Longitudinal Investigation of Behavior Change Across Multiple Cancer Risk

There is accumulated evidence to support the efficacy of population-based behavioral interventions, however, our understanding of how and why effective interventions promote behavior change is still lacking. The goal of these two studies was to investigate mechanisms of single and multiple behavior change with a focus on cancer risk behaviors, so as to further our understanding of how effective behavioral interventions can promote successful behavior change; improving public health while reducing healthcare costs. These studies pooled primary data from three large population-based randomized intervention trials that included important cancer-related risk behaviors, including smoking, unhealthy eating, and sun exposure. A total of N=9522 adults across the three samples reported at least one baseline behavioral risk, and were assessed at baseline, 12and 24-months. Two alternative latent variable modeling techniques were applied to examine behavior change within and jointly across the three cancer risk behaviors. Latent growth curve (LGC) modeling approaches were employed in the first study to systematically examine 2-year growth trajectories of observed behavioral outcomes within each risk behavior individually and jointly across pairs of cooccurring behavioral risks. Smoking behavior decreased over time across all participants, with treatment predicting a slightly steeper decrease in the number of cigarettes smoked. Conditional LGC models also supported significant intervention effects on increasing healthy eating and sun protection behaviors over time. Parallelprocess LGC models revealed that growth trajectories were associated across behaviors within pairs of co-occurring risks. The second study applied latent transition analysis techniques to examine transitions through the discrete stages for changing individual cancer-related risk behaviors and to compare stage transition patterns across risk behaviors. Stage transition models supported the stability, progression and regression in behavioral stages over time across all three cancer risks. Conditional stage transition models also provided evidence for intervention efficacy for all three behaviors, in terms of moving at-risk participants to reach behavioral criteria, promoting stage progress among those who did not reach criteria, and in maintaining successful behavior change during the follow-up interval. In addition, findings from the second study revealed the stability of precontemplation stage membership across all three behaviors; stage progress from the precontemplation stage was even less likely among control participants.

including cancer, cardiovascular disease, and diabetes (Fisher et al, 2011). The primary risks for these diseases are common modifiable health risk behaviors. Cancer, cardiovascular disease and diabetes are strongly linked to four health risk behaviors: tobacco use, unhealthy eating, physical inactivity and alcohol use (Fisher et al, 2011).
Improving health behaviors play a central role in disease prevention and health promotion efforts, and effective health behavior change interventions can help to prevent many diseases, promote well-being and reduce healthcare costs.
Although tailored communications are effective, their efficacy can still be improved. For example, the TTM-tailored interventions for smoking cessation have consistently produced 22 to 25% point prevalence abstinence at long term follow-up (Prochaska et al, 1993(Prochaska et al, , 2001a(Prochaska et al, , 2001bVelicer et al, 1999Velicer et al, , 2006aVelicer et al, , 2006b. While these were good results, this also means that almost 75% of treated smokers did not successfully quit. In addition, CTIs targeting risky sun exposure and unhealthy diet behavior have demonstrated efficacy: the proportion of treated participants who had taken effective action at long term follow-up was about 23 to 31% for adopting sun protective behaviors, or 29 to 34% who reached behavioral criteria for reduced dietary fat intake (Prochaska et al., , 2005Weinstock, Rossi, Redding & Maddock, 2002). Given that close to 70% of treated at-risk participants had not successfully reduced their behavioral risks for sun exposure or unhealthy eating, there is similar potential and need to improve on the efficacy of these interventions. Empirically based enhancement of these benchmark programs represents a major challenge and an opportunity in tailored health communications research.
One There are several general analytic approaches that are well-suited to investigate the underlying mechanisms of behavior change, including: 1) latent growth curve modeling (LGCM) (MacCullum, Kim, Malarkey & Kiecolt-Glaser, 1997;McArdle & Epstein, 1987;Meredith & Tisak, 1990), and 2) latent transition analysis (LTA)/latent class analysis (LCA) (Collins & Lanza, 2010;Goodman, 1974). These approaches have the capability to analyze multiple latent variables in longitudinal research designs. They also have the potential to extend to multiple group designs that investigate model invariance across different populations. These analytical capabilities are essential for examining underlying mechanisms.
A number of studies have employed LGCM or LCA/LTA to model the complex trajectories and/or mechanisms of behavior change (e.g. Adams et al, 2009;Brick, 2015;Brick, Babbin & Velicer, 2014;deRuiter, Cairney, Leatherdale & Faulkner, 2014;Evers, Harlow, Redding & LaForge, 1998;Kobayashi, Yin, Redding & Rossi, 2014;Lanza & Collins, 2008;Lanza, Collins, Lemmon & Schafer, 2007;Lanza, Patrick & Maggs, 2010;Richert, Schüz & Schüz, 2013;Roesch et al, 2009;Schumann, John, Rumpf, Hapke & Meyer, 2006;Yin, Rossi, Kobayashi & Redding, 2014a). For example, Martin and colleagues (1996) examined longitudinal stage transitions for smoking cessation over a six month interval using data for 545 current and former smokers. Their best-fitting model suggested progression and regression between adjacent stages as well as two-stage progression. They concluded that movement through the stages was not always linear, that forward movement was more likely to occur than backward movement, and that over the six month interval, moving to adjacent stages was more likely to occur than two-stage progression. In another study, Roesch and colleagues (2009)  The aim of the current research was to investigate mechanisms of single and multiple behavior change across three cancer-related risk behaviors of smoking, unhealthy eating, and sun exposure using two alternative latent variable modeling approaches. In Study 1, we employed LGC modeling approach to examine 2-year growth trajectories for quantitative behavioral outcomes within each individual risk behavior. We tested the effects of TTM-tailored intervention on the rate (slope) of behavior change, as previously reported outcomes include significant increases over time in treatment relative to controls on sun protection and diet behavior (Prochaska et al., , 2005Weinstock, Rossi, Redding & Maddock, 2002). We also modeled growth trajectories jointly within pairs of co-occurring risk behaviors to understand whether the trajectories were associated across behaviors in the pair. In Study 2, we  (Linnan et al., 2002;Prochaska et al., 2004;2005;Velicer et al., 2004). All three randomized trials targeted smoking, unhealthy diet and sun exposure. All trials used common TTM-tailored interventions and no-treatment, assessment-only control groups. Participants in all three trials completed assessments at baseline, 12-, and 24months follow-up. The main effects of stage of change on observed behavioral outcomes were estimated using available data from the baseline assessment, and compared across samples. Examination of the longitudinal changes in behaviors were conducted using all available data from the baseline, 12-, and 24-months assessments combined across intervention and control groups for all three trials.

