Statistical Methods for Longitudinal Research

Course web page: http://web.stanford.edu/~rag/stat222/

Rogosa Office Hour: Tues Nov 11 3 - 4

Wed Nov 19 4:10 - 5:30

Tues Dec 2 2 - 3:30

To see full course materials from Spring 2013 go here

Registrar's informationSTATS 222 (Same as EDUC 351A): Statistical Methods for Longitudinal Research 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, and the effects of interventions. 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

Weeks 8-9. Further topics in analysis of durations: Recurrent Events, Frailty Models, Behavioral Observations, Series of Events (renewal processes)

Dead Week. Assorted Special Topics (enrichment): 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; 2nd ed 2011)

Text Website second edition 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,

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' August 2014, 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 Autumn qtr exam period we will have an in-class (all materials available, "open" everything) exam.

My reading of the Registrar's chart indicates Wednesday, December 10, 2014 12:15-3:15 p.m.

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 are done with Rogosa in Sequoia 224, which has 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.

Collection of scanned course handouts,

Course Problem Set posted 11/19/14

Class presentation will be in, and students are encouraged to use, R (occasionally, some references to SAS and Mathematica).

1/7/09. NY Times endorses R: Data Analysts Captivated by R's Power

Current version of R is version 3.1.1 (Sock it to Me) released on 2014-07-10

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 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 and 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

Non-linear models, esp logistic. From week 1, aslo week 3 Self-Starting Logistic model SSlogis help page, do

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

1. For the straight-line (constant rate of change) fit example to subj 372 in the sleepstudy data. Obtain a confidence interval for the rate of change from the OLS fit. Now compare the OLS fit with day-to-day differences. Under the constant rate of change model these 9 day to day differences also estimate the rate of change. Obtain a estimate of the mean and a confidence interval for rate of change from these first differences. Compare with OLS results.

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

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)?

Health officials say diabetes rates may be leveling off overall Diabetes Rate In The U.S. May Be Leveling Off Publication: JAMA Sept 24. 2014 312 (12).

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 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

Individual plots (frame-by-frame) Plot of straight-line fits Sleepstudy, Bates Ch 4, lme4 analyses handout, ascii Sleepstudy class handout, pdf scan more Doug Bates Slides (pdf pages 8-28)

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 There are a number of add-on packages.

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

Data formatting:

Fitting linear mixed-effects models using lme4, Journal of Statistical Software Douglas Bates Martin Machler Ben Bolker also Rnews_2005 pp.27-30

Douglas Bates item #4, Texts and Resources. Other 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

I start by fitting the lmer model for the collection of growth curves:

Then try out

Then look at the

Consider the sleepstudy and Ramus examples, collections of growth trajectories with no exogenous variable. 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 .

Fitting the lmer models with

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

Artificial data example from Review Question 3 (used in Myths chapter to illustrate time-1,time-2 data analysis) 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.

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

Data formatting:

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 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. identify the fastest and slowest growth among the 277 females. Compare medians of growth rates for females with verbal ability (Z) at or above 106 with that for females with verbal ability below 106. Show side-by-side boxplots.

b. In the class handout version of the NC analyses (and other postings, but not all) the first thing to do was make the 'time' variable have intitial value = 0 (making the intercept of a straight line fit correspond to level at initial time): i.e. 1 to 8 becomes 0 to 7. Obtain lmList results and fit the ncUnc lmer model (straight-line growth, no Z) using time 1 to 8. Comment on differences of these analyses with those using timeInt in the class handout. In particular, look at the correlation of change and initial status. The correlation between observed change and observed initial status using timeInt was .279 from lmer (

a. Construct an lmer model with the individual growth curve a quadratic function of grade (year), most convenient to use uncorrelated predictors

b. Investigate (via lmer model) gender differences (isMale) in vocabulary growth. Fit appropriate lmer models and interpret results,

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 . 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. 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).

Solution for problem 2

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

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.

a. Smart First Year Student analyses. 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.

b. lmer analyses. Try to obtain a good confidence interval for the amount of decline. Obtain a point and interval estimate for the correlation beween initial status and change in Spb.

