Statistics 222,   Education 351A  Spring 2013
    Statistical Methods for Longitudinal Research


David Rogosa Sequoia 224,   rag{AT}stat{DOT}stanford{DOT}edu   Office hours: Thursday 2:10-3
Course web page: http://statistics.stanford.edu/~rag/stat222/


                To see full course materials from Spring 2012 go here

Registrar's information
STATS 222 (Same as EDUC 351A): Statistical Methods for Longitudinal Research
Class Number  35282
Lecture
Units: 2-3
Mo 3:15PM - 5:05PM  GSB Littlefield 107
Schedule: Monday 3:15-5:05pm
Grading Basis: Letter or Credit/No Credit

Course Description:
Research designs and statistical procedures for time-ordered (repeated-measures) data.
The analysis of longitudinal panel data is central to empirical research on
learning,development, aging. Topics: measurement of change, growth curve models,
analysis of durations including survival analysis, experimental and non-experimental group 
comparisons, reciprocal effects, stability.
Prerequisite: intermediate statistical methods. 


Preliminary Course Outline
Week 1. Course Overview, Longitudinal Research; Individual Histories and Growth Trajectories
Week 2. Introduction to Data Analysis Methods for Individual Change and Collections of Growth Curves (mixed-effects models)
Week 3. Collections of growth curves: linear and non-linear mixed-effects models
Week 4. Special case of time-1, time-2 data; Traditional measurement of change
Week 5. Assessing Group Growth and Comparing Treatments: Traditional Repeated Measures Analysis of Variance and Linear Mixed-effects Models
Week 6. Comparing group growth: Power calculations, Cohort Designs, Cross-over Designs, Methods for missing data. Observational studies.
Week 7. Analysis of Durations: Introduction to Survival Analysis and Event History Analysis
Week 8. Further topics in analysis of durations: Recurrent Events, Frailty Models, Behavioral Observations, Series of Events (renewal processes)
Week 9. Special Topics: Assessments of Stability (including Tracking), Reciprocal Effects, (mis)Applications of Structural Equation Models, Longitudinal Network Analysis

Texts and Resources for Course Content (reserves in Math/Stat library)
1. Garrett M. Fitzmaurice Nan M. Laird James H. Ware Applied Longitudinal Analysis (Wiley Series in Probability and Statistics)
  Text Website   Text lecture slides   
2. Peter Diggle , Patrick Heagerty, Kung-Yee Liang , Scott Zeger. Analysis of Longitudinal Data 2nd Ed, 2002
   Amazon page     Peter Diggle home page    Book data sets     A Short Course in Longitudinal Data Analysis Peter J Diggle, Nicola Reeve, Michelle Stanton (School of Health and Medicine, Lancaster University), June 2011
3. Judith D. Singer and John B. Willett . Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence New York: Oxford University Press, March, 2003.
  Text web page    Text data examples    Powerpoint presentations   good gentle intro to modelling collections of growth curves (and survival analysis) is Willett and Singer (1998)
4. Douglas M. Bates. lme4: Mixed-effects modeling with R  February 17, 2010 Springer (chapters). An merged version of Bates book: lme4: Mixed-effects modeling with R January 11, 2010
Manual for R-package lme4    and   mlmRev, Bates-Pinheiro book datasets.    
    Additional Doug Bates materials. Collection of all Doug Bates lme4 talks      Mixed models in R using the lme4 package Part 2: Longitudinal data, modeling interactions Douglas Bates 8th International Amsterdam Conference on Multilevel Analysis 2011-03-16    another version
Fitting linear mixed-effects models using lme4, Journal of Statistical Software Douglas Bates Martin Machler Ben Bolker.    Linear mixed model implementation in lme4 Douglas Bates Department of Statistics University of Wisconsin Madison October 4, 2011
  Technical topics: Mixed models in R using the lme4 package Part 4: Theory of linear mixed models
5. Longitudinal Data Analysis    Edited by Geert Verbeke , Marie Davidian , Garrett Fitzmaurice , and Geert Molenberghs Chapman and Hall/CRC 2008.   online supplement for LDA book  .
6. Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer Series in Statistics. New-York: Springer.  Extended presentation: Introduction to Longitudinal Data Analysis A shorter exposition: Methods for Analyzing Continuous, Discrete, and Incomplete Longitudinal Data
7. A handbook of statistical analyses using R (second edition). Brian Everitt, Torsten Hothorn CRC Press, Index of book chapters   Stanford access     Longitudinal chapters: Chap11   Chap12  Chap13. Data sets etc Package 'HSAUR2' February 15,2013, Title A Handbook of Statistical Analyses Using R (2nd Edition)
8. Survival analysis Rupert G. Miller. Available as Stanford Tech Report
9. John D. Kalbfleisch , Ross L. Prentice The Statistical Analysis of Failure Time Data 2nd Ed
  Amazon page    online from Wiley

Additional Specialized Resources
10. Harvey Goldstein. The Design and Analysis of Longitudinal Studies: Their Role in the Measurment of Change (1979). Elsevier
  Amazon page    Goldstein Chap 6 Repeated measures data      Multilevel Statistical Models by Harvey Goldstein with data sets   
11. David Roxbee Cox, Peter A. W. Lewis The statistical analysis of series of events. Chapman and Hall, 1966
  Google books    Poisson process computing program
12. David J Bartholomew. Stochastic Models for Social Processes, Chichester 3rd edition: John Wiley and Sons.
   David J Bartholomew web page


Grading, Exams, and Credit Units
Stat222/Ed351A is listed as Letter or Credit/No Credit grading (Stat MS students should check whether S/NC is a viable option for their degree program.)
Grading (for the 2-unit base) will be based on two components:
  Each week I will post a few exercises for that week's content--towards the end of the qtr I'll identify a subset of those exercises to be turned in.
  During the Spring qtr exam period we will have an in-class (all materials available, "open" everything) exam. My reading of the Registrar's chart indicates Monday, June 10, 2013 at 12:15PM in our classroom
           see Class Calendar for details
The Registrar requires clear identification of the requirements for incremental units. The additional requirement for a 3-unit registration (the one unit above 2-units) is satisfied by a student presentation: a mini-lecture, approximately 15 minutes with handout. These were done last year with Rogosa in Sequoia 224, which worked out well. Good topics would include empirical longitudinal research, such as a data set or set of studies you are involved with, or an extension of class lecture topics such as preparing an additional data analysis example or a report on some technical readings. Discussion with Rogosa is encouraged.   


Course Problem Set   posted 5/22/13

Cumulative Collection of Course Handounts

Statistical computing
Class presentation will be in, and students are encouraged to use, R (occasionally, some references to SAS and Mathematica). To the extent feasable, students can use whatever they are comfortable with.
1/7/09.  NY Times endorses R: Data Analysts Captivated by R's Power
Current version of R is version 2.15.3 (Security Blanket) released on 2013-03-01.(Also postings on R 3.0.0 Final release is scheduled for April 3, 2013).
    For references and software: The R Project for Statistical Computing   Closest download mirror is Berkeley
The CRAN Task View: Statistics for the Social Sciences provides an overview of some relevant R packages. Also the new CRAN Task View: Psychometric Models and Methods and CRAN Task View: Survival Analysis and CRAN Task View: Computational Econometrics.
A good R-primer on various applications (repeated measures and lots else). Notes on the use of R for psychology experiments and questionnaires Jonathan Baron, Yuelin Li.   Another version
A remarkably useful set of R-resources from Murray State
A Stat209 text, Data analysis and graphics using R (2007) J. Maindonald and J. Braun, Cambridge 2nd edition 2007. 3rd edition 2010   has available a short version in CRAN .
According to Peter Diggle: "The best resource for R that I have found is Karl Broman's Introduction to R page."

