Intensive Longitudinal Data Analysis

Intensive Longitudinal Data Analysis Adam C. Carle, M.A., Ph.D. adam.carle.cchmc@gmail.com James M. Anderson Center for Health Systems Excellence Cincinnati Children s Hospital Medical Center University of Cincinnati College of Medicine University of Cincinnati College of Arts and Sciences MCH Epidemiology Conference 2016, Philadelphia

Overview What is intensive longitudinal data? Definition. Advantages. Analytical challenges. An analytical approach. Time varying effect model. Example. Conclusion. Questions.

About Me

Help Along the Way Constance Mara. Michael Seid.

The Challenge

Introduction Health services researchers often wish to understand change. Much of the historical literature has used change scores. Difference between two time points. Limited information. Statistical concerns. Different courses of change may demonstrate the same incremental difference when measured with two time points.

Introduction Mobility Low High Time 1 Time 2 Observation

Time 1

Time 2

Time 3

Time 4

Introduction Recent years have seen increased use of designs that attempt to evaluate the course of change. 3 to 4 observations. Longitudinal growth models. Multilevel models. Latent growth curve models. Begin to address the overall shape and rate of change. Still require a parametric assumption. Theory. Extensive trial and error. May miss important and meaningful variation.

Introduction Mobility Low High Time 1 Time 2 Time 3 Time 4 Observation

What to do?

Intensive Longitudinal Data Intensive longitudinal data (ILD) refer to data with many measurements over time. Threshold of 10 observations sometimes used to define intensive, sometimes 40.

EMA repeatedly collects data from participants in their natural environment. Assessments focus on current state and setting. Home, school, hospital, etc. Represent sample of participant s state. Different times of day. Different settings. Random intervals. Ecological Momentary Assessment Saul Shiffman and Arthur Stone pioneered the use of ecological momentary assessment (EMA). Collected moment to moment data on the behavior and experiences of smokers. Led to rich understanding of etiology, dependence, withdrawal, treatment effects, and relapse process.

Intensive Longitudinal Data The hallmark of ILD and EMA is multiple, repeated assessment. Dense over short period or sparse over long period. Event-based. Do not attempt to characterize entire experience. Focus on discrete events. Can be difficult to operationally define. Time-based. Characterize experience more broadly. Combination of event- and time-based.

Intensive Longitudinal Data Advances in technology allow health services researchers to collect enormous amounts of data. Mobile technology (e.g., cell phones). Wireless technology (e.g., wireless sensor technology). Data storage advances (e.g.. the cloud ). Researchers can collect real-time, continuous, biological, behavioral, and environmental data. Decreased cost and increased uptake make large sample intensive data collection possible.

Advantages: Methodological Self-report often uses retrospective recall. People report on what they did or how they felt during a certain period. Evidence that self-reports include error and biases. Autobiographical memory is not an HD video. Particularly problematic for summary recall. Complete and accurate recall not typical. Heuristic strategies used instead. Retrospective memory influenced by primacy, recency, availability, physical context, and mental state.

Advantages: Theory Research has often focused on antecedents and consequences. Little is known about dynamic processes that occur during a disease s course. ILD provide data provide fine-grain information on the entire course of experience. Disease, hospital stay, etc. Allows shift to thinking about process of disease. Size and direction of effects and relationships may vary across time. Explicit testing of temporal sequence/ordering.

Intensive Longitudinal Data Analysis But, how do we analyze data like this?

Intensive Longitudinal Data Analysis i =1,...,n; j =1,...,m i, { t ij, y ij, x ij1..., x } ijp ( ) ( ) y = t + t x + β β ε ij 0 ij 1 ij ij ij.

No EQUATIONS!

