Time Immortal Bias in the analysis of Influenza

Time – Immortal Bias in the analysis of “Influenza and COPD Mortality Protection as Pleiotropic, Dose-dependent effects of statins” by Floyd J, Frost et. al. Chest 2007: 131 (4) 1006 -1012. Contents: 1. 2. 3. 4. Basic concept of time-immortal bias Description of the analysis used in this paper Proper study design – Matched cohort design Statistical Analysis - Cox PH regression with time varying covariate - Poisson regression 5. Simulation using ICU delirium study

Time-immortal bias KM graphs for time to deaths Time-varying (actual data) Time-invarying approach Non-user User 0 Time after enrollment in a cohort Initiation of drug use 0 Time after enrollment in a cohort Bias can be introduced If analyzed as ever / never user or non-user.

Time immortal bias In the time-invarying (ever/never) drug (statin) user or non-user approach, patients who survived longer were followed longer which systematically increases the likelihood of using the drug. They are systematically more likely to live longer. Wrong analysis, but still popular in clinical research.

Examples: (1) the effect of inhaled corticosteroid use on chronic obstructive pulmonary disease (COPD)(4), Suissa S. Am J Respir Crit Care Med. 2003 Time – invarying RR: 0. 73 (95%CI: 0. 57 -0. 93) Time- varying RR: 0. 98 (95%CI: 0. 77 -1. 25) (2) the effect of statin use in reducing mortality among patients with acute coronary syndromes. Laupacis A, Mamdani M. Observational studies of treatment effectiveness: some cautions. Ann Intern Med. 2004 Jun 1; 140(11): 923 -4. Time – invarying OR: 0. 78 (95%CI: 0. 70 – 0. 86) Time - varying NA (3) Do OSCAR winners live longer than less successful peers? A reanalysis of the evidence. Sylvestre MP, Huszti E, Hanley JA. Ann Intern Med. 2006 Time – invarying HR: 23 (95%CI: 8 - 40) Time-varying HR: 15 (-5 - 32) Van Walraven et al. conducted a literature review of nine prominent medical journals between 1998 and 2002 and found that 41% (95% CI = [32%, 50%]) of reported observational studies using survival analyses were susceptible to immortal-time bias.

Two popular methods to deal with time-immortal bias: (1) Proper study design - i. e. , Matched Cohort Method In the analysis of the effect of nosocomial infection on ICU length of stay, controls were matched by number of days spent in the ICU before the onset of the infection corresponding patients with the infection, and remaining days in ICU were used as outcome. Pittet D et. al. (1994) Nosocomial Bloodstream Infection in Critically Ill Patients. JAMA (1994) 271: 1598 -1601 Unbiased but loss of statistical power by matching (2) Through proper regression technique…. . (will talk later)

Description of the study design by Floyd et al. – How did they deal with the time-immortal bias. 1993 Jan Statin-use enrolled Non statin-use 2003 Dec died Cohort definition: Patient identified in the above period with COPD with HMO enrollment > 90 days Exposure – total 90 + days with statin exposure Non-exposure - Pick 3 from the rest of the cohort to each of exposed pt matched on sex, birth year, and HMO enrollment period Event – died at hospital discharge

Description of the analysis by Floyd et al. – How did they deal with the time-immortal bias. Logistic regression was used to compare proportion of death between exposed and non-exposed groups adjusting for the number of days enrolled before ( ) and after statin initiation of the statin-exposed individual ( ). 1993 Jan Statin-use Non statin-use died enrolled Questions: • Are these two time variables, , 0 for non-exposed patients? • Are adjustment of time after the initiation properly control different follow-up time? Are there better models over logistic regression accounting for varying follow-up time? • Are adjustment of time before the initiation of statin proper to control for timeimmortal bias?

Two popular methods to deal with time-immortal bias: Through proper regression techinique…. . (2) Analysis with Statin Use as a time-varying covariate controlling for the onset of delirium. - Cox PH regression with time-varying covariate - Poisson regression

Simulation Study using ICU delirium data (1) Time-invarying Cox: Median 95% CI Time-varying Cox: Median 95% CI Rate of Delirium

Simulation Study using ICU delirium data (2) Linear regression with log transformed outcome Median 95% CI Time-varying Cox Median 95% CI

Simulation Study using ICU delirium data (3) 15 Linear regression with log transformed outcome Adjusting for time to delirium 5 10 Median 95% CI Time-varying Cox Median 0 Exp(beta) for delirium (vs no delirium) 20 ICU Length of Stay 0. 0 0. 2 0. 4 0. 6 Rate of risk factor 0. 8 1. 0 95% CI

Simulation Study using ICU delirium data (4) Poisson regression: Median 95% CI Time-varying Cox: Median 95% CI

Examples: (1) the effect of inhaled corticosteroid use on chronic obstructive pulmonary disease (COPD)(4), Suissa S. Am J Respir Crit Care Med. 2003 Time – invarying RR: 0. 73 (95%CI: 0. 57 -0. 93) Time- varying (Poisson Regression) RR: 0. 98 (95%CI: 0. 77 -1. 25) (2) the effect of statin use in reducing mortality among patients with acute coronary syndromes (6, 7). Laupacis A, Mamdani M. Observational studies of treatment effectiveness: some cautions. Ann Intern Med. 2004 Jun 1; 140(11): 923 -4. Time – invarying OR: 0. 78 (95%CI: 0. 70 – 0. 86) Time - varying NA (3) Do OSCAR winners live longer than less successful peers? A reanalysis of the evidence. Sylvestre MP, Huszti E, Hanley JA. Ann Intern Med. 2006 Time – invarying HR: 23 (95%CI: 8 - 40) Time-varying (Cox with time-varying cov) HR: 15 ((95%CI: -5 - 32) Van Walraven et al. conducted a literature review of nine prominent medical journals between 1998 and 2002 and found that 41% (95% CI = [32%, 50%]) of reported observational studies using survival analyses were susceptible to immortal-time bias.