                  Course Content: Files, Readings, Examples

4/1. First class, Organizational Meeting
A.    Initial meet-and-greet. Class logistics and longitudinal research overview
B.     Examples, illustrations for longitudinal research overview, taken from course resources above:
          Verbeke (#6) slides from Ch 2, Sec3.3;   Laird,Ware (#1) slides 1-16;    Diggle (#2) slides 4-14, 22-28
C.     Data Analysis Examples of Model Fitting for Individual Trajectories and Histories.
         ascii version of class handout    pdf version with plots     datasets
            For Count Data (glm) example. Link functions for generalized linear mixed models (GLMMs), Bates slides (pdf pages 11-18)      AIDS in Belgium example, (from Simon Wood) single trajectory, count data using glm. A very comprehensive introduction to analysis of count data Regression Models for Count Data in R Achim Zeileis Christian Kleiber Simon Jackman (Stanford University)
           Trend in Proportions: College fund raising example     prop.trend.test help page ?prop.trend.test in R-session.       Trend in proportions, group growth, Cochran-Armitage test. Expository paper: G. Salanti and K. Ulm (2003): Tests for Trend in Binary Response


Longitudinal in the news
1. Study Ties Social Isolation to Increased Risk of Death      English Longitudinal Study of Ageing (ELSA)  Publication: Social isolation, loneliness, and all-cause mortality in older men and women Proc Natl Acad Sci U S A. 2013 Mar 25.
2.  Women Abused As Kids More Likely To Have Children With Autism     Nurses' Health Study II   Publication: Association of Maternal Exposure to Childhood Abuse With Elevated Risk for Autism in Offspring. JAMA Psychiatry. 2013;():1-8. doi:10.1001/jamapsychiatry.2013.
From 2012
3. Red Meat Tied to Increased Mortality Risk   Red Meat Can Be Unhealthy, Study Suggests  Publication: Red Meat Consumption and Mortality Results From 2 Prospective Cohort Studies Archives of Internal Medicine, March 2012.   Health Professionals Follow-up Study
4. Women Who Drink Moderately Have Lower Stroke Risk   Publication: Alcohol Consumption and Risk of Stroke in Women, Stroke, March 2012.  Nurses' Health Study
5. Do Happy People Have Healthier Hearts? Optimism, Happiness Linked to Lower Heart Attack, Stroke Risk    Publication: Boehm, J. K., and Kubzansky, L. D. (2012, April 16). The Heart's Content: The Association Between Positive Psychological Well-Being and Cardiovascular Health. Psychological Bulletin. 2012 American Psychological Association 2012, Vol. 138, No. 4, 655–691


WEEK 1 Exercises
1. Straight-line fits for NC Fem data: North Carolina Achievement Data (see Williamson, Applebaum, Epanchin, 1991). These education data are eight yearly observations on achievement test scores in math (Y), for 277 females each followed from grade 1 to grade 8, with a verbal ability background measure (W).
North Carolina, female math performance (also in Rogosa-Saner)    North Carolina data (wide format);         NC data (long)
a. Here we will use the 8 yearly observations on female ID 705810, which you can obtain from either the long form or wide form of these data.
For that female, what is the rate of improvement over grades 1 through 8? Compare the observed improvement for grades 1 through 8 (the difference score) with the amount of improvement indicated by the model fit. Obtain a 95% confidence interval for each (if possible).
b. More on OLS and the difference score. Refer to an old publication: A growth curve approach to the measurement of change. Rogosa, David; Brandt, David; Zimowski, Michele Psychological Bulletin. 1982 Nov Vol 92(3) 726-748 APA record   direct link;  Equation 4, page 728, shows a useful form for the OLS slope. (actually reading the first three pages of that pub is a decent intro to the growth curve topic.) For equally spaced data, that Eq (4) gives a useful equivalence between difference scores (amounts of change) and OLS slopes (multiply rates of change by time interval). For the part a NC data show that the OLS slope can be expressed as a weighted sum of the four differences: { 8-1,7-2,6-3,5-4}. [to say that better {score at time 8 minus score at time 1; score at time 7 minus score at time 2; ...} and so forth]
Seperately, consider three observations at taken at equally spaced time intervals: What is a simple expression for the OLS slope (rate of change)?
2. Revisit the Berkeley Growth Data example from week 1 lecture. Consider the quadratic (polynomial degree 2) fit to these data, and also a (innapropriate?) constant-rate-of-change (straight-line) fit to these data. Then refer to Seigel, D. G. Several approaches for measuring average rates of change for a second degree polynomial. The American Statistician, 1975, 29, 36-37. JStor Link for equivalences for the slope of the straight-line fit to an average rate of change for the quadratic fit. Compare Seigel 'Approach 3" to 'Approach 1'.
3. Revisit the Belgium Aids data example (counts of new cases by year). Use the parameter estimates for am2 (quadratic in time glm fit) to compute by hand (or calculator) the values of the glm fit at year = 5 and year = 9. Compare those values with results from the model am2 using predict
Solution for problem 3
4. Paul Rosenbaum has a little data set on growth in vocabulary that I grabbed from his Wharton coursesite. Following the chicks class example, plot these data and try to fit a logistic growth curve to these data. What is the estimate of the final vocab level (asymptote)? Compare the data and the fits from the logistic growth curve.
For reference,       Self-Starting Logistic model      SSlogis help page, do ?SSlogis   post of annotated logistic curve with SSlogis arguments       additional tools in the grofit package

Solution for problem 4



4/8. Analysis of collections of growth curves (Mixed-effects Models, lmer)

Class Examples
1. Sleepstudy data analysis from Doug Bates lme4 book lme4: Mixed-effects modeling with R February 17, 2010 (draft chapters) Chapter 4: Sleepstudy example or Chap 3 in merged version of Bates book: lme4: Mixed-effects modeling with R January 11, 2010.   Or a set of Bates slides for the sleepstudy example
Data frame sleepstudy available in lme4 package.
Source Publication: Belenky, G., Wesensten, N. J., Thorne, D. R., Thomas, M. L., Sing, H. C., Redmond, D. P., Russo, M., & Balkin, T. (2003). Patterns of performance degradation and restoration during sleep restriction and subsequent recovery: A sleep dose-response study. Journal of Sleep Research, 12(1), 1-12.
     Sleepstudy, Bates Ch 4, lme4 analyses handout     more Doug Bates Slides (pdf pages 8-28)          Individual plots (frame-by-frame)   Plot of straight-line fits   
   Music to accompany long-distance truck driver data: 1971 The Flying Burrito Brothers "Six Days on the Road"
2.      North Carolina, female math performance (also in Rogosa-Saner)    North Carolina data (wide format);     making the "Long" version     NC data (long)    lmer analyses of NC data     plots for NC data
Why lmer (lme4) does not provide p-values for fixed effects : Doug Bates    lmer, p-values and all that
North Carolina example. Smart First Year Student Analysis for NC    lmer analyses of NC data          NC bootstrap results (SAS)
North Carolina Data also in (with full development of the modelling) Longitudinal Data Analysis Examples with Random Coefficient Models. David Rogosa; Hilary Saner . Journal of Educational and Behavioral Statistics, Vol. 20, No. 2, Special Issue: Hierarchical Linear Models: Problems and Prospects. (Summer, 1995), pp. 149-170. Jstor
3. Brain Volume Data, in-class modeling exercise: analyses from "Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI"     cartoon plot of Lateral Ventricles data;     actual data plot of Lateral Ventricles data;    development of lmer (random effect) growth models

Background Readings
Fitting linear mixed-effects models using lme4, Journal of Statistical Software Douglas Bates Martin Machler Ben Bolker
Linear mixed model implementation in lme4 Douglas Bates Department of Statistics University of Wisconsin Madison October 4, 2011
Doug Bates materials: Three packages, "SASmixed", "mlmRev" and "MEMSS" with examples and data sets for mixed effect models
North Carolina Data also in (with full development of the modelling) Longitudinal Data Analysis Examples with Random Coefficient Models. David Rogosa; Hilary Saner . Journal of Educational and Behavioral Statistics, Vol. 20, No. 2, Special Issue: Hierarchical Linear Models: Problems and Prospects. (Summer, 1995), pp. 149-170. Jstor    Data sets for Rogosa-Saner
Additional talk materials: An Assortment of Longitudinal Data Analysis Examples and Problems 1/97, Stanford biostat.      Overview and Implementation for Basic Longitudinal Data Analysis CRESST Sept '97.    Another version (short) of the expository material is from the Timepath '97 (old SAS progranms) site: Growth Curve models ;    Data Analysis and Parameter Estimation ; Derived quantities for properties of collections of growth curves and bootstrap inference procedures

