Variable selection and inference in a follow-up study on back pain

Drießlein, David; Küchenhoff, Helmut ; Tutz, Gerhard und Wippert, Pia Maria (31. August 2017): Variable selection and inference in a follow-up study on back pain. Department of Statistics: Technical Reports, Nr. 206

Abstract

The Lasso of Tibshirani (1996) is a useful method for estimation and implicit selection of predictors in a linear regression model, by using a `1-penalty, if the number of observations is not markedly larger than the number of possible pre-dictors. We apply the Lasso to a predictive linear regression model in a study with baseline and follow up measurement for unspecific low back pain with a focus on theselection of psycho sociological predictors. Practitioners want to report measures of uncertainty for estimated regression coeÿcients, i.e. p-values or confidence intervals, where post selection classical t-tests are not valid anymore. In the last few years several approaches for inference in high-dimensional data settings have been devel-oped. We do a selective overview on assigning p-values to Lasso selected variables and analyse two methods in a simulation study using the structure of our data set. We find out that Multi Sample Splitting (Wasserman and Roeder, 2009; Meinshausen et al., 2009) may not be helpful for generating p-values, while the LDPE approach of Zhang and Zhang (2014) produces promising results for type-I-errors and power calculations on single hypotheses. Therefore, we apply the LDPE for the analysis of our back pain study.

• Dokumententyp: Paper
• Keywords: Lasso; Multi Sample Splitting; LDPE; inference; post selection infer-ence, MiSpEx Network
• Fakultät: Mathematik, Informatik und Statistik ; Mathematik, Informatik und Statistik > Statistik > Technische Reports
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• JEL Classification: C 41
• Sprache: Englisch

Literaturliste

Airaksinen, O., Brox, JI., Cedraschi, C., Hildebrandt, J., Klaber-Moffett, J., Kovacs, F., Mannion, AF., Reis, S., Staal, JB., Ursin, H., and Zanoli, G. (2006). Chapter 4. European guidelines for the management of chronic nonspecific low back pain. European Spine Journal, 15, 192–300.

Bartholomew, K. and Horowitz, LM. (1991). Attachment styles among young adults: a test of a four-category model. Journal of Personality and Social Psychology, 61, 226–244.

Bühlmann, P., Meier, L., and van de Geer, S. (2014). Invited discussion on ’a significance test for the lasso (Lockhart, R., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2014)). The Annals of Statistics, 42, 469–477.

Chatterjee, A., and Lahiri, S. (2010). Asymptotic Properties of the Residual Bootstrap for Lasso Estimators. Proceedings of the American Mathematical Society, 138, 4497–4509.

Chatterjee, A., and Lahiri, S. (2011). Bootstrapping Lasso Estimators. Journal of the American Statistical Association, 106, 608–625.

Dezeure, R., Bühlmann, P., Meier, L., and Meinshausen, N. (2015). High-Dimensional Inference: Confidence Intervals, p-Values and R-Software hdi. Statistical Science, 30, 533–558.

Fan, J. and Lv, J. (2010). A Selective Overview of Variable Selection in High Dimensional Feature Space. Statistica Sinica, 20, 101–148. Gesundheitsreport (2014). Risiko Rücken. Veröffentlichungen zum Betrieblichen Gesundheitsmanagement der Techniker Krankenkasse, 29, Hamburg.

Goeman, J. (2010). L1 Penalized Estimation in the Cox Proportional Hazards Model. Biometrical Journal, 52, 70–84.

Groll, A. and Tutz, T. (2014). Variable selection for generalized linear mixed models by L (1)-penalized estimation. Statistics and Computing, 24, 137–154.

Hasenbring. M,, Hallner. D. and Rusu, AC. (2009). Fear-avoidance- and endurancerelated responses to pain: development and validation of the Avoidance-Endurance Questionnaire (AEQ). European Journal of Pain, 13, 620–628.

Hemingway, H., Croft, P., Perel, P., et al. (2013). Prognosis research strategy (PROGRESS) 1: a framework for researching clinical outcomes. BMJ, 346:e5595. Herrmann, C., Buss, U. and Snaith, RP. (1995). Hospital Anxiety and Depression Scale - Deutsche Version (HADS-D). Manual.Hans Huber, Bern.

Hill, JC., Dunn, KM., Lewis, M., et al. (2008). A primary care back pain screening tool: identifying patient subgroups for initial treatment. Arthritis Rheum, 59, 632– 641.

Hill, JC., Vohora, K., Dunn, KM., et al. (2010). Comparing the STarT back screening tools subgroup allocation of individual patients with that of independent clinical experts. Clin J Pain, 26, 783–787.

Hingorani, AD., Windt, DA., Riley, RD., et al. (2013). Prognosis research strategy (PROGRESS) 4: stratified medicine research. BMJ, 346:e5793.

Ibrahim, T., Tleyjeh, IM., and Gabbar, O. (2008).Surgical versus nonsurgical treatment of chronic low back pain: a meta-analysis of randomised trials. Int Orthop, 32, 107–113.

Janwantanakul, P., Sihawong, R., Sitthipornvorakul, E., and Paksaichol, A. (2015). A screening tool for non-specific low back pain with disability in office workers: A 1-year prospective cohort study. BMC Musculoskeletal Disorders, 16:298.

Javanmard, A., and Montanari, A. (2014). Confidence Intervals and Hypothesis Testing for High-Dimensional Regression. The Journal of Machine Learning Research, 15, 2869–2909.

Knight, K., and Fu, W. (2000). Asymptotics for Lasso-Type Estimators. The Annals of Statistics, 28, 1356–1378.