Participants and Procedure
This study pooled data from three separate population-based intervention trials with adult participants comprising (a) one sample of parents of adolescents (N = 2,460), (b) one sample of patients from an insurance provider list (N = 5,382), and (c) worksite employees (N = 1,906). These samples were population-based and reflect the demographics of the New England region. The samples included slightly more than 50% female, 2-4% Black/African Americans and 2-5% Hispanic, providing adequate demographic heterogeneity for the planned analyses. The subpopulations that were at risk (i.e. that were in the TTM pre-action stages of precontemplation, contemplation, or preparation) on the target behaviors (smoking, unhealthy diet, sun exposure) at baseline were included in the analyses.
Participants were adults who were proactively recruited for each intervention trial as described below. Eligibility included being at risk for at least one of the health risk behaviors targeted for intervention. At-risk status for each individual behavior was defined as being in the precontemplation, contemplation, or preparation stage of change. In each trial, participants were randomized to intervention or control conditions after providing informed consent. Participants randomized to the intervention group received TTM-tailored intervention materials mailed to their homes at baseline, 6-, and 12-months for each risk behavior that they were at risk for (e.g., nonsmokers did not receive any intervention for smoking). They were also provided with a multiple behavior self-help manual based on TTM strategies. Details of the intervention have been reported previously (Linnan et al., 2002;Prochaska et al., 2004;2005;Velicer et al., 2004;Yin et al., 2013  . Patient Sample. A health insurance provider provided a list of patient names for a TTM-tailored intervention study that targeted smoking, unhealthy diet, sun exposure and mammography. Initial screening identified a total of 12,978 potential households, which were contacted by phone. Across the 8,539 patients who agreed to participate, 5,382 were eligible and were enrolled in the trial. One patient was recruited from each eligible household. Assessments were administered for all participants at baseline, 12, and 24 months. The original study outcomes were reported previously (Prochaska et al, 2005).
Employee Sample. The employee sample was part of a multiple risk behavior study that targeted smoking, unhealthy diet, sun exposure and physical inactivity.
Participants were recruited from a total of 22 worksites (Linnan et al., 2002). Across the 2,224 eligible employees, 1,906 individuals agreed to participate, and were then randomized at the individual level. Assessments were administered for all participants at baseline, 12, and 24 months. The original study outcomes were reported previously .

Measures
Background measures were assessed during baseline. The measures included demographics, problem behavior history, screening questions and health history.
Demographic data consisted of age, gender, racial and ethnic group status, marital status, education, and employment status. Preparation, intending to change behavior to meet criteria within the next 30 days; 4.