WEEK 2 Exercises
1. Ramus Data example. Example consists of 4 longitudinal observations on each of 20 cases. The measurement is the height of the mandibular ramus bone (in mm) for boys each measured at 8, 8.5, 9, 9.5 years of age. These data, which have been used by a number of authors (e.g., Elston and Grizzle 1962), can be found in Table 4.1 of Goldstein (1979).      Ramus data example      long form for Ramus data   tutorial on creating long form data manipulation .     Use lmList to obtain the 20 OLS fits, with the initial time set to 8 years of age, i.e. intercepts are fits for the time of initial measurement (not t=0). Fit the lmer model for the collection of growth curves (using initial time = 8); verify that fixed effects are the sample means (over persons) of the lmList intercepts and slopes. Verify that the random effects variance for "age" (i.e. slopes) is the method-of-moments estimate for Var(theta). Compare the random effect estimates (ranef) which borrow strength for each subject with the OLS estimates from lmList (c.f. Bates Chap 4 discussion of sleepstudy data)
2.   Artificial data example (used in Myths chapter to illustrate time-1,time-2 data analysis)    Two part artificial data example.   The bottom frame (the X's) is 40 subjects each with three equally spaced time observations (here in wide form).For these the fallible "X" measurements (constructed by adding noise to the Xi measurements).
       Solution provided for problem 2a
  a. Follow the class examples and obtain the plot showing each subject's data and straight-line fit. Use lmList to obtain the 40 slopes for the straight-line fits.
  b. Standardizing is always a bad idea is a good motto for life, especially with longitudinal data. Start out with the "X" data, and standardize (i.e. transform to mean 0, var 1) at each of the 3 time points. Note "scale" will do this for you (in wide form). For the standardized data obtain the plot showing each subject's data and straight-line fit. What do you have here? Compare the results the mixed-effects models fitting the collection of straight-line growth curves for the measured and standardized data.
3. lmer/lme vs lm  Consider the sleepstudy and Ramus examples, collections of growth trajectories with no exogenous variable. Fitting the lmer models with Formula: Reaction ~ 1 + Days + (1 + Days | Subject) or Formula: ramus ~ I(age - 8) + (age | subj) has motivated the student question, what is going on here beyond what lm would do? So let's look at what lm would do in these examples. Verify (or disprove) the assertion that the fixed effects from lmer, which we have seen are the averages of the individual fit parameter estimates (i.e. lmList), and therefore the coefficients of the average growth curve are identical to the fit from lm (which ignores the existence of individual trajectories). Compare the results of the lm and lmer analyses for these two data sets.
4. Early Education data (From Bates and Willett-Singer). Data on early childhood cognitive development described in Doug Bates talk materials (pdf pages 49-52). Obtain these data from the R-package "mlmRev" or the Willett-Singer book site (in our week 1 intro links). Data are in long form and consist of 3 observations 58 treatment and 45 control children; see the Early entry in the mlmRev package docs. Produce the plot of individual trajectories shown pdf p.49, Bates talk. (note:Bates does connect-the-dots, we have done straight-line fit, your choice). Show five-number summaries of rates of impovement in cognitive scores for treatment and control groups. Develop and fit the fm12 lmer model shown in Bates pdf p.50 (note fm12 allows trt to effect rates of improvement but not level;). Interpret results. Note: this moves us into the comparing groups topics, where the individual attribute is group membership.


4/15. Collections of growth curves: linear and non-linear mixed-effects models

Lecture Topics
1.      Model Comparisons for North Carolina, female math performance (also in Rogosa-Saner).
  Additional NC materials North Carolina data (wide format);     making the "Long" version     NC data (long)       plots for NC data    Smart First Year Student Analysis for NC    lmer analyses of NC data          NC bootstrap results (SAS)
North Carolina Data also in (with full development of the modelling) Longitudinal Data Analysis Examples with Random Coefficient Models. David Rogosa; Hilary Saner . Journal of Educational and Behavioral Statistics, Vol. 20, No. 2, Special Issue: Hierarchical Linear Models: Problems and Prospects. (Summer, 1995), pp. 149-170. Jstor
2.    Brain Volume Data, in-class modeling exercise: analyses from "Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI"     cartoon plot of Lateral Ventricles data;     actual data plot of Lateral Ventricles data;    development of lmer (random effect) growth models
3. General formulation of mixed effects model in terms of growth trajectories (see pdf pages 7-8, handout) in An Assortment of Longitudinal Data Analysis Examples and Problems 1/97, Stanford biostat. Also Ware-Laird ALA slides 234-240.    Douglas M. Bates lme4: Mixed-effects modeling with R section 3.5
4.   Non-linear Models: Example: Orange Tree growth.     Data from MEMSS package Data sets and sample analyses from Pinheiro and Bates, Mixedeffects Models in S and S-PLUS (Springer, 2000).
   Doug Bates Slides Orange trees analysis (pdf pages 8-16), Logistic SS (pdf p.6), pharmacokinetics ex (pdf pages 7, 17-24)   Plots and nlmer analysis, Orange tree data   Bates NLMM.Rnw  R graphical manual entry      From week 1 Self-Starting Logistic model      SSlogis help page, do ?SSlogis   post of annotated logistic curve with SSlogis arguments   another analysis of Orange Trees in the ASReml package manual section 8.9
Also LDA book Chapter 5. Chapter 5. Non-linear mixed-effects models Marie Davidian
    additional tools in the grofit package and nlmeODE package Title Non-linear mixed-effects modelling in nlme using differential equations

a well-meaning experiment, script for Lecture 3
WEEK 3 Exercises
1.Vocabulary learning data from test results on file in the Records Office of the Laboratory School of the University of Chicago. Source D R Bock, MSMBR. The data consist of scores, obtained from a cohort of pupils at the eigth through eleventh gade level on alternative forms of the vocabulary section of the Cooperative Reading Tests." There are 64 students in all, 36 male, 28 female (ordered) each with four equally spaced observations (test scores). Wide form of these data are in BOCKwide.dat and I kindly also made a long-form version BOCKlong.dat . Construct the usual collection of individual trajectory displays (either connect-the-dots or compare to a straight-line). Obtain the means (over persons) and plot the group growth curve. Does there appear to be curvature (i.e. deceleration in vocabulary skill growth)? Construct an lmer model with the individual growth curve a quadratic function of grade (year), most convenient to use uncorrelated predictors grade - mean(grade) and (grade - mean(grade))^2. Fit the lmer model and interpret the fixed and random effects you obtain. Compare the results with a lmer model in which the individual trajectories are straight-line. Use the anova model comparison functionality in R (e.g. anova(modLin, modQuad) to test whether the quadratic function for individual growth produces a better model fit.
2. Orange tree extras. Take the fixed effects from the orange tree nlmer model, "m1" in the class materials, as the parameters of the "average" growth curve for this group of trees. Plot that logistic growth curve (either use a formula for logistic or the growfit package has a simple function). Compare the fixed effects from nlmer to the results from nls for these data. More challenging Try to superimpose the group logistic curve (above) onto the plots of the individual tree trajectories (you may want to refer to the plots week1 Aids data).
3. Data on the growth of chicks on different diets. Hand and Crowder (1996), Table A.2, p. 172 Hand, D. and Crowder, M. (1996), Practical Longitudinal Data Analysis, Chapman and Hall, London. The dataset is available as a .R file; easiest to bring this page down to your machine and then load into your R-session (or try to load remotely). Here we consider the 20 chicks on Diet 1. (select these). Construct the plots analogous to those for the class example Orange trees: individual chicks frame-by-frame and all chicks on one plot. Fit a nlmer model that allows final weight (asymptote) to differ over chicks (other params fixed). Use ranef (individual estimates) to identify the largest asymptote value and smallest value. Plot the "average" growth curve under diet 1. Compare that nlmer maodel with a model that does not allow asymptotes to differ. What is your conclusion. Also compare with a nls model that ignores repeated measurements structure (i.e. ignores individual chicks). Compare the average growth curves.
4. Asymptotic regression, SSasymp slide (pdf p.5 of Bates slides, Nonlinear mixed models talk linked in Week 3, Topic 4). Data are from Neter-Wasserman text in file CH13TA04.txt. The outcome variable is manufacturing relative efficiency (RelEff) over 90 weeks duration for two different locations. Plot the RelEff outcome against week for the two locations. Use the SSasymp function for a nlmer fit (or nls if needed) to see whether the asymptote differs for the two locations.



