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  • 1
    Electronic Resource
    Electronic Resource
    Relationship between Derivatives of the Observed and Full Loglikelihoods and Application to Newton-Raphson Algorithm (2006)
    Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)
    The @international journal of biostatistics 2 (2006), S. 4 
    Details
    ISSN: 1557-4679
    Source: Berkeley Electronic Press Academic Journals
    Topics: Biology , Mathematics , Medicine
    Notes: In the case of incomplete data we give general relationships between the first and second derivatives of the loglikelihood relative to the full and the incomplete observation set-ups. In the case where these quantities are easy to compute for the full observation set-up we propose to compute their analogue for the incomplete observation set-up using the above mentioned relationships: this involves numerical integrations. Once we are able to compute these quantities, Newton-Raphson type algorithms can be applied to find the maximum likelihood estimators, together with estimates of their variances. We detail the application of this approach to parametric multiplicative frailty models and we show that the method works well in practice using both a real data and a simulated example. The proposed algorithm outperforms a Newton-Raphson type algorithm using numerical derivatives.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/ijb/vol2/iss1/4
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  • 2
    Electronic Resource
    Electronic Resource
    Rejoinder (1995)
    Springer
    Lifetime data analysis 1 (1995), S. 159-159 
    Details
    ISSN: 1572-9249
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00985766
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Standardized Martingale Residuals Applied to Grouped Left Truncated Observations of Dementia Cases (2000)
    Springer
    Lifetime data analysis 6 (2000), S. 229-235 
    Details
    ISSN: 1572-9249
    Keywords: martingale residuals ; survival data ; left-truncation ; dementia ; aluminum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The use of martingale residuals have been proposed for modelchecking and also to get a non-parametric estimate of the effectof an explanatory variable. We apply this approach to an epidemiologicalproblem which presents two characteristics: the data are lefttruncated due to delayed entry in the cohort; the data are groupedinto geographical units (parishes). This grouping suggests anatural way of smoothing the graph of residuals which is to computethe sum of the residuals for each parish. It is also naturalto present a graph with standardized residuals. We derive thevariances of the estimated residuals for left truncated datawhich allows computing the standardized residuals. This methodis applied to the study of dementia in a cohort of old people,and to the possible effect of the concentration of aluminum andsilica in drinking water on the risk of developing dementia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009637608473
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Deconvolution analysis of radionuclide angiocardiography curves: Problems arising from fragmented bolus injections (1983)
    Springer
    European journal of nuclear medicine 8 (1983), S. 93-98 
    Details
    ISSN: 1619-7089
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Deconvolution analysis of radionuclide angiocardiography time-activity curves (TAC) in the cases of fragmented bolus injections was studied by using a new deconvolution technique based on the maximum a posteriori estimator. This method was first tested by simulation studies which showed its capability for accurate handling of deconvolution both for single and double peak input functions. These simulations have proved this technique to have advantages over a Fourier transform division method used with a low-pass filter. In patient studies, deconvolution of pulmonary TAC by superior vena caval TAC produced poor results in double peak (fragmented) bolus injections, compared with single peak bolus injections (SPBI). This discrepancy seems to be due to the fact that the postulates of linearity and invariance, on which deconvolution analysis is based, do not hold for the ‘cardiopulmonary system’ which extends from the superior vena cava to the lung. The differences between the model and the real system appear unimportant for SPBI. However, differences become apparent for fragmented bolus injections. Deconvolution analysis should be avoided with this type of input function in this cardiopulmonary system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00256729
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    Paper (German National Licenses)
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