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VARIABLE SELECTION FOR DECISION MAKING IN MENTAL HEALTH 1,2 Gunter , Lacey STATISTICS Departments of and Institute for Social Introduction A=1 A=0 0.8 0.0 A=0 0.0 0.4 0.4 A=0 R 0.4 A=1 R 0.4 A=1 0.0 0.0 X4 0.4 0.8 0.0 0.4 X5 big interaction big proportion We have 3 components: 1. observations X = (X1, X2,…, Xp), 2. treatment action, A, 3. response, R 0.8 0.8 0.8 We propose ranking the variables in X based on potential for a qualitative interaction with the treatment. We give a score for ranking the variables based on 2 factors for evaluating qualitative interactions 1. The magnitude of the interaction between the variable and treatment 2. The proportion of patients whose optimal treatment changes given knowledge of the variable These 2 factors are illustrated in the plots below. 0.0 This poster discusses variable selection for medical decision making; in particular, decisions regarding when to provide treatment and which treatment to provide patients with mental health disorders. Variable selection is often needed in this setting to reduce costs incurred by collecting unnecessary information and to inform clinicians which variables are important for individualizing treatment. We present a new technique designed to find variables that aid in decision making. We demonstrate the utility of this technique on data from a randomized controlled trial which compared three alternate treatments for chronic depression. 0.8 2 Research , University of Michigan, Ann Arbor We demonstrate this method on data from a depression study to determine which variables might help decipher the optimal depression treatment for each patient. Aim of the Nefazodone CBASP trial(1) – to compare efficacy of three alternate treatments for chronic major depressive disorder (MDD): 1. Nefazodone, 2. Cognitive behavioral-analysis system of psychotherapy (CBASP) 3. Nefazodone + CBASP For our analysis we used data from 440 patient with: X 64 baseline variables listed in the table to the right A Nefazodone vs. Nefazodone + CBASP R Last observed Hamilton’s Rating Scale for Depression score, post treatment X6 small interaction big proportion big interaction small proportion We estimate the interaction factor by: Dj = change in the effect of the optimal treatment over range of variable Xj See plot below for illustration; a* is the overall optimal treatment, the blue and red lines represent the fitted model, green ticks represent observations Policy: guidelines for choosing treatment, A, given observations, X and Susan 1,2 Murphy Depression Study Results New Methods R Abstract 1 Statistics Ji 1 Zhu , We used bootstrap sampling to minimize the variability of the results. On each of 100 bootstrap samples, we performed the following analysis: 1. run new method U and the standard method 2. record the interaction variables selected The plots below give the percentage of time each interaction was selected for each method. R patient's condition and symptoms post treatment R A=0 0.0 0.4 X2 0.8 40 60 variable number 0.10 0.4 0.2 0.8 0.0 0.8 A=1 A=0 0.0 0.4 Algorithm 0.8 A=1 0.0 X1 0.8 0.0 2 Pj 7 20 0 20 40 60 variable number The green threshold lines in above plots were determined as follows: 1. Remove interaction effects from the data 2. Run methods on new data 3. Threshold : largest percentage of time a variable was selected This helped assess the maximum selection percentage we expect to see when no interaction effects exist. Only interaction variables with selection percentages above these thresholds should be selected. Results: The standard method selected 30 interaction variables. The new method selected only 4 interaction variables: 2 indicators dealing with alcohol, a somatic anxiety score and an indicator dealing with specific phobia. For more details see (2). 