4/22. Special case of time-1, time-2 data; Traditional measurement of change

1. Properties of Collections of Growth Curves. class handout
2. Time-1, time-2 data.
The R-package PairedData has some interesting plots and statistical summaries for "before and after" data; here is a McNeil plot for Xi.1, Xi.5 in data example
Paired dichotomous data, McNemar's test (in R, mcnemar.test {stats}), Agresti (2nd ed) sec 10.1 Also see R-package "PropCIs" Prime Minister ex
3. Issues in the Measurement of Change. Class lecture covers Myths 1-6+.
Slides from Myths talk    Distribute Myths/MeasurementOfChange CD   also on the CD with pubs.
Class Handout, Companion for Myths talk
4. Examples for Exogenous Variables and Correlates of Change
   Time-1,time-2 data analysis examples    Measurement of change: time-1,time-2 data
      data example for handout    scan of regression handout
Correlates and predictors of change: time-1,time-2 data      data analysis     Rogosa R-session to replicate handout, demonstrate wide-to-long data set conversion, and descriptive fitting of individual growth curves. Some useful plots from Rogosa R-session
5. Comparing groups on time-1, time-2 measurements: repeated measures anova vs lmer OR the t-test
     urea synthesis, BK data     Stat141 analysis     data, long-form,    lmer for BK repeated measures analysis     BK plots (by group)     archival example analyses. SAS and minitab
Comparative Analyses of Pretest-Posttest Research Designs, Donna R. Brogan; Michael H. Kutner, The American Statistician, Vol. 34, No. 4. (Nov., 1980), pp. 229-232.   JSTOR link

Background Readings and Resources
Myths Chapter-- distributed on CD. Rogosa, D. R. (1995). Myths and methods: "Myths about longitudinal research," plus supplemental questions. In The analysis of change, J. M. Gottman, Ed. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 3-65.
More stuff (if you don't like the ways I said it)   
I noticed John Gottman did a pub rewriting the myths: Journal of Consulting and Clinical Psychology 1993, Vol. 61, No. 6,907-910 The Analysis of Change: Issues, Fallacies, and New Ideas
Also John Willett did a rewrite of the Myths 'cuz I didn't want to reprint it again (or write a new version): Questions and Answers in the Measurement of Change REVIEW OF RESEARCH IN EDUCATION 1988 15: 345
Reliability Coefficients: Background info. Short primer on test reliability    Informal exposition in Shoe Shopping and the Reliability Coefficient    extensive technical material in Chap 7 Revelle text
A growth curve approach to the measurement of change. Rogosa, David; Brandt, David; Zimowski, Michele Psychological Bulletin. 1982 Nov Vol 92(3) 726-748 APA record   direct link
Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203-228.
available from John Willet's pub page
Demonstrating the Reliability of the Difference Score in the Measurement of Change. David R. Rogosa; John B. Willett Journal of Educational Measurement, Vol. 20, No. 4. (Winter, 1983), pp. 335-343. Jstor
Maris, Eric. (1998). Covariance Adjustment Versus Gain Scores--Revisited. Psychological Methods, 3(3) 309-327. apa link  
A good R-primer on repeated measures (a lots else). Notes on the use of R for psychology experiments and questionnaires Jonathan Baron, Yuelin Li.   Another version
Multilevel package   has behavioral scienes applications including estimates of within-group agreement, and routines using random group resampling (RGR) to detect group effects.


WEEK 4 Exercises
1. Time1-time2 regressions; Class example 4/22
Repeat the handout demonstration regressions using the fallible measures (the X's) from the bottom half of the linked data page. The X's are simply error-in-variable versions of the Xi's: X = Xi + error, with error having mean 0 and variance 10. Compare 5-number summaries for the amount of change from the earliest time "1" to the final observation "5" using the "Xi" measurements (upper frame) and the fallible "X" observations (lower frame).
2. Captopril and Blood pressure
The file captopril.dat contains the data shown in Section 2.2 of Verbeke, Introduction to Longitudinal Data Analysis, slides. Captopril is an angiotensin-converting enzyme inhibitor (ACE inhibitor) used for the treatment of hypertension. Use the before and after Spb measurements to examine the improvement (i.e. decrease) in blood pressure. Obtain a five-number summary for observed improvement. What is the correlation between change and initial blood pressure measurement? Obtain a confidence interval for the correlation and show the corresponding scatterplot.
3. (more challenging). Use mvrnorm to construct a second artificial data example (n=100) mirroring the 4/22 class handout BUT with the correlation between true individual rate of change and W set to .7 instead of 0. Carry out the corresponding regression demonstration.
       Solution provided for problem 3
4. Reliability versus precision demonstration
  Consider a population with true change between time1 and time2 distributed Uniform [99,101] and measurement error Uniform [-1, 1]. If you used discrete Uniform in this construction then you could say measurement of change is accurate to 1 part in a hundred.
Calculate the reliability of the difference score.
Also try error Uniform [-2,2], accuracy one part in 50.
A similar demonstration can be found in my Shoe Shopping and the Reliability Coefficient
5. Regression toward the mean? Galton's data on the heights of parents and their children
In the "HistData" or "psych" packages reside the "galton" dataset, the primordial regression toward mean example.
Description: Galton (1886) presented these data in a table, showing a cross-tabulation of 928 adult children born to 205 fathers and mothers, by their height and their mid-parent's height. A data frame with 928 observations on the following 2 variables. parent Mid Parent heights (in inches) child Child Height. Details: Female heights were adjusted by 1.08 to compensate for sex differences. (This was done in the original data set)
Consider "parent" as time1 data and "child" as time2 data and investigate whether these data indicate regression toward the mean according to either definition (metric or standardized)? Refer to Section 4 of the Myths chapter supplement (pagination 61-63) for an assessment of regression toward the mean (i.e. counting up number of subjects satisfying regression-toward-mean).
Aside: if you like odd plots, try this (and then look at the docs ?sunflowerplot; this may require the package "car" to be installed on your machine)
with(Galton,
{
sunflowerplot(parent,child, xlim=c(62,74), ylim=c(62,74))
reg <- lm(child ~ parent)
abline(reg)
lines(lowess(parent, child), col="blue", lwd=2)
if(require(car)) {
dataEllipse(parent,child, xlim=c(62,74), ylim=c(62,74), plot.points=FALSE)
}
}) 
6. Paired and unpaired samples, continuous vs categorical measurements.
Let's use again the 40 subjects in the problem 1 "X" data.
a. Measured data. Take the time1 and time5 observations and obtain a 95% Confidence Interval for the amount of change. Compare the width of that interval with a confidence interval for the difference beween the time5 and time1 means if we were told a different group of 40 subjects was measured at each of the time points (data no longer paired).
b. Dichotomous data. Instead look at these data with the criterion that a score of 50 or above is a "PASS" and below that is "FAIL". Carry out McNemar's test for the paired dichotomous data, and obtain a 95% CI for the difference between dependent proportions. Compare that confidence interval with the "unpaired" version (different group of 40 subjects was measured at each of the time points) for independent proportions.


