The 4th International Meeting on Methodological Issues In Oral Health Research, Istanbul , Turkey 21-23 April 2010

1. Statistical Analysis of Clustered Binary Response in
Oral Health Research
Ronen Ofec*, DMD ; David M. Steinberg, PhD ; Devorah Schwartz-Arad, DND, PhD
* M.Sc. program in Biostatistics, School of Mathematical sciences, Tel-Aviv university
* Praviate dental practice, Tel-Aviv, Israel
The 4th International Meeting on Methodological Issues In Oral Health Research,
Istanbul , Turkey

2. Dental implants treatment

3. Dental implants treatment

4. Dental implants treatment

5. Dental implants treatment

6. Dental implants treatment

7. Dental implants treatment

8. Dental implants treatment

9. Dental implants treatment

10. Dental implants treatment

11. The durability of
Dental implants treatment
 Failures (removal of an implant) do occur
 Marginal bone loss (MBL) can be an early sign for a failure
 MBL: The amount of bone an implant loses during function time

12. Marginal bone loss (MBL)
Fransson et al.(2005)
 What are the risk factors for MBL?
 Are some patients more prone to MBL?
 Are implants within patients correlated to each other?

13. Marginal bone loss (MBL)
Fransson et al.(2005)
 What are the risk factors for MBL?
 Are some patients more prone to MBL?
 Are implants within patients correlated to each other?

14. Marginal bone loss (MBL)
Fransson et al.(2005)
 What are the risk factors for MBL?
 Are some patients more prone to MBL?
 Are implants within patients correlated to each other?

15. Main question of interest and
Objectives of the study
What will be the consequences of a naïve analysis
that doesn't recognize correlation within a patient?
1 To identify risk factors for MBL in a long term follow up study
2 To estimate the Intra patient correlation with regard to MBL
To compare results from a naïve analysis to one that
3 includes intra patient correlation

16. Main question of interest and
Objectives of the study
What will be the consequences of a naïve analysis
that doesn't recognize correlation within a patient?
1 To identify risk factors for MBL in a long term follow up study
2 To estimate the Intra patient correlation with regard to MBL
To compare results from a naïve analysis to one that
3 includes intra patient correlation

17. Main question of interest and
Objectives of the study
What will be the consequences of a naïve analysis
that doesn't recognize correlation within a patient?
1 To identify risk factors for MBL in a long term follow up study
2 To estimate the Intra patient correlation with regard to MBL
To compare results from a naïve analysis to one that
3 includes intra patient correlation

18. Main question of interest and
Objectives of the study
What will be the consequences of a naïve analysis
that doesn't recognize correlation within a patient?
1 To identify risk factors for MBL in a long term follow up study
2 To estimate the Intra patient correlation with regard to MBL
To compare results from a naïve analysis to one that
3 includes intra patient correlation

19. Study design and participants
 Historical prospective cohort study design
 Schwartz-Arad Surgical center, between January
1996, and July 1998 by a single surgeon (DSA)
 Follow-up time was up to 147 months with a mean
of 70 months

20. The exposures,
Binary response and data set
 The exposures: Patient-specific and implant-specific
 Clustered response: MBL measurement at implant level
 Binary response: Acceptable vs. advanced bone loss
 Cut point at MBL=0.2 mm/year
 The data set: Multilevel data set
 195 Patients as the primary sample units (clusters)
 721 Implants as the Elementary units
 No. of implants per patient [1,16], mode=3

21. The Intra Patient Correlation
1 Way Random Effect ANOVA
Patient effect
Implant effect
Patient and implant effect
are independent
The Intra Class Correlation (ICC)

22. The estimator and the estimate
for ICC
 Kappa type estimator proposed by Fleiss and Cuzick (1979)
 Confidence Intervals for the estimator formulated
by Zou and Donner (2004)
 Simulation results: empirical coverage is close to nominal
with C.I for the kappa type
 In our study:

23. The Generalized Estimating
Equations (GEE)
 Population average (Marginal) model Liang and Zeger (1986)
1. The mean model:
2. Working variance structure:
3. Working correlation structure:
 The empirical/sandwich estimator for the precision of estimates

24. Robustness of the
Sandwich estimator
 The estimator is robust to misspecification of the variance and
correlation structures
 Our estimates are still valid (consistent) if we use a structure
which is not reflecting reality
 Mancl and Leroux (1996): Gain of precision for the “right”
correlation structure

25. The prevalence of advanced
bone loss by GEE

26. Risk factors for MBL
by GEE
0 *** 0.001 ** 0.01 * 0.05
Exposure Function time<3 years Function time≥3 years
Beta S.E PV. Beta S.E PV.
Smoker 1.44 0.41 ***
Coating (HA &TPS) -2.22 0.76 ** 1.34 0.39 ***
Early spontaneous exposure 0.85 0.29 **
Diameter -1.39 0.40 ***
Interaction between function time and risk factors
 For smoker:
 The odds for MBL for smokers is 4.22 times greater
than for non smokers
 The effect of HA & TPS turns from protective to risk

27. Risk factors for MBL
by GEE
0 *** 0.001 ** 0.01 * 0.05
Exposure Function time<3 years Function time≥3 years
Beta S.E PV. Beta S.E PV.
Smoker 1.44 0.41 ***
Coating (HA &TPS) -2.22 0.76 ** 1.34 0.39 ***
Early spontaneous exposure 0.85 0.29 **
Diameter -1.39 0.40 ***
Interaction between function time and risk factors
 For smoker:
 The odds for MBL for smokers is 4.22 times greater
than for non smokers
 The effect of HA & TPS turns from protective to risk

