Skip to main content

Advertisement

SpringerLink
Log in

Estimation of a recurrent event gap time distribution: an application to morbidity outcomes following lower extremity fracture in Veterans with spinal cord injury

  • Published:
Health Services and Outcomes Research Methodology Aims and scope Submit manuscript

Abstract

Recurrent event data is frequently encountered in biomedical research. Estimators describing the time to the next event occurrence could be useful information in healthcare settings to deliver targeted, preemptive, patient-specific care. Distribution estimation of recurrence times is varied based on both the underlying assumptions of the estimator (e.g., dependence vs. independence of recurrence times within individual) and estimator construct. In an example among Veterans with spinal cord injury, distributional changes in recurrence times of health complications subsequent lower extremity (LE) fracture are explored. Veterans with LE fracture (cases) were matched to Veterans without LE fracture (controls) on demographic (age, race), level of injury (paraplegia vs. tetraplegia), extent of injury, Veterans Affairs connected service status, and comorbidities using Mahalanobis metric matching. Stratified distributional estimates of recurrence times between successive morbidity outcomes are compared between Veterans with/without LE fracture using three estimators: independent identically distributed product limit estimator, Wang–Chang product limit estimator, and a gamma frailty maximum likelihood estimator. It can be seen that the estimator selection can provide a very different showcasing of a recurrence time distribution. There is a change in the time-to-recurrence of recurrent urinary tract infections and pressure ulcers for fracture cases directly following LE fracture, however testing if this difference is statistically significant remains unclear. Causal inference of gap time analyses in observational data with recurrent events is considered and a call for methods in this area is much warranted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Aalen, O.O.: Nonparametric inference for a family of counting processes. Ann. Statist. 6, 701–726 (1978)

    Article  Google Scholar 

  • Andersen, P.K., Gill, R.: Cox’s regression model for counting processes: a large sample study. Ann. Stat. 1100–1120 (1982)

  • Biering-Sorensen, F., Bohr, H., Schaadt, O.: Bone mineral content of the lumbar spine and lower extremities years after spinal cord lesion. Paraplegia 26, 293–301 (1988)

    Article  CAS  PubMed  Google Scholar 

  • Byar, D., Blackard, C.: Comparisons of placebo, pyridoxine, and topical thiotepa in preventing recurrence of stage I bladder cancer. Urology 10(6), 556–561 (1977)

    Article  CAS  PubMed  Google Scholar 

  • Byrne, D.W., Salzberg, C.A.: Major risk factors for pressure ulcers in the spinal cord disabled: a literature review. Spinal cord 34(5), 255–263 (1996)

    Article  CAS  PubMed  Google Scholar 

  • Carbone, L.D., Chin, A.S., Burns, S.P., Svircev, J.N., Hoenig, H., Heggeness, M., Weaver, F.: Morbidity following lower extremity fractures in men with spinal cord injury. Osteoporos. Int. 24(8), 2261–2267 (2013)

    Article  CAS  PubMed  Google Scholar 

  • Charlson, M.E., Pompei, P., Ales, K.L., MacKenzie, C.R.: A new method of classifying prognostic comorbidity in longitudinal studies: development and validation. J. Chronic Dis. 40(5), 373–383 (1987)

    Article  CAS  PubMed  Google Scholar 

  • Cook, R.J., Lawless, J.F.: The statistical analysis of recurrent events. Springer, New York (2007)

    Google Scholar 

  • Cook, R.J., Lawless, J.F., Lakhal-Chaieb, L., Lee, K.A.: Robust estimation of mean functions and treatment effects for recurrent events under event-dependent censoring and termination: application to skeletal complications in cancer metastatic to bone. JASA. 104(485), 60–75 (2009)

    Article  CAS  Google Scholar 

  • Court-Brown, C.M., Caesar, B.: Epidemiology of adult fractures: a review. Injury 37(8), 691–697 (2006)

    Article  PubMed  Google Scholar 

  • Clement, D.Y., Strawderman, R.L.: Conditional GEE for recurrent event gap times. Biostatistics 10(3), 451–467 (2009)

    Article  PubMed Central  PubMed  Google Scholar 

  • Echigoya, Y., Kato, H.: Postoperative complications after femoral neck fracture in advanced elderly patients. Masui: the. Jpn. J. Anesthesiol. 57(2), 163 (2008)

    Google Scholar 

  • Evans, C.T., Li, K., Burns, S.P., Smith, B., Lee, T.A., Weaver, F.M.: Antibiotic prescribing for acute respiratory infection and subsequent outpatient and hospital utilization in veterans with spinal cord injury and disorder. Phys. Med. Rehabil. 2(2), 101–109 (2010)