Stages of Change.
Action, currently meeting behavioral criteria, but for less than 6 months; and 5.
Maintenance, has met behavioral criteria for 6 months or more. To account for seasonal variations in sun exposure, the SOC algorithm for sun protection behavior uses 12 months instead of 6 months as the threshold separating (a) the precontemplation from the contemplation SOC, and (b) the action from the maintenance SOC. Generally, individuals in the pre-Action stages (precontemplation , contemplation, preparation) are considered "at-risk" because they have not yet taken effective action to meet behavioral criteria for reducing the specific health risk. The SOC criteria are unique for each behavior and as much as possible consensus criteria were used (e.g., abstinence for smoking). In measurement development studies, the behavior criteria for stage were always compared against standard measures of the problem behavior. The reliability, utility, and predictive validity of the SOC algorithm have been demonstrated for various behaviors, including smoking cessation, healthy diet, and sun protection (DiClemente et al., 1991;Greene et al., 1999;Hall & Rossi, 2008;Prochaska & DiClemente, 1983;Velicer et al., 2007;Weinstock, Rossi, Redding, Maddock, & Cottrill, 2000). These stages of change have also demonstrated predictable relationships with other important TTM constructs, including Decisional Balance and Self Efficacy (Blissmer et al., 2010;DiClemente et al, 1991;Fava, Velicer & Prochaska, 1995;Hall & Rossi, 2008;Prochaska & Velicer, 1997). Velicer, Martin and Collins (1996) suggested that using SOC as an outcome measure has the advantage of being sensitive to all stage transitions, may increase precision and statistical power, and improve theoretical meaningfulness and interpretability.
In the first study, SOC was used as a grouping variable instead of the primary behavior change outcome. Study 2 examined stage transitions in three cancer risk behaviors of smoking, unhealthy eating, and sun exposure, and focused on the SOC as the primary indicator of behavior change.  Greene et al., 1999;Velicer DiClemente, Prochaska & Brandenberg, 1985;Yin et al., 2014b) developed for each of the behaviors. The DBI measures the relative importance of the positives, benefits, or advantages (pros) of changing and the negatives, costs, or disadvantages (cons) of changing a specific behavior. The DBI assesses the pros and cons of smoking; higher endorsement of the pros of smoking indicates that the perceived benefits of smoking are considered to be more important. For diet and sun behaviors, the DBI assesses the pros and cons of reducing dietary fat and adopting sun protective behavior respectively. A comprehensive meta-analysis of 120 studies including 48 health behaviors found predictable, replicable relationships, named the strong and weak principles of change, between the Pros and the Cons across the stages of change (Hall & Rossi, 2008;Prochaska et al, 1994).
Situational Temptations/Self-efficacy. Situational Temptations/Self-efficacy represents a variation of the self-efficacy construct (Bandura, 1977;1982) and reflects how confident people are that they can maintain the behavior change in challenging situations. Instruments developed to assess situational temptations for smoking and dietary fat reduction and self-efficacy for sun protection behaviors have demonstrated measurement validity and reliability (Babbin et al., 2015;DiClemente, Prochaska & Gibertini, 1985;Velicer, DiClemente, Rossi & Prochaska, 1990;Rossi & Rossi, 1994). The temptations measures for smoking and diet behaviors assess how tempted a person feels to smoke or eat higher-fat foods across different situations, with higher endorsement reflecting a greater degree of temptation. For the self-efficacy scale for sun protection, higher mean scores indicate greater confidence in the ability to protect oneself from sun exposure.

Data Analysis
Behavior change was examined using two complementary longitudinal latent variable modeling techniques. Latent Growth Curve (LGC) modeling was the main analytical procedure employed in Study 1 to examine growth trajectories of quantitative behavioral measures.
LGC models can be fitted as restricted factor models within the structural modeling framework, and are used to estimate within-person change and determinants of between-person differences in key change parameters (McArdle & Epstein, 1987;Meredith & Tisak, 1990). Each set of measured (manifest) indicators was sequentially examined in single behavior analyses, and multiple sets of indicators were then simultaneously examined across co-occurring risk behavior pairs.
In Study 2, Latent Transition Analysis (LTA) was the primary analytical approach employed to examine behavior change modeled as stage transitions for each of the three cancer-related risk behaviors of smoking, unhealthy eating and sun exposure.
LTA are multivariate statistical models in a family of finite mixture models that allow unobserved underlying heterogeneity in outcomes to be modeled as discrete/categorical latent variables (i.e., a latent status/class variable) that are allowed to change over time. These are powerful and flexible analytical tools particularly suited for making large contingency tables interpretable (Goodman, 1974).
Preliminary analyses. The analyses examined the "functional relationships" between measured behavioral outcomes and the stages of change, an approach recommended for measure development and validation (Redding, Maddock & Rossi, 2006). Two-way factorial ANOVA was used to assess any differences in the behavioral scores (e.g. DBQ, SPBI) assessed at baseline across (i) the three baseline stages of precontemplation, contemplation, and preparation, (ii) the samples from different randomized trials, and (iii) any potential interaction between stage and sample. Behavioral scores were expected to show significant main effects for stage and nonsignificant or negligible stage by sample interactions effects.
Study 1: Latent Growth Trajectories. In Study 1, latent growth curve (LGC) models were developed sequentially to examine the two year trajectories of measured smoking, sun protective, and healthy eating behavior over time. Quantitative behavioral outcomes assessed at baseline, 12-and 24-months served as indicators for the growth trajectories for each risk behavior. A series of growth curve models were fitted to estimate the rate of behavior change (slope) and initial level (intercept) for each risk behavior separately. With just three waves of data, only linear models could be estimated, and indicator residual variances were constrained to be equal over time in the growth models. Full-information maximum-likelihood estimation using the lavaan software package (Rosseel, 2012) in the R statistical computing environment was employed for all LGC models, allowing all available data from each participant to be used under the assumption that data was missing at random.
First, unconditional single behavior LGC models ( Figure 1) were developed beginning with fewer estimated parameters, then sequentially increasing model complexity. The fit of the growth curve models to the data was evaluated using multiple fit indices, including the Comparative Fit Index (CFI; Bentler, 1990), the root mean square error of approximation (RMSEA; Browne & Cudeck, 1993), and the nonnormed fit index or Tucker-Lewis index (NNFI/TLI; Tucker & Lewis, 1973). Better model fit is indicated by higher values (closer to 1) for CFI and NNFI, and RMSEA values less than .06 (Bentler, 1990;Hu & Bentler, 1999). The χ 2 is also reported for completeness, although it is known to be very sensitive to sample size (Kline, 2011).
Next, conditional LGC models that included intervention condition as a timeinvariant covariate were evaluated to estimate the effect of treatment on the rate of behavior change (see Figure 2). Effect size d (with 95% confidence intervals) representing the standardized difference in behavioral outcomes were computed to estimate the magnitude of the intervention effect (Feingold, 2009;Raudenbush & Liu, 2001). The TTM constructs Decisional Balance (Pros, Cons) and Situational Temptations/Self-efficacy were then examined as predictors of behavior trajectories.
Baseline mean levels of behavior-specific Pros, Cons, or Situational Temptations/Selfefficacy were included as additional time-invariant covariates, and the coefficients were estimated when the slope factor was regressed on multiple covariates (intervention plus TTM constructs) simultaneously.
Finally, unconditional parallel-process LGC models (see Figure 3) were also developed to estimate trajectories for two behaviors simultaneously within pairs of cooccurring risk behaviors (MacCallum et al, 1997;deRuiter et al, 2014). The parallelprocess growth models were estimated using data drawn from participants at baseline risk for both behaviors in the risk pair. The main parameter of interest in these unconditional parallel-process LGC models was the association (ψ) between the parallel behavior trajectories, especially the covariance between slope factors for each behavior pair. This allowed us to examine multiple behavior change, specifically whether rate of change in one behavior was associated with change in the second behavior within each behavior pair. Next, the stability of the unconditional parallelprocess LGC models for each behavior pair were examined across subsamples defined by intervention condition using multiple sample invariance testing procedures (Hancock, Kuo & Lawrence, 2001;Yin, Rossi, Kobayashi & Redding, 2014).
Parameters of interest were sequentially restricted to be equal across subsamples, starting from the least restrictive model and progressing to more restrictive models.
Model invariance was assessed by examining the deterioration in model fit as additional cross-sample equality constraints were imposed, based on the χ 2 -difference test for nested models. Because the χ 2 statistic is very powerful when sample sizes are large (Kline, 2011), differences in practical fit indices such as the CFI, which is not affected by sample size, were also assessed. Difference values for ∆CFI less than 0.01 have been suggested to be indicative of factorial invariance (Chen, 2007;Cheung & Rensvold, 2002).
Study 2: Behavioral Stage Transitions. In Study 2, latent transition analysis (LTA) was applied to examine patterns of stage transitions between latent status (i.e. behavior stage) subgroups over the two intervals between baseline, 1-, and 2-years.
Because only those participants considered "at-risk" (i.e., baseline SOC was precontemplation, contemplation or preparation) for each behavior were selected, only three behavioral stages are represented in the stage transition models at baseline, although four different stage levels (precontemplation, contemplation, preparation, and action/maintenance) are represented in the models at years 1 and 2 (see Figure 4). indicators were specified to allow the same low level of measurement error over time in the latent transition models (Kaplan, 2008). Full-information maximum-likelihood estimation with robust standard errors via the expectation-maximization algorithm (Dempster, Laird, & Rubin, 1977) in Mplus  was employed for all latent transition models. This maximum-likelihood procedure accounted for data missing at random due to attrition, allowing all available data from each participant to be used to estimate parameters, standard errors, and fit statistics that are robust to non-normality and non-independence of observations. The best fitting model to the data, including the number of transition paths, was determined by comparing alternative nested models (see Figure 4) using several fit criteria and statistics. The

