An analytical approach on estimation of cure rate from mixture model based on Type 2 censoring
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Abstract This study deals with the analysis of estimation of cure rate. Mixture models have been proposed for cure rate estimation. In this paper we have tried to estimate the cure parameter by considering censored data specifically for Type 2 censoring from mixture model. We have used parametric Maximum likelihood estimation (PMLE) method and non parametric maximum likelihood (NPMLE) method to estimate the parameter. From the analysis we have found an explicit solution for the parameter of cure rate model based on Type 2 censoring for known distribution function. On the other hand when the distribution function are unknown, we have found a non-parametric estimating equations for on based on Type 2 censoring scheme.Keywords:
Censoring (clinical trials)
On the mixture model H=λF+(1-λ)G,we derive the consistent estimator ■ of the mixture proportionλunder random right censoring,we also discuss the asymptotic normality of the estimator ■.
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We find that the empirical results reported in Chang (Journal of Applied Econometrics 2011; 26(5): 854–871) are contingent on the specification of the model. The use of Heckman's initial conditions combined with observed and not latent lagged dependent variables leads to a counter-intuitive estimation of the true state dependence. The use of Wooldridge's initial conditions together with the observed lagged dependent variable and a proper modelling of censoring provides a much more natural estimate of the true state dependence parameters together with a clearer interpretation of the decision to participate in the labour market in the two-tiered model. Copyright © 2015 John Wiley & Sons, Ltd.
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Fixed transactions costs that prohibit exchange engender bias in supply analysis due to censoring of the sample observations. The associated bias in conventional regression procedures applied to censored data and the construction of robust methods for mitigating bias have been preoccupations of applied economists since Tobin [Econometrica 26 (1958) 24]. This literature assumes that the true point of censoring in the data is zero and, when this is not the case, imparts a bias to parameter estimates of the censored regression model. We conjecture that this bias can be significant; affirm this from experiments; and suggest techniques for mitigating this bias using Bayesian procedures. The bias-mitigating procedures are based on modifications of the key step that facilitates Bayesian estimation of the censored regression model; are easy to implement; work well in both small and large samples; and lead to significantly improved inference in the censored regression model. These findings are important in light of the widespread use of the zero-censored Tobit regression and we investigate their consequences using data on milk-market participation in the Ethiopian highlands.
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A simulation study was performed to examine the effects of withdrawal censoring and fixed right censoring on the level of significance and power of two-sample tests. Statistics based on Gehan, logrank, and Peto-Prentice scores are used. It is demonstrated that the performance of these tests can be adversely affected by a high percenage of withdrawals and/or unequal sample sizes
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Journal Article Maximum likelihood estimation of the general nonlinear functional relationship with replicated observations and correlated errors Get access G. R. DOLBY, G. R. DOLBY Department of Primary IndustriesQueensland Search for other works by this author on: Oxford Academic Google Scholar S. LIPTON S. LIPTON University of Queensland Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 59, Issue 1, April 1972, Pages 121–129, https://doi.org/10.1093/biomet/59.1.121 Published: 01 April 1972 Article history Received: 01 May 1971 Revision received: 01 October 1971 Published: 01 April 1972
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Time use researchers frequently debate whether it is more appropriate to fit censored regression (Tobit) models using maximum likelihood estimation or linear models using ordinary least squares (OLS) to explain individuals’ allocations of time to different activities as recorded in time-diary data. One side argues that estimation of Tobit models addresses the significant censoring (i.e., large numbers of zeros) typically found in time-diary data and that OLS estimation leads to biased and inconsistent estimates. The opposing side argues that optimization occurs over a longer period than that covered by the typical time diary, and thus that reported zeros represent measurement error rather than true non-participation in the activity, in which case OLS is preferred. We use the Australian Time Use Surveys, which record information for two consecutive diary days, to estimate censored and linear versions of a parental child care model for both 24-hour and 48-hour windows of observation in order to determine the empirical consequences of estimation technique and diary length. We find a moderate amount of measurement error when we use the 24-hour window compared to the 48-hour window, but a large number of zeros in the shorter window remain zeroes when we double the window length. Most of the qualitative conclusions we draw are similar for the two windows of observation and the two estimation methods, although there are some slight differences in the magnitudes and statistical significance of the estimates. Importantly, Tobit estimates appear to be more sensitive to window length than OLS estimates.
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We give semiparametric identi…cation and estimation results for econometric models with a regressor that is endogenous, bound censored and selected, called a Tobin regressor.First, we show that true parameter value is set identi-…ed and characterize the identi…cation sets.Second, we propose novel estimation and inference methods for this true value.These estimation and inference methods are of independent interest and apply to any problem where the true parameter value is point identi…ed conditional on some nuisance parameter values that are set-identi…ed.By …xing the nuisance parameter value in some suitable region, we can proceed with regular point and interval estimation.Then, we take the union over nuisance parameter values of the point and interval estimates to form the …nal set estimates and con…dence set estimates.The initial point or interval estimates can be frequentist or Bayesian.The …nal set estimates are set-consistent for the true parameter value, and con…dence set estimates have frequentist validity in the sense of covering this value with at least a prespeci…ed probability in large samples.We apply our identi…cation, estimation, and inference procedures to study the e¤ects of changes in housing wealth on household consumption.Our set estimates fall in plausible ranges, signi…cantly above low OLS estimates and below high IV estimates that do not account for the Tobin regressor structure.
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