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A multilevel modelling approach to analysis of patient costs under managed care.

The growth of the managed care model of health care delivery in the USA has led to broadened interest in the performance of health care providers. This paper uses multilevel modelling to analyse the effects of managed care penetration on patient level costs for a sample of 24 medical centres operated by the Veterans Health Administration (VHA). The appropriateness of a two level approach to this problem over ordinary least squares (OLS) is demonstrated. Results indicate a modicum of difference in institutions' performance after controlling for patient effects. Facilities more heavily penetrated by the managed care model may be more effective at controlling costs of their sicker patients.

Cost Sharing↗

Multilevel modeling for the analysis of longitudinal blood pressure data in the Framingham Heart Study pedigrees.

BACKGROUND: The data arising from a longitudinal familial study have a complex correlation structure that cannot be modeled using classical methods for the analysis of familial data at a single time point. METHODS: To fit the longitudinal systolic blood pressure (SBP) pedigree data arising from the Framingham Heart Study, we proposed to use multilevel modeling. That approach was used to distinguish multiple levels of information with individual repeated measurements (Level 1) being made within individuals (Level 2), and individuals clustered within pedigrees (Level 3). Residuals from the subject-specific and pedigree-specific regression models were summed both for the mean SBP and slope of SBP change over time, in order to define two new outcomes that were then used in a genome-wide linkage analysis. RESULTS: Evidence for linkage for the two outcomes (mean SBP and slope) was found in several chromosomal regions with a maximum LOD score of 3.6 on chromosome 8 and 3.5 on chromosome 17 for the mean SBP, and 2.5 on chromosome 1 for SBP slope. However, the linkage on chromosome 8 was only detected when the sample was restricted to subjects between age 25 and 75 and with at least four exams (Cohort 1) or 3 exams (Cohort 2). DISCUSSION: Multilevel modeling is a powerful approach to detect genes involved in complex traits when longitudinal data are available. It allows for complex hierarchical data structure to be taken into account and therefore, a better partitioning of random within-individual variation from other sources of variability (genetic or nongenetic).

Adult↗

The application of multilevel modeling in the analysis of longitudinal periodontal data--part I: absolute levels of disease.

BACKGROUND: Statistical analyses of periodontal data that average site measurements to subject mean values are unable to explore the site-specific nature of periodontal diseases. Multilevel modeling (MLM) overcomes this, taking hierarchical structure into account. MLM was used to investigate longitudinal relationships between the outcomes of lifetime cumulative attachment loss (LCAL) and probing depth (PD) in relation to potential risk factors for periodontal disease progression. METHODS: One hundred males (mean age 17 years) received a comprehensive periodontal examination at baseline and at 12 and 30 months. The resulting data were analyzed in two stages. In stage one (reported here), the absolute levels of disease were analyzed in relation to potential risk factors; in stage two (reported in a second paper), changes in disease patterns over time were analyzed in relation to the same risk factors. Each approach yielded substantially different insights. RESULTS: For absolute levels of disease, subject-level risk factors (covariates) had limited prediction for LCAL/PD throughout the 30-month observation period. Tooth position demonstrated a near linear relationship for both outcomes, with disease increasing from anterior to posterior teeth. Sites with subgingival calculus and bleeding on probing demonstrated more LCAL and PD, and supragingival calculus had an apparently protective effect. Covariates had more "explanatory power" for the variation in PD than for the variation in LCAL, suggesting that LCAL and PD might be generally associated with a different profile of covariates. CONCLUSION: This study provides, for a relatively young cohort, considerable insights into the factors associated with early-life periodontal disease and its progression at all levels of the natural hierarchy of sites within teeth within subjects.

Adolescent↗

[Glutathione S-transferase M1 polymorphism and the risk on colorectal cancer: a multilevel meta regression].

OBJECTIVE: In order to investigate the relationship between Glutathione S-transferase M1 (GSTM1) status and the risk on colorectal cancer as well as to detect the related factors to this association. METHODS: A pooled analysis of multilevel Meta-regression was performed to estimate GSTM1 deficiency associated with the risks of colorectal cancer. Then subgroup Meta-regression was undertaken to evaluate the possible relationship between heterogeneity and the related characteristics. RESULTS: The overall pooled odds ratios of colorectal cancer risk associated with GSTM1 deficiency was 1.17 (95% CI: 1.08-1.26). Ethnicity, percent of GSTM1 deficiency in population had significant relationships with heterogeneity across the studies (P < 0.05). Results of subgroup Meta-regression showed that GSTM1 deficiency was significantly associated with colorectal cancer risk in ethnic subgroups of Asians, Caucasians and in low level (lower than 50%) of GSTM1 deficiency population (P < 0.05). The respective pooled ORs were 1.14, 1.25 and 1.29. CONCLUSION: GSTM1 deficiency seemed to be a risk factor for colorectal cancer, while interactions on the characteristics of ethnicity, percentage of GSTM1 deficiency in the studied population were related to this association.