Responses to behavior-specific SOC indicators
Akaike Information Criterion (AIC; Akaike, 1981), Bayesian Information Criterion (BIC; Schwarz, 1978), and the likelihood ratio statistic G 2 that is distributed asymptotically as χ² (Agresti & Yang, 1987) are commonly used for this purpose.
Better model fit is indicated by smaller values of AIC, BIC, and G 2 , and by G 2 values smaller than the model degrees of freedom (Lanza, Flaherty & Collins, 2003). Nested models were also evaluated using the scaled difference likelihood ratio test (∆G 2 ) based on loglikelihood values and scaling correction factors obtained with the robust maximum-likelihood estimator (Asparouhov & Muthen, 2010;Satorra & Bentler, 2001;. All models were estimated several times using random start values to minimize the risk of misspecification due to local maxima. Consistency in estimated parameters indicates that the estimation procedure correctly specified the global maximum. Once the stage transition model with the appropriate number of transition paths that best fit the data was determined for each risk behavior, the stability of the transition parameters over time was assessed. The corresponding stationary model, in which stage transition probability parameters (τ) were constrained to be equal across time intervals, was then estimated for each risk behavior. Because only three behavioral stages (precontemplation, contemplation, and preparation) are represented in the first wave, the equality across time constraints were only specified for stage transition parameters conditioned on those three stages; the transition parameters conditioned on action/maintenance stage from the second to third wave were freely estimated in the stationarity model. The scaled difference likelihood ratio (∆G 2 ) test was used to compare the nested stationary and nonstationary models for each risk behavior.
Next, TTM-intervention condition was included as a time-invariant covariate (TICV) in the best fitting single behavior stage transition model to estimate the effect of treatment on stage transition probabilities (Muthén & Asparouhov, 2011). Finally, if the stage transition models for individual risk behaviors showed similar patterns in terms of the number of stage transition paths, the models were compared across risk behaviors. Comparison of results across different behaviors was generally conducted on an absolute basis.

Participants
The final analytic sample included 9522 participants pooled across three population-based intervention trials who had valid baseline stage of change responses for each of the three cancer risk behaviors of smoking, unhealthy diet, and sun exposure. All available data from each participant was used for model estimation; full information maximum likelihood estimation procedures accounted for data missing at random due to attrition. The characteristics of these participants are presented in Table   1. The majority of participants included in this study were non-Hispanic White women, with mean age 44.6 years (SD = 11.2). Almost half of participants (47.3%) perceived their general health to be "Very good" or "Excellent." Table 2 summarizes the distribution of baseline stage of change for each cancer-related behavioral risk among the participants. A total of 2164 participants (23% of overall sample) reported being current smokers at baseline and were included in the smoking dataset. There were 6729 participants, more than two-thirds (71%) of the overall sample, who were at risk for unhealthy eating at baseline. There were 7065 participants (74%) who were at risk due to sun exposure.