1 Gender 2 Racial category 3-4 Marital status 5 Body mass index 6 Age in years at screening 7 Treated current depression 8 Medication current depression 9 Psychotherapy current depression 10 Treated past depression 11 Medication past depression 12 Psychotherapy past depression 13 Age of MDD onset 14-16 Number of depressive episodes 17 Length current episode 18-19 MDD type of current episode 20-21 MDD current severity 22-23 MDD chronic status 24 MDD threshold frequency 25 Dysthymic disorder current 26 Dysthymia initial onset 27 Length current dysthymia episode 28-29 Alcohol 30 Drug 31-32 Social phobia 33-34 Specific phobia 35 Obsessive compulsive 36-37 Post traumatic stress 38-39 Generalized anxiety 40 Anxiety disorder NOS 41-42 Panic disorder 43 Body dysmorphic current 44 Anorexia or Bulimia nervosa 45 Global assessment of function 46-47 Main study diagnosis 48 Severity of illness 49 Chronic or double depression 50 Total HAMA score 51 HAMA Sleep disturbance factor 52 HAMA Psychic Anxiety Score 53 HAMA Somatic Anxiety Score 54 Total HAMD-24 score 55 Total HAMD-17 score 56 HAMD Cognitive Disturbance 57 HAMD Retardation Score 58 HAMD Anxiety/Somatic symptom 59 IDSSR Total Score 60 IDSSR Anxious depression type 61 IDSSR General/Mood Cognition 62 IDSSR Anxiety/Arousal Score 63-64 IDSSR Sleep scores Qualitative Interaction 0.4 0.8 R 0.4 A=0 We combine Dj and Pj to make a score, Uj for each variable. The scores, U, can be used to rank the variables. Non-qualitative Interaction 0.4 0.8 R 0.4 0.0 0.0 2 out of 7 subjects would change choice of optimal treatment given Xj Xj What is a qualitative interaction? A=0 A=1=a* 0.4 R Predictive selection techniques have been proposed, but are only part of the puzzle. We need variables that help determine the optimal treatment for each patient, variables that qualitatively interact with the treatment. 0 We estimate the proportion factor by: Pj = percentage of patients in the sample whose optimal treatment changes when variable Xj is added to the fitted model For example, see plot below. 0.8 Reasons for variable selection in decision making: ● limited resources ● better interpretability ● improved performance A=1 0.8 Xj Goal: discover optimal treatment for any future patient No Interaction 0.4 Dj = max effect – min effect 0.00 assigned treatment 0.0 maximum effect of treatment a* on R New Method U % of time chosen A A=0 0.0 X baseline variables such as patient’s background, medical history, current symptoms, etc. 0.4 Example: clinical trial to test two alternative drug treatments A=1=a* 0.0 minimum effect of treatment a* on R R Goal: find the policy which results in the highest average response % of time chosen Standard Method Variable % Chosen Standard Method Method U 21 0 11 1 2,13 0,1 2 1 9 0 2 0 23 0 16 0 16 1 10 0 38 0 5 0 16,22,14 0,0,0 14 2 19,18 1,1 9,3 0,1 15,20 0,0 8 0 4 0 23 0 1 0 28,46 12,17 1 0 11,28 2,3 3,32 0,6 51 0 9,2 0,0 28,15 0,0 26 0 26,27 0,0 8 0 22 3 5 0 5,8 0,0 1 0 6 0 3 2 3 0 3 1 34 14 4 1 4 0 10 0 2 0 1 0 2 0 5 0 5 4 0 3 10,3 0,0 0.0 0.4 0.8 X3 X qualitatively interacts with the treatment if at least two subsets of X values result in different optimal treatments. For a complete variable selection method using this new ranking procedure, we suggest the following algorithm which we call New Method U: 1. Select important predictors of R in X using a predictive variable selection method 2. Rank the variables in X using score U; select the top k in rank 3. Use a predictive variable selection method to select from important predictors chosen in step 1, A, and k interactions chosen in step 2 We compare this method versus a standard method: a Lasso of the main effects of X, A and the interactions between X and A Conclusion In this poster, we presented a new technique explicitly designed to select variables for decision making. We demonstrated this method on a depression data set. We found new method U did a better job eliminating interaction variables that are not important for prescribing treatment, which allow clinicians to focus on important variables that can help make treatment more individualized. Acknowledgements: We wish to thank Martin Keller and the investigators of [2] for use of their data, and gratefully acknowledge Bristol-Myers Squibb for helping fund the study. We also acknowledge financial support from NIH grants R21 DA019800, K02 DA15674, P50 DA10075, and NSF grant DMS 0505432 and technical support from A. John Rush, MD, University of Texas Southwestern. References: (1) Keller, M.B., McCullough, J.P., Klein, D.N.et al.: A Comparison of Nefazodone, the Cognitive Behavioral-analysis System of Psychotherapy, and Their Combination for Treatment of Chronic Depression. N. Engl. J. Med. 342 (2000) 331-366 (2) Gunter, L., Murphy, S.A., Zhu, J.: Variable Selection for Optimal Decision Making. Technical Report 463, University of Michigan Statistics Department