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.

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,

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' August 2014, Title A Handbook of Statistical Analyses Using R (2nd Edition)

For SAS (and GEE) fans another analysis

Also, Bates, fertility in Bangladesh (for HW).

Missing data and imputation, including

a. Demonstrate the Brogan-Kutner Section 5 equivalences (from paper, shown in class) for repeated measures anova and/or BK lmer analyses.

b. Is amount of gain/decline related to initial status? For the 8 new procedure patients and for the 13 old procedure patients, seperately, estimate the correlation between change and initial status and obtain a confidence interval if possible.

c. Analysis of Covariance. 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.

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

a. try to do lmList on these data to get odds(good) for each of the each 111 subjects. Investigate effectiveness of treatment.

b Use lmer analyses to compare treament and placebo. Obtain a confidence interval for effectiveness of treament. Investigate gender differences in response to the intervention (i.e. the treatment)

c. Extend the lmer model in part b by adding the age and baseline measurements to the level 2 model. Compare with part b results.

To supplement the longitudinal texts (HSAUR, ALA etc) full model for the epilepsy data, lets try to build up the analysis from basic description comparing placebo vs drug up through some basic some basic glmer models.

A somewhat similar effort was made in the second class posting "Recap group comparisons (epcomp)" linked above. In this exercise treat period as a time measurement (1,2,3,4) rather than an ordered factor.

How many subjects in placebo and drug groups? Use lmList to obtain slopes and intercepts for fits of time trends to seizures for each subject and compare drug and placebo groups.

Fit and compare glmer models with treatment as the only level 2 predictor (for intercept) without and with a time trend. Compare.

Add the baseline to the glmer models above (in level 2 model for intercept; is effect of the drug significant (use confint)? Does adding age help this model?

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.

Missing data and imputation, including

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.

C. Economist's differences in differences (or diffs in diffs with matching) for observational studies. R-package

D. Interrupted time-series. Interrupted Time Series Quasi-Experiments Gene V Glass Arizona State University. Time Series Analysis with R section 4.6 Did fertility go up after the Oklahoma City bombing? An analysis of births in metropolitan counties in Oklahoma, 1990-1999. Demography, 2005. R package

E. Value-added analysis. Value-added does New York City. New York schools release 'value added' teacher rankings from the unions: THIS IS NO WAY TO RATE A TEACHER Value-Added Models to Evaluate Teachers: A Cry For Help H Wainer, Chance, 2011. American Statistical Association Statement on Using Value-Added Models for Educational Assessment

a. Longpower package (vignette). Reconstruct the sample size calculation for the Alzheimer's disease trial (7 waves) on p.4 of the vignette.

b. MBESS package. Recreate the sample size calculation for width of confidence interval for differential growth using

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 RQ2 solution

The display from lecture of the regression adjustments also has a numerical example (page 2 of pdf). Recreate the results shown for the Anderson et al Head Start example. Also for lecture materials, Regression Adjustments with Non-equivalent groups Week 6, show the Belson adjustment procedure (using control group slope) is equivalent to evaluating the vertical distance between the within-group regression fits at the mean of the treatment group. written out proof.

Artificial data example from week 2 RQ3 and Week 4 Lecture item 4 (used in Myths examples 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 these data (with lm) 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. What does

b. Repeat part a with data set W6prob1b. Can you find any reason to doubt a "missing at random" assumption for this data set?

