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J Dent Res 83(11):859-863, 2004
© 2004 International and American Associations for Dental Research

RESEARCH REPORTS
Clinical

A Comprehensive Index for the Modeling of Smoking History in Periodontal Research

Th. Dietrich1,2,3,4,*, and K. Hoffmann1

1 Dept. of Epidemiology, German Institute of Human Nutrition, Nuthetal, Germany;
2 Dept. of Periodontology and
3 Dept. of Oral Surgery, Charité, Humboldt University of Berlin, Berlin, Germany; and
4 Dept. of Health Policy & Health Services Research, Goldman School of Dental Medicine, Boston University, 715 Albany St., 560 3rd floor, Boston, MA 02118, USA;

* corresponding author, tdietric{at}bu.edu


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Cigarette smoking is both a strong and common risk factor for chronic periodontitis. It is a multi-dimensional exposure that is difficult to model accurately. We propose a new comprehensive smoking index (CSI) that accounts for intensity, duration, and recency of smoking and allows for estimation of the half-life of the smoking effect. Using NHANES III data from 12,623 subjects aged 20+ yrs, we compared the performance of the CSI with that of various conventional approaches using multiple logistic regression models of chronic periodontitis. The estimate of the smoking effect’s half-life was 1.5 yrs (95% CI, 0.5–2.5 yrs). Use of the new index resulted in best model fit and the highest Wald statistic for the smoking effect on chronic periodontitis. The results suggest that use of the CSI may be a more comprehensive, efficient, and parsimonious approach to the modeling of smoking history in periodontal research.

KEY WORDS: chronic periodontitis • confounder • epidemiology • regression models • tobacco smoking


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Cigarette smoking is an established risk factor for chronic periodontitis. Prevalence, extent, and severity of chronic periodontitis have been shown to be much higher in smokers vs. non-smokers, and a dose-response relationship has been established (Tomar and Asma, 2000). The fact that smoking is both a strong and a common risk factor makes it a very important exposure in periodontal research. It is therefore crucial that investigators accurately model the history of cigarette smoking in periodontal research, regardless of whether smoking is the exposure of interest or a confounder. However, this is not straightforward, since smoking is a multi-dimensional phenomenon with many characteristics, such as intensity, duration, and time since cessation.

Usually, the decision on how smoking history should be modeled is a compromise among validity, efficiency, and interpretability. For instance, the use of a dichotomous variable for ‘ever-smoking’ will result in an estimate that is easy to interpret, but most of the variability in smoking history will not be captured. Alternatively, one could include more than a single characteristic (e.g., intensity, duration, time since cessation) as independent variables in a regression model. However, duration, time since cessation, and intensity of smoking inherently interact, and their effects cannot be separated. In addition, regression models that include terms for more than one characteristic of an exposure are prone to multi-colinearity and model instability (Leffondre et al., 2002), and yield estimates that are difficult to interpret or even meaningless (McKnight et al., 1999).

It is therefore desirable to capture various important characteristics of cigarette smoking history in a single, comprehensive variable. Such a comprehensive smoking index (CSI) has been proposed previously for the modeling of smoking history in environmental epidemiology (Hoffmann et al., 2001).

The purpose of the present paper was to evaluate the performance of a single CSI in comparison with conventional approaches to the modeling of smoking history in periodontal research, using data from the Third National Health and Nutrition Examination Survey (NHANES III).


   MATERIALS & METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Data Source
The NHANES III survey was conducted in 2 phases between 1988 and 1994 to study the health and nutritional status of the civilian non-institutionalized US population. The analysis of this public-use database conformed to procedures approved by the Institutional Review Board of the Charité Medical School. The survey was designed as a complex, multi-stage, stratified, clustered sample survey. A detailed description of the survey can be found elsewhere (US Department of Health and Human Services, 1996). Briefly, periodontal measurements were performed at the mesiobuccal and midbuccal sites of all teeth except third molars in 2 randomly selected quadrants. Periodontal probing depths, clinical attachment levels, and bleeding on probing (present/absent) were assessed with a periodontal probe.

Data on Smoking History
Subjects were classified as ‘never smokers’ if they self-reported smoking fewer than 100 cigarettes in their lifetime. For ‘ever smokers’, intensity (in cigarettes per day) and duration (in years), and for ‘former smokers’, time since cessation (= recency, in yrs) were calculated from the subjects’ responses.

