Applied Multivariable Modeling in Public Health: Use of CART and Logistic Regression to Help Diagnose HIV Infection
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This document discusses using logistic regression and classification and regression tree (CART) analysis to develop models for predicting undiagnosed HIV infection. The models were developed using data from over 10,000 patients. Logistic regression was used to create the Denver HIV Risk Score based on demographics, sexual behaviors, and other risk factors. CART analysis was then used to develop a decision tree to classify patients into risk groups. Both methods showed good ability to predict undiagnosed HIV. Future work includes external validation of the decision tree and comparing screening approaches.
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Applied Multivariable Modeling in Public Health: Use of CART and Logistic Regression to Help Diagnose HIV Infection
- 1. Applied Multivariable Modeling in Public Health Use of CART® and Logistic Regression to Help Diagnose HIV Infection Jason S. Haukoos, MD, MSc Associate Professor & Director of Research Department of Emergency Medicine Denver Health Medical Center University of Colorado School of Medicine Department of Epidemiology Colorado School of Public Health Denver, Colorado Salford Analytics and Data Mining Conference 2012 May 25, 2012
- 2. Supported by an Independent Scientist Award (K02 HS017526) from the Agency for Healthcare Research and Quality
- 4. Awareness in the United States Number with HIV infection 1,200,000 Number unaware of HIV infection 250,000 Annual new infections 56,000
- 6. HIV Epidemic in the U.S. The numbers of people infected with HIV is growing fastest among Racial and ethnic minorities Social and economically disadvantaged These are the same groups that are Under- or uninsured Do not have primary medical care Commonly seek medical care in emergency departments
- 8. Earlier Diagnosis of HIV Infection Benefits both Patient and Public Benefits for the Patient Timely linkage to care Reduced morbidity and mortality due to HAART Reduced at-risk behavior Benefits for the Public Earlier treatment, decreased viral load, decreased transmission Reduced unscheduled medical care and length of inpatient hospitalizations
- 10. Strategies for Uncovering HIV Figure 1. Conceptual model for performing HIV testing in emergency departments. Nontargeted HIV No HIV Screening Testing (“Routine Screening”) Diagnostic Testing Traditional Targeted Enhanced Targeted (Signs or Symptoms) Screening Screening Selection of Selection of Individuals Populations Referral for outpatient Operational Considerations for All Testing Models HIV testing Opt-in versus Opt-out Consent Education versus Counseling Rapid versus Conventional Assay Point-of-Care Testing versus Laboratory-based Testing Result Notification, Reporting, and Linkage of Positives Native versus External Resources Rothman et al. Acad Emerg Med 2007;14:653-657.
- 12. Haukoos. Arch Intern Med 2012;172:20-22.
- 13. Objective To systematically evaluate a large number of characteristics to derive a clinically meaningful and valid prediction tool to accurately categorize patients into risk groups for undiagnosed HIV infection
- 14. Derivation Methods Denver Metro Health STD Clinic, Denver, CO 10,000 annual visits & 0.5% HIV prevalence Consecutive patients from 1/1/1996 – 12/31/2008
- 18. Candidate Variables Demographics Hepatitis B Sexual Practices Age Hepatitis C Vaginal sex Sex Previous HIV Testing Given oral sex Race/ethnicity Ever tested Received oral sex Symptoms Last tested Given anal sex Urethral discharge Sexual History Received anal sex Anal discharge Time since last sex Sexual Contact Anal lesion Number of partners in prior month Male Genital rash Number of new partners prior month Female Genital Itch Number of partners in prior 4 months Sexual orientation Past STIs Number of new partners in prior 4 months Transgender Gonorrhea Number of lifetime partners Transexual Chlamydia Other Risks Contraception HSV Injection drug use (IDU) None Genital warts Sexual contact with prostitute Condom and percent use Scabies Acting as a prostitute Condom rupture/slip off Crabs Sexual contact with IDU Scabies Sexual contact HIV positive Trichomonas Sexual contact HCV positive Epidiymitis Blood transfusion and year Syphilis
