1. Latent Class Regression Computing examples
Karen Bandeen-Roche
October 28, 2016

2. Objectives For you to leave here knowing…
How to use the LCR SAS Macro for latent class regression
How to interpret, report output
Model checking: how to conduct, interpret pseudo-value analysis

3. Basics on using the software
Part I:
Basics on using the software

4. General recommendations
Fit an LCA
Add covariates one at a time
Initialize at prior fits and an “agnostic” value for coefficient of newly added covariate

5. Reminder – Toy Example

6. Reminder – Toy Example

7. Initialization using Previous Fit
Result:
beta
sebeta
Covariates
int
COV1

8. Initialization using Previous Fit
beta
sebeta
Covariates
int
COV1
Initial coefficient for newly added covariate

9. Back to the PTSD Example
Part II:
Back to the PTSD Example

11. PTSD Latent Class Analysis
SYMPTOM
DOMAIN
(prevalence)
SYMPTOM PROBABILITY (π)
Class 1 - NO PTSD
Class 2 - PRECLINICAL
Class 3 - PTSD
RE-
EXPERIENCE
 (1 of 5)
Recurrent thoughts (.49)
.20
.74
.96
Distress to event cues (.42)
.12
.68
.88
Reactivity to cues (.31)
.05
.51
.77
AVOIDANCE/
NUMBING
 (3 of 7)
Avoid related thoughts (.28)
.08
.37
.75
Avoid activities (.24)
.34
.66
Detachment (.15)
.01
.14
.64
INCREASED AROUSAL
 (2 of 5)
Difficulty sleeping (.19)
.02
.18
.78
Irritability (.21)
.22
.83
Difficulty concentrating (.25)
.03
.30
.89
MEAN PREVALENCE-BASELINE
.52
.33
[Omitted: nightmares, flashback; amnesia, interest, affect, short future; hypervigilance, startle]
Report concordance with diagnosis: 79.1 Sens, 93.7 Spec, 63.7 PPV, 97.1 NPV; NOT FIT
Female 3 times the RP as males; Assault between 2.5 and 10 time the RP as other traumas

14. LCR Coding – Three Class Model
Covariates:
Sex
(1 if female, 0 if male)
Trauma type
(indicators for
injury / other shock
trauma to loved one
death to loved one;
personal assault = ref.)
(Intercept)

15. LCR Coding – Three Class Model
Initialization: from model
With only “female” as covariate
(three trauma type indicators
1st vs. 3rd and 2nd vs. 3rd class
initialized at 0
1st vs 3rd class
2nd vs 3rd class

16. Parameter interpretation, inference
Part III:
Parameter interpretation, inference

17. Covariate Coefficient Estimates
Example: “FEMALE”
exp(1.137) = 3.117
Odds of “PTSD” vs “NONE”
3.12 higher in females vs
males
(holding trauma type
constant)
95%CI =
Exp( *0.172,
*0.172)
= (2.224,4.367)
Log Relative Prevalence
Ratios, “PTSD” vs “NONE”

18. Data support
that females are at substantially higher risk than males;
that persons with traumas other than assault are at substantially
lower risk

19. Covariate Coefficient Estimates
exp(0.109) =
Relative prevalence
“Some symptoms” vs None
(Class 2 vs Class 3) in
male assault victims
(reference group)
= 1.115
Prevalence
“Some symptoms” in
male assault victims =
exp(0.109)/
[1+exp(-0.535)+exp(0.109)]
=0.413
Log Relative Prevalence
Ratios, “Some Symptoms”
vs “NONE”
(Class 2 vs 3)
FEMALE
injshock
traumlov
deathlov

20. Interaction analysis “PTSD” versus “None”
Interactions for “some symptoms” versus “none”: negligible

21. Interactions? AIC, BIC slightly increased (vs no interactions)
-2 log likelihood comparison:
No interactions Interactions
> Difference = on (43-37) df
> p-value = 0.10 (χ2 with 6 df)
> A suggestion that the extent of F vs M increase in risk is trauma-type dependent
loglik
dfm df 43
loglik
dfm df 37

