Data Mining through Linear Modeling

Factors associated with the clinical characteristic “Dominance” published in “Psychosocial Treatments for Cocaine Dependence” [Arch Gen Psychiatry 56: June 1999] Tim Hare STA531 Fall 2009

Cross-sectional (Month = 6) modeling of DOMI (Dominance) as a primary outcome
The outcome measure under consideration is the clinical attribute/behavior “dominance”.
Preliminary hypothesis directed the search somewhat: Is Dominance correlated with depression scores and psychological characteristics scores?
A focus on scores for personality traits as well as assessed alcohol use yielded a subset of candidate predictors with strong correlation.
VIND = vindictive
ALC_SUB = ASI Alcohol composite
INTR = intrusive
COLD
Exploratory analysis of these to develop the hypothesis?

Correlation data for raw score VIND vs. DOMI Binned by score trend of the 95% CI’s suggests possible significance of categorical based on binning 1.00000 0.80637 <.0001 VIND 0.80637 <.0001 1.00000 DOMI VIND DOMI Pearson Correlation Coefficients, N = 456 Prob > |r| under H0: Rho=0

Correlation data for raw score INTR vs DOMI Again, trend in the 95% CI’s 1.00000 0.79210 <.0001 INTR 0.79210 <.0001 1.00000 DOMI INTR DOMI Pearson Correlation Coefficients, N = 456 Prob > |r| under H0: Rho=0

Correlation data for raw score COLD vs DOMI Again, trend in the 95% CI’s 1.00000 457 0.73152 <.0001 456 COLD 0.73152 <.0001 456 1.00000 456 DOMI COLD DOMI Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations

Cross-sectional (Month = 6) modeling of DOMI (Dominance) as a primary outcome
The outcome measure under consideration is the clinical attribute/behavior “dominance”.
A number of potential factors were evaluated, however a focus on related psychological scores as well as assessed alcohol use yielded a subset of relatively strong predictors.
VIND = vindictive
ALC_SUB = ASI Alcohol composite
INTR = intrusive
COLD
Based upon the preliminary exploration , the above patient scores were transformed to create a new set of 2-LEVEL categorical variables codified by assignment according to whether they were above or below their mean (e.g. “high” “low”)
VINDGROUP
ALC_SUBGRUOP
INTRGROUP
COLDGROUP
Additional crossed 2- and 3-way group variables were created based upon the ABOVE GROUP variables (e.g. combinations of “high” and “low” levels).
VA = vindictive + ASI Alcohol composite
VI = vindictive + intrusive
VAI = vindictive + ASI Alcohol composite + intrusive
Before we get started, what about any MODELING ASSUMPTIONS?

OUTCOME MEASURE = DOMI Raw score NORMAL PROBABILITY PLOT 1.00000 0.94328 <.0001 zdomi Rank for Variable DOMI 0.94328 <.0001 1.00000 DOMI zdomi DOMI Pearson Correlation Coefficients, N = 456 Prob > |r| under H0: Rho=0

Potential 2-way & 3-way CROSS FACTOR GROUP VIEWS VINDGROUP-INTRGROUP VINDGROUP-ALC_SUBGROUP VINDGROUP-ALC_SUBGROUP-INTRGROUP 1) Evidence for non-homogeneous variance. 2) As well, groups are unbalanced (dissimilar counts)  USE PROC MIXED

Any hypothesis suggest itself?
Let’s take a look at the new CATEGORICAL VARIABLES we created, graphically…
Let’s also take a look at the new observational CROSS FACTOR data groups...
Let’s also look for any confounding 2-way or 3-way INTERACTIONS between the variables…
Will a story emerge?

NEW CATEGORICAL VARIABLES (NOT RAW DATA) MEAN DOMI SCORE by LEVEL ALC_SUBGROUP INTRGROUP VINDGROUP Some good evidence that our 2-LEVEL categorization correlates with our OUTCOME measure. What about combinations of the above CATEGORIES by LEVEL?