Intensive Longitudinal Data Analysis i =1,...,n; j =1,...,m i, { t ij, y ij, x ij1..., x } ijp i corresponds to a specific participant. n represents total number of participants. j designates a specific observation. m i represents the total number of observations for participant i. t ij corresponds to the measurement time of the jth observation for the ith participant. y ij corresponds to the outcome on the jth observation for the ith participant. x ijp corresponds to the pth covariate on the jth observation for the ith participant.

Time Varying Effect Model (TVEM) TVEMs are a semiparametric approach that do not require a predetermined specification for the shape of change. Introduced in mid 1990s. Hastie & Tibshirani, 1993; Hoover, Rice, Wu, & Yang, 1998. Allow researchers to answer questions about associations that unfold and change across time.

Time Varying Effect Model D0 not require a parametric assumption about change across time. Linear, quadratic, etc. Do not require covariate effects to be constant across time. Direction and strength estimated from the data. Regression coefficients can change with time. Allow variability in completeness, timing, and spacing of observations. Systematic missingness is a different story though.

Time Varying Effect Model ( ) ( ) y = t + t x + β β ε ij 0 ij 1 ij ij ij. Key things about this model: Single covariate for simplicity. Continuous outcome. β o (t ij ) correspond to the intercept at time j. Intercept = mean of y. When covariate(s) = 0. β 1 (t ij ) corresponds to the relationship between covariate 1 at a particular point in time (j).

Time Varying Effect Model β o (. ) and β 1 (. ) assumed to be continuous functions of time. Labeled as coefficient functions. Commonly depicted graphically. Can be summarized numerically.

Time Varying Effect Model

Time Varying Effect Model Goal of TVEM is to estimate the shape of the coefficient functions over time. Does not impose parametric assumptions. Assumes only that the relationship changes smoothly over time. Continuous first order derivative. Estimation? Extensive literature on topic. Broadly categorized into two methods. Spline-based methods. Kernel-based methods. We will briefly discuss P-spline methods.

P-Spline Estimation of TVEM Flexible and computationally efficient. Any smooth function over an interval can be approximated by a polynomial function. Runge phenomenon makes this problematic. Oscillation at boundaries. Instead, locally approximate function over smaller subinterval with lower order polynomials. Provide a good approximation over small interval. Piecewise polynomials. Spline functions. This is the spline part of P-spline.

P-Spline Estimation of TVEM Requires sufficient density of observations within the subinterval. To avoid overfitting the P-spline method smooths the estimated functions. Estimates may be rough, especially with large number of knots. Penalizing the coefficients, shrinking them toward zero, smooths the overall function. This can be done manually with tuning parameters. More effectively done by including random effects for the coefficients. This approach less sensitive to misspecification of error dependence.

Example

An Ecological Momentary Approach to Understanding Health Related Quality Of Life and Disease Activity among Children with Inflammatory Bowel Disease. Adam C. Carle, M.A., Ph.D. Constance A. Mara, M.A., Ph.D. Michael Seid, Ph.D.

Example Pediatric inflammatory bowel disease (IBD) is a chronic relapsing condition. Comprised of Crohn s disease and ulcerative colitis. Chronic recurrent episodes of gastrointestinal tract inflammation. Bloating, pain, diarrhea, fever, and malabsorption of nutrients. Treatment requires longitudinal follow-up to: Maximize therapeutic response, minimize drug toxicity, improve HRQOL, promote physical and psychological growth, and prevent complications.

Example Studies have shown that children with IBD report significantly poorer HRQOL. Even during periods of disease inactivity, children with IBD continue to report poorer HRQOL. Poor HRQOL in children with IBD is associated with increased healthcare utilization, even when HRQOL is not associated with disease outcome itself.

Example Nearly all of these studies have used crosssectional designs, despite IBD's lifelong duration and unpredictable course. Some children have frequent relapses, others experience prolonged periods of remission, and some children experience sporadic relapses. When active, severity can range dramatically.