4/29. Assessing Group Growth and Comparing Treatments

Lecture Topics.
1. Recap lmer models versus Repeated measures analysis of variance, Brogan-Kutner data     longform with subjects numbered sequentially   BK equivalences (old)    BK data, comparing lmer with aov .  Reference: Comparative Analyses of Pretest-Posttest Research Designs, Donna R. Brogan; Michael H. Kutner, The American Statistician, Vol. 34, No. 4. (Nov., 1980), pp. 229-232.   JSTOR link
Bock Vocabulary data, Repeated Measures anova (with linear, quadratic, cubic contrasts): class example.
More repeated measures resources: Background primer on analysis of variance (with R); see sections 6.8, 6.9 of Notes on the use of R for psychology experiments and questionnaires Jonathan Baron, Yuelin Li.   Pdf version    The ez package provides extended anova capabities.   Examples (blog notes) : Repeated measures ANOVA with R (functions and tutorials)   Repeated Measures ANOVA using R    Obtaining the same ANOVA results in R as in SPSS - the difficulties with Type II and Type III sums of squares
Application publications, time-1, time-2 Experimental Group Comparisons:
a.  Mere Visual Perception of Other People's Disease Symptoms Facilitates a More Aggressive Immune Response Psychological Science, April 2010   Pre-post data and difference scores (see Table 1)
b. Guns and testosterone. Guns Up Testosterone, Male Aggression
Guns, Testosterone, and Aggression: An Experimental Test of a Mediational Hypothesis Klinesmith, Jennifer; Kasser, Tim; McAndrew, Francis T,   Psychological Science. Vol 17(7), Jul 2006, pp. 568-571.
2. Cross-over designs. Laird-Ware text slides (pdf pages 135-150). Crossover design data from slide 137, anova for crossover design ex also see slides 5-14 Repeated Measures Design Mark Conaway
3. Group Comparisons for Longitudinal Experimental Designs. Group growth and Experimental comparisons for count and dichotomous outcomes.
Link functions for generalized linear mixed models (GLMMs), Bates slides (pdf pages 11-18)
A Handbook of Statistical Analyses Using R, Second Edition Torsten Hothorn and Brian S . Everitt Chapman and Hall/CRC 2009. Analysing Longitudinal Data II -- Generalised Estimation Equations and Linear Mixed Effect Models: Treating Respiratory Illness and Epileptic Seizures     Data sets etc Package 'HSAUR2' February 15,2013, Title A Handbook of Statistical Analyses Using R (2nd Edition)
  A.    Analysis of Count data.      Epilepsy example, group comparisons, collection of individual trajectories. HSAUR chap 13    Rogosa R-session using gee and lmer   For SAS (and GEE) fans another analysis
  B.    Binary Response, dichotomous outcomes. Respiratory Illness Data from HSAUR package. Data and description also at the ALA (Laird-Ware) site   Rogosa R-session using lmer   Also, Bates, fertility in Bangladesh (for HW).

WEEK 5 Exercises
1.Treatment of Lead Exposed Children (TLC) Trial. Data (wide form) and description reside at Laird-Ware text site
Start out by just using the subset of the longitudinal data Lead Level Week 0 and Week 6. Carry out the repeated measures anova for the relative effectiveness of chelation treatment with succimer or placebo (A,P). Show the three equivalences in the Brogan-Kutner paper between the repeated measures anova results and simple t-tests for these data. Next compare with a lmer fit following the B-K class example (posted). Finally use all 4 longitudinal measures (weeks 0,1,4,6) for a Active vs Placebo comparison using lmer. Compare with the results that use only 2 observations.
2. Vocabulary learning data-- see Week 3 problem 1-- from test results on file in the Records Office of the Laboratory School of the University of Chicago. Source D R Bock, MSMBR. The data consist of scores, obtained from a cohort of pupils at the eigth through eleventh gade level on alternative forms of the vocabulary section of the Cooperative Reading Tests." There are 64 students in all, 36 male, 28 female (ordered) each with four equally spaced observations (test scores). Wide form of these data are in BOCKwide.dat and I kindly also made a long-form version BOCKlong.dat .
For this problem consider gender differences in Vocabulary growth. Obtain the means (over persons) and plot the group growth curves, separately by gender. Does there appear to be curvature (i.e. deceleration in vocabulary skill growth) for both males and females? Construct an lmer model with the individual growth curve a quadratic function of grade (year), most convenient to use uncorrelated predictors grade - mean(grade) and (grade - mean(grade))^2. In the level II model allow each of the three parameters of the individual quadratic curves to differ by gender. Fit the lmer model and interpret the fixed and random effects you obtain. Compare the results with a lmer model in which the individual trajectories are straight-line. Use the anova model comparison functionality in R (e.g. anova(modLin, modQuad) to test whether the quadratic function for individual growth produces a better model fit.
3. Crossover Design. The dataset consists of safety data from a crossover trial on the disease cerebrovascular deficiency. The response variable is not a trial endpoint but rather a potential side effect. In this two-period crossover trial, comparing the effects of active drug to placebo, 67 patients were randomly allocated to the two treatment sequences, with 34 patients receiving placebo followed by active treatment, and 33 patients receiving active treatment followed by placebo. The response variable is binary, indicating whether an electrocardiogram (ECG) was abnormal (Y=1) or normal (Y=0). Each patient has a bivariate binary response vector.
Data set is available at http://www.hsph.harvard.edu/fitzmaur/ala/ecg.txt (needs to be cut-and-paste into editor). Carry out the basic analysis of variance for this crossover design following week 5 Lecture topic 2. You may want to use glm to take into account the binary outcome. Does the treatment increase the probability of abnormal ECG? Give a point estimate and significance test for the treatment effect.
4. Analysis of Covariance
part a. For the Brogan-Kutner data carry out an analysis of covariance (using premeasure as covariate) for the relative effectiveness of the surgery methods. Compare with class analyses.
part b. Slides 203-204 in the Laird-Ware text materials purport to demonstrate that analysis of covariance produces a more precise treatment effect estimate than difference scores (repeated measures anova). What very limiting assumption is slipped into their analysis? Can you create a counter-example to their assertion/proof?
   Solution Notes on the ALA (Laird-Ware) assertion
5. Level I, Level II model formulation for experimental group comparisons. In the respiratory (dichotomous outcome) and seizure (count outcome) examples, both of which focus on drug/placebo group comparisons, the specification of the individual trajectory (Level 1) model was not a major feature of the analysis. Rogosa note on formulating (g)lmer models.
a. The lmer model for the resp data in the class handout and section 13.4 of the HSAUR chapter
Formula: status ~ baseline + month + treatment + gender + age + centre + (1 | subject)
The within-subject term (1 | subject) in this model specifies a flat "trend" for logit(Pr(good)) over the months of observation (but adding "month" in the fixed effects negates that specification to some extent).
Compare the results from the 'reduced' model with no month term: Formula: status ~ baseline + treatment + gender + age + centre + (1 | subject) with a model that includes a trend over months,
Formula: status ~ baseline + month + treatment + gender + age + centre + (month | subject) . Compare estimate for the odds of "good" outcome for drug vs placebo; compare the model fits using anova. Which model appears perferable?
b. With the seizure data (epilepsy) there is a similar comparison to be considered. In the class handout the model used is:
seizure.rate ~ base + age + treatment + offset(per) + (period | subject) and the specification allows for a within-subject trend of log(seizure) over periods of observation. Compare these results with a 'reduced' model that specifies no time trend, (1 | subject). Compare estimates of seizure rate reduction and compare model fits.
6. Chick Data, finale. One more use of the chick data (week 3, problem 3; week 1 class lecture). Use the data for all 4 Diets to construct a nlmer model that allows asymptotes to differ across the four diets. Do the diets produce significantly different results? Which diet produces the heaviest 'mature' chick weight?
5/6. Comparing Group Growth, continued. Power Calculations, Cohort Designs, Missing Data, Observational Studies.