Note: in Week 10 we will demonstrate multiple imputation procedures (

'data.frame': 6402 obs. of 15 variables: $ id : int 31 31 31 31 31 31 31 31 36 36 ... $ lnw : num 1.49 1.43 1.47 1.75 1.93 ... $ exper : num 0.015 0.715 1.734 2.773 3.927 ... $ ged : int 1 1 1 1 1 1 1 1 1 1 ... $ postexp : num 0.015 0.715 1.734 2.773 3.927 ... $ black : int 0 0 0 0 0 0 0 0 0 0 ... $ hispanic : int 1 1 1 1 1 1 1 1 0 0 ... $ hgc : int 8 8 8 8 8 8 8 8 9 9 ... $ hgc.9 : int -1 -1 -1 -1 -1 -1 -1 -1 0 0 ... $ uerate : num 3.21 3.21 3.21 3.29 2.9 ... $ ue.7 : num -3.79 -3.79 -3.79 -3.71 -4.11 ... $ ue.centert1 : num 0 0 0 0.08 -0.32 ... $ ue.mean : num 3.21 3.21 3.21 3.21 3.21 ... $ ue.person.cen: num 0 0 0 0.08 -0.32 ... $ ue1 : num 3.21 3.21 3.21 3.21 3.21 ...Variables we will use are

a. How many individuals in this data set? Give a five-number summary of the number of observations per person. How many of the individuals in these data have black = 1?

b. SFYS descriptive analyses. We are interested in wages (measured by lnw) as a function of experience (lnw ~ exper). Show a five-number summary of the gradient (slope; i.e. change in log-wage for unit change in exper)) and level (here fit for exper = 0, initial status) for the set of individuals. Then stratify on black = 1 vs black = 0 (combining the white and hispanic drop-outs). Also show side-by-side boxplots for gradient and initial level stratifying on

c. Use a formal mixed-effects model analysis to obtain random and fixed effects for the

d. Are there differences in the lnw ~ exper relation for students black = 1 vs black = 0? Show by estimates and confidence intervals from mixed-effects models.

e. Does inclusion of

The class handout on regression adjustments shown in class and linked in RQ3 above 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). Also show the result for the basic diffs-in-diffs estimator from Week 6.

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

Set of Slides An introduction to survival analysis, Geert Verbeke

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 handouts (scanned) week 7

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

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 these data 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 integrated 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: Alcohol Consumption and Risk of Stroke in Women, Stroke, March 2012. Nurses' Health Study). (figure underneath Table 2).

What is the increase in hazard between 2 drinks/day and 3 drinks/day?

> str(melanom) 'data.frame': 205 obs. of 6 variables: $ no : int 789 13 97 16 21 469 685 7 932 944 ... $ status: int 3 3 2 3 1 1 1 1 3 1 ... $ days : int 10 30 35 99 185 204 210 232 232 279 ... $ ulc : int 1 2 2 2 1 1 1 1 1 1 ... $ thick : int 676 65 134 290 1208 484 516 1288 322 741 ... $ sex : int 2 2 2 1 2 2 2 2 1 1 ... ,We are interested in

days: time on study after operation for malignant melanoma

status: the patient's status at the end of study

Documentation shows the possible values of status are: 1: dead from malignant melanoma 2: alive at end of study 3: dead from other causes. Consider 'dead from other causes' as censored (along with alive). Thus, status vector should be status == 1 and the survival object is

a. How many survival times are censored? Obtain an estimate of the survival curve at each event time (along with CI) using the Kaplan-Meier estimate and plot the survival curve and confidence interval.

b. Does survival differ in men and women? Compare asymptotic (log-rank) and exact tests for gender differences? Compare the exact test with a bootstrap approximation. Plot the male and female survival curves.

c. Use Cox regression to carry out the gender comparison of the survival curves in part b. Obtain a confidence interval for the effect of gender on the hazard.

Recap AML analyses. Baseline hazard plot.

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 Cox regression analyses and diagnostics for heroin (addict) data . Cox fits, zph plot

Additional analyses for herion: Bootstrapping, Math 159 Pomona analysis in SAS (phreg) HSAUS (stata) link week 7

Publication Source: Caplehorn, J., Bell, J. 1991. Methadone dosage and the retention of patients in maintenance treatment. The Medical Journal of Australia,154,195-199.