Preliminary Analyses
Means and SDs for three quantitative behavioral measures (number of cigarettes smoked/day, DBQ, and SPBI) assessed at baseline are presented in Tables 3,   4, and 5 respectively. Two-way factorial ANOVAs revealed large effect sizes for stage of change on the quantitative measures of behavior assessed at baseline, with small effects of sample, and negligible Stage X Sample interactions, confirming that expected stage of change effects on measured behavioral outcomes were consistent across samples. This suggests that it was reasonable to pool the data across sample for analyses as in several previous studies (e.g. Paiva et al, 2012;Kobayashi, 2013;Yin et al., 2013). Table 3 shows that the number of cigarettes smoked per day at baseline were significantly higher among participants in the precontemplation and contemplation stages of change, compared to those in preparation to quit smoking, Significant between-stage differences were also found for the DBQ mean score at baseline, F(2, 6642) = 55.36, p < .001, η 2 = 0.016. Follow-up Tukey tests revealed that participants in preparation reported significantly higher DBQ mean scores when compared to those in precontemplation or contemplation at baseline (Table 4). DBQ mean scores were also significantly different across sample, F(2, 6642) = 8.16, p < .001, η 2 = 0.002, with slightly higher mean DBQ scores in the patient sample compared to the employee sample. The effect of stage of change on DBQ mean scores was consistent across samples, F(4, 6642) = 0.39, p = .814.
The SPBI mean scores were significantly different across stage at baseline, F(2,7012) = 2125.05, p < .001, η 2 = 0.377. Table 5 shows that baseline SPBI mean scores were significantly higher in later stages compared to earlier stages. The SPBI mean scores were also slightly higher for the patient sample compared to the employee sample, F(2,7012) = 10.44, p < .001, η 2 = 0.003. A small but significant effect of Stage X Sample interaction was detected, F(4, 7012) = 4.83, p < .01, η 2 = 0.003, although this was more likely an artifact of the large sample size.

Study 1: Behavioral Growth Trajectories
Descriptive statistics for the quantitative behavioral outcome measures at each time point were computed for the LGCM analytic samples for each risk behavior. For smoking, participants were included in the analytic sample if they were in the precontemplation, contemplation or preparation stages, and reported non-zero cigarette counts at baseline. Out of 2164 smokers, 8 had missing baseline cigarette count data, and another 39 reported smoking zero cigarettes, producing an analytic sample of 2117 smokers for LGCM. The distribution of cigarette count data was found to be positively skewed with high kurtosis at each time point (Table 6), so a square root transformation was applied to the data to bring it closer to a normal distribution.
The square root transformed cigarette counts at each time point were then used as indicators in all LGC models for smoking behavior. Table 6 also reveals that the standard deviation for cigarette counts was much larger at 1-and 2-year compared to baseline.
There were 78 participants out of 6729 at risk for unhealthy eating at baseline with insufficient data to compute the baseline DBQ mean score, the remaining 6651 participants comprised the LGCM analytic sample for diet behavior. Table 7 shows that mean DBQ scores appear to be slightly higher at 1-and 2-years compared to baseline, the standard deviations were similar across time points, and skewness and kurtosis were acceptable.
For sun exposure, 44 of the 7065 at risk participants did not have sufficient baseline SPBI data to be included in the LGCM analytic sample (N = 7021). Table 8 shows that SPBI mean scores also appear to be slightly higher at year 1 and 2 compared to baseline, the standard deviations were similar across time points, and skewness and kurtosis were acceptable.

Unconditional
LGC Models. Table 9 shows the model fit statistics for nested unconditional 2-year LGC models developed sequentially for smoking, diet, and sun exposure separately. In order for the linear growth model for smoking behavior to converge, the constraint of equality over time for indicator residual variances was released for the first time point, with only 12-and 24-month residuals set to be equal. Examination of the unstandardized parameter estimates found that sun protective behavior increased significantly over time, mean slope ̂ = 0.14, SE = 0.005, p < .001. The estimated slope factor variance was 0.026, SE = 0.003, p < .001, indicating significant between-individual variation in the rate of behavior change. The model estimated intercept factor mean ̂ = 3.01, SE = 0.009, p < .001 (variance 0.39, SE = 0.01, p < .001), indicated that initial mean scores were above the theoretical midpoint of 2.50 (on 5 point scale) on the SPBI, and that there was significant variation between individuals in baseline sun protective behavior. In addition, the estimated covariance between both intercept and slope factors was positive and significant ̂ = 0.01, SE = 0.004, Δχ 2 (1) = 7.591, p < .01. Further probing of the standardized parameter estimates revealed that the estimated correlation between the intercept and slope factors was 0.113, suggesting that higher initial SPB mean scores were weakly associated with steeper increases in sun protective behavior. The unconditional growth trajectory model for sun protection behavior with standardized parameter estimates are shown in Figure 9.

Conditional
LGC Models. to the intervention effect on increasing sun protection behavior. The conditional growth trajectory model for sun protection behavior (Model 1B.5) is shown in Figure   12 with standardized parameter estimates.