Lecture Topics.
1. Recap Group Comparisons, Epilepsy example. Comparison of lmer models
2. Study Design: Power Calculations for Longitudinal Group Comparsions. R-package longpower . Functions in MBESS package--ss.power.pcm. Background pubs:Sample Size Planning for Longitudinal Models: Accuracy in Parameter Estimation for Polynomial Change Parameters Ken Kelley Notre Dame Joseph R. Rausch Psychological Methods 2011   Power for linear models of longitudinal data with applications to Alzheimer's Disease Phase II study design Michael C. Donohue, Steven D. Edland, Anthony C. Gamst
3. Cohort effects. Cohort-sequential, Accelerated longitudinal designs. Robinson, K., Schmidt, T. and Teti, D. M. (2008) Issues in the Use of Longitudinal and Cross-Sectional Designs, in Handbook of Research Methods in Developmental Science (ed D. M. Teti), Blackwell Publishing Ltd, Oxford, UK
4. Missing Data.    Nontechnical overviews: Phil Lavori et al. Psychiatric Annals, Volume 38, Issue 12, December 2008 Missing Data in Longitudinal Clinical Trials, Part A    Part B    Robin Henderson, Missing Data in Longitudinal Studies
Multiple Imputation. van Buuren S and Groothuis-Oudshoorn K (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. see also multiple imputation online    Flexible Imputation of Missing Data. Stef van Buuren Chapman and Hall/CRC 2012. Chapter 9, Longitudinal Data Sec 3.8 Multilevel data. He is the originator of mice
   CHAPTER 17 Incomplete data: Introduction and overview. Longitudinal Data Analysis Edited by Geert Verbeke , Marie Davidian , Garrett Fitzmaurice , and Geert Molenberghs Chapman and Hall/CRC 2008. Also CHAPTER 21 Multiple imputation Michael G. Kenward and James R. Carpenter and CHAPTER 22 Sensitivity analysis for incomplete data. online supplement for LDA book  . van Buuren S (2010). Multiple Imputation of Multilevel Data. In JJ Hox, K Roberts (eds.), The Handbook of Advanced Multilevel Analysis, chapter 10, pp. 173{196. Routledge, Milton Park, UK
Handling drop-out in longitudinal studies (pages 1455-1497) Joseph W. Hogan, Jason Roy and Christina Korkontzelou, Statistics in Medicine 15 May 2004 Volume 23, Issue 9. (SAS implementations)
Bayesian approach. Missing Data in Longitudinal Studies. Strategies for Bayesian Modeling and Sensitivity Analysis Joseph W . Hogan and Michael J . Daniels Chapman and Hall/CRC 2008 Ch 5 Missing Data Mechanisms and Longitudinal Data     Corresponding talk, A Brief Tour of Missing Data in Longitudinal Studies Mike Daniels
Overview and applications paper: Assessing missing data assumptions in longitudinal studies: an example using a smoking cessation trial Xiaowei Yanga, Steven Shoptawb. Drug and Alcohol Dependence Volume 77, Issue 3, 7 March 2005, Pages 213-225
R resources.  Multivariate Analysis Task View, Missing data section, esp packages mice and mi   R-package pan Multiple imputation for multivariate panel or clustered data. Schafer tech report   Schafer talk: Missing Data in Longitudinal Studies: A Review   Efficient ways to impute incomplete panel data. Kristian Kleinke · Mark Stemmler · Jost Reinecke ·Friedrich Losel AStA Adv Stat Anal (2011) 95:351-373 DOI 10.1007/s10182-011-0179-9
5. Observational Studies: Group Comparisons in Longitudinal Observational (non-experimental,  "quasi"-experimental) Designs
  A. Regression adjustments in quasi-experiments. Technical resource: Weisberg, H. I. Statistical adjustments and uncontrolled studies. Psychological Bulletin, 1979, 86, 1149-1164.
  B. Lord's paradox; pre-post group comparisons. Lord, F. M. (1967). A paradox in the interpretation of group comparisons. Psychological Bulletin, 68, 304-305.
   Wainer, H. (1991). Adjusting for differential base rates: Lord's Paradox again. Psychological Bulletin, 109, 147-151.
  C. Additional topics (quick mentions). Differences in Differences (Diff-in-Diff) R-package wfe, Value-added analysis, Interrupted time-series, group-based trajectory modelling (matching).
6. Econometric Approaches to Longitudinal Panel Data. Panel Data Econometrics in R: The plm Package Yves Croissant Giovanni Millo (esp. section 7. "plm versus nlme/lme4" ).   R-package plm


WEEK 6 Exercises
1. Missing Data. Wide-form longitudinal data
   Artificial data example from week 2 problem 2 and Week 4 Lecture item 4 and problem 1 (used in Myths chapter to illustrate time-1,time-2 data analysis)    Two part artificial data example.   The top frame (the Xi's) is 40 subjects each with three equally spaced time observations (here in wide form). For these these perfectly measured "Xi" measurements each subject's observation fall on a straight-line.
   a. Use data set W6prob1a , for which about 15% of the observations have been made missing. Use multiple imputation procedures to recreate the multiple regression demonstration in Week 4 lecture, part 4: "Correlates and predictors of change: time-1,time-2 data" . Compare with the results for the full data on 40 subjects.
   b. Repeat part a with data set W6prob1b. Can you find any reason to doubt a "missing at random" assumption for this data set?
2. Observational Studies: Lord's Paradox.
    Part 1. Lord's paradox example
a. construct a two-group pre-post example with 20 observations in each group that mimics the description in Lord (1967):
statistician 1 (difference scores) obtains 0 group effect
statistician 2 (analysis of covariance) obtains large group effect for the group higher on the pre-existing differences in pretest
b. construct second example for which
statistician 1 (difference scores) obtains large group effect
statistician 2 (analysis of covariance) obtains 0 group effect
c. construct a third example (if possible) for which
statistician 1 (difference scores) obtains large postive group effect
statistician 2 (analysis of covariance) obtains large negative group effect
    Part 2. Group Comparisons by repeated measures analysis of variance or lmer
For the examples in part 1, (a and c), carry out the group comparison (i.e. is there differential change?) for the artificial data using a repeated measures anova (one within, one between factor) or lmer equivalent.
Demonstrate the equivalence from Brogan-Kutner paper that testing the groupXtime interaction term is equivalent to a t-test between groups on individual improvement (i.e. a statistician 1 analysis).
Solution to Problem 2 available from Stat 209 HW9 (probs 1 and 2)
3. Observational Studies: Regression Adjustments.
The class handout on regression adjustments contained summary statistics for the Head Start data considered in Anderson et al (1980) Statistical Methods for Comparative Studies. I constructed a corresponding data set located at W6prob3dat
Try out the various regression adjustments described on the handout for these pretest-posttest data. (Handout shows some approximate estimates).


5/13. Analysis of Durations: Introduction to Survival Analysis (aka event history) Methods

Useful introductions to Survival Analysis (mostly with R)
John Fox tutorial: Cox Proportional-Hazards Regression for Survival Data
Survival analysis text by Rupert G. Miller (Ch 2,3,4,6). Available as Stanford Tech Report
CHAPTER 11 Survival Analysis: Glioma Treatment and Breast Cancer Survival A handbook of statistical analyses using R (second edition). Brian Everitt, Torsten Hothorn CRC Press, Complete version (through Stanford access)    R-code for chapter11
An Introduction to Survival Analysis  Mark Stevenson EpiCentre, IVABS, Massey University.   Author R-package   epiR  Quick overview Survival analysis in clinical trials: Basics and must know areas
CHAPTER 11 Survival Analysis: Retention of Heroin Addicts in Methadone Maintenance Treatment. Handbook of Statistical Analyses Using Stata, Second Edition. Sophia Rabe-Hesketh Chapman and Hall/CRC 2000.
Event History Analysis with R. Goran Brostrom CRC Press 2012. R-package   eha
Slides on renewal processes and hazard functions

Main R-package: survival; Terry Therneau, Stanford Stat Ph.D
CRAN Task View: Survival Analysis . Survival analysis, also called event history analysis in social science, or reliability analysis in engineering, deals with time until occurrence of an event of interest. However, this failure time may not be observed within the relevant time period, producing so-called censored observations. This task view aims at presenting the useful R packages for the analysis of time to event data.
KM bootstrap in Hmisc package, bootkm. Exact tests, coin package, surv_test.

Class Data examples:
1. Miller leukemia data (Kaplan-Meier); pdf p.42 in online version     class example in R, data in package survival      extensions of leukemia example (week 7)    Using eha package for aml     Cox fits, zph plot
          Legacy versions SAS    Minitab
2. Herion (addict) data. Source: D.J. Hand, (et al.) Handbook of Small Data Sets. Properly formatted version   Analyses in Stevenson and Stata expositions above.   Rogosa R-session class handout
       Additional analyses for herion: Bootstrapping, Math 159 Pomona    analysis in SAS (phreg)
Publication Source: Caplehorn, J., Bell, J. 1991. Methadone dosage and the retention of patients inmaintenance treatment. The Medical Journal of Australia,154,195-199.
Additional survival data.
3. Recidivism data from John Fox tutorial.
4. Kalbfleisch and Prentice (1980) rat survival Data and description plus SAS analysis (Cox regression). Also best subsets Cox regression example, myeloma
5. R Textbook Examples. Applied Survival Analysis Chapter 3: Regression Models for Survival Data

Some further topics:
Interval Censoring: Tutorial on methods for interval-censored data and their implementation in R Statistical Modelling 2009; 9(4): 259-297.    Interval-Censored Time-to-Event Data Methods and Applications Chapman and Hall/CRC 2012 (esp Chap 14--glrt New R Package for Analyzing Interval-Censored Survival Data. Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package    Also intcox {intcox}Cox proportional hazards model for interval censored data
Time dependence, time-varying covariates. Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model Terry Therneau Cindy Crowson Mayo Clinic February 26, 2013. Also See section 5.2 of Event History Analysis with R.

