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Finite Mixture Models with Student t Distributions: an Applied Example.

ABSTRACT: The use of finite mixture modeling (FMM) to identify unobservable or latent groupings of individuals within a population has increased rapidly in applied prevention research. However, many prevention scientists are still unaware of the statistical assumptions underlying FMM. In particular, finite mixture models (FMMs) typically assume that the observed indicator variables are normally distributed within each latent subgroup (i.e., within-class normality). These assumptions are rarely met in applied psychological and prevention research, and violating these assumptions when fitting a FMM can lead to the identification of spurious subgroups and/or biased parameter estimates. Although new methods have been developed that relax the within-class normality assumption when fitting a FMM, prevention scientists continue to rely on FMM methods that assume within-class normality. The purpose of the current article is to introduce prevention researchers to a FMM method for heavy-tailed data: FMM with Student t distributions. We begin by reviewing the distributional assumptions that underlie FMM and the limitations of FMM with normal distributions. Next, we introduce FMM with Student t distributions, and show, step by step, the analytic and substantive results of fitting a FMM with normal and Student t distributions to data from a smoking-cessation trial. Finally, we extend the results of the applied example to draw conclusions about the use of FMM with Student t distributions in applied settings and to provide guidelines for researchers who wish to use these methods in their own research.

SUBMITTER: Burgess-Hull AJ

PROVIDER: S-EPMC7368836 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundCentral monitoring (CM), in which data across all clinical sites are monitored, has an important role in risk-based monitoring. Several statistical methods have been proposed to compare patient outcomes among the sites for detecting atypical sites that have different trends in observed data. These methods assume that the number of clinical sites is not small, e.g., 100 or more. In addition, the proportion of atypical sites is assumed to be relatively small. However, in actuality, the central statistical monitoring (CSM) has to be implemented in small or moderate sized clinical trials such as small phase II clinical trials. The number of sites is no longer large in such situations. Therefore, it is of concern that existing methods may not work efficiently in CM of small or moderate sized clinical trials. In the light of this problem, we propose a Bayesian CSM method to detect atypical sites as the robust method against the existence of atypical sites.MethodsWe use Bayesian finite mixture models (FMM) to model patient outcome values of both atypical and typical sites. In the method, the distributions of outcome values in normal sites are determined by choosing the body distribution, which has the largest mixture parameter value of finite mixture models based on the assumption that normal sites are in the majority. Atypical sites are detected by the criterion based on the posterior predictive distribution of normal site's outcome values derived from only the chosen body distribution.ResultsProposed method is evaluated by cumulative detection probability and type I error averaged over sites every round of CSM under the various scenarios, being compared with the conventional type analysis. If the total number of patients enrolled is 48, the proposed method is superior at least 10% for any shift sizes at the 2nd and the 3rd rounds. If the total number of patients is 96, both methods show similar detection probability for only one atypical site and large shift size. However, the proposed method is superior for the other scenarios. It is observed that all the type I errors averaged over sites are little difference between the methods at all the scenarios.ConclusionWe propose a Bayesian CSM method which works efficiently in a practical use of CM. It is shown that our method detects atypical sites with high probability regardless of the proportion of the atypical sites under the small clinical trial settings which is the target of our proposed method.

Project description:BackgroundA strategy to combat infectious diseases, including neglected tropical diseases (NTDs), will depend on the development of reliable epidemiological surveillance methods. To establish a simple and practical seroprevalence detection system, we developed a microsphere-based multiplex immunoassay system and evaluated utility using samples obtained in Kenya.MethodsWe developed a microsphere-based immuno-assay system to simultaneously measure the individual levels of plasma antibody (IgG) against 8 antigens derived from 6 pathogens: Entamoeba histolytica (C-IgL), Leishmania donovani (KRP42), Toxoplasma gondii (SAG1), Wuchereria bancrofti (SXP1), HIV (gag, gp120 and gp41), and Vibrio cholerae (cholera toxin). The assay system was validated using appropriate control samples. The assay system was applied for 3411 blood samples collected from the general population randomly selected from two health and demographic surveillance system (HDSS) cohorts in the coastal and western regions of Kenya. The immunoassay values distribution for each antigen was mathematically defined by a finite mixture model, and cut-off values were optimized.FindingsSensitivities and specificities for each antigen ranged between 71 and 100%. Seroprevalences for each pathogen from the Kwale and Mbita HDSS sites (respectively) were as follows: HIV, 3.0% and 20.1%; L. donovani, 12.6% and 17.3%; E. histolytica, 12.8% and 16.6%; and T. gondii, 30.9% and 28.2%. Seroprevalences of W. bancrofti and V. cholerae showed relatively high figures, especially among children. The results might be affected by immunological cross reactions between W. bancrofti-SXP1 and other parasitic infections; and cholera toxin and the enterotoxigenic E. coli (ETEC), respectively.InterpretationA microsphere-based multi-serological assay system can provide an opportunity to comprehensively grasp epidemiological features for NTDs. By adding pathogens and antigens of interest, optimized made-to-order high-quality programs can be established to utilize limited resources to effectively control NTDs in Africa.

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Finite Mixture Models with Student t Distributions: an Applied Example.

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