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A Comprehensive Index for the Modeling of Smoking History in Periodontal Research
1 Dept. of Epidemiology, German Institute of Human Nutrition, Nuthetal, Germany; Correspondence: * corresponding author, tdietric{at}bu.edu
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
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).
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
Construction of a Comprehensive Smoking Index (CSI)
Then, the cigarettes smoked t years ago have an effect on chronic periodontitis which is proportional to 0.5t/ Thus, the effect of smoking n cigarettes is proportional to:
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:
with
The CSI is an increasing function of intensity (n) and duration (d), but a decreasing function of recency (c) (Table 1
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 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
The final analytic sample consisted of 12,623 subjects aged 20+ yrs (Table 2  ).
The half-life parameter  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 (Fig.). 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 1 ). 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.
Model fit improves dramatically when an indicator variable for current smoking is added to the model (Table 3 , 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.
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
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 3 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 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.
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 for publication November 5, 2003. Revision received August 11, 2004. Accepted for publication August 23, 2004.
Journal of Dental Research, Vol. 83, No. 11,
859-863 (2004) This article has been cited by other articles:
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ABSTRACT
INTRODUCTION
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. 