Conditional LGC Models including baseline Decisional Balance and
Situational Temptations/Self-efficacy as covariates. Descriptive statistics for baseline mean scores for behavior specific Pro, Cons, and Situational Temptations/Selfefficacy are presented in   Table 14. Two alternative unconditional parallel-process LCGMs with random intercepts and slopes were assessed for each risk behavior dyad: covariance between all growth factors across behaviors were estimated in Model 1D.5, and in Model 1D.6, independence was assumed between intercept-slope factors across behaviors, and only the covariance's between intercept-intercept and between slope-slope were estimated across behaviors in the pair (see Figure 3).
The unconditional parallel-process LCGMs with random intercepts and slopes for smoking and diet behavior dyad fit well. χ 2 -difference test of the nested models 1D.5 and 1D.6 found that estimating the two additional parameters did not significantly improve model fit: while sun protection behavior also increased slightly over the same interval, ̂= 0.14, SE = 0.012, p < .001, from an initial level of ̂= 2.79, SE = 0.021, p < .001.
The estimated covariance between smoking and sun intercept factors was negative and significant, ̂= −0.15, SE = 0.026, p < .001, suggesting that higher initial levels of smoking were associated with lower initial levels of sun protection behavior (i.e., lower SPBI mean scores). The estimated covariance between smoking and sun protection slope factors was also negative but not significant, ̂= −0.01, SE = 0.013, p = .387, suggesting that the rate of decrease in smoking behavior was not consistently related to the rate of increase in sun protection behavior. The parallelprocess LGC model (Model 1D.6) for smoking and sun protection behaviors are shown in Figure 18 with standardized parameter estimates.
Stability of parallel-process LGCM of co-occurring risk behavior dyads across intervention condition. Finally, multiple-sample invariance analyses were conducted to assess the stability of the slope parameters across intervention condition. The parallel-process growth model (Model 1D.6) was fitted simultaneously to intervention and control group data for each risk behavior dyad. Four invariance models were tested sequentially for each health behavior pair: Equal form, Equal slope factor means, Equal slope factor means and covariance, and Equal slope factor means and factor covariances. Model fit statistics are presented in Table 15 for each invariance model by behavior dyad. Overall model fit, and the χ 2 -difference and ∆CFI for nested model comparisons, were both considered when examining the invariance models.
Cohen's q was also computed to estimate the magnitude of the difference in slope factor correlations between intervention conditions (Cohen, 1988). was estimated by ̂ = 0.41. However, comparing the nested models when ̂ was constrained to equality suggests that this association was not significantly different across intervention groups, Δχ 2 (1, N=1496) = 2.711, p = .100. Figure 19 shows the standardized parameter estimates across intervention condition for the parallel-process growth curve model for smoking and diet behaviors.  For smoking, transition parameter estimates suggest that across participants in precontemplation were more likely to remain in the same stage after one year (.65) than to make stage progress (.35). Participants in contemplation were also more likely to remain in the same stage after one year (.53) than to make stage progress (.29) or to regress in to precontemplation (.18 Unconditional two year stage transition models supported the stationarity of transition paths for smoking cessation and sun protection behavioral stages, but not for diet behavior. covariance between the intercept and slope factors for smoking suggested that individuals who initially smoked more (greater problem severity) had more difficulty reducing smoking behavior, whereas those who smoked less at baseline were able to achieve a greater reduction in their number of cigarettes smoked, which is consistent with previous research findings that behavior change at 24-months was related to problem severity (Blissmer et al., 2010). Healthy eating behavior and sun protective behavior were also found to increase slightly over time across all participants, with significant inter-individual variation in both the initial levels on the behavioral measures (DBQ or SPBI) as well as the rate of increase (slope) of the behaviors over time. Interestingly, the covariance between the intercept and slope factors for diet behavior was not significant, suggesting that the rate of change in diet behavior was unrelated to initial DBQ scores. For sun protection behavior, the significant but small estimated covariance between intercept and slope factors indicated that higher baseline levels on the SPBI were only weakly associated with steeper increases over time in sun protective behavior.
TTM-tailored intervention had a significant and positive effect on increasing both healthy eating behavior and sun protective behavior over time, consistent with previously reported outcomes (Prochaska et al., , 2005Weinstock, Rossi, Redding & Maddock, 2002). Healthy eating and sun protection behavioral outcomes at the 2-year follow-up were approximately 0.25 of a standard deviation higher (̂ = 0.23 for diet and ̂ = 0.25 for sun protection) in the treatment group. This could be interpreted as medium-to-large intervention effects on the rate of increase in healthy eating and sun protection (Rossi, 2013). However in contrast, the intervention did not appear to have a significant effect on the mean slope for smoking behavior. This is not what was expected based on numerous studies that found significant intervention effects on point prevalence abstinence for smoking cessation (Prochaska et al, 1993(Prochaska et al, , 2001a(Prochaska et al, , 2001bVelicer et al, 1999Velicer et al, , 2006aVelicer et al, , 2006b. One key consideration to keep in mind is that the behavioral outcome measure for smoking examined in the current study is based on the number of cigarettes smoked per day, whereas previous studies assessed intervention efficacy in terms of cessation, a dichotomous outcome that that does not differentiate between smoking two or 20 cigarettes/day in smokers who were not unsuccessful in quitting. Another possible explanation may be that individuals who smoked fewer cigarettes daily (lower problem severity) were more likely to be able to quit smoking, whereas those who smoked more were less likely to change their smoking behavior (Blissmer et al., 2010).
The TTM constructs of Pros, Cons, and Situational Temptations/Self-efficacy were also assessed as baseline predictors of growth trajectories. Baseline Temptations and Pros were found to significantly predict initial smoking behavior, which was not surprising as Temptations can also serve as an indicator of smoking problem severity.
When assessed simultaneously in LGCM with multiple time-invariant covariates, baseline Cons were also found to be significant predictors of mean slope for healthy eating and sun protective behaviors.
Parallel-process LGC models were developed to examine inter-relationships between growth trajectories within pairs of co-occurring risk behaviors. For the series of parallel-process LGC models, we were primarily interested in the covariance parameters estimated between the parallel behavior trajectories for each risk dyad.
Previous multiple behavior change research described the phenomenon of "co-action," observed within the context of co-occurring behavioral risk pairs, in which taking action on one behavior was associated with increased odds of successful action on the second behavior (Paiva et al., 2012;Yin et al., 2013). In the interest of understanding the process of multiple behavior change, examining the association between parallel behavior trajectories could provide some insight into whether and how co-occurring risk behaviors change together over time.
Unconditional parallel-process LGCM for the smoking and diet risk dyad fitted to data from the full sample found that higher initial levels of smoking were significantly associated with lower initial DBQ mean scores (i.e., less healthy diet behavior), but that the rate of decrease in smoking behavior was not consistently related to the rate of increase in healthy eating. For the smoking and sun protection behavior dyad, higher initial levels of smoking were significantly associated with lower initial levels of sun protection behavior (lower SPBI mean scores), although the rate of decrease in smoking behavior was weakly and not significantly related to the rate of increase in sun protection behavior. Sun protection and diet was the only behavior pair shown to have significant covariances between parallel behavior trajectories. In the full sample, higher initial levels of healthy eating were associated with higher initial levels of sun protection behavior and the rates of increase in sun protection and healthy eating behaviors were also consistently related. Multiplesample analyses of the parallel-process LGC model for diet and sun protection across intervention condition revealed significantly steeper increases (slope) over time in each behavior in the treatment group. Although the initial levels for both behaviors were more strongly related in the treatment group compared to controls, no significant intervention group difference was found for the association between slope factors for diet and sun protection behaviors. Therefore, previous research findings of significant co-action in the treatment group for the sun protection-diet behavior pair ) are more likely explained by the effect of TTM-tailored interventions on increasing the rate of change (slope) for each treated behavior, which we also observed in the single behavior conditional LGC models.
Study 2 employed LTA techniques to examine behavioral stage transitions in three cancer-related risks over time, intervention condition, and across behaviors. For all three behaviors, the saturated stage movement model that freely estimated all possible transition paths was preferred over more restrictive models that constrained movement patterns to two or fewer stages. These findings indicate that a lot of stage movement is possible, and does occur. Given that the duration between assessment time points was one year in the data, finding this amount of stage movement over such a long interval was not unexpected, and also consistent with previous research that found movement of up to four stages in smokers when assessments were taken at intervals of one year (Schumann, John, Rumpf, Hapke & Meyer, 2006). Longitudinal data that include more frequent assessment time points (e.g. intervals of 3-6 months instead of 12-month intervals) would provide better resolution to study the stage transition process, and may even support a more parsimonious model of stage movement patterns. For example, other research with smokers assessed at shorter intervals of 6-months favored a more restricted transition model with a two-stage forward, one-stage back movement pattern . In the present study, examination of the transition parameters revealed that the transition paths on or closest to the diagonal (of the parameter estimate matrix) had the highest probabilities, while those paths furthest from the diagonal generally had very much lower (although nonzero) probabilities. This tells us that over a one year interval, either no stage movement or one-stage movement was much more likely to occur compared to greater movement over multiple stages within the same interval.
Based on data for the full analytical sample combining intervention and control group participants, the stationary unconditional stage transition model was supported for smoking cessation, and was also preferred over the nonstationary model for sun protection behavior based on better overall model fit. For healthy diet behavior, the nonstationary model was shown to fit significantly better (based on significant scaled difference ∆G 2 ), although the overall G 2 and AIC both favored the more parsimonious stationary model. It is possible that the power of the scaled likelihood ratio difference test was amplified due to the large sample size. These findings suggest that stage movement patterns may be reasonably stable over time for the different behaviors.
In stage membership was the most stable: participants in precontemplation were more likely to remain in that stage than to make any progress in readiness to reduce their behavioral risk.
For all three behaviors, conditional stage transition models that included intervention condition as a time-invariant covariate supported the efficacy of TTMtailored intervention. Transition parameter estimates indicated that treated at-risk participants were more likely to reach behavioral criteria (move to action/maintenance stage), and to maintain their behavior change during follow-up, which was consistent with previous study outcomes (Prochaska et al., , 2005Velicer et al., 2004;Weinstock, Rossi, Redding & Maddock, 2002). In addition, treated participants were more likely to increase their readiness to reduce behavioral risk (make forward stage progress) even if they had not taken effective action. These effects were observed across all stages and both time intervals for both diet and sun protection behaviors, however, the pattern of effects looked slightly different for smoking cessation.
Although treatment effects were observed during the first year (intervention period) on overall stage progress and especially on quitting smoking, during the follow-up interval, transition parameters indicated more stage progress among controls in precontemplation and contemplation. During the follow-up, transition parameter estimates showed that treated smokers were more likely to move from preparation to action/maintenance stage (point prevalence abstinence), and also to maintain their quit status. Probing of the transition parameter estimates reveals an interesting pattern of effects that suggests that treatment may accelerate smoking cessation stage progress, with some possible "catching-up" by controls during follow-up, but the net outcome is still higher smoking cessation rates at follow-up in favor of treatment.