Example Given chronicity and variation in course and symptomology, it would seem critical to examine children with IBD's HRQOL longitudinally. Only a handful of studies have collected longitudinal data on HRQOL in children with IBD. Just one of these collected more than two observations (3 total). All of the studies conducted relatively simple analyses focusing on difference in average reports of HRQOL from baseline to follow-up Otley, et al., with 3 data points, compared average reports between adjacent observations only.

Example No IBD studies have attempted to understand children with IBD's HRQOL and disease activity as they unfold in real time. Research has not yet fully addressed the lived experience of children with IBD. Studies may have missed substantial and meaningful variation in patients' HRQOL and symptomatology. In this study, we addressed these issues. We used ecological momentary assessment (EMA) and a time varying effect model for ILDA.

Example We collected patient reported outcomes (PROs) daily and others weekly. Examined extent to which disease activity and HRQOL change and fluctuate across time. Extent to which changes in disease activity and HRQOL corresponded to similar changes in other PROs. We also used TVEMs to examine extent to which passively collected information about cell phone use (e.g., call duration, the number of texts, etc.) correlated with PROs. Might passively collected data compliment actively reported PRO data and serve as proxy for active patient reporting?

Methods Longitudinal sample of 56 children with CD and UC from the ImproveCareNow (ICN) network. ICN includes 66 care centers in 34 states and includes 35% of the ~50,000 children with IBD in the US. Weekly measures "pushed" to children s phones: PROMIS fatigue and pain interference measures. PRO Measurement Information System (PROMIS). A disease activity index weekly in situ using surveys. Pediatric ulcerative colitis activity index (PUCAI) and short pediatric Crohn s disease AI (spcdai).

Methods Daily symptom measures pushed to phones: # of bowel movements, presence of diarrhea, bleeding in stool, stomach pain, fatigue, stress question, and the # of hours slept the previous night. Passive smart phone data collected continuously daily and matched to active data for that day. Phone call, SMS, and movement data used to measure: Call count. Call length. SMS count. SMS length. Missed calls. Average movement radius; Communication diversity.

Methods Children provided M=148 data points. SD=114.20. Total of 9,645 matched observations. Because some variables collected weekly rather than daily, some analyses have fewer total observations. For the current study, we limited the observations included in the analyses to those made within 300 days of a patient's first observation. In the analytical sample, each child provided an average of 107 data points (SD=73.40). Total of 7,697 matched momentary assessment observations across time and children.

Analyses For all of the PRO, symptom, and smart phone use variables, calculated bivariate ordinary least squares correlations. Used a Taylor linearization to adjust the standard errors to account for within patient clustering (repeated measurement). Used the Benjamini-Hochberg False Discovery Procedure to control for inflated Type I errors. Used "null" model multilevel models to partition each variable's variance into variance between and within individuals, as well as compute each variable's intraclass correlation.

Analyses Used TVEMs to examine each variable individually and the relationship between each variable and each of the remaining variables. Started with a series of intercept-only TVEMs to describe how the average values of each of the variables changed across the length of the study.

Analyses Then fit two sets of intercept and slope TVEMs. First set focused on relationships between the different patient reported variables. First set of models examined: Extent to which a given patient reported variable ( outcome ) changed across time at average levels of another patient reported variable ( predictor ). Whether change in predictor corresponded to change in outcome. How the strength of the relationship between an outcome and predictor changed across time.

Analyses The second set of TVEMs focused on relationships between the passively collected variables as outcomes and each of the patient reported variables as predictors) The models in this set examined: Extent to which passive variable changed across time at average levels of patient reported variable. Whether change in a patient reported variable corresponded to change in a passive variable. How the strength of the relationship between the passive variable and the patient reported variable changed across time.

Analyses Conducted all analyses in Stata 13. For TVEMs, we used P-spline smoothing. TVEM results presented as figures because the approach results in a large number of coefficients that are difficult to interpret in tables.

Results Patient reported variables: A large proportion of the variance was between individuals and the ICCs were relatively large. Mean=.59, SD=.17. Relatively dissimilar to each other on average. Across time, an individual's values relatively similar.