Construction of a Comprehensive Smoking Index (CSI)
The CSI is based on the assumption that the effect of smoking on susceptibility to chronic periodontitis is caused by toxins contained in cigarette smoke, and that their common effect over time can be modeled by an exponentially decreasing function. This assumption of an exponential decline of the smoking effect over time has been shown for other smoking-related chronic diseases, specifically coronary heart disease and stroke (Lightwood and Glantz, 1997). It is also a plausible assumption for periodontal disease (Tomar and Asma, 2000). However, it is important to note that a different function may be more appropriate in models of cancer, where a multi-stage pathogenesis is assumed (Flanders et al., 2003).

Then, the cigarettes smoked t years ago have an effect on chronic periodontitis which is proportional to 0.5t/{tau} • n, where n is the number of cigarettes smoked per day, and {tau} is a half-life parameter (in yrs). To allow for the effect of all years of active smoking, we must integrate this term over time.

Thus, the effect of smoking n cigarettes is proportional to:


(1)

where d and c denote duration of smoking (in yrs) and time since cessation of smoking (in yrs), respectively. To account for changes in smoking over time (e.g., multiple relapses after cessation), one can split smoking history into k periods of constant exposure.

The CSI is then represented by:


(2)

with

di
duration of i-th period (in yrs),

ci
time since i-th period (in yrs), and

ni
number of cigarettes/day smoked in i-th period.

The CSI is an increasing function of intensity (n) and duration (d), but a decreasing function of recency (c) (Table 1Go). Clearly, the parameter {tau} will be unknown in various applications. We suggest estimating {tau} by maximizing the model fit or, once established, pre-specifying it using prior knowledge.


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  		Table 1. Comparison of Pack-years and CSI Values for Different Values of Smoking Intensity, Duration, and Recency in Current and Former Smokers
 
Statistical Analysis
Chronic periodontitis was defined as at least 1 site with both attachment loss ≥ 4 mm and a probing depth of ≥ 4 mm (Tomar and Asma, 2000). We constructed multivariate logistic regression models with chronic periodontitis as the dependent variable and age (five-year categories), gender, race/ethnicity (non-Hispanic Whites, non-Hispanic Blacks, Mexican Americans, Others), diabetes, use of oral contraceptives or hormone replacement for females (never, former, current), poverty-income ratio, and bleeding on probing as independent variables. Missing values for poverty-income ratio and female hormone use were coded as such. Adjustments were also made for survey phase and dental examiner.

Then, different smoking variables were added: an indicator for current smoking alone; indicators for former and current smoking; indicators for former smokers and current smokers who smoked ≤ 10, 11–20, 21–30, or > 30 cigarettes per day; an indicator for ever smoking and pack-years of smoking as a continuous variable; indicators for current and former smoking and continuous variables for intensity and duration of smoking; or the continuous CSI as described above. For comparison purposes, variables were also standardized to have a mean of 0 and a standard deviation of 1. We computed Akaike’s information criterion [AIC = –2(log-likelihood) + 2(number of estimated parameters)] to compare the goodness of fit of different models.

To illustrate the potential merit of CSI to model an important confounder, we used gingival bleeding on probing as the exposure of interest.

We estimated the half-life parameter {tau} by maximizing model fit. To produce a 95% confidence for this estimate, we performed bootstrap sampling with repositioning with 1000 replications. To evaluate the effect of the sampling error in estimating {tau}, we conducted a sensitivity analysis by comparing models with CSIs calculated with {tau} within a reasonable range, as suggested by the 95% confidence interval.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
The final analytic sample consisted of 12,623 subjects aged 20+ yrs (Table 2Go).


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  		Table 2. Distribution of Covariates by Chronic Periodontitis Status
 
The half-life parameter {tau} was estimated at 1.5 yrs (95% CI, 0.46 to 2.53 yrs). A quantile plot of CSI by smoking category shows that CSI tends to increase with increasing smoking intensity (FigGo.). Furthermore, there is large variation within the category ‘former smokers’, due to variations in smoking intensity, duration, and recency. In addition, as the graph illustrates, due to variation in smoking duration, there is some overlap between current smoking categories, in particular between lighter smokers (from 0 to 10 and 11 to 20 cigarettes per day). Depending on intensity, duration, and recency, the CSI can yield values that are considerably different from pack-years, a conventional composite smoking measure (Table 1Go). For example, a former smoker with 10 pack-years (20 cigarettes for 10 years) who quit 5 yrs ago can have a CSI of 1.96, while a former smoker with half the cumulative dose (10 cigarettes for 10 yrs) can have a CSI twice as high (3.93) if he quit only 2 yrs ago.