28. Risk factors for MBL
by GEE
0 *** 0.001 ** 0.01 * 0.05
Exposure Function time<3 years Function time≥3 years
Beta S.E PV. Beta S.E PV.
Smoker 1.44 0.41 ***
Coating (HA &TPS) -2.22 0.76 ** 1.34 0.39 ***
Early spontaneous exposure 0.85 0.29 **
Diameter -1.39 0.40 ***
Interaction between function time and risk factors
 For smoker:
 The odds for MBL for smokers is 4.22 times greater
than for non smokers
 The effect of HA & TPS turns from protective to risk

29. The naïve estimation
and GEE
Function time >= 3 years
Naïve GEE
Exposure Beta S.E PV. Beta S.E PV.
Smoker 1.50 0.29 *** 1.44 0.41 ***
Coating (HA &TPS) 1.31 0.27 *** 1.34 0.39 ***
Early exposure 0.85 0.26 ** 0.85 0.29 **
Diameter -1.57 0.35 *** -1.39 0.40 ***
 Estimates for exposure effects – it is not bad to be naïve
 Correlation doesn’t induce bias to an unbiased estimator
 Standard errors of estimates- a naïve analysis leads to bias
 Underestimation or overestimation of standard errors
 Risk for invalid inference concerning the estimated effect

30. The naïve estimation
and GEE
Function time >= 3 years
Naïve GEE
Exposure Beta S.E PV. Beta S.E PV.
Smoker 1.50 0.29 *** 1.44 0.41 ***
Coating (HA &TPS) 1.31 0.27 *** 1.34 0.39 ***
Early exposure 0.85 0.26 ** 0.85 0.29 **
Diameter -1.57 0.35 *** -1.39 0.40 ***
 Estimates for exposure effects – it is not bad to be naïve
 Correlation doesn’t induce bias to an unbiased estimator
 Standard errors of estimates- a naïve analysis leads to bias
 Underestimation or overestimation of standard errors
 Risk for invalid inference concerning the estimated effect

31. The naïve estimation
and GEE
Function time < 3 years
Naïve GEE
Exposure Beta S.E PV. Beta S.E PV.
Smoker -0.41 0.41 0.32 -0.43 0.43 0.30
Coating (HA &TPS) -2.2 1.09 0.04 -2.2 0.76 **
Early exposure 0.35 0.42 0.40 0.35 0.39 0.35
Diameter -0.63 0.42 0.13 -0.60 0.47 0.21
 Estimates for exposure effects – it is not bad to be naïve
 Correlation doesn’t induce bias to an unbiased estimator
 Standard errors of estimates- a naïve analysis leads to bias
 Underestimation or overestimation of standard errors
 Risk for invalid inference concerning the estimated effect

32. The source of exposures
variation
Source of exposure/treatment variation
Between Within
patient/cluster patient/cluster
 Patient specific exposure: variation between patient
 Similar to treatment effect in Between cluster design
 Implant specific exposure: variation within and between patient
 Might be similar to treatment effect in Within/Between cluster
design
 Depends on the source of variation of Implant specific exposure

33. The Design Effect (Deff)
Between Within
cluster design cluster design
 Deff >1  Deff<1
 Variance inflation factor (VIF)  Variance attenuation factor (VAF)
 Therefore, a naïve analysis is  Therefore, a naïve analysis is
anti-conservative (underestimate) conservative (overestimate)

34. The Design Effect (Deff)
Between Within
cluster design cluster design
 Deff >1  Deff<1
 Variance inflation factor (VIF)  Variance attenuation factor (VAF)
 Therefore, a naïve analysis is  Therefore, a naïve analysis is
anti-conservative (underestimate) conservative (overestimate)

35. The Design Effect (Deff)
Between Within
cluster design cluster design
 Deff >1  Deff<1
 Variance inflation factor (VIF)  Variance attenuation factor (VAF)
 Therefore, a naïve analysis is  Therefore, a naïve analysis is
anti-conservative (underestimate) conservative (overestimate)

36. The answer to the main
question of interest
What will be the consequences of a
naïve analysis that doesn't recognize
correlation within a patient?
 No problem with the estimated effect
 For a patient specific exposure: underestimation of standard
errors
 For an implant specific exposure: underestimation if variance is
from between patients
 But, overestimation if variance of exposure is from within patient
 Mancl, Leroux, DeRouen (2000) recommended to separate the
effect of a site specific exposure, into within and between effect

37. Conclusions
1 Intra patient correlation for advanced MBL exists
2 The effect of some exposures isn’t constant during function time
Ignoring ICC might bias the precision of estimated effect. Simulation
3 studies should confirm the direction of the bias

38. Conclusions
1 Intra patient correlation for advanced MBL exists
2 The effect of some exposures isn’t constant during function time
Ignoring ICC might bias the precision of estimated effect. Simulation
3 studies should confirm the direction of the bias

39. Conclusions
1 Intra patient correlation for advanced MBL exists
2 The effect of some exposures isn’t constant during function time
Ignoring ICC might bias the precision of estimated effect. Simulation
3 studies should confirm the direction of the bias

40. Thanks !
ofec@post.tau.ac.il