New R Package for Analyzing Interval-Censored Survival Data. Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package 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). Also

a. In the class example, after seeing a problem with proportional hazards assumption for the clinic variable, we used strata(clinic) which allows different baseline hazards in each clinic with predictors prison and dose. Look at this further by fitting the coxhernSt model seperately within each clinic (i.e. dropping the strata(clinic) term). Are the effects of clinic and dose similar within each clinic?

b. In class question asked whether some model-modification (e.g. interaction terms) in the coxhern model might mitigate the proportional hazards violation in the coxhern model. (Note the Fox tutorial section 4 does a time-dependent modification.) Try out some augmented models using interactions between the predictors in coxhern.

c. The

Data Example: Grade at First Intercourse. Research Question: Whether, and when, adolescent males experience heterosexual intercourse for the first time? Citation: Capaldi, et al. (1996). Sample: 180 high-school boys. Research Design: Event of interest is the first experience of heterosexual intercourse. Boys tracked over time, from 7th thru 12th grade. 54 (30% of sample) were virgins (censored) at end of data collection.

The Willet-Singer displays show lifetables and logistic regression estimates for survival analyses.

a. investigate time-to-event as a function of parental transitions (pt = 1, 1 or more transitions) using Kaplan-Meier and cox regression methods shown in class. Compare with the logistic regression results in the Willet-Singer materials.

b. clearly the firstsex data are really interval censored, rather than inately discrete-time. Sex was had sometime during the reported grade. Indicate how you would set up these data for the proper interval censored analysis. See class examples, week 8 section 3.

For these data 'status': 0=censored, 1=liver transplant, 2=death; so status = 2 represents observed values of

a. Use Kaplan-Meier methods to carry out a simple two-group comparison of the effectiveness of the drug, along with any useful plots.

b. Extend the two-group comparison with a Cox regression using additional predictors

a. Repeat the gender comparison in parts b or c in Ex 2, week 7, stratifying on ulceration of the tumor (or not). Compare with the result in Ex 2 week 7 and interpret.

b. Carry out a Cox regression using predictors log(thick) and the gender indicator, stratifying on ulceration. Interpret the results. Check the viability of the proportional hazards assumption for this cox model.

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.

a. Section 4, Fox tutorial (week 7) Recidivism data. Fox tutorial script

class handout, recidivism data fold/unfold functions (wide-to-long): Package

b. Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model Terry Therneau Cindy Crowson Mayo Clinic January 22, 2014

coxme Class handout plain text version

Additional materials. 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,

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"

Package

Class handout. JM for aids example.

R-package

Book (Stanford access) Joint Models for Longitudinal and Time-to-Event Data. With Applications in R. Dimitris Rizopoulos. Chapman and Hall/CRC 2012. Book Table of Contents Book website

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

The Week 9 class example did time-dependent cox regression analysis and compared that with crude stratification on age (to adress violations of proportional hazards). As an exercise, carry out the cox regression, stratifying on age in thirds (more carefully than I did in the class examples) and also stratifying on age split in fifths. Check the proportional hazards assumptions and compare results.

a. Class example; eortc breast cancer data

Compare results ignoring center, stratifying on centers, and using coxme (in class example) for patients nested within centers.

b. Rat data (see R Journal December 2012).

The data set presented by Mantel et al. (1977) is based on a tumorigenesis study of 50 (q = 50) litters of female rats. For each litter, one rat was selected to receive the drug and the other two rats were placebo treated controls (ni = 3). Here each litter is treated as a cluster. The survival time (time) is the time to development of tumor, measured in weeks. Death before occurrence of tumor yields a right-censored observation; forty rats developed a tumor, leading to censoring of about 73%. The survival times for rats in a given litter may be correlated due to a random effect representing shared genetic or environmental effects.

Compare Cox regression models that investigate effect of the drug (rx)

(i) ignoring litters and (ii) mixed effects models incorporating the nested structure of these data (rats within litters)

0. Do-over: scheduling individual presentation 12/4, 12/11

1. Observational Studies (topics from week 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

2. Structural equation models for longitudinal data (don't do it; Myth 7) (handout in week 10 handout collection)

3. Stability over time (Myth 8). Change and Sameness

4. Reciprocal effects ( Myth 9) Rogosa, Encyclopedia of Social Science

5. Missing data (week 6),

6. Longitudinal Network Data

7. In class exam 12/10, discussion and sample questions

Resources

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.

Missing Data. See also Week 6

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,

For the Ramus data (week 2 exercise, 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].