    Google Scholar 

  • Feng, W.W., Jun, Y., Xu, R.: A method/macro based on propensity score and Mahalanobis distance to reduce bias in treatment comparison in observational study. SAS PharmaSUG 2006 Conference. http://jansenlex.readyhosting.com/pharmasug/2006/publichealthresearch/pr05.pdf (2006). Accessed 4 Feb 2014

  • Fisher, W.D., Agnelli, G., George, D.J., Kakkar, A.K., Lassen, M.R., Mismetti, P., Mouret, P., Turpie, A.G.: Extended venous thromboembolism prophylaxis in patients undergoing hip fracture surgery–the SAVE-HIP3 study. Bone Joint J. 95(4), 459 (2013)

    Article  PubMed  Google Scholar 

  • Fuhrer, M.J., Garber, S.L., Rintala, D.H., Clearman, R., Hart, K.A.: Pressure ulcers in community-resident persons with spinal cord injury: prevalence and risk factors. Arch. Phys. Med. Rehabil. 74(11), 1172–1177 (1993)

    CAS  PubMed  Google Scholar 

  • Gail, M.H., Santner, T.J., Brown, C.C.: An analysis of comparative carcinogenesis experiments based on multiple times to tumor. Biometrics, 255–266 (1980)

  • Garber, S.L., Rintala, D.H.: Pressure ulcers in veterans with spinal cord injury: a retrospective study. J. Rehibil. Res. Dev. 40(5), 433–442 (2003)

  • Garcia Leoni, M.E., Esclarin De Ruz, A.: Management of urinary tract infection in patients with spinal cord injuries. Clin. Microbiol. Infect. 9(8), 780–785 (2003)

    Article  CAS  PubMed  Google Scholar 

  • Garland, D.E., Stewart, C.A., Adkins, R.H., Hu, S.S., Rosen, C., Liotta, F.J., Weinstein, D.A.: Osteoporosis after spinal cord injury. J. Orthop. Res. 10(3), 371–378 (1992)

    Article  CAS  PubMed  Google Scholar 

  • González, J.R., Fernandez, E., Moreno, V., Ribes, J., Peris, M., Navarro, M., Cambray, M., Borràs, J.M.: Sex differences in hospital readmission among colorectal cancer patients. J. Epidemiol. Community Health 59(6), 506–511 (2005)

    Article  PubMed Central  PubMed  Google Scholar 

  • González, J.R., Peña, E.A., Strawderman, R.L.: survrec: Survival analysis for recurrent event data. R package version 1.2-2, (2012)

  • Griffiths, H.J., Zimmerman, R.E.: The use of photon densitometry to evaluate bone mineral in a group of patients with spinal cord injury. Paraplegia 10, 279–284 (1973)

    Article  CAS  PubMed  Google Scholar 

  • Johnson, E.E., Kay, R.M., Dorey, F.J.: Heterotopic ossification prophylaxis following operative treatment of acetabular fracture. Clin. Orthop. Relat. Res. 305, 88–95 (1994)

    PubMed  Google Scholar 

  • Kadyan, V., Clinchot, D.M., Mitchell, G.L., Colachis, S.C.: Surveillance with duplex ultrasound in traumatic spinal cord injury on initial admission to rehabilitation. J. Spinal Cord Med. 26(3), 231 (2003)

    PubMed  Google Scholar 

  • Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. JASA 53(282), 457–481 (1958)

    Article  Google Scholar 

  • Kleinbaum, D.G., and Klein, M.: Logistic regression for correlated data GEE. In: Logistic regression, pp. 489–538. Springer, New York (2010)

  • Lazo, M.G., Shirazi, P., Sam, M., Giobbie-Hurder, A., Blacconiere, M.J., Muppidi, M.: Osteoporosis and risk of fracture in men with spinal cord injury. Spinal Cord 39(4), 208–214 (2001)

    Article  CAS  PubMed  Google Scholar 

  • Le Moigne, E., Delluc, A., Tromeur, C., Nowak, E., Mottier, D., Lacut, K., Le Gal, G.: Risk of recurrent venous thromboembolism among young women after a first event while exposed to combined oral contraception versus not exposed to: a cohort study. Thromb. Res. 132(1), 51–55 (2013)

    Article  PubMed  Google Scholar 

  • Logan Jr, W.C., Sloane, R., Lyles, K.W., Goldstein, B., Hoenig, H.M.: Incidence of fractures in a cohort of veterans with chronic multiple sclerosis or traumatic spinal cord injury. Arch. Phys. Med. Rehabil. 89(2), 237–243 (2008)