Krampen, G. (1991). Fragebogen zu Kompetenz- und Kontrollberzeugungen (FKK) (Inventory on Competence and Control Beliefs]). Hofgrefe, Göttingen. Lechert, Y., Schroedter, J. and Lüttinger, P. (2006). Die Umsetzung der Bildungsklassifikation CASMIN für die Volkszählung 1970, die Mikrozensus-Zusatzerhebung 1971 und die Mikrozensen 1976 2004. ZUMA-Methodenbericht, Mannheim.

Lentz, TA., Beneciuk, JM., Bialosky, JE., Zeppieri, G.Jr., Dai, Y., Wu, SS., et al. (2016). Development of a yellow flag assessment tool for orthopaedic physical therapists: Results from the optimal screening for prediction of referral and outcome (OSPRO) cohort. The Journal of orthopaedic and sports physical therapy, 46, 327–343.

Lockhart, R., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2014a). A significance test for the lasso. The Annals of Statistics, 42, 413–468.

Lockhart, R., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2014b). Rejoinder: ’A significance test for the lasso’. The Annals of Statistics, 42, 518–531.

Meier, L., Meinshausen, N., and Dezeure, R. (2014). hdi: High-Dimensional Inference. R package.

Meinshausen, N., Meier, L., and Bühlmann, P. (2009). p-Values for High-Dimensional Regression. Journal of the American Statistical Association - Theory and Methods, 104, 1671–1681.

Melloh, M., Roder, C., Elfering, A., Theis, JC., Muller, U., Staub, LP., Aghayev, E., Zweig, T., Barz, T., Kohlmann, T., Wieser, S., Juni, P., and Zwahlen, M. (2008). Differences across health care systems in outcome and cost-utility of surgical and conservative treatment of chronic low back pain: a study protocol. BMC Musculoskelet Disord, 9:81.

Menezes Costa, LC., Maher, CG., Hancock, MJ., McAuley, JH., Herbert, RD., and Costa, LO. (2012). The prognosis of acute and persistent low-back pain: a metaanalysis. CMAJ, 184, E613–E624.

Nicholas, MK:, Linton, SJ., Watson, PJ., and Main, CJ. (2011). Early Identification and Management of Psychological Risk Factors (Yellow Flags) in Patient With Low Back Pain: A Reappraisal. Physical Therapy, 91, 1–17.

Pfingsten, M., Leibing, E., Franz, C., Bansemer, D., Busch, O. and Hildebrandt, J. (1997). Erfassung der fear-avoidance-beliefs bei Patienten mit Rückenschmerzen: Deutsche Version des fear-avoidance-beliefs questionnaire (FABQ-D). Der Schmerz, 11, 387–395.

Pfingsten, M., Nagel, B., Emrich, O., Seemann, H. and Lindena, G. (2007). Deutscher Schmerz-Fragebogen - Handbuch: Deutsche Gesellschaft zum Studium des Schmerzes DGSS.

Riley, RD., Hayden, JA., Steyerberg, EW., et al. (2013). Prognosis Research Strategy (PROGRESS) 2: prognostic factor research. PLoS Med, 10:e1001380.

Schnorpfeil, P., Noll, A., Wirtz, P., Schulze, R., Ehlert, U., Frey, K. and Fischer, JE. (2002). Assessment of exhaustion and related risk factors in employees in the manufacturing industrya cross- sectional study. Int Arch Occup Environ Health, 75, 535–540.

Schultz, IZ., Crook, J., Berkowitz, J., Milner, R., and Meloche, GR. (2005). Predicting return to work after low back injury using the Psychosocial Risk for Occupational Disability Instrument: a validation study. J Occup Rehabil, 15, 365–376.

Schulz, P., Schlotz, W. and Becker, P. (2004). Trierer Inventar zum chronischen Stress (TICS). Hofgrefe, Göttingen.

Schwarzer, R. and Schulz, U. (2000). Berliner Social-Support Skalen. Berlin: Freie Universität, Abteilung für Gesundheitspsychologie.

Statistisches Bundesamt (2010). Krankheitskosten in Mio. Euro für Deutschland. Adhoc- table. http://www. gbe-bund.de, April 30, 2014.

Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society – Series B (Methodological), 58, 267–288.

Traeger, A., Henschke, N., Hubscher, M., Williams, CM., Kamper, SJ., Maher, CG., Moseley, GL., and McAuley, JH. (2015). Development and validation of a screening tool to predict the risk of chronic low back pain in patients presenting with acute low back pain: a study protocol. BMJ open, 5(7):e007916.

Traeger, A., Henschke, N., Hubscher, M., Williams, CM., Kamper, SJ., Maher, CG., Moseley, GL., and McAuley, JH. (2016). Estimating the risk of chronic pain: Development and validation of a prognostic model (PICKUP) for patients with acute low back pain. PLoS medicine, 13(5):e1002019.

Von Korff, M., Ormel, J., Keefe, FJ., and Dworkin, SF. (1992). Grading the severity of chronic pain. Pain, 50, 133–149.

Wasserman, L., and Roeder, K. (2009). High-Dimensional Variable Selection. The Annals of Statistics, 37, 2178–2201.

Wippert, PM., Puschmann, AK., Weiffen, A., Drießlein, D., Arampatzis, A., Banzer, W., Beck, H., Schiltenwolf, M., Schmidt, H., Schneider, C. and Mayer, F. (subm.), Development of a Risk Stratification Index and a Risk Prevention Index for chronic low back pain in primary care. Focus: yellow flags (MiSpEx Network).

Zhang, C. and Zhang, S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. Journal of the Royal Statistical Society – Series B (Methodological), 76, 217–242.