WEEK 7-8 Exercises
1. Part a. In file teacha.dat in the class directory are 75 "survival times" (variable name 'career') indicating actual length of teachers careers (in years) in a rather rough school district. What is the median survival time? what proportion of teachers are still in the district after 2 years? 4 years? 6 years? Plot a survival curve from this complete set of times.
Part b. In file teachb.dat in the class directory are the more realistic data: censored versions of the 75 "survival times" in part a. Column 1 has the times (career) and Column 2 has the censoring indicator (Note here we have status = 1 if censored). Compute naive answers (ignoring censoring) to the questions in part a: what is the median survival time? what proportion of teachers are still in the district after 2 years? 4 years? 6 years?
Use the Kaplan-Meier product-limit estimate to answer the questions in part a for these censored data: what is the median survival time? what proportion of teachers are still in the district after 2 years? 4 years? 6 years? Plot a survival curve with 95% confidence intervals. Obtain bootstrap (percentile) confidence intervals for the median survival time, and for the lower quartile (25th) of the survival time distribution.
2. Fun with hazards.
Part a. Social Security Life Tables. Use the 2007 Actuarial Life Table, useful discussion on benefits. Plot the hazard functions for males and females. Do these hazard functions appear to be exponential? Also plot the corresponding survival curves. Can you verify (approximately numerically) the relation between surival curve and intergrated hazard from the week 7 handout-- S(t) = exp(-H(t)) ?
Part b. Refer to the hazard function shown in class for Alcohol and Incidence of Total Stroke (publication 4 in the Week 1, "longitudinal in the news" listing). (figure underneath Table 2). What is the increase in hazard between 2 drinks/day and 3 drinks/day?
3. Days to vaginal Cancer Mortality in Rats. The link for data example 4 above has these data and description and an assortment of (gratuitous) SAS analyses. From that file make yourself an R data set. Plot the Kaplan-Meier survival curves for the two groups (with the point-wise condidence intervals for each curve). Carry out the (asymptotic) log-rank test of identical survival curves. Compare those results with the exact (permutation) test. What are the median survival times in the two groups? Obtain a bootstrap estimate of the confidence interval for the difference of median survival times in the two groups (95% is a good default or 90%). How does this confidence interval compare with the tests for differences between the survival done above? One more thing...Redo the group comparsion of survival using Cox regression with predictor (covariate) Group membership (pretreatment regimes). Do the results agree with the previous analyses. Obtain a confidence interval for the hazard ratio (ratio of the hazard functions) between the two groups.
4. Replicate (some of) the analyses in the John Fox survival analysis tutorial for the Recidivism data (sec 3.2), links above. The experimental variable is fin indicating financial aid (or not). Start with a Kaplan Meier 2-group comparison, with plot and significance test. Then fit the 'full' model (mod.allison) and assess the significance of the experimental manipulation (fin). Plot the survival function from the cox regression (Fox Fig 1). Carry out the comparison (Fig 2) of estimated survival functions for those receiving (fin = 1) and not receiving (fin = 0) financial aid, with other covariates are fixed at their average values. For the model diagnostics in Section 5: use the cox.zph function to assess the proportional hazards assumptions, and plot the scaled Schoenfeld residuals (Fox figure 3).
5. Interval Censored Data. Consider the breast cancer data shown in Week 8 lecture; interval-censored breast cosmesis data set of Finkelstein and Wolfe (1985). The data are from a study of two groups of breast cancer patients, those treated with radiation therapy with chemotherapy (treatment = "RadChem") and those treated with radiation therapy alone (treatment = "Rad"). The response is time (in months) until the appearance of breast retraction, and the data are interval-censored between the last clinic visit before the event was observed (left) and the first visit when the event was observed (right) (or Inf if the event was not observed). One location of these data is:
R> library("interval")
R> data("bcos", package = "interval")
Class examples show parametric and non-parametric survival analyses for these interval censored data. Before these methods were available, various Kludges (imputations) existed. One is to take the midpoint of the interval for any observed event in [left, right] or if right is NA (censored) treat as left+ and carry out a survival analysis for right censored data. Repeat the breast cancer example Cox regression using this strategy and compare with the results from week 8 using the interval censoring.
6. Mixed-effect survival (aka frailty). Reconsider the heroin (addict) data from week 7 (ex 2). Compare the Cox regression model from class with mixed effects models that allow indidivual frailties and variability over centers.

5/20. Survival analysis and analysis of durations: Recurrent Events, Frailty Models, Behavioral Observations, Series of Events (renewal processes)
Longitudinal in the news
Mild brain shock may improve math skills     Publication: Current Biology, 16 May 2013. Long-Term Enhancement of Brain Function and Cognition Using Cognitive Training and Brain Stimulation. Albert Snowball1, Ilias Tachtsidis2, Tudor Popescu1, Jacqueline Thompson1, Margarete Delazer3, Laura Zamarian3, Tingting Zhu2 and Roi Cohen Kadosh

Lecture Topics
1. Additional Cox regression analyses and diagnostics for heroin (addict) data (week 7 ex 2).       Cox fits, zph plot
2. Interval Censoring; breast cancer data. Class analysis.
Interval Censoring: Tutorial on methods for interval-censored data and their implementation in R Statistical Modelling 2009; 9(4): 259-297.    Interval-Censored Time-to-Event Data Methods and Applications Chapman and Hall/CRC 2012 (esp Chap 14--glrt New R Package for Analyzing Interval-Censored Survival Data. Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package    Also intcox {intcox}Cox proportional hazards model for interval censored data
3. Frailty (mixed effects) survival models. Package coxme February 15, 2013 Mixed Effects Cox Models. Maintainer Terry Therneau. Mixed Effects Cox Models Terry Therneau Mayo Clinic May 15, 2012
frailtyHL: A Package for Fitting Frailty Models with H-likelihood by Il Do Ha, Maengseok Noh and Youngjo Lee Recurrent events, Frailty models: additional R-packages, frailtypack, parfm, survrec, gmrec, TestSurvRec, bivrec
4. Frailty models (individual differences, random effects) and Recurrent events (observe multiple on/off transitions and timing). Asthma data example from Duchateau et al (2003). Evolution of Recurrent Asthma Event Rate over Time in Frailty Models Journal of the Royal Statistical Society. Series C (Applied Statistics) 355-363.   see also Ch 3 in Frailty Models in Survival Analysis Andreas Wienke Chapman and Hall/CRC 2010
Recurrent Events: Chapter 9 of Kalbfleisch and Prentice (2nd edition), "Modeling and Analysis of Recurrent Event Data"
5. Series of Events, Point Processes, Behavioral Observations.
Behavioral Observations. David Rogosa; Ghassan Ghandour. Statistical Models for Behavioral Observations
Journal of Educational Statistics, Vol. 16, No. 3, Special Issue: Behavioral Observations. (Autumn, 1991), pp. 157-252. Jstor link    Reply to Discussants. Jstor link
Rogosa, D. R., Floden, R. E., & Willett, J. B. (1984). Assessing the stability of teacher behavior. Journal of Educational Psychology, 76, 1000-1027. APA link also available from John Willet's pub page
Computing Resources. Point processes, Series of events: R-packages, NHPoisson ppstat, processdata, spatstat, PtProcess

A remarkable overview of advanced survival analysis topics. Multiple and Correlated Events Terry M. Therneau Mayo Clinic Spring 2009

6/3. Special Topics for Longitudinal Data: Observational Studies, Applications of Stuctural Equation Models, Assessments of Stability, Reciprocal Effects, Longitudinal Network Data

Longitudinal in the news
Nearly all US states see hefty drop in teen births     NCHS Data Brief Number 123, May, 2013 Declines in State Teen Birth Rates by Race and Hispanic Origin

Lecture topics:
0. cloglog tranformations, survival analysis, cox regression
1. Observational Studies (topics from week 6)
Observational Studies: Group Comparisons in Longitudinal Observational (non-experimental,  "quasi"-experimental) Designs
Differences in Differences (Diff-in-Diff) R-package wfe paper On the Use of Linear Fixed Effects Regression Models for Causal Inference(sec 3.2), Value-added analysis, Interrupted time-series, group-based trajectory modelling (matching).
Econometric Approaches to Longitudinal Panel Data. Panel Data Econometrics in R: The plm Package Yves Croissant Giovanni Millo (esp. section 7. "plm versus nlme/lme4" ).      R-package plm
2. Structural equation models for longitudinal data (don't do it; Myth 7)
3. Stability over time (Myth 8). Change and Sameness
4. Reciprocal effects ( Myth 9) Rogosa, Encyclopedia of Social Science
5. Longitudinal Network Data