- 20. Web Figure 1. 0.012 High 0.010 High Moderate 0.008 Probability of HIV Infection 0.006 Moderate 0.004 0.002 Low 0.000 0 20 40 60 80 100 Age, years
- 21. Variable β (95% CI)‡ Score§ Age <22 or >60 years Ref - 0 22-25 or 55-60 years 0.43 (0.14 – 0.72) +4 26-32 or 47-54 years 1.01 (0.65 – 1.35) +10 33-46 years 1.09 (0.77 – 1.39) +11 Sex Female Ref - 0 Male 2.67 (2.19 – 3.14) +27 Race/Ethnicity Black 0.84 (0.64 – 1.04) +8 Hispanic 0.26 (0.03 – 0.49) +3 Other* 0† - 0 White Ref - 0 Sexual Behaviors Sex with Male 2.10 (1.69 – 2.53) +21 Sex with Female in Past Year -0.60 (-0.18 – -1.00) -6 Sex with HIV-Infected Partner 0.55 (0.33 – 0.77) +6 Type of Sexual Contact Vaginal Intercourse -0.57 (-0.16 – -0.99) -6 Insertive Anal Intercourse -0.26 (-0.02 – -0.51) -3 Receptive Anal Intercourse 0.85 (0.59 – 1.12) +9 Oral Intercourse -0.37 (-0.09 – -0.64) -4 Other Behaviors Injection Drug Use 0.71 (0.43 – 1.01) +7 Prostitution in Past Year 0.70 (0.14 – 1.31) +7 Past HIV Test -0.48 (-0.29 – -0.68) -5 Symptoms History of Syphilis 0.38 (0.00 – 0.83) +4 Rash 0.53 (0.21 – 0.88) +5 Genital Discharge 0.27 (0.10 – 0.45) +3 *Represents American or Alaskan Native, Native Hawaiian, or non-Hawaiian
- 22. Area under the Slope (β) of the R2 of the linear receiver linear regression regression line operating line for the for the calibration characteristics calibration plot plot Model* curve Model 14 0.82 0.88 0.86 Model 15 0.71 0.67 0.85 Model 16 0.78 0.91 0.86 Model 17 0.93 0.78 0.86 Model 18 0.84 0.87 0.86 Model 19 1.05 0.78 0.85 Model 20 0.95 0.94 0.85 Model 21 0.79 0.96 0.85 Model 22† 1.02 0.91 0.85 Model 23 0.91 0.69 0.85 Model 24 1.42 0.82 0.85 Model 25 1.41 0.90 0.85 Calibration plots were graphed using the predicted and observed prevalence of HIV infection in 10 distinct groups categorized using deciles of the predicted prevalence. *See text for descriptions of variables included in each model. † Model 22 was chosen as the final model and includes: age, sex, race/ethnicity, sex with a male, vaginal intercourse, receptive anal intercourse, injection drug use, and past HIV test.
- 23. Denver HIV Risk Score Variable β (95% CI) Score Age <22 or >60 years ref - 0 22-25 or 55-60 years 0.4 (0.3 – 0.8) +4 26-32 or 47-54 years 1.0 (0.7 – 1.3) +10 33-46 years 1.2 (0.9 – 1.5) +12 Gender Female ref - 0 Male 2.1 (1.8 – 2.4) +21 Race/Ethnicity Black 0.9 (0.7 – 1.1) +9 Hispanic 0.3 (0.1 – 0.5) +3 Other* -0.1 (-0.3 – 0.1) 0 White ref - 0 Sexual Practices Sex with a male 2.2 (2.0 – 2.5) +22 Vaginal intercourse -1.0 (-0.8 – -1.2) -10 Receptive anal intercourse 0.8 (0.6 – 1.0) +8 Other Risks Injection drug use 0.9 (0.7 – 1.1) +9 Past HIV test -0.4 (-0.2 – -0.6) -4 *Represents American or Alaskan Native, Native Hawaiian, or non- Hawaiian Pacific Islander. Haukoos et al. Am J Epidemiol 2012;175:838-846.
- 24. 7 Derivation 6 Validation HIV Prevalence, % 5 4 3.59% 3 2 1.59% 1 0.99% 0 0.41% 0.31% <20 20 - 29 30 - 39 40 - 49 >50 _ HIV Risk Score
- 25. A) 18 Derivation 16 Validation 14 Observed HIV Prevalence, % 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 18 Predicted HIV Prevalence, %
- 26. B) Derivation 100 Derivation Validation Sensitivity, % 80 60 Validation 40 Derivation AUC = 0.85 20 (95% CI: 0.83-0.88) Validation AUC = 0.75 (95% CI: 0.70-0.78) 0 0 20 40 60 80 100 1-Specificity, %
- 27. Classification Tree
- 33. Denver HIV Decision Tree Yes 0/1,229 Age <16 or >61 years (0%, 95% CI: 0% - 0.2%) Yes 170/83,444 MSW or Female (0.2%, 95% CI: 0.2% - 0.2%) Yes 334/7,962 MSM or MSB (4.2%, 95% CI: 3.8% - 4.7%)
- 34. Future Directions External validation of the Denver HIV Decision Tree Comparative clinical and cost effectiveness of the different HIV screening approaches
- 35. Conclusions Multivariable analyses have become increasingly important in clinical research Parametric regression techniques have historically been the root for analyzing multivariable problems Specific public health-related research questions lend themselves to both traditional and non-traditional multivariable techniques
- 36. Applied Multivariable Modeling in Public Health Use of CART® and Logistic Regression to Help Diagnose HIV Infection Jason S. Haukoos, MD, MSc Associate Professor & Director of Research Department of Emergency Medicine Denver Health Medical Center University of Colorado School of Medicine Department of Epidemiology Colorado School of Public Health Denver, Colorado Salford Analytics and Data Mining Conference 2012 May 25, 2012