    Article  PubMed  Google Scholar 

  • Merchant, R.A., Lui, K.L., Ismail, N.H., Wong, H.P., Sitoh, Y.Y.: The relationship between postoperative complications and outcomes after hip fracture surgery. Ann. Acad. Med. Singapore 34(2), 163–168 (2005)

    CAS  PubMed  Google Scholar 

  • National Spinal Cord Injury Statistical Center (NSCISC): Spinal Cord Injury Facts and Figures at a Glance. https://www.nscisc.uab.edu/PublicDocuments/fact_figures_docs/Facts%202013.pdf (2013). Accessed 4 Feb 2013

  • Nelson, W.: Theory and applications of hazard plotting for censored failure data. Technometrics 14, 945–966 (1972)

    Article  Google Scholar 

  • Niazi, Z.B., Salzberg, C.A., Byrne, D.W., Vienhbeck, M.: Recurrence of initial pressure ulcer in persons with spinal cord injuries. Adv. Wound Care 10, 38–42 (1997)

    CAS  PubMed  Google Scholar 

  • Nielsen, G., Gill, R., Andersen, P.: Sorensen, T: A Counting Process Approach to Maximum Likelihood Estimation in Frailty Models. Scand. J. Stat. 19, 25–43 (1992)

    Google Scholar 

  • Peña, E.A., Strawderman, R.L., Hollander, M.: Nonparametric estimation with recurrent event data. JASA 96(456), 1299–1315 (2001)

    Article  Google Scholar 

  • Perlin, J.B., Kolodner, R.M., Roswell, R.H.: The Veterans Health Administration: quality, value, accountability, and information as transforming strategies for patient-centered care. Am. J. Manag. Care 10(11 Pt 2), 828–836 (2004)

    PubMed  Google Scholar 

  • Rimler, J.C., Scholz, T., Shbeeb, A., Chua, W., Wirth, G.A., Paydar, K.Z.: The incidence of venous thromboembolism in postoperative plastic and reconstructive surgery patients with chronic spinal cord injury. Plast. Reconstr. Surg. 128(6), 1230–1235 (2011)

    Article  CAS  PubMed  Google Scholar 

  • Rish, B.L., Dilustro, J.F., Salazar, A.M., Schwab, K.A., Brown, H.R.: Spinal cord injury: a 25-year morbidity and mortality study. Mil. Med. 162, 141–148 (1997)

    CAS  PubMed  Google Scholar 

  • Rogers, J.K., Pocock, S.J., McMurray, J.J., Granger, C.B., Michelson, E.L., Östergren, J., Pfeffer, M.A., Solomon, S.D., Swedberg, K., Yusuf, S.: Analysing recurrent hospitalizations in heart failure: a review of statistical methodology, with application to CHARM-Preserved. Eur. J. Heart Fail. 16(1), 33–40 (2014)

    Article  PubMed  Google Scholar 

  • Rosenbaum, P.R., Rubin, D.B.: The central role of the propensity score in observational studies for causal effects. Biometrika 70(1), 41–55 (1983)

    Article  Google Scholar 

  • Sabo, D., Blaich, S., Wenz, W., Hohmann, M., Loew, M., Gerner, H.J.: Osteoporosis in patients with paralysis after spinal cord injury: a cross sectional study in 46 male patients with dual-energy X-ray absorptiometry. Arch. Orthop. Trauma Surg. 121, 75–78 (2001)

    Article  CAS  PubMed  Google Scholar 

  • Scheike, T.H., Petersen, J.H.: Martinussen: retrospective ascertainment of recurrent events: an application to time to pregnancy. JASA 94(447), 713–725 (1999)

    Article  Google Scholar 

  • Silverstein, M.D., Heit, J.A., Mohr, D.N., Petterson, T.M., O’Fallon, W.M., Melton, L.J.: Trends in the incidence of deep vein thrombosis and pulmonary embolism: a 25-year population-based study. Arch. Intern. Med. 158(6), 585–593 (1998)

    Article  CAS  PubMed  Google Scholar 

  • Siroky, M.B.: Pathogenesis of bacteriuria and infection in the spinal cord injured patient. Amer. J. Med. 113(1), 67–79 (2002)

    Article  Google Scholar 

  • Smith, B.M., Evans, C.T., Kurichi, J.E., Weaver, F.M., Patel, N., Burns, S.P.: Acute respiratory tract infection visits of veterans with spinal cord injuries and disorders: rates, trends, and risk factors. J. Spinal Cord Med. 30(4), 355 (2007)

