Stat 532 Presentation - ualberta.cakcarrier/STAT532/JM.pdf · Time-Dependent Variables. Springer: New York, USA • Hosmer & Lemeshow 1999. Applied Survival Analysis: Regression modeling

Time-dependent variables

Stat 532 Presentation

JM Gamble, BSc, BSc(Pharm), MSc

Outline

1.  A Historical example

2.  Definitions and theory

3.  A scientific question: bisphosphonates and pneumonia-related adverse events

A Historical example

1.  Do Oscar winner’s live longer?

A Historical example

•  28% (95% CI: 10% - 42%) relative reduction in death rates between Oscar winners and less successful performers

•  4 year survival advantage

•  20% (95% CI: 0% - 35%) relative reduction using time-dependent variable

•  Data has been re-analyzed extensively

•  Debate on the best analytical approach

A Historical example

Oscar Winner

No Award

death or censored

Birth

death or censored

Date of Award

A Historical example

  Subjects must remain event free until the start of exposure to be classified as exposed

Received transplant

Did not receive transplant

death

Accepted for transplant

Cohort exit; death or censored

transplant

A Historical example

exposed

unexposed death

Cohort exit exposure.( i.e. first drug use)

Cohort entry (i.e. diagnosis)

Cohort entry (i.e. diagnosis)

Adapted from figure 1. Suissa S. Pharmacoepidemiology & Drug Safety 2007;16:241-249.

Definitions & Theory

Time-dependent:

•  Value of variable differs over time

Time-independent:

•  Value of variable is constant over time

Definitions & Theory

Cox PH model

Extended Cox PH model

Hazard Ratio

Definitions & Theory

A. Defined time-dependent variable

•  Commonly a product of a time-independent variable and time (or some function of time)

•  Values are completely defined over study period

•  Sex x time

•  Baseline drug level x exp(-0.35 x time)

•  Exposure x g(t) where g(t) is a heavy-side function

Types of Time-dependent variables:

Definitions & Theory

B. Internal

•  Values may change over time due to subject specific characteristics

•  Subject must be under periodic observation

•  Physiological status

•  Drug treatment

Types of Time-dependent variables:

Definitions & Theory

C.  External

•  May or may not be subject specific

•  Subject not required to be under observation

•  Environmental factor (i.e. air pollution)

•  Age

•  time

Types of Time-dependent variables:

Definitions & Theory

•  The hazard at time t depends on the value of Xj(t) at the same time … not an earlier or later time –  May account for lag-time effect if

appropriate

•  Reason for change in value of time-dependent variable (i.e. treatment switching) must be unrelated to risk of the outcome event

Some key assumptions of the Cox PH model using a time-dependent variable:

Research question

In patients admitted to the hospital with community-acquired pneumonia, does exposure to a bisphosphonate decrease the risk of pneumonia-related mortality or hospitalization?

Background

•  Bisphosphonates –  Class of medications used to prevent

fractures •  Signal from RCT data

–  Colón-Emeric et al. Potential Mediators of the Mortality Reduction with Zoledronic Acid After Hip Fracture. J Bone Miner Res (2009) online early.

–  Decreased the relative risk of death by 25% (95% CI: 0.58-0.97)

–  Found a statistically significant decrease in pneumonia-related death (p=0.04).

Study Design

Time 0

Cohort design: time-varying drug exposure

Statistical analysis

•  Cox Proportional hazards model •  Primary predictor/explanatory/exposure

variable –  bisphosphonate use

•  Dichotomous variable (coded as 1 for exposed) •  Time-dependent •  Heavy-sided form

•  Primary outcome variable –  Composite of pneumonia-related mortality and

hospitalizations

•  Other covariates included in the model based on scientific/clinical rationale

Cox PH model

pneum_comp: composite outcome of CAP-related death and CAP-related hospitalization

Ebisp: time-dependent bisphosphonate exposure (0=no exposure; 1= exposed)

age: age in years at date of presentation sex: male=0; female=1 Functional_Status: 0=walking with/without

assistance; 1=wheelchair/prosthesis; 2=bedridden

Risk_class_combined: Pneumonia severity index; categories 1 through 4 indicated more severe pneumonia.

Variables in the model:

Results

Cohort Selection:

•  3415 subjects admitted for community-acquired pneumonia

–  27 subjects excluded due to prior bisphosphonate exposure

–  131 subjects dropped due to unable to link to long-term outcomes

•  N=3257 subjects available for analysis

Results Cohort Characteristics Variable Bisphosphonate

N= 200 No Bisphosphonate

N=3057

Age, years (mean, sd) 75 (9) 68 (18)

Age, n(%) < 45 yrs 45 – 64 yrs ≥ 65 yrs

0 (0) 27 (14)

173 (87)

426 (14) 648 (21) 648 (21)

Female, n(%) 145 (73) 1391 (46)

Functional Status, n(%) Walking Wheelchair/prosthesis Bedridden

193 (97) 3 (2) 4 (2)

2711 (89) 223 (7) 123 (4)

Risk Class, n(%) Class I/II Class III Class IV Class V

24 (12) 58 (29) 94 (47) 24 (12)

591 (19) 546 (18)

1200 (39) 720 (24)

Results Descriptive results

Results Descriptive results

Results Descriptive results

Setting up data for survival analysis:

Data structure

Setting up exposure variable as time-dependent:

. replace bisph_date1=mdy(4,1,2006)+1 if bisph_date1==.

. stsplit Ebisp, after(time=bisph_date1) at(0)

. replace Ebisp=Ebisp+1

Setting up data for survival analysis:

Data structure

Results: crude HR

Results - aHR

Results: time-independent exposure

Results

Conclusion

•  Bisphosphonates do not appear to decrease

the risk of pneumonia-related death or

hospitalizations.

References

•  Kleinbaum & Klein 2005. Survival Analysis: A Self-Learning Text. 2nd Edition. Chapter IV: The Extended Cox Model for Time-Dependent Variables. Springer: New York, USA

•  Hosmer & Lemeshow 1999. Applied Survival Analysis: Regression modeling of time to event data. Chapter 7: Extensions of the Proportional Hazards Model. John Wiley & Sons: New York, USA.

•  Kalbfleisch & Prentice 2002. The Statistical Analysis of Failure Time Data. Second Edition. Chapter 6: Likelihood Construction and Further Results. John Wiley & Sons: New Jersey, USA.

•  Cleves, Gould, & Gutierrez. An Introduction to Survival Analysis Using Stata. Revised Edition. Stata Press: Texas, USA.