Limitations
One of the strengths of the current research is that the findings are based on data for participants pooled across multiple large randomized trials, and the data also include three of the most important behaviors for cancer prevention. However, one major limitation of this study was that the data only included three common assessment time points, at intervals of one year between each wave, thus restricting the growth trajectory or stage transition patterns that could be modeled. Data that include more frequent and shorter intervals between assessments would most likely provide a richer framework for investigating the process of behavior change. A second limitation of this study was the restricted range in the data because the sample consisted entirely of individuals identified to be "at-risk" for one or more cancer risk behavior at baseline, and individuals identified to be in action or maintenance stages at baseline were not assessed for the specific behavior at any follow-up time point.
Although a sample of participants in all stages of change at baseline would provide greater variance in responses on outcome measures, it may not be representative of intervention populations and thus difficult to justify from a cost perspective. Another limitation of the current sample relates to the racial and ethnic demographics. A sample that is more diverse in terms of racial identity, with adequate numbers of other racial groups besides white and black, would support assessment of stability for growth trajectory and/or stage transition models across racial/ethnic identity subgroups, potentially improving the generalizability of these findings.
Perhaps one current limitation specific to the mixture modeling (LTA) approach lies with the number and type of fit criteria available for assessing model fit.
The likelihood ratio G 2 (based on the log likelihood) and information criteria such as the AIC and BIC are more commonly used to assess model fit, however, interpretation of these indices are relative as they do not have any absolute or theoretical limits for "perfect" fit, preventing comparison of non-nested models.
Additional avenues for future research could include evaluating plausible covariates such as number of co-occurring behavioral risks as predictors of growth trajectories or stage transitions. In addition, indicators for different behaviors could be used to identify a multiple behavior risk status, in order to model stage transitions over time in multiple behaviors jointly.

