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Relationship between Bisphosphonate (BP) Treatment and General Infection & Osteonecrosis of the Jaw:
Findings from Marginal Structural Models
Trevor McMullan
Background
• Bisphosphonates (BP) maintain bone strength• BP are most commonly prescribed meds for
osteoporosis• BP treatment has been associated with
Osteonecrosis of the Jaw (ONJ) • Infection is suggested to play a pivotal role in
the pathogenesis of ONJ• Reported BP incidence rates; 8799 (Infection)
and 1 (ONJ) per 100000 subject years
Objective
• To develop causal relationships between osteoporotic meds including BP and their risk factors General Infection and ONJ using observational claims data
• Need to address; confounding by indication and informative censoring bias
• Observational data is unblinded, contains selection bias and time dependent confounding
Time Dependent Confounding
Fragility Fracture
OsteoporosisTreatment 1
OsteoporosisTreatment 2
Infections or ONJ
Data & Study Population• Marketscan commercial claims database• Meds, diagnoses, procedures, in/out patient• Data from 1st Jan 2004 to 30th June 2011• N=469432 subjects; 1050567 subject years of data
• Postmenopausal women with osteoporosis• Age > 55 years• dx osteoporosis, osteo fracture or osteo med• ≥ 12 months of continuous enrollment
Data:
Study Population Inclusion Criteria (PMO Index date):
Baseline Demographic & Subject Characteristics Table
Covariate BP (Ptyrs=464728) Other OP (Ptyrs=67860) No Treat (Ptyrs=517979)
% % %
Age (55-64 yrs) 51.6 52.5 42.2
(>= 65 yrs) 48.4 47.5 57.8
Diabetes Type II 12.8 13.2 19.1
Fragility fracture 3.7 5.5 15.5
Serious infection 4.2 5.0 5.4
CCI (mean,std) 0.5 (0.8) 0.5 (1.0) 0.6 (1.0)
Corticosteroids 26.3 27.0 22.2
Immunosuppresants 1.1 0.9 0.8
No physician visits (mean, std)
7.2 (6.1) 7.7 (6.6) 7.5 (6.4)
CCI=Charlson Comorbidity Index
Exposure & Endpoint(s)
• Treatment accessed via drug/procedure codes• 3 Cohorts; BP, Other Osteo Meds, No treat• Treat duration: Days supplied + 60 days
• Followed from inclusion criteria until disenrollment, dx/trt malignancy/Paget’s disease, end of study period, ONJ or general infection event
Exposure:
Endpoint(s): Time to Event
Covariates
• Time fixed (baseline) and time varying covars• Time fixed: demographics, prior BP use,
healthcare utilization• Time varying: comorbidities, concomitant
meds, risk factors for ONJ or general infection• Chronic diseases (diabetes) once identified,
where carried forward throughout the study period
Visit Window (Data Organization)Unstructured Visit Record Window
X
Time varying covariates: 6 months
Time axis
t t1 t2 t3 t4 t5
Time fixed covariates: 12 months
Data record at time t is activated by a treatment switch, ONJ/infection event, or censoring, time dep var status fragility fracture updated at each new rec,time at risk defined as days supplied + 60 days (on-treatment)
Time at risk
Data Structure: 1 Hypothetical SubjectId Base-
lineDate
Treat-ment
SwitchDate
Cohort Time(t)
Days
Event Base-line
Covars
Time VaryingCovars
BPProb
Other OsteoProb
NoOsteoTreatProb
1 3Jun10 3Jun05 BP 456 0 x y1 0.42 0.30 0.28
1 3Jun10 1Sep06 Other 123 0 x y2 0.30 0.44 0.26
1 3Jun10 1Jan07 No Trt 702 0 x y3 0.40 0.30 0.30
1 3Jun10 2Dec08 Other 151 1 x y4 0.50 0.25 0.25
x, y1,y2,y3,y4 are vectors of covariatesy1,y2,y3,y4 change over timeLOCF used if data value is missing for a time varying covariate1=Event, 0=censored
Statistical Analysis: MSM model
• IPTW regression models with time dep vars• Treatment weights: multinominal regression• Censoring weights: logistic regression• Wghts inverse cond Prob of obersved treat cat• Subj with high predicted prob: lower weight• Subj with low predicted prob: higher weight• Stabilized weights and truncation introduced to control extreme weights
Stage 1:
Statistical Analysis: MSM Weights
𝑠𝑤𝑖 (𝑡 )=∏𝑘=0
𝑖𝑛𝑡 (𝑡 ) 𝑝𝑟 (𝐴 (𝑘 )=𝑎𝑖(𝑘)∨𝐴 (𝑘−1 )=𝑎𝑖 (𝑘−1 ) ,𝑉=𝑣 𝑖)𝑝𝑟 ( 𝐴 (𝑘 )=𝑎𝑖 (𝑘)∨𝐴 (𝑘−1 )=𝑎𝑖 (𝑘−1 ) ,𝐿 (𝑘 )=𝑙𝑖(𝑘))
𝑠𝑤𝑖∗ (𝑡 )=∏
𝑘=0
𝑖𝑛𝑡 (𝑡 ) 𝑝𝑟 (𝐶 (𝑘 )=0∨𝐶 (𝑘−1 )=0 , 𝐴 (𝑘−1 )=𝑎𝑖 (𝑘−1 ) ,𝑉=𝑣 𝑖)𝑝𝑟 ¿¿
¿
Treatment stabilized weights: Multinominal logistic regression model
Censoring stabilized weights: Logistic regression model
=Treatment =Treatment history =Time fixed covariates =censoring =Time Varying covariate history (includes Time Fixed covars) =Censoring history
Statistical Analysis: MSM Cox model
(t|V) =
Where:
(t|V) is the hazard of ONJ or General infection at time t among subjectswith baseline covariates V in the source population had, contrary to fact, all subjects followed each treatment cohort history through time t
the scalar and row vector are unknown parameters
is an unspecified baseline hazard
Need to account for within subject correlation: Robust Sandwich Covariance Estimator
Weight and MSM models use different time axes
Stage 2:
General Infection Results TableTreatment Number
of PtyrsNumber of Cases
Multivariate Cox Reg Model I
Multivariate Cox Reg Model II MSM:Model III
No Osteo Treatment
330429 78634 1 1 1
BP 335976 82963 1.11 (1.10, 1.13) 1.08 (1.06, 1.09) 0.84 (0.83, 0.85)
Other OP Meds
47433 12882 1.17 (1.14, 1.19) 1.13 (1.11, 1.15) 0.92 (0.90, 0.93)
Model I: Unweighed Cox model with time fixed covariatesModel II: Unweighted Cox model with time fixed and time varying covariatesModel III: IPTW weighed Cox model with time fixed and time varying covariates
Time fixed covars: demographics, healthcare utilizationTime varying covars: risk factors for general infection (hiv,lupus,diabetes etc.), comorbidity status, select concomitant medications, malnutrition, obesity, fragility fracture, etc.
ONJ Results TableTreatment Number
of PtyrsNumber of Cases
Multivariate Cox Reg Model I
Multivariate Cox Reg Model II MSM
No Osteo Treatment
515903 108 1 1 1
BP 465060 99 1.04 (0.73, 1.48) 1.03 (0.69, 1.53) 0.94 (0.64, 1.37)
Other OP Meds
67683 8 0.56 (0.26 1.17) 0.55 (0.26, 1.18) 0.58 (0.27, 1.22)
Model I: Unweighed Cox model with time fixed covariatesModel II: Unweighted Cox model with time fixed and time varying covariatesModel III: IPTW weighed Cox model with time fixed and time varying covariates
Time fixed covars: demographics, healthcare utilizationTime varying covars: risk factors for ONJ (age, gingival bleeding, dental fistula, diabetes etc.), comorbidity status, select concomitant medications, fragility fracture, etc.
MSM Assumptions
• No unmeasured confounders
• Positivity
• Model mis-specification
• Weight Truncation
Claims data does not collect all variables that may impact treatment and outcome, For instance, bone mineral density (BMD)
All modeled covariates should have a +ve probability for outcome category
The correct model is selected for determining the IPTWs such as using amultinominal logistic regression model and not an ordinal logistic regressionmodel when treatments > 2 and are not ordinal
Trade-off between control of confounding and precision of MSM weight estimates
Conclusion & Other Approaches
• Unweighted Cox models indicated an increased risk of general infection for subjects on BP and other OP meds
• Adjusting for time varying confounding covariates such as fragility fracture using inverse probability of treatment weights indicated a reduced risk of general infection for BP and other OP med subjects
• ONJ results were inconclusive due to their low occurrence rate
• IPTW Kaplan Meier curves are another possible way to conduct this statistical analysis
ReferencesHernan MA, Brumback B & Robins JM Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-Positive Men. Epidemiology 2000;11(5): 561-570Westreich D et al. Time Scale and Adjusted Survival Curves for Marginal Structural Cox Models. Practice of Epidemiology 2010;171(6): 691-700Wang O, Kilpatrick RD et al. Relationship between Epoetin Alfa Dose and Mortality: Findings from a Marginal Structural Model. Clin J Am Soc Nephrol. 2010; 5: 182-188Xue F, Tchetgen Tchetgen E, McMullan T et al. Marginal Structural Model to Estimate the Effect of Cumulative Osteoporosis Medication on Infection and Potential Osteonecrosis of the Jaw (ONJ) Using Claims Data (manuscript under progress)Spreeuwenberg MD et al. The Multiple Propensity Score as Control for Bias in the Comparison of More Than Two Treatment Arms. Medical Care 2010; 48(2): 166-174
Additional Slides
Statistical Analysis: Weighed KM
𝑆𝑥 (𝑡 )=∏𝑡
1−𝑑𝑡𝑥
𝑟 𝑡𝑥
𝑑𝑡𝑥=∑𝑖=1
𝑁
𝑊 𝑖𝑡𝑌 𝑖𝑡 (𝑋 𝑖𝑡=𝑥¿)¿
Survivor Function:
where:
= IPTW weighed number of events for treatment x at week t=IPTW weight at time t for subject i= Event indicator with 1=Event 0=No event = Subject risk set at time t for treatment t
Measured & Unmeasured Confounding
Fragility Fracture
OsteoporosisTreatment 1
OsteoporosisTreatment 2
Infections or ONJ
Unmeasured Confounders
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