Mplus VERSION 8.8
MUTHEN & MUTHEN
04/19/2022 11:13 PM
INPUT INSTRUCTIONS
TITLE: this is an example of continuous-time survival
analysis using a Cox regression model to
estimate a treatment effect
DATA: FILE = ex7.30.dat;
VARIABLE: NAMES are t u x tcent class;
USEVARIABLES = t-tcent;
SURVIVAL = t;
TIMECENSORED = tcent;
CATEGORICAL = u;
CLASSES = c (2);
ANALYSIS: TYPE = MIXTURE;
MODEL:
%OVERALL%
t ON x;
%c#1%
[u$1@15];
[t@0];
%c#2%
[u$1@-15];
[t];
OUTPUT: TECH1 LOGRANK;
PLOT: TYPE = PLOT2;
INPUT READING TERMINATED NORMALLY
this is an example of continuous-time survival
analysis using a Cox regression model to
estimate a treatment effect
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 500
Number of dependent variables 2
Number of independent variables 1
Number of continuous latent variables 0
Number of categorical latent variables 1
Observed dependent variables
Binary and ordered categorical (ordinal)
U
Time-to-event (survival)
Non-parametric
T
Observed independent variables
X
Categorical latent variables
C
Variables with special functions
Time-censoring variables
TCENT
Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 100
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-06
Relative loglikelihood change 0.100D-06
Derivative 0.100D-05
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-05
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-05
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Random Starts Specifications
Number of initial stage random starts 20
Number of final stage optimizations 4
Number of initial stage iterations 10
Initial stage convergence criterion 0.100D+01
Random starts scale 0.500D+01
Random seed for generating random starts 0
Link LOGIT
Base Hazard EQUAL ACROSS CLASSES
Input data file(s)
ex7.30.dat
Input data format FREE
UNIVARIATE PROPORTIONS AND COUNTS FOR CATEGORICAL VARIABLES
U
Category 1 0.460 230.000
Category 2 0.540 270.000
UNIVARIATE SAMPLE STATISTICS
UNIVARIATE HIGHER-ORDER MOMENT DESCRIPTIVE STATISTICS
Variable/ Mean/ Skewness/ Minimum/ % with Percentiles
Sample Size Variance Kurtosis Maximum Min/Max 20%/60% 40%/80% Median
X 0.030 0.084 -2.799 0.20% -0.852 -0.260 0.003
500.000 1.121 -0.298 3.254 0.20% 0.275 0.956
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
-98.989 851945 18
-98.989 939021 8
-98.989 608496 4
-98.989 unperturbed 0
THE BEST LOGLIKELIHOOD VALUE HAS BEEN REPLICATED. RERUN WITH AT LEAST TWICE THE
RANDOM STARTS TO CHECK THAT THE BEST LOGLIKELIHOOD IS STILL OBTAINED AND REPLICATED.