2-way- & 3-way CROSS FACTOR GROUPS MEAN DOMI SCORES (VIND*INTR) (VIND*ALC_SUB) VIND*ALC_SUB*INTR Good story to explore… What about “interaction”???

Possible interaction between VINDGROUP and ALC_SUBGROUP

Possible interaction between INTRGROUP and ALC_SUBGROUP

Possible interaction between INTRGROUP and VINDGROUP

Graphical analysis to examine potential 3-WAY interaction VINDGROUP*INTRGROUP*ALC_SUBGROUP( LOW/HIGH ) ALC_SUBGROUP = LOW ALC_SUBGROUP = HIGH

PREVIEW for longitudinal modeling: Correlation noted in CROSS SECTIONAL (Month=6) data seems to persist across time … Therefore suspect “repeated measures” (longitudinal modeling) may model well from the same variables

Exploration leads to Hypothesis
Incidence of the clinical characteristic “Dominance” can likely be explained by modeling with the categorical variables (VINDGROUP, INTRGROUP, ALC_SUBGROUP, COLD) derived from the raw scores.
Interaction terms (VINDGROUP*ALC_SUBGROUP, VINDGROUP*INTRGROUP, INTRGROUP*ALC_SUBGROUP) will likely play a role in the modeling process given the preliminary 2-/3-way interaction plots ( COLDGROUP*<other> not compelling, data not shown ).
Finally, there are some compelling graphs that suggest that interaction can be explained and may be significant in many cases ( we’ll explore these further with contrasts later ).

Cross sectional (Month=6) modeling results confirm our suspicions PROC MIXED ( α =0.05) 2X/3X 0.0044 5.50 447 2 VINDGROUP*ALC_SUBGROUP*INTRGROUP 0.0027 9.11 447 1 VINDGROUP*ALC_SUBGROUP <.0001 33.72 447 1 VINDGROUP*INTRGROUP <.0001 163.16 447 1 INTRGROUP 0.0136 6.13 447 1 ALC_SUBGROUP <.0001 136.66 447 1 VINDGROUP 0.0002 13.79 447 1 COLDGROUP Pr > F F Value Den DF Num DF Effect Type 3 Tests of Fixed Effects

CROSS SECTIONAL (Month=6) DOMI SCORE LSMEANS for 3-way crossed observational groups
Least Squares Means
Effect VINDGROUP ALCSUBGROUP INTRGROUP Estimate Error DF t Value
VINDGR*ALC_SU*INTRGR 1_Q12VIND 1_Q12ALC_SUB 1_Q12INTR 1.2440 0.2747 447 4.53
Effect VINDGROUP ALCSUBGROUP INTRGROUP Pr > |t| Alpha Lower Upper
VINDGR*ALC_SU*INTRGR 1_Q12VIND 1_Q12ALC_SUB 1_Q12INTR <.0001 0.05 0.7042 1.7838
VINDGR*ALC_SU*INTRGR 1_Q12VIND 1_Q12ALC_SUB 2_Q34INTR 0.0001 0.05 1.2802 3.8559

If you’re Vindictive=Low, Intrusive=Low… you probably don’t have to worry about being overly Dominant after drinking … At 95% conf. Level: not significant <.0001 5.55 447 0.3445 1.9119 LHL <.0001 4.53 447 0.2747 1.2440 LLL Pr > |t| t Value DF Standard Error Estimate Label Estimates 0.0938 2.82 447 1 LHL-LLL Pr > F F Value Den DF Num DF Label Contrasts

Does intrusiveness trump alcohol in low vindictives? VL AL/H IL VL AL/H IH <.0001 9.04 447 0.45 4.08 AVG(LHH,LLH) <.0001 6.58 447 0.24 1.58 AVG(LLL,LHL) 0.0001 3.92 447 0.66 2.57 LLH <.0001 9.00 447 0.62 5.59 LHH <.0001 5.55 447 0.34 1.91 LHL <.0001 4.53 447 0.27 1.24 LLL Pr > |t| t Value DF Standard Error Estimate Label Estimates <.0001 24.87 447 1 AVG(LHH,LLH)-AVG(LLL,LHL) 0.0009 11.21 447 1 LHH-LLH 0.093 2.82 447 1 LHL-LLL Pr > F F Value Den DF Num DF Label Contrasts