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  		Figure. Smoothed quantile plot of log-transformed CSI for former smokers (solid line) and different categories of current smokers [0–10 cig/day (long dashes), 11–20 cig/day (medium dashes), 21–30 cig/day (short dashes), and > 30 cig/day (dots)].

 
Model fit improves dramatically when an indicator variable for current smoking is added to the model (Table 3Go, AIC = 8785 for model A, AIC = 8633 for model B). Model fit further improves with increasingly finer categories for smoking (AIC = 8627 for model C, AIC = 8599 for model D). With an indicator variable for ‘ever smokers’ and log-transformed pack-years (model E), the model fit is similar to a model with only an indicator for current smoking (model B). With indicators for former and current smokers and log-transformed continuous variables for intensity and duration of smoking, model fit improves to an AIC of 8577 (model F). Modeling smoking history with the CSI gives the best model fit (AIC = 8555, model G) and the highest value of the Wald test statistic.


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  		Table 3. Estimates for Smoking and Bleeding on Probing (BoP) and Akaike’s Information Criterion (AIC) from Multivariate Logistic Regression using Different Approaches to the Modeling of Smoking History
 
When smoking is not taken into account, bleeding on probing is significantly associated with prevalence of chronic periodontitis (OR 3.35, 95% CI 2.56–4.39, model A). When smoking is added to the model, the OR for bleeding increases considerably. The highest OR estimates result from the model using terms for both intensity and duration [4.06 (3.08–5.35), model F], and the CSI model [4.02 (3.05–5.29), model G].

In the sensitivity analysis, varying the half-life parameter {tau} for the calculation of CSI between {tau} = 0.4 and {tau} = 2.6 changed the results only slightly. For {tau} = 0.4, the AIC was 8568, the OR for CSI was 1.40 (95% CI 1.34–1.47), and for gingival bleeding it was 4.04 (3.07–5.32). For {tau} = 2.6, the AIC was 8560, the OR for CSI was 1.41 (95% CI 1.35–1.48), and for gingival bleeding it was 4.00 (3.04–5.27).


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
The effect of smoking on chronic periodontitis risk is multi-dimensional and depends on intensity, duration, and recency (Tomar and Asma, 2000; Schuller and Holst, 2001). Taking these characteristics into account is therefore important, even if smoking is not the primary exposure of interest (Hujoel et al., 2002). Usually, this is accomplished by including several smoking-related parameters into a regression model. However, this approach can create major difficulties in the interpretation of regression coefficients, on the one hand (McKnight et al., 1999), and in fitting the model, on the other (Leffondre et al., 2002). Furthermore, adding more parameters to a model tends to decrease statistical power for parameter estimation and may hamper the validity of the model (Concato et al., 1995; Peduzzi et al., 1995, 1996). The application of a single CSI thus has several advantages over conventional approaches. CSI accounts for several important aspects of smoking history (intensity, duration, and recency) in a highly efficient way, i.e., it incorporates multiple characteristics of exposure into a single variable.

In the present analysis, the problems of interpreting regression coefficients become most obvious in the model with terms for both intensity and duration. The coefficients for former and current smoking become negative, indicating a protective effect of former and current smoking if interpreted naïvely. The models with only mutually exclusive categorical variables do not share these difficulties; however, these 3 models do not account for important smoking-related information like duration and recency of smoking. Pack-years and the model using terms for both intensity and duration account for more characteristics; however, both approaches assume that the effects of intensity and duration are independent. For instance, ‘pack-years’ is a strictly cumulative measure (5 cigarettes per day smoked over 20 yrs are assumed to have the same effect as 20 cigarettes per day smoked over 5 yrs), and the latter model assumes that any given smoking intensity has the same effect, regardless of smoking duration. This assumption is unlikely to hold in most disease conditions. Furthermore, including several variables measuring related phenomena may induce model instability and collinearity (Leffondre et al., 2002).

Using the CSI avoided such problems and yielded the best model fit in our analyses. One may argue that any given value of the CSI may not be readily interpretable by researchers or clinicians, because it is a composite index. However, the same holds true for other indices commonly used in clinical medicine and research that project a multivariate issue on a univariate scale. One example is body mass index, a composite index of body height and weight. Nevertheless, risk assessment by composite indices is important in research and clinical practice, and the use of such indices aids in the identification of proper prevention or treatment/maintenance strategies to individual patients (Lang and Tonetti, 1996; Page et al., 2003). CSI would allow researchers and clinicians to calculate and assign a single value (comparable with body mass index) that comprehensively captures several aspects of an individual’s smoking history and may thus be useful in risk prediction.

