statistical analysis of clustered binary response in oral health research

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

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

Dental implants treatment

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

What are the risk factors for MBL?

Are some patients more prone to MBL?

Are implants within patients correlated to each other?

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?

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?

Marginal bone loss (MBL)

Fransson et al.(2005)

Main question of interest and Objectives of the study

To identify risk factors for MBL in a long term follow up study

To estimate the Intra patient correlation with regard to MBL

To compare results from a naïve analysis to one that includes intra patient correlation

1

2

3

What will be the consequences of a naïve analysis that doesn't recognize correlation within a patient?

Main question of interest and Objectives of the study

To identify risk factors for MBL in a long term follow up study

To estimate the Intra patient correlation with regard to MBL

To compare results from a naïve analysis to one that includes intra patient correlation

1

2

3

What will be the consequences of a naïve analysis that doesn't recognize correlation within a patient?

Main question of interest and Objectives of the study

To identify risk factors for MBL in a long term follow up study

To estimate the Intra patient correlation with regard to MBL

To compare results from a naïve analysis to one that includes intra patient correlation

1

2

3

What will be the consequences of a naïve analysis that doesn't recognize correlation within a patient?

Main question of interest and Objectives of the study

To identify risk factors for MBL in a long term follow up study

To estimate the Intra patient correlation with regard to MBL

To compare results from a naïve analysis to one that includes intra patient correlation

1

2

3

What will be the consequences of a naïve analysis that doesn't recognize correlation within a patient?

Study design and participants

Historical prospective cohort study design

Schwartz-Arad Surgical center, between January1996, and July 1998 by a single surgeon (DSA)

Follow-up time was up to 147 months with a meanof 70 months

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

1 Way Random Effect ANOVA

Patient effect

Implant effect

Patient and implant effect are independent

The Intra Class Correlation (ICC)

The Intra Patient Correlation

Kappa type estimator proposed by Fleiss and Cuzick (1979)

Confidence Intervals for the estimator formulatedby Zou and Donner (2004)

Simulation results: empirical coverage is close to nominal with C.I for the kappa type

In our study:

The estimator and the estimatefor ICC

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

The Generalized Estimating Equations (GEE)

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

The prevalence of advanced bone loss by GEE

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

Risk factors for MBL by GEE

Function time≥3 yearsFunction time<3 yearsExposure

PV.S.EBetaPV.S.EBeta

***0.411.44Smoker

***0.391.34**0.76-2.22Coating (HA &TPS)

**0.290.85Early spontaneous exposure

***0.40-1.39Diameter

0 *** 0.001 ** 0.01 * 0.05

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

Risk factors for MBL by GEE

Function time≥3 yearsFunction time<3 yearsExposure

PV.S.EBetaPV.S.EBeta

***0.411.44Smoker

***0.391.34**0.76-2.22Coating (HA &TPS)

**0.290.85Early spontaneous exposure

***0.40-1.39Diameter

0 *** 0.001 ** 0.01 * 0.05

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

Risk factors for MBL by GEE

Function time≥3 yearsFunction time<3 yearsExposure

PV.S.EBetaPV.S.EBeta

***0.411.44Smoker

***0.391.34**0.76-2.22Coating (HA &TPS)

**0.290.85Early spontaneous exposure

***0.40-1.39Diameter

0 *** 0.001 ** 0.01 * 0.05

Function time >= 3 years

The naïve estimation and GEE

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

GEENaïve

PV.S.EBetaPV.S.EBetaExposure

***0.411.44***0.291.50Smoker

***0.391.34***0.271.31Coating (HA &TPS)

**0.290.85**0.260.85Early exposure

***0.40-1.39***0.35-1.57Diameter

Function time >= 3 years

The naïve estimation and GEE

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

GEENaïve

PV.S.EBetaPV.S.EBetaExposure

***0.411.44***0.291.50Smoker

***0.391.34***0.271.31Coating (HA &TPS)

**0.290.85**0.260.85Early exposure

***0.40-1.39***0.35-1.57Diameter

GEENaïve

PV.S.EBetaPV.S.EBetaExposure

0.300.43-0.430.320.41-0.41Smoker

**0.76-2.20.041.09-2.2Coating (HA &TPS)

0.350.390.350.400.420.35Early exposure

0.210.47-0.600.130.42-0.63Diameter

The naïve estimation and GEE

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

Function time < 3 years

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

The source of exposures variation

Within

patient/cluster

Between

patient/cluster

Source of exposure/treatment variation

Deff<1

Variance attenuation factor (VAF)

Therefore, a naïve analysis is conservative (overestimate)

Deff >1

Variance inflation factor (VIF)

Therefore, a naïve analysis is anti-conservative (underestimate)

The Design Effect (Deff)

Within

cluster design

Between

cluster design

Deff<1

Variance attenuation factor (VAF)

Therefore, a naïve analysis is conservative (overestimate)

Deff >1

Variance inflation factor (VIF)

Therefore, a naïve analysis is anti-conservative (underestimate)

The Design Effect (Deff)

Within

cluster design

Between

cluster design

Deff >1

Variance inflation factor (VIF)

Therefore, a naïve analysis is anti-conservative (underestimate)

Deff<1

Variance attenuation factor (VAF)

Therefore, a naïve analysis is conservative (overestimate)

The Design Effect (Deff)

Within

cluster design

Between

cluster design

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

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?

Conclusions

Intra patient correlation for advanced MBL exists

The effect of some exposures isn’t constant during function time

Ignoring ICC might bias the precision of estimated effect. Simulation

studies should confirm the direction of the bias

1

2

3

Conclusions

Intra patient correlation for advanced MBL exists

The effect of some exposures isn’t constant during function time

Ignoring ICC might bias the precision of estimated effect. Simulation

studies should confirm the direction of the bias

1

2

3

Conclusions

Intra patient correlation for advanced MBL exists

The effect of some exposures isn’t constant during function time

Ignoring ICC might bias the precision of estimated effect. Simulation

studies should confirm the direction of the bias

1

2

3

Thanks ! ofec@post.tau.ac.il