean Models -- FLW Chpts 5 and 6
- Analysis: TLC Data (see Lecture section of web page)
- [Note] The TLC data are in a "wide" format with one record.
per row (one subject's data).
- [1] Analyze blood lead at each
of the three follow-up times using simple
cross-sectional methods (i.e. t-test, and estimated means).
Compare this to our estimates/inference obtained using a
mixed model (notes pp. 201-202, and 205-207).
- [2] Another approach would analyze the change-since-baseline
in blood lead at each
of the three follow-up times using simple
cross-sectional methods (i.e. t-test, and estimated means).
Compare this to our estimates/inference obtained using a
mixed model (notes pp. 201-202, and 205-207).
- [3] A third approach would analyze the blood lead at each
of the three follow-up times using ANCOVA. This is
conducted by regressing the outcome at Time(j) on the
treatment indicator and the baseline response.
Compare this to our estimates/inference obtained using a
mixed model (notes pp. 201-202, and 205-207).
- [4] Inspect the coefficient of the baseline response in each of
the three ANCOVA models fit in [3]. Are these coefficients
approximately the same magnitude, or is there a trend in the
values. Would you expect these coefficients to be the same?
Justify.
- Comments on Exercise:
- Week 5:
- EXAMPLE -- Midterm Analysis for 2007: Epo Responsiveness
- Midterm Analysis for 2018:
- Week 6:
- Reading: GEE Discussion in chpts 7, 8 of DHLZ, and/or chpt 11 of FLW
- Week 7:
- Reading: Missing Data: chpt 13 of DHLZ, and/or chpt 14 of FLW
- Optional article:
Raghunathan (2004)
--- Annual Review of Public Health.
Discusses methods for general types of missing data (not just
drop-out).
- Optional article:
Hogan et al. (2004)
--- Statistics in Medicine.
Tutorial article regarding drop-outs in longitudinal studies.
- Optional article:
Houck et al. (2004)
--- Psychiatry Research.
Compares different methods.
- Optional article:
Wood et al. (2004)
--- International Journal of Epidemiology.
Compares different methods.
- Week 8:
- Reading: Hu et al. (1998) AJE paper
- Analysis: Infection and vitamin A
- xerop.raw --- Xeropthalmia data
- xerop.txt --- documentation
- [1] Input the data and summarize the prevalence of respiratory infection as a function of age (using descriptive methods).
- [2] Characterize the within-subject correlation of the binary infection outcomes.
- [3] Controlling for age and season, use GEE to evaluate whether there is an association between xeropthalmia (vitamin A deficiency) and risk of respiratory infection.
- [4] Controlling for age and season, use a GLMM to evaluate whether there is an association between xeropthalmia (vitamin A deficiency) and risk of respiratory infection.
- Comments on Exercise:
- Week 10:
- Final Analysis: USRDS and Hospitalization
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