22. Part IV:
Model Checking

23. Checking How the Model Fails to Fit
Basic ideas:
Suppose the model is true
If we knew persons’ latent class memberships, we would check directly:
Within classes:
Check correlations or pairwise odds ratios among the item responses (Conditional Independence)
Regress item responses on covariates (non-differential measurement)
Regress class memberships on covariates, hope for
Similar findings re regression coefficients
No strong effects of outliers
Identify strongly nonlinear covariates effects

24. Checking How the Model Fails to Fit
But in reality, we don’t know the true latent class membership!
Latent class memberships must be estimated
Randomize people into “pseudo” classes C* using their posterior probabilities or assign to “most likely class” corresponding to the highest posterior probability
Posterior probability is defined as
Analyze as described before, except using “pseudo” class membership rather than true ones
Bandeen Roche, Miglioretti, Zeger & Rathouz, 1997
Huang & Bandeen-Roche, 2004; Wang, Brown & Bandeen-Roche, 2005
Bandeen-Roche et al., J Am Statist Assoc., 1997

25. PTSD analysis Implementation
Step 1: Obtain posterior probabilities in a dataset
data post;
merge theta dataset;
run;
data junk;
set post;
file 'ptsd1pos.dat';
put theta1 theta2 theta3 b1 b4 b5 c1 c2 c5 d1 d2 d3
female injshock traumlov deathlov;

26. PTSD analysis Implementation
Step 2: Randomize individuals into pseudo classes C*
(see next slide…)

27. # read data data_matrix(scan("ptsd1pos
# read data data_matrix(scan("ptsd1pos.dat"),ncol=16,byrow=T) data_cbind(1:nrow(data),data) # establish a randomization vector rvec_runif(nrow(data)) rvec_order(rvec) data_cbind(data,rvec) # labels dimnames(data)_list(NULL,c("id","theta1","theta2","theta3","b1","b4","b5","c1", "c2","c5","d1","d2","d3","female","injshock","traumlov","deathlov","random")) nrow(data) # posterior probabilities pi_data[,c("theta1","theta2","theta3")] print(dim(pi)) # randomization ptsd1pos_matrix(0,ncol=ncol(pi),nrow=nrow(pi)) ptsd1pos[,1]_1*(rvec<= pi[,1]) ptsd1pos[,2]_1*((rvec > pi[,1]) & (rvec <= (pi[,1]+pi[,2]))) ptsd1pos[,3]_1*(rvec > (1-pi[,3])) # complete data ptsd1pos_cbind(data,ptsd1pos) dimnames(ptsd1pos)_list(NULL,c(dimnames(data)[[2]],"class1","class2","class3"))

28. PTSD analysis Implementation
Step 3: Evaluation of [Y|x] “per” C*
Time-saving method: GEE to analyze [Y|x,c*]
“GEE2”: Heagerty & Zeger, 1996
ordgee in R

29. PTSD analysis Implementation
Two concurrent regressions
Mean model: Logistic regression of each item Yim on covariates
“Basic”: item, pseudo-class indicators and their interactions - reproduce measurement model
Item-by-x terms: assesses differential measurement
Association model describes pairwise odds ratios: factors by which odds of positive response on one item vary by response on another item
M-choose-2 “outcomes” per person (pairs)

32. Model Checking Conclusions
Symptoms were differentially sensitive to different traumas
Within latent classes:
Those with a non-assaultive trauma were
less prone to report distress to cues, reactivity to cues, avoiding thoughts, & avoiding activities
more prone to report recurrent thoughts & difficulty concentrating
There was considerable tendency for symptoms within categories (esp. avoidance) to be reported together
Concern: Criteria may insensitively detect psychiatric sequelae to assault than to traumas other than assault
Differential
measurement
Conditional
dependence

33. Objectives For you to leave here knowing…
How to use the LCR SAS Macro for latent class regression
How to interpret, report output
Model checking: how to conduct, interpret pseudo-value analysis

34. EXTRA SLIDES