Asian People↗

Graphical approaches to support the analysis of linear-multilevel models of lamb pre-weaning growth in Kolda (Senegal).

Linear-multilevel models (LMM) are mixed-effects models in which several levels of grouping may be specified (village, herd, animal, ellipsis). This study highlighted the usefulness of graphical methods in their analysis through: (1) the choice of the fixed and random effects and their structure, (2) the assessment of goodness-of-fit and (3) distributional assumptions for random effects and residuals. An LMM was developed to study the effect of ewe deworming with morantel on lamb pre-weaning growth in a field experiment involving 182 lambs in 45 herds and 10 villages in Kolda, Senegal. Growth was described as a quadratic polynomial of age. Other covariates were sex, litter-size and treatment. The choice of fixed and random effects relied on three graphs: (1) a trellis display of mean live-weight vs. age, to select main effects and interactions (fixed effects); (2) a trellis display of individual growth curves, to decide which growth-curve terms should be included as random effects and (3) a scatter plot of parameters of lamb-specific regressions (live-weight vs. quadratic polynomial of age) to choose the random-effects covariance structure.Age, litter-size, agexlitter-size, litter-sizextreatment and agexlitter-sizextreatment were selected graphically as fixed effects and were significant (p<0.05) in subsequent statistical models. The selection of random-effect structures was guided by graphical assessment and comparison of the Akaike's information criterion for different models. The final random-effects selected included no random effect at the village level but intercept, age and squared-age at the herd and lamb levels. The structure of the random-effects variance-covariance matrices were blocked-diagonal at the herd level and unstructured at the lamb level. An order-1 autoregressive structure was retained to account for serial correlations of residuals. Smaller residual variance at 90 days than at younger ages was modeled with a dummy variable taking a value of 1 at 90 days and 0 elsewhere.Ewe-deworming with morantel during the rainy season lead to higher lamb live-weights (probably related to a better ewe-nutrition and -health status). A positive correlation was demonstrated between early weight and growth rate at the population level (with important lamb and herd-level random deviations). The persistence of this correlation at older ages should be checked to determine whether early weights are good predictors of mature weights and ewe-reproductive lifetime performance.

Animal Husbandry↗

Utilization of prenatal care in poorer and wealthier urban neighbourhoods in Turkey.

BACKGROUND: The objectives of this study are to identify the individual- and neighbourhood-level determinants of utilization of prenatal care, and to identify self-reported reasons for not receiving prenatal care in Turkey. METHODS: A household-based cluster sample of 1249 women who had a child less than two years old were interviewed in five Turkish cities. Multilevel regression analysis was run to predict the influences of individual- and neighbourhood-level characteristics on utilization of prenatal care. RESULTS: Utilization of prenatal care and the quality of the care received were found to be significantly lower in poorer neighbourhoods. Using multilevel regression analysis (two levels), educational level, income, parity and having health insurance were found to be individual-level determinants, while quality of care offered and stability of the local population were found to be neighbourhood-level determinants of utilization of prenatal care. The most frequent self-reported reason for receiving no prenatal care was 'not having any complaint', and the second was 'insufficient financial resources'. CONCLUSION: There was a big difference between poor and wealthy neighbourhoods in utilization of prenatal care. This difference was partly due to a contextual effect of neighbourhood status; but mostly due to individual-level variables. Improving the quality of prenatal care may increase not only the benefits of prenatal care, but also its utilization, especially in the public sector. Health and social policies have to take into account diversity among individuals and neighbourhoods in the course of efforts to improve service quality.

Adolescent↗

The application of multilevel modeling in the analysis of longitudinal periodontal data--part II: changes in disease levels over time.

