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 informationSTATS 222 (Same as EDUC 351A): Statistical Methods for Longitudinal Research Class Number 35282 Lecture Units: 2-3 Mo 3:15PM - 5:05PMGSB Littlefield 107Schedule: 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.

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

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,

Technical topics: Mixed models in R using the lme4 package Part 4: Theory of linear mixed models

5.

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

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

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."

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

Trend in Proportions: College fund raising example prop.trend.test help page

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.

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

North Carolina, female math performance (also in Rogosa-Saner) North Carolina data (wide format); NC data (long)

For that female, what is the rate of improvement over grades 1 through 8? Compare the observed improvement for grades 1 through 8 (the

Seperately, consider three observations at taken at equally spaced time intervals: What is a simple expression for the OLS slope (rate of change)?

For reference, Self-Starting Logistic model SSlogis help page, do

Data frame

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"

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

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

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.

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

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

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

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,

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.

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

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.

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.

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).

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.

Solution provided for problem 3

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

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

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) } })

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.

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

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

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,

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)

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.

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

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.

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

Solution Notes on the ALA (Laird-Ware) assertion

a. The lmer model for the resp data in the class handout and section 13.4 of the HSAUR chapter

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

b. With the seizure data (epilepsy) there is a similar comparison to be considered. In the class handout the model used is:

6. Chick Data,

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

CHAPTER 17 Incomplete data: Introduction and overview.

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,

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.

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

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?

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)

The class handout on regression adjustments contained summary statistics for the Head Start data considered in Anderson et al (1980)

Try out the various regression adjustments described on the handout for these pretest-posttest data. (Handout shows some approximate estimates).

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

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

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,

Class Data examples:

1. Miller leukemia data (Kaplan-Meier); pdf p.42 in online version class example in R, data in package

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

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

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.

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?

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.

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

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

3. Frailty (mixed effects) survival models. Package

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,

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,

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

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

0.

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

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

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

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

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

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.

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

Longitudinal Networks

R-package

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.

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].