CROSS SECTIONAL MODEL: (Month=6) Good fit? Residuals plots… 1.00000 0.97126 <.0001 zresid Rank for Variable Resid 0.97126 <.0001 1.00000 Resid Residual zresid Resid Pearson Correlation Coefficients, N = 456 Prob > |r| under H0: Rho=0

Repeated Measures Analysis of the entire Month1-Month6 data set
The original cross sectional model was evaluated for COV / VAR structure (e.g. adjust for possible correlation in longitudinal data) by comparison
CS, UN, AR(1) TOEP, CSH, ARH(1)
COV / VAR type “UN” was retained as smallest -2ResLogLikelihood, significantly smaller than all the rest, adjusting for DF.
ALC_SUBGROUP was retained due to participation in higher order terms of significance. 0.0012 7.16 102 2 VINDGR*ALC_SU*INTRGR 0.0098 6.93 102 1 VINDGROUP*ALC_SUBGRO <.0001 39.29 102 1 VINDGROUP*INTRGROUP <.0001 125.09 102 1 INTRGROUP 0.8081 0.06 102 1 ALC_SUBGROUP <.0001 132.23 102 1 VINDGROUP <.0001 22.20 102 1 COLDGROUP Pr > F F Value Den DF Num DF Effect Type 3 Tests of Fixed Effects

LONGITUDINAL MODEL: Good fit? Residuals plots… 1.00000 0.95069 <.0001 zresid Rank for Variable Resid 0.95069 <.0001 1.00000 Resid Residual zresid Resid Pearson Correlation Coefficients, N = 456 Prob > |r| under H0: Rho=0

Repeated Measures (COV=UN, no terms removed)
Least Squares Means
Effect VINDGROUP ALC_SUBGROUP INTRGROUP Estimate Error DF t Value
Effect VINDGROUP ALC_SUBGROUP INTRGROUP Pr > |t| Alpha Lower Upper
At 95% conf. Level: not significant <.0001 6.04 102 0.3452 2.0854 LHL <.0001 5.59 102 0.2996 1.6757 LLL Pr > |t| t Value DF Standard Error Estimate Label Estimates 0.2124 1.57 102 1 LHL-LLL Pr > F F Value Den DF Num DF Label Contrasts

What about our cross sectional contrast of alcohol being trumped by intrusiveness in low vindictives? Does it still hold in the longitudinal analysis? Still significant At 95% CI <.0001 8.44 102 0.4247 3.5832 AVG(LHH,LLH) <.0001 6.74 102 0.2790 1.8806 AVG(LLL,LHL) <.0001 5.34 102 0.5583 2.9805 LLH <.0001 7.36 102 0.5689 4.1859 LHH <.0001 6.04 102 0.3452 2.0854 LHL <.0001 5.59 102 0.2996 1.6757 LLL Pr > |t| t Value DF Standard Error Estimate Label Estimates 0.0002 15.41 102 1 AVG(LHH,LLH)-AVG(LLL,LHL) 0.1069 2.65 102 1 LHH-LLH 0.2124 1.57 102 1 LHL-LLL Pr > F F Value Den DF Num DF Label Contrasts

Conclusions
The interrelationship between the clinical attribute “dominance” and the related attributes “intrusive” “vindictiveness”, “cold”, along with the ASI Alcohol Composite score, combine to model the incidence of dominance in the clinical data.
Both longitudinal modeling (using the entire data set) and cross sectional modeling (Month=6) support the same conclusions.
We can use CONTRASTS to profitably to validate the BARCHARTS showing possible differences in relationship between the interactions of 3 key variables (VINDGROUP, INTRGROUP, and ALC_SUBGROUP) types that correlated with DOMINANCE, but have complex INTERACTIONS.

Data Mining through Linear Modeling

by tim_hare

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