BACKGROUND: The aim of this study was to investigate the longitudinal relationships between the outcome measurements of changes in lifetime cumulative attachment loss (cLCAL) and changes in probing depth (cPD) in relation to potential risk factors or other risk markers for periodontal disease progression from a cohort of 100 young males. In order to account for the hierarchical data structure, and to explore explicitly the site, tooth, and subject levels simultaneously, multilevel modeling was undertaken. METHODS: The analyses were undertaken in two parts. Within a previous article, the absolute levels of disease were analyzed in relation to potential risk factors; within this article, changes in disease are analyzed in relation to these factors. Each analytical approach yielded substantively different insights. RESULTS: Subject-level risk factors had limited predictive value for cLCAL/cPD throughout the 30-month observation period. Tooth position demonstrated a near linear relationship for both outcomes, with disease increasing from anterior to posterior teeth. Supragingival plaque had no significant effect on cLCAL/cPD, while subgingival calculus and bleeding on probing were negatively associated with cLCAL/cPD. In contrast to the outcomes LCAL/PD, supragingival calculus had no significant protective effect on cLCAL/cPD. There was no significant influence of smoking in this cohort. CONCLUSIONS: This study provides, for a relatively young cohort, considerable insights into the factors associated with longitudinal patterns of early-life periodontal disease at all levels of the natural hierarchy of sites within teeth within subjects. Furthermore, it is demonstrated how multilevel modeling can provide considerable insight into some of the inconsistencies and controversies found in the previous periodontal literature.

Adolescent↗

An introduction to meta-analysis within the framework of multilevel modelling using the probability of success of root canal treatment as an illustration.

OBJECTIVE: To introduce the statistical methodology of meta-analysis within the framework of multilevel modelling (MLM) using an illustrative example. BASIC RESEARCH DESIGN: In meta-analysis it is important that the quantitative pooling of study results should be carried out in conjunction with careful consideration of the variation apparent between studies. If statistical heterogeneity is found to be significant, it is due, at least in part, to clinical heterogeneity. It is possible to account for clinical heterogeneity by including covariates that are thought to be responsible, using meta-regression. CLINICAL SETTING: A total of 38 studies of root canal treatment outcome were identified as being suitable for introducing the meta-analysis methodology. Two covariates were considered for modelling: a 'loose' or 'strict' (loose--incomplete radiographic healing; strict--complete radiographic healing) criterion for judging outcome of treatment and the year in which the study was performed. RESULTS: There was considerable statistical heterogeneity between the study results. The effect of employing loose criteria for judging success significantly increased the probability of success when compared to employing strict criteria. Furthermore, the variance between studies was significantly reduced when this covariate was included in the modelling process when compared to the variation estimated in the model which did not consider covariates. CONCLUSION: MLM is a good facilitator for meta-analysis and meta-regression.

Analysis of Variance↗

School-related stress, social support, and distress: prospective analysis of reciprocal and multilevel relationships.

This three-wave prospective study investigated the reciprocal relationships among school-related stress, school-related social support, and distress in a cohort of 767 secondary school students (mean age 13.9 years). Stress, support, and distress were measured at three occasions with six-month lags between. Reciprocal relationships were analyzed with multivariate multilevel modeling (MLwiN). Each of the three factors at baseline predicted change in one or two of the other factors at subsequent measurements, indicating a complex pattern of reciprocal relationships among stress, support, and distress across time. A high level of distress at baseline predicted a lower level of support and a higher level of stress six months later. High levels of stress at baseline predicted a higher level of distress and a lower level of support 12 months later. The results are consistent with a transactional and dynamic model of stress, support, and distress, and indicate the need to view school-related stress, support, and distress as mutually dependent factors.

Adolescent↗

Marginal modeling of multilevel binary data with time-varying covariates.

We propose and compare two approaches for regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors, and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated using data from the Breast Cancer Surveillance Consortium to estimate mammography accuracy from a repeatedly screened population.

Adult↗

A multilevel model framework for meta-analysis of clinical trials with binary outcomes.