Summary
The current research employed two alternative latent variable modeling approaches to investigate mechanisms of single and multiple behavior change across three cancer-related risk behaviors of smoking, unhealthy eating, and sun exposure.
Study 1 applied LGC modeling approaches to examine 2-year growth trajectories of quantitative outcomes for all three behaviors. Conditional LGC models supported significant TTM-intervention effects on increasing the rates of change over time for healthy eating and sun protection behaviors. Parallel-process LGC models developed to estimate 2-year growth trajectories jointly across behaviors within co-occurring risk pairs provided evidence that initials levels were significantly correlated between both behaviors in each risk dyad. In addition, for the sun protection and diet behavior pair, the rate of increase over time was shown to be associated between both behaviors in the pair. results also provided evidence for TTM-tailored intervention efficacy across smoking cessation, dietary fat reduction, and sun protection behavior, in terms of moving atrisk participants to reach behavioral criteria, promoting stage progress among those who did not reach criteria, and in maintaining successful behavior change during the follow-up interval. In addition, our findings revealed the stability of precontemplation stage membership across all three behaviors; stage progress from the precontemplation stage was even less likely among control participants.             Note: DF = degrees of freedom; LL = log likelihood; G 2 = likelihood ratio; AIC = Akaike information criterion; BIC = Bayesian information criterion.       Transition probabilities (τ St2|St1 ) to be estimated for intervals: (a) Baseline to 1-year, and (b) 1-to 2-years.

TABLES
Model 1: Baseline model, all paths free.

Figure 16.
Unconditional parallel-process model of 2-year growth trajectories for smoking and healthy diet behaviors with standardized parameter estimates. Note: α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001; Indicators at baseline, 1-and 2-years for smoking behavior are number of cigarettes/day (square-rooted transformed for normalization), and mean DBQ scores for diet behavior.

Figure 17.
Unconditional parallel-process model of 2-year growth trajectories for healthy diet and sun protection behaviors with standardized parameter estimates. Note: α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001. Indicators at baseline, 1-and 2-years for healthy eating behavior are mean DBQ mean scores, and mean SPBI scores for sun protection behavior. Figure 18. Unconditional parallel-process model of 2-year growth trajectories for smoking and sun protection behaviors with standardized parameter estimates. Note: α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001. Indicators at baseline, 1-and 2-years for smoking behavior are number of cigarettes/day (square-rooted transformed for normalization), and mean SPBI score for sun protection behavior. Figure 19. Unconditional parallel-process model of 2-year growth trajectories for smoking and healthy diet behaviors with standardized parameter estimates across intervention condition. Note: Parameter estimates for control condition are presented in parentheses; α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001. Indicators at baseline, 1-and 2-years for smoking behavior are number of cigarettes/day (square-rooted transformed for normalization), and mean DBQ scores for diet behavior.

Figure 20.
Unconditional parallel-process model of 2-year growth trajectories for healthy diet and sun protection behaviors with standardized parameter estimates across intervention condition. Note: Parameter estimates for control condition are presented in parentheses; α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001. Indicators at baseline, 1-and 2-years for healthy eating behavior are mean DBQ mean scores, and mean SPBI scores for sun protection behavior.

Figure 21.
Unconditional parallel-process model of 2-year growth trajectories for smoking and sun protection behaviors with standardized parameter estimates across intervention condition. Note: Parameter estimates for control condition are presented in parentheses; α = estimated factor mean; ψ = estimated factor variance; * p < .05; ** p < .01; *** p < .001. Indicators at baseline, 1-and 2-years for smoking behavior are number of cigarettes/day (square-rooted transformed for normalization), and mean SPBI score for sun protection behavior.