Gingival bleeding is associated with chronic periodontitis, and it has been shown that smoking strongly suppresses gingival bleeding on probing (Bergström and Boström, 2001; Dietrich et al., 2004). Hence, smoking should act as a strong negative confounder in an appropriate model. The ‘crude’ OR estimate for gingival bleeding (i.e., not adjusted for smoking) is 3.35 (95% CI 2.56–4.39). As expected, this OR estimate increases when smoking is adjusted for (Table 3Go). However, some adjustments are insufficient and incomplete, resulting in residual confounding.

Residual confounding by smoking is of particular concern in certain applications in periodontal research (Hujoel et al., 2002; Spiekerman et al., 2003). The associations found in epidemiologic studies between periodontal status and risk of various systemic diseases have been ascribed to such confounding. A possible source of residual confounding is the categorization of continuous smoking characteristics such as intensity and duration (Brenner and Blettner, 1997). Therefore, CSI may be an efficient way to improve adjustment for confounding by smoking.

However, the proposed CSI has several limitations. First, it does not include all characteristics of smoking that may be important for disease risk, such as age at which smoking was started, types of cigarettes smoked, and smoking topography (e.g., depth of inhalation). Second, we estimated the half-life parameter {tau} from the sample, which may inflate the type 1 error. To evaluate how much the results of this study depend on the estimated {tau}, we conducted a sensitivity analysis. The results were stable insofar as models run with CSI calculated with {tau} ranging between 0.4 and 2.6 (limits of the 95% confidence interval) still gave better model fit than any other model and similar OR estimates for smoking and gingival bleeding. The true value of {tau} will likely be different for different outcome measures and is of scientific interest in itself. Once this constant is established from longitudinal studies, it can be pre-specified in applications. Third, the CSI does not account for inaccurate self-report and hence does not substitute the use of biomarkers in selected studies (Patrick et al., 1994; Scott et al., 2001). However, there is substantial inter-individual variation in biomarker metabolism that does not necessarily correspond to the smoking effect on disease risk. Furthermore, since the half-life of currently established biomarkers is extremely short, the effect on disease risk among former smokers cannot be quantified. This is one of the potential strengths of the CSI, since it accounts for duration, intensity, and recency in both current and former smokers.

In conclusion, our results suggest that a single CSI that accounts for smoking intensity, duration, and recency may be advantageous over conventional approaches to the modeling of smoking history in periodontal research. Longitudinal studies are needed to evaluate the performance of the CSI in different study designs and populations.


   ACKNOWLEDGMENTS
 
We acknowledge Dr. Raul Garcia and Dr. Martha Nunn for their helpful comments. Both authors were funded by their institutions. This work was supported by NIDCR Grant K24 DE000419.

Received November 5, 2003; Last revision August 11, 2004; Accepted August 23, 2004


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 ABSTRACT
 INTRODUCTION
 MATERIALS & METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
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Brenner H, Blettner M (1997). Controlling for continuous confounders in epidemiologic research. Epidemiology 8:429–434.[ISI][Medline]

Concato J, Peduzzi P, Holford TR, Feinstein AR (1995). Importance of events per independent variable in proportional hazards analysis. I. Background, goals, and general strategy. J Clin Epidemiol 48:1495–1501.[ISI][Medline]

Dietrich T, Bernimoulin J-P, Glynn RJ (2004). The effect of smoking on gingival bleeding. J Periodontol 75:10–16.

Flanders WD, Lally CA, Zhu B-P, Henley SJ, Thun MJ (2003). Lung cancer mortality in relation to age, duration of smoking, and daily cigarette consumption: results from Cancer Prevention Study II. Cancer Res 63:6556–6562.[Abstract/Free Full Text]

Hoffmann K, Krause C, Seifert B (2001). The German Environmental Survey 1990/92 (GerES II): primary predictors of blood cadmium levels in adults. Arch Environ Health 56:374–379.[ISI][Medline]

Hujoel PP, Drangsholt M, Spiekerman C, DeRouen TA (2002). Periodontitis—systemic disease associations in the presence of smoking-causal or coincidental? Periodontol 2000 30:51–60.

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This Article
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