In this paper we explore the potential of multilevel models for meta-analysis of trials with binary outcomes for both summary data, such as log-odds ratios, and individual patient data. Conventional fixed effect and random effects models are put into a multilevel model framework, which provides maximum likelihood or restricted maximum likelihood estimation. To exemplify the methods, we use the results from 22 trials to prevent respiratory tract infections; we also make comparisons with a second example data set comprising fewer trials. Within summary data methods, confidence intervals for the overall treatment effect and for the between-trial variance may be derived from likelihood based methods or a parametric bootstrap as well as from Wald methods; the bootstrap intervals are preferred because they relax the assumptions required by the other two methods. When modelling individual patient data, a bias corrected bootstrap may be used to provide unbiased estimation and correctly located confidence intervals; this method is particularly valuable for the between-trial variance. The trial effects may be modelled as either fixed or random within individual data models, and we discuss the corresponding assumptions and implications. If random trial effects are used, the covariance between these and the random treatment effects should be included; the resulting model is equivalent to a bivariate approach to meta-analysis. Having implemented these techniques, the flexibility of multilevel modelling may be exploited in facilitating extensions to standard meta-analysis methods.

Clinical Trials as Topic↗

Conventional models overestimate the statistical significance of volume-outcome associations, compared with multilevel models.

OBJECTIVE: To compare the use of conventional statistical models with multilevel regression models in volume-outcome analyses of surgical procedures in an empirical case study. STUDY DESIGN AND SETTING: Using conventional regression models and multilevel regression models, we estimated the effect of hospital volume and surgeon volume on 30-day mortality and length of postoperative hospital stay in persons who had an esophagectomy, pancreaticoduodenectomy, or major lung resection for cancer in Ontario, Canada, from 1994 to 1999. RESULTS: The point estimates of volume-outcome associations were similar using either method; however, the 95% confidence intervals estimated by multilevel models were wider than those estimated by conventional models. A significant association between volume and mortality was identified in 2 of 18 (11%) comparisons using conventional analysis but in none of the 18 (0%) comparisons using multilevel analysis, and between volume and length of stay in 15 of 18 (83%) comparisons using conventional analysis and in 1 of 18 (6%) comparisons using multilevel analysis. CONCLUSION: Conventional and multilevel statistical models can yield substantially different results in the analysis of volume-outcome associations for surgical procedures.

Age Factors↗

Health care is an individual necessity and a national luxury: applying multilevel decision models to the analysis of health care expenditures.

Health care is neither "a necessity" or "a luxury"; it is "both" since the income elasticity varies with the level of analysis. With insurance, individual income elasticities are typically near zero, while national health expenditure elasticities are commonly greater than 1.0. The debate over whether health care is or is not a luxury good arises primarily from the failure to specify levels of analysis clearly so as to distinguish variation within groups from variation between groups. Apparently, contradictory empirical results are shown to be consistent with a simple nested multilevel model of health care spending.

Health Care Rationing↗

The infrabony defect and its determinants.

BACKGROUND AND OBJECTIVE: The purpose of this study was to assess the defect width of infrabony defects in a cross-sectional study and to evaluate whether the defect width is a function of defect depth. MATERIAL AND METHODS: Complete sets of intra-oral radiographs of patients with severe periodontitis, which exhibited at least one infrabony defect, were digitised and evaluated. The following parameters were measured: depth and width of the infrabony defect, defect angle, and width of the interdental spaces. RESULTS: Fifty-one patients (26 women), ranging from 21 to 73 yr of age (48.5 +/- 13.4 yr), contributed a total of 1272 teeth with 135 infrabony defects (10.6%). Seventeen infrabony defects were located at sites without a neighboring tooth. Infrabony defects were statistically more prevalent in the mandible (n = 82) than in the maxilla (p = 0.013), and more prevalent at mesial sites (n = 92) than at distal sites (p < 0.001). At infrabony defects, the width of interdental spaces at the most coronal extension of the alveolar crest could be measured only at sites with neigboring teeth 2.67 +/- 0.78 mm (range: 1.19-5.70 mm). Analysis failed to reveal a statistically significant difference between defect width at sites with (2.64 +/- 0.82 mm) and sites without (2.76 +/- 0.70 mm) a neighboring tooth. Multilevel regression analysis revealed narrow defect angles to be related to deep infrabony defects, whereas width of the interdental space and distal location were related to wide defects. CONCLUSION: Defect angle depended on defect depth and defect width was not different at sites with or without a neighboring tooth. Even in severe periodontitis, infrabony defects are found only at a minority of teeth.

Adult↗

Trial by trial effects in the antisaccade task.