Results Mean SD Median Min Max Adolescents PROMIS Fatigue 49.5 14.12 51.41 30 84.36 53 PROMIS Pain Interference 46.02 11.17 45.54 34.04 73.75 53 PCDAI 10.97 8.77 10 0 50 40 PUCAI 13.35 13.97 10 0 80 14 Fatigue 3.84 2.48 3 1 10 56 Stress 3.03 2.18 3 1 10 56 Stomach Pain 2.77 2.11 2 1 10 56 Hours Sleep 7.59 1.78 8 0 12 56 # Bowel Movements 2.59 1.54 2 0 15 56

Results Variance Between Participants Variance Within Participants Intraclass Correlation PROMIS Fatigue 147.61 43.08 0.77 PROMIS Pain Interference 99.18 34.12 0.74 PCDAI 61.06 23.68 0.72 PUCAI 54.59 156.85 0.26 Fatigue 4.69 2.25 0.68 Stress 2.92 2.39 0.55 Stomach Pain 3.34 1.91 0.64 Hours Sleep 1.13 2.36 0.32 # Bowel Movements 1.93 1.19 0.62

Results PROMIS Fatigue PROMIS Pain PCDAI Score PUCAI Score Fatigue Stress Stomach Pain Hours of Sleep # of Bowel Movements PROMIS Fatigue 1.000 PROMIS Pain 0.77* 1.000 PCDAI Score 0.73* 0.76* 1.000 PUCAI Score 0.28 0.37* N/A 1.000 Fatigue 0.68* 0.52* 0.58* 0.09 1.000 Stress 0.57* 0.42* 0.49* 0.05 0.67* 1.000 Stomach Pain 0.53* 0.57* 0.65* 0.45* 0.58* 0.49* 1.000 Hours of Sleep -0.05-0.08-0.14-0.14* -0.11-0.12-0.14* 1.000 # of Bowel Movements 0.18 0.29* 0.34* 0.47* 0.12 0.12 0.25* -0.03 1.000 *p<0.05 Based on Benjamini-Hochberg False Discovery Procedure All standard errors and p-values adjusted for within individual clustering.

Results Passive variables: Much smaller proportion of the variance between individuals and ICCs were comparatively small (mean=. 23; SD=.13). Children relatively similar to each other across time. Fair amount of variance within individual across time.

Results Mean SD Median Min Max Adolescents Text Length 1639.59 2018.34 976.00 0 22887 15 Unreturned Calls 0.44 0.83 0.00 0 7 14 Call Duration (Minutes) 8.45 16.54 1.68 0 266 15 Mobility 1.63 1.75 1.23 0 28.01 48 Interaction Diversity 4.70 2.79 4.00 0 34 15 Missed Interactions 0.57 1.09 0 0 18 15 Aggregate Communication 34.50 35.80 23.00 0 276 15 Number of Texts 32.03 35.07 21 0 271 15

Results Variance Between Participants Variance Within Participants Intraclass Correlation Text Length 1.45E+06 3.98E+06 0.27 Unreturned Calls 0.02 0.58 0.03 Call Duration (Minutes) 163.07 229.07 0.42 Mobility 0.47 3.42 0.12 Interaction Diversity 3.67 6.23 0.37 Missed Interactions 0.05 1.07 0.04 Aggregate Communication 385.73 1100.92 0.26 Number of Texts 369.97 1063.24 0.26