Value-added analysis.
Value-added does New York City. New York schools release 'value added' teacher rankings     Formula uncovers the 'value added'    from the unions: THIS IS NO WAY TO RATE A TEACHER
Chap 9 in Uneducated Guesses: Using Evidence to Uncover Misguided Education Policies.   Howard Wainer (Author) amazon page    available in paper and Kindle
Other versions of the Chap 9 materials Value-Added Models to Evaluate Teachers: A Cry For Help H Wainer, Chance, 2011.         Journal of Consumer Research Vol. 32, No. 2, Sept 2005
More Value-added analysis. Journal of Educational and Behavioral Statistics Vol. 29, No. 1, Spring, 2004 Value-Added Assessment Special Issue
Value-Added Measures of Education Performance: Clearing Away the Smoke and Mirrors, PACE
LA Times Teacher Ratings, summer 2010        NEPC vs LATimes
J.R. Lockwood, Harold Doran, and Daniel F. McCaffrey. Using R for estimating longitudinal student achievement models. R News, 3(3):17-23, December 2003.
Fitting Value-Added Models in R  Harold C. Doran and J.R. Lockwood
Andrew Gelman on Value-added arithmetic: It's no fun being graded on a curve     more NY  Principals rebel against 'value-added' evaluation

Interrupted time-series
Time Series Analysis with R (Section 4) A. Ian McLeod, Hao Yu, Esam Mahdi .      R package BayesSingleSub: Computation of Bayes factors for interrupted time-series designs
Interrupted Time Series Quasi-Experiments Gene V Glass Arizona State University
original publication (ozone data): Box, G. E. P. and G. C. Tiao. 1975. Intervention Analysis with Applications to Economic and Environmental Problems." Journal of the American Statistical Association. 70:70-79. SAS example for ozone data     another ozone analysis with data
Box-tiao time series models for impact assessment Evaluation Quarterly 1979
Interrupted time-series analysis and its application to behavioral data Donald P. Hartmann, John M. Gottman, Richard R. Jones, William Gardner, Alan E. Kazdin, and Russell S. Vaught J Appl Behav Anal. 1980 Winter; 13(4): 543-559.

Applications of Structural Equation Models (LISREL, path analysis, Myth 7)
David Rogosa. Casual Models Do Not Support Scientific Conclusions: A Comment in Support of Freedman. Journal of Educational Statistics, Vol. 12, No. 2. (Summer, 1987), pp. 185-195. Jstor link       Theme Song Ballad of the casual modeler    http://www.stanford.edu/class/ed260/ballad.mp3
Rogosa, D. R. (March 1994). Longitudinal reasons to avoid structural equation models, UC Berkeley.
Rogosa, D. R. (1993). Individual unit models versus structural equations: Growth curve examples. In Statistical modeling and latent variables, K. Haagen, D. Bartholomew, and M. Diestler, Eds. Amsterdam: Elsevier North Holland, 259-281.
  original publication on the longitudinal path analysis:   Some Models for Analysing Longitudinal Data on Educational Attainment. Harvey Goldstein       Journal of the Royal Statistical Society. Series A (General), Vol. 142, No. 4. (1979), pp. 407-442.  Jstor link
Rogosa, D. R., & Willett, J. B. (1985). Satisfying a simplex structure is simpler than it should be.      Journal of Educational Statistics, 10, 99-107. Jstor link      Follow-up paper: Two Aspects of the Simplex Model: Goodness of Fit to Linear Growth Curve Structures and the Analysis of Mean Trends. Frantisek Mandys; Conor V. Dolan; Peter C. M. Molenaar. Journal of Educational and Behavioral Statistics, Vol. 19, No. 3. (Autumn, 1994), pp. 201-215.    Jstor link

Stability: Consistency, Change and Sameness (Myth 8)
J.H. Ware Tracking in S. Kotz, N.L. Johnson (Eds.), The Encyclopedia of Statistical Sciences (13th Edn.), Vol. 9 John Wiley, New York (1988)
Rogosa, D. R., Floden, R. E., & Willett, J. B. (1984). Assessing the stability of teacher behavior. Journal of Educational Psychology, 76, 1000-1027. APA link also available from John Willet's pub page
Rogosa, D. R., & Willett, J. B. (1983). Comparing two indices of tracking. Biometrics, 39, 795-6.      JStor link
Rogosa, D. R. Stability section of Individual unit models versus structural equations (link above)
Rogosa, D. R. Stability of school scores from educational assessments: Confusions about Consistency in Improvement David Rogosa, June 2003 ; Education Writers Association April 2004
Personality research. Stability versus change, dependability versus error: Issues in the assessment of personality over time David Watson Journal of Research in Personality 38 (2004) 319-350.
Some applications: A Stochastic Model for Analysis of Longitudinal AIDS Data J.M.G. Taylor, W.G. Cumberland, Sy J.P.; Journal of the American Statistical Association, Vol. 89, 1994
Tracking of objectively measured physical activity from childhood to adolescence: The European youth heart study. Scandinavian Journal of Medicine & Science in SportsVolume 18, Issue 2, 2007.
Factors Associated With Tracking of BMI: A Meta-Regression Analysis on BMI Tracking. Obesity (2011) 19 5, 1069-1076. doi:10.1038/oby.2010.250
Long-term tracking of cardiovascular risk factors among men and women in a large population-based health system The Vorarlberg Health Monitoring and Promotion Programme. European Heart Journal (2003) 24, 1004-1013.
Journal of Traumatic Stress. Reliability of Reports of Violent Victimization and Posttraumatic Stress Disorder Among Men and Women With Serious Mental Illness Volume 12 Issue4 587 - 599 1999-10-01 Lisa A. Goodman Kim M. Thompson Kevin Weinfurt Susan Corl Pat Acker Kim T. Mueser Stanley D. Rosenberg
Computing: Foulkes-Davis gamma (not in R). A GAUSS program for computing the Foulkes-Davis tracking index for polynomial growth curves   TRACK: A FORTRAN program for calculating the Foulkes-Davis tracking index Gerard E. Dallal Computers in Biology and Medicine Volume 19, Issue 5, 1989, Pages 367-371

Reciprocal effects (Myth 9).
Rogosa, D. R. (1980). A critique of cross-lagged correlation. Psychological Bulletin, 88, 245-258. APA site version
Granger Causality. Nobel 2003. Complete Granger
Relationships--and the Lack Thereof--Between Economic Time Series, with Special Reference to Money and Interest Rates. David A. Pierce Journal of the American Statistical Association, Vol. 72, No. 357. (Mar., 1977), pp. 11-26. Jstor

Longitudinal Networks
  R-package RSiena manual,   RSiena Resource page
Huisman, M. E. and Snijders, T. A. B. (2003). Statistical analysis of longitudinal network data with changing composition. Sociological Methods and Research, 32:253-287.
Application: Kids' friends influence physical activity levels   Publication: The Distribution of Physical Activity in an After-school Friendship Network Sabina B. Gesell, Eric Tesdahl, Eileen Ruchman, Pediatrics; originally published online May 28, 2012.

Exercises Week 9.
1. Stability of Individual Differences
For the Ramus data (week 2 exercise 1, 20 individuals, 4 time points), the Foulkes-Davis (gamma) index of tracking has point estimate .83 and (bootstrap) standard error .06 for the 18-month time interval 8yrs to 9.5 years. Compare that estimate of consistency of individual differences with time1-time2 correlations for the time intervals [8, 9.5] and [9, 9.5].
2. Path Analysis. Replicate the 3-wave path analysis example based on the Goldstein model for UK reading scores. Use the perfectly measured data Xi(t) in Week 1 Myths chapter data examples and description. Repeat with the fallible X(t) and compare results.
3. Try a path analysis on the 4-waves of the Ramus data. Compare with the growth curve analyses in week 2 exercises.
4. Do a diffs-in-diffs analysis fot the Head Start data in Week 6 problem 3. See if you can also get the wfe package to work.
brief week 9 solutions