The antisaccade task requires participants to inhibit the reflexive tendency to look at a sudden onset target and instead direct their gaze to the opposite hemifield. As such it provides a convenient tool with which to investigate the cognitive and neural systems that support goal-directed behaviour. Recent models of cognitive control suggest that antisaccade performance on a single trial should vary as a function of the outcome (correct antisaccade or erroneous prosaccade) of the previous trial. In addition, repetition priming effects suggest that the spatial location of the target on the previous trial may also influence current trial performance. Thus an analysis of contingency effects in antisaccade performance may provide new insights into the factors that influence the monitoring and modulation of the antisaccade task and other ongoing behaviours. Using a multilevel modelling analysis we explored previous trial effects on current trial performance in a large antisaccade dataset. We found (1) repetition priming effects following correct antisaccades; (2) contrary to models of cognitive control antisaccade error rates were increased on trials following an error, suggesting that failures to adequately maintain the task goal can persist across more than one trial; and (3) current trial latencies varied according to the previous trial outcome (correct antisaccade, slowly corrected error or rapidly corrected error). These results are discussed in terms of current models of antisaccade performance and cognitive control and further demonstrate the utility of multilevel modelling for analysing antisaccade data.

Adult↗

Methodological approaches to the analysis of hierarchical studies of air pollution and respiratory health--examples from the CESAR study. Central European Study on Air pollution and Respiratory Health.

OBJECTIVES: Many studies of air pollution and health are carried out over several geographical areas, and sometimes over several countries. This paper explores three approaches to analysis in such studies: a non hierarchical model, a two-stage analysis, and multilevel modelling. Illustrations are given using a preliminary subset of data from the CESAR study. DESIGN: The Central European Study on Air pollution and Respiratory Health (CESAR) was conducted in 25 areas within six Central European countries, enrolling 20,271 schoolchildren. Pollution averages were calculated for each area. Associations between pollution and health outcomes were estimated under different models. MAIN RESULTS: A regression analysis of log FVC (forced vital capacity) on PM10, ignoring the geographical hierarchy, estimated a significant mean drop in FVC (adjusted for confounders) of 2.2% (95% CI 0.5% to 1.3%), p=0.007, from the area with the lowest PM10 to that with the highest. A multilevel model (mlm), using data for all children, but with random effects at area and country level, estimated a drop of 2.8% (-0.6% to 6.1%), p=0.110. A two-stage analysis (mean log FVC, adjusted for confounders, was estimated for each area using regression, and these means then regressed on PM10) estimated a drop of 2.6% (-0.5% to 5.5%), p=0.101. Simulation exercises showed the non hierarchical method to be very inadequate in the context of the CESAR study, with only half of all 95% confidence intervals for the estimated PM10 slope containing the true value (i.e., that used to create the simulated data). The two-stage and multilevel modelling methods gave results which were substantially better, though both underperformed slightly. All three methods appeared to give unbiased slope estimates. CONCLUSIONS: Acknowledgement of hierarchical structures is essential in statistical inference--standard errors can be substantially incorrect when they are ignored. Multilevel, random-effects models correctly address hierarchical structures, though having few units at higher levels can cause problems in convergence, especially where complex modelling is required. Two-stage analyses, acknowledging hierarchy, provide simple alternatives to random-effects models.

Air Pollutants↗

Variation in test ordering behaviour of GPs: professional or context-related factors?

OBJECTIVE: The aim of this study was to describe GPs' test ordering behaviour, and to establish professional and context-related determinants of GPs' inclination to order tests. METHODS: A cross-sectional analysis was carried out of 229 GPs in 40 local GP groups from five regions in The Netherlands of the combined number of 19 laboratory and eight imaging tests ordered by GPs, collected from five regional diagnostic centres. In a multivariable multilevel regression analysis, these data were linked with survey data on professional characteristics such as knowledge about and attitude towards test ordering, and with data on context-related factors such as practice type or experience with feedback on test ordering data. The main outcome measure was the percentage point differences associated with professional and context-related factors. RESULTS: The total median number of tests per GP per year was 998 (interquartile range 663-1500), with significant differences between the regions. The response to the survey was 97%. At the professional level, 'individual involvement in developing guidelines' (yes versus no), and at the context-related level 'group practice' (versus single-handed and two-person practices) and 'more than 1 year of experience working with a problem-oriented laboratory order form' (yes versus no) were associated with 27, 18 and 41% lower numbers of tests ordered, respectively. CONCLUSION: In addition to professional determinants, context-related factors appeared to be strongly associated with the numbers of tests ordered. Further studies on GPs' test ordering behaviour should include local and regional factors.

Attitude of Health Personnel↗