Results SMS Unret. Call Length Calls Duration Mob. Int. Missed Agg. SMS Mobility Diver. Int. Comm. Count Radius PROMIS Fatigue 0.09-0.07 0.23* -0.05 0.10 0.03 0.20 0.19 0.00 PROMIS Pain 0.23 0.00 0.22-0.01 0.24 0.09 0.30* 0.28* 0.04 PCDAI Score 0.12-0.10 0.26-0.05 0.28* 0.05 0.24* 0.22* -0.01 PUCAI Score 0.04-0.13 0.14* 0.12* 0.04-0.10-0.11-0.13 0.00 Fatigue 0.13 0.06 0.22* -0.09 0.17 0.10* 0.30 0.29-0.03 Stress 0.11 0.06 0.16-0.11 0.07 0.06 0.25 0.25-0.04 Stomach Pain 0.19 0.05 0.17-0.07 0.18* 0.07 0.30* 0.29* -0.03 Hours of Sleep -0.03-0.07 0.02-0.05-0.07-0.06-0.01-0.01-0.04 # of Bowel Movements 0.01 0.01 0.17 0.03 0.02 0.05 0.00-0.02 0.07 *p<0.05 Based on Benjamini-Hochberg False Discovery Procedure All standard errors and p-values adjusted for within individual clustering.

Intercept Only TVEM

Results

Results Some variability in each variable's average levels across time. For majority, changes in average value across time did not differ significantly from the initial value. In general, gray confidence interval bands encompass the line depicting initial value.

Results Three exceptions. Average values of PROMIS pain interference and selfreported hours of sleep both tended to decrease. PCDAI values decreased significantly as well, but not significantly until around the 200th day. Focusing on shape rather than significance, average values fluctuate relatively cyclically. Figures show increases and decreases across time, even for the variables that generally decreased across the study period

Results

Intercepts and Slopes TVEM

Results

Results Patient reported slope functions generally consistent and stable across time. Largest association between PROMIS fatigue and PROMIS pain (~0.5). Single item measures have more random measurement error than multi-item measures and are therefore less sensitive. Not surprising that largest effect size between PROMIS measures. All but reported hours of sleep and the number of bowel movements in a day were consistently significantly associated with the remaining patient reported variables.

Passive-Active TVEMs

Results

Results Relationship between aggregate communication and each patient reported variables generally small (< 0.2). Hours of sleep, bowel movements, PROMIS pain interference, and PROMIS fatigue relatively constant relationships with aggregate communication. Only relationship with pain interference is statistically significant across most of the study period. Other variables either have no or only brief periods where their association with aggregate communication differs significantly from zero.

Results

Results For remaining, focusing shape, one can see variation in the strength of the relationship. Slope functions rise and fall across time. Because confidence interval bands tend to overlap across time, periodicity could be due to chance. With the exception of stomach pain. Relationship significantly different from zero across several points in time. Vacillates from negative to positive multiple times. Sometimes increased stomach pain is associated with decreased aggregate communication. Other times increased stomach pain is associated with increased aggregate communication Size of relationship generally small though.

Results

Conclusions from Example Results suggest treatments that improve some of the common IBD symptoms will likely have a moderate and consistent impact on children's HRQOL regardless of when the improvements occur. Evidenced by consistent and moderately sized values in the slope functions. Analyses also demonstrate how more typical two time point studies miss substantial and meaningful variation in patients' HRQOL. In our IBD sample, there was significant variation for each variable within individuals across time.

Conclusions from Example Although we did observe some statistically significant relationships between passively collected data and active patient reports, the sizes of the relationships were relatively small. In addition, many of these relationships cyclically varied in size and occasionally in sign across time. This limits their ability to serve as potential proxies for patient reported outcomes. But, small number of individuals (not data points) so further study may show reveal different effects.

Challenges in ILD Studies Respondent burden. Reactivity. Compliance. Including concerns about falsification. Ethical issues. Psychometric issues. Integration across data sources. Increasingly complex research questions. Availability of ILD does not imply its appropriateness for all HSR questions. Don t force it.

Conclusions ILD designs allow for new and enriched understanding with respect to individual variables and relationships among variables. Shift the focus from single time points or parametric trajectories to more dynamical processes. Ecologically valid study results may differ from recall-based studies. Today we only focused on TVEM. Multiple options available.

Perplexed? Happy to take questions.