    PubMed Central  PubMed  Google Scholar 

  • Smith, B.M., Evans, C.T., Ullrich, P., Burns, S., Guihan, M., Miskevics, S., LaVela, S.L., Rajan, S., Weaver, F.M.: Using VA data for research in persons with spinal cord injuries and disorders: lessons from SCI QUERI. J. Rehabil. Res. Dev. 47(8), 679–688 (2010)

    Article  PubMed  Google Scholar 

  • St. Andre, J.R., Smith, B.M., Stroupe, K.T., Burns, S.P., Evans, C.T., Ripley, D.C., Li, K., Huo, Z., Hogan, T.P., Weaver, F.M.: A comparison of costs and health care utilization for Veterans with traumatic and nontraumatic spinal cord injury. TSCIR. 16(4), 27–42 (2011)

    Google Scholar 

  • Sumi, M., Tango, T.: Inference on the rate ratio of recurrent events for the matched pairs design. Stat. Med. 29(30), 3186–3193 (2010)

    Article  PubMed  Google Scholar 

  • Trautner, B.W., Darouiche, R.O.: Prevention of urinary tract infection in patients with spinal cord injury. J. Spinal Cord Med. 25(4), 277–283 (2001)

    Google Scholar 

  • Vidal, J., Sarrias, M.: An analysis of the diverse factors concerned with the development of pressure sores in spinal cord injured patients. Paraplegia 29(4), 261–267 (1991)

    Article  CAS  PubMed  Google Scholar 

  • VIReC Research User Guide: FY2002 VHA Medical SAS_ inpatient datasets. Veterans Affairs Information Resource Center, Hines (2003)

    Google Scholar 

  • Viroslav, J., Rosenblatt, R., Tomazevic, S.M.: Respiratory management, survival, and quality of life for high-level traumatic tetraplegics. Respir. Care Clin. N. Am. 2(2), 313–322 (1996)

    CAS  PubMed  Google Scholar 

  • VISTA. Spinal cord injury dysfunction (SCD) user manual. Version 2. Department of Veterans Affairs Software Service Clinical Support Product Line. Washington (2006)

  • Wang, M.C., Chang, S.H.: Nonparametric estimation of a recurrent survival function. JASA 94(445), 146–153 (1999)

    Article  PubMed Central  PubMed  Google Scholar 

  • Weaver, F.M., Smith, B., Evans, C.T., Kurichi, J.E., Patel, N., Kapur, V.K., Burns, S.P.: Outcomes of outpatient visits for acute respiratory illness in veterans with spinal cord injuries and disorders. Am. J. Phys. Med. Rehabil. 85(9), 718–726 (2006)

    Article  PubMed  Google Scholar 

  • Zeger, S.L., Liang, K.Y.: Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42(1), 121–130 (1986)

  • Zhu, T., Martinez, I., Emmerich, J.: Venous thromboembolism risk factors for recurrence. Arterioscler. Thromb. Vasc. Biol. 29(3), 298–310 (2009)

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This work was supported by the Department of Veteran Affairs, Veterans Health Administration, Health Services Research and Development #IIR 08-033. The views expressed in this paper are those of the authors and do not necessarily reflect those of the Department of Veterans Affairs.

Conflict of interest

All authors state that they have no conflicts of interest.

Author information

Authors and Affiliations

  1. Center of Innovation for Complex Chronic Healthcare (CINCCH), Edward Hines, Jr. VA Hospital, 151-H, 5000 South 5th Avenue, Bldg. 1, D318, Hines, IL, 60141-3030, USA

    Lauren Bailey, Frances M. Weaver & Amy S. Chin

  2. Division of Epidemiology and Biostatistics, University of Illinois at Chicago, Chicago, IL, USA

    Lauren Bailey

  3. Stritch School of Medicine, Loyola University, Maywood, IL, USA

    Frances M. Weaver

  4. Charlie Norwood VA Medical Center, Augusta, GA, USA

    Laura D. Carbone

  5. Section of Rheumatology and Adult Allergy, Georgia Regents University, Augusta, GA, USA

    Laura D. Carbone

Authors
  1. Lauren Bailey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frances M. Weaver
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amy S. Chin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Laura D. Carbone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lauren Bailey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bailey, L., Weaver, F.M., Chin, A.S. et al. Estimation of a recurrent event gap time distribution: an application to morbidity outcomes following lower extremity fracture in Veterans with spinal cord injury. Health Serv Outcomes Res Method 15, 1–22 (2015). https://doi.org/10.1007/s10742-014-0128-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10742-014-0128-7

Keywords

Search

Navigation