THE MODEL ESTIMATION TERMINATED NORMALLY
MODEL FIT INFORMATION
Number of Free Parameters 3
Loglikelihood
H0 Value -98.989
H0 Scaling Correction Factor 1.0162
for MLR
Information Criteria
Akaike (AIC) 203.978
Bayesian (BIC) 216.621
Sample-Size Adjusted BIC 207.099
(n* = (n + 2) / 24)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical
(Ordinal) Outcomes
Pearson Chi-Square
Value 0.000
Degrees of Freedom 0
P-Value 1.0000
Likelihood Ratio Chi-Square
Value 0.000
Degrees of Freedom 0
P-Value 1.0000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THE ESTIMATED MODEL
Latent
Classes
1 229.99999 0.46000
2 270.00001 0.54000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent
Classes
1 229.99999 0.46000
2 270.00001 0.54000
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES
BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Class Counts and Proportions
Latent
Classes
1 230 0.46000
2 270 0.54000
CLASSIFICATION QUALITY
Entropy 1.000
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row)
by Latent Class (Column)
1 2
1 1.000 0.000
2 0.000 1.000
Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 1.000 0.000
2 0.000 1.000
Logits for the Classification Probabilities for the Most Likely Latent Class Membership (Column)
by Latent Class (Row)
1 2
1 13.816 0.000
2 -13.816 0.000
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
T ON
X 0.541 0.057 9.479 0.000
Intercepts
T 0.000 0.000 999.000 999.000
Thresholds
U$1 15.000 0.000 999.000 999.000
Latent Class 2
T ON
X 0.541 0.057 9.479 0.000
Intercepts
T 0.974 0.117 8.325 0.000
Thresholds
U$1 -15.000 0.000 999.000 999.000
Categorical Latent Variables
Means
C#1 -0.160 0.090 -1.787 0.074
QUALITY OF NUMERICAL RESULTS
Condition Number for the Information Matrix 0.222E+00
(ratio of smallest to largest eigenvalue)
RESULTS IN PROBABILITY SCALE
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
U
Category 1 1.000 0.000 0.000 1.000
Category 2 0.000 0.000 0.000 1.000
Latent Class 2
U
Category 1 0.000 0.000 0.000 1.000
Category 2 1.000 0.000 0.000 1.000
LATENT CLASS INDICATOR ODDS RATIOS FOR THE LATENT CLASSES
95% C.I.
Estimate S.E. Lower 2.5% Upper 2.5%
Latent Class 1 Compared to Latent Class 2
U
Category > 1 0.000 0.000 0.000 0.000
LOGRANK OUTPUT
LOGRANK TEST FOR SURVIVAL VARIABLE T COMPARING CLASS 2 AGAINST CLASS 1
Chi-Square Value 64.136
Degrees of Freedom 1
P-value 0.000
TECHNICAL 1 OUTPUT
PARAMETER SPECIFICATION FOR LATENT CLASS 1
NU
X
________
0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS 2
NU
X
________
0
LAMBDA
X
________
X 0
THETA
X
________
X 0
ALPHA
X
________
0
BETA
X
________
X 0
PSI
X
________
X 0
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U$1
________
0
TAU(U) FOR LATENT CLASS 2
U$1
________
0
PARAMETER SPECIFICATION FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
1 0
GAMMA(C)
X
________
C#1 0
C#2 0
PARAMETER SPECIFICATION FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
T#1 T
________ ________
0 0
KAPPA(P) FOR LATENT CLASS 1
X
________
T#1 0
T 2
NU(P) FOR LATENT CLASS 2
T#1 T
________ ________
0 3
KAPPA(P) FOR LATENT CLASS 2
X
________
T#1 0
T 2
STARTING VALUES FOR LATENT CLASS 1
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.560
STARTING VALUES FOR LATENT CLASS 2
NU
X
________
0.000
LAMBDA
X
________
X 1.000
THETA
X
________
X 0.000
ALPHA
X
________
0.000
BETA
X
________
X 0.000
PSI
X
________
X 0.560
STARTING VALUES FOR LATENT CLASS INDICATOR MODEL PART
TAU(U) FOR LATENT CLASS 1
U$1
________
15.000
TAU(U) FOR LATENT CLASS 2
U$1
________
-15.000
STARTING VALUES FOR LATENT CLASS REGRESSION MODEL PART
ALPHA(C)
C#1 C#2
________ ________
0.000 0.000
GAMMA(C)
X
________
C#1 0.000
C#2 0.000
STARTING VALUES FOR THE CENSORED/NOMINAL/COUNT MODEL PART
NU(P) FOR LATENT CLASS 1
T#1 T
________ ________
-20.000 0.000
KAPPA(P) FOR LATENT CLASS 1
X
________
T#1 0.000
T 0.000
NU(P) FOR LATENT CLASS 2
T#1 T
________ ________
-20.000 0.000
KAPPA(P) FOR LATENT CLASS 2
X
________
T#1 0.000
T 0.000
PLOT INFORMATION
The following plots are available:
Survival curves
Sample proportions, estimated and conditional estimated probabilities
Beginning Time: 23:13:22
Ending Time: 23:13:23
Elapsed Time: 00:00:01
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