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SUPERVISOR
Reyhaneh Rikhtegaran,Zahra Saberi
ریحانه ریخته گران (استاد مشاور) زهرا صابری (استاد راهنما)
 
STUDENT
Maryam Sabetrasekh
مریم ثابت راسخ

FACULTY - DEPARTMENT

دانشکده ریاضی
DEGREE
Master of Science (MSc)
YEAR
1393
Longitudinal data are very common in clinical researches and other field where measurments for a subject are collected over time. Missing data are unavoidable with longitudinal studies, because complete follow-up data are often not available for all subjects. Different mechanisms for denoting missingness are introduced. Mechanism of missingness is said to be missing completely at random (MCAR) if missing process is independent of both unobserved and observed data, missing at random (MAR) if conditional on the observed data, the missing process is independent of the unobserved data, and missing not at random (MNAR) when the missing process depends only upon the unobserved data. Also in longitudinal data, missing data can be categorized into two different patter general (intermittent) missing pattern and monoton (dropout) pattern. If mechanism and pattern of missingness is MNAR and monoton, respectively, missingness is called informative dropout. Analysing such data requires the more compplex models wich incorporate the dropout mechanism in the analysis, because not considering dropout mechanism into the model, lead to invalid estimation for the parameters. In this situation an indicator variable that describe response variable is observed or not, is recorded. This indicator variable show mechanism of missingness and take 1 if corresponding response variable is observed and 0 in another. In modelling missing data with respect to joint distribution of response variable and mechanism of missingness, three type of models are introduced. In this thesis for simulated longitudinal count data with informative dropout, we use from selection model that denote joint distribution of response variable and dropout indicator into a marginal distribution for response variable and conditional distribution for dropout mechanism. In conditional model of dropout mechanism, response variables are appeared as covariate variables. In longitudinal data, between group correlation are included through using random effects, So we use special case of selection model with random effects that random effects only infects on marginal distribution of response variable and mechanism of missingness is affected by response variable. In addition of between group correlation , serial correlation is existed in longitudinal data, So for considering that, we use first order auto regressive construction for marginal model for response variables. Also in longitudinal count data, is possible to be overdispersion, so we introduce one of the solution of this problem. In Bayesian framework, by considering noninformative prior distribution for parameters and using the Gi sampler algorithm, fit the joint model by using the Bayesian software OpenBUGS. The Gi sampler is done by interative algorithm that simulating parameters of model of full conditional distribution, then estimation of parameters is calculated approximately, according to ergodic theorem.
وجود گم‌شدگی در جمع‌آوری اطلاعات، به‌ویژه مطالعات طولی، امری اجتناب ناپذیر است و این امر منجر به استنباط‌های غیرمعتبر می‌شود. یکی از مفاهیم مهم مرتبط با داده‌های گم‌شده، مکانیسم گم‌شدگی است و در صورت اشتباه در نظر گرفته شدن آن، به ویژه زمانی‌که مکانیسم گم‌شدگی غیرتصادفی(MNAR) باشد، برآوردها اریب شده و کارایی برآوردگرها کاهش می‌یابد. مفهوم دیگر مرتبط با داده‌های گم‌شده، الگوی گم‌شدگی است. در داده‌های طولی، چنان‌چه گم‌شدگی با الگوی یکنوا و مکانیسم MNAR رخ دهد، به آن انصراف آگاهی‌بخش می‌گویند و در مدل‌بندی آن، باید به مکانیسم گم‌شدگی توجه شود که این کار از طریق مدل‌بندی توام متغیرهای پاسخ و مکانیسم گم‌شدگی، انجام می‌شود. نگاه ویژه این پایان‌نامه به مدل‌بندی انصراف آگاهی‌بخش داده‌های شمارشی طولی در رویکرد بیز است که در این میان، به مشکل بیش‌پراکنش داده‌های شمارشی نیز توجه شده است و به منظور در نظر گرفتن مکانیسم گم‌شدگی و تغییرات درون‌گروهی داده‌های طولی، از مدل گزینش با اثرات آمیخته استفاده می‌شود.

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