{"id":668,"date":"2015-11-25T21:33:45","date_gmt":"2015-11-25T10:33:45","guid":{"rendered":"http:\/\/casestudyhelp.com\/sample-questions\/?p=668"},"modified":"2018-01-25T21:30:12","modified_gmt":"2018-01-25T10:30:12","slug":"statistic-survival-analysis-assignment-help","status":"publish","type":"post","link":"https:\/\/casestudyhelp.com\/sample-questions\/statistic-survival-analysis-assignment-help\/","title":{"rendered":"Statistic :Survival Analysis Assignment Help"},"content":{"rendered":"

Stat 4100\/5100 – Survival Analysis – Fall 2015
\nW11: Additional Notes
\nText References and Additional Reading: x8.5-8.8,9.1-9.2
\nAssignment 8 (Due Wed, Nov 25):
\n1. Consider a censored sample from the exponential distribution with rate parameter \u0015 and \fxed cen-
\nsoring time c, common to all individuals that were in the study. That is, individual i is censored if
\nfailure time, Xi > c. Otherwise Xi is observed.
\n(a) Suppose that only the number of failures, D, is observed. Show that D has a binomial distribu-
\ntion with parameters n and p = 1 exp[\u0015c]. Using the relationship between the variance of
\nmaximum likelihood estimators and expected information obtain an expression for the variance
\nof the maximum likelihood estimate of \u0015. This should be a true variance not a standard error;
\ni.e. an expression that depends upon the parameters of the model, not data.
\n(b) Suppose now the usual case: (
\nP
\ni ti;D) are observed, where the ti are the failure and censoring
\ntimes. You showed on Assignment 4 that l00(\u0015) = D=\u00152 and ^\u0015
\n= D=
\nP
\ni ti. Using the relation-
\nship between the variance of maximum likelihood estimators and expected information obtain
\nan expression for the variance of the maximum likelihood estimate of \u0015. Again, this should
\ndepend on the parameters of the model, not data.
\n(c) The e\u000eciency of an estimator ^\u0015
\n1 to another estimator ^\u0015
\n2 is the ratio of the large sample variances
\nof the two estimators: Var(^\u0015
\n2)=Var(^\u0015
\n1). Obtain an expression for the e\u000eciency of the estimator
\nin (a) to the estimator in (b). Note that the e\u000eciency depends upon \u0015 and c. In R, produce a
\nplot of the e\u000eciency as a function of \u0015 for c = 1. For what values of \u0015 does the method in (a)
\ngive almost as good results as method (b), if any?
\n2. 8.6. The data is available on the web site. Be sure to use factor to ensure variables that are
\nsupposed to have interpretations as categorical variables do have such interpretations. In (a), by
\nANOVA table, the question means the output of summary in R. In (c) you can answer the question
\nby \fnding a 95% con\fdence interval for the relevant relative risk and checking whether 1 falls in the
\ninterval.<\/p>\n

 <\/p>\n

To get answer chat with online assignment adviser<\/strong><\/p>\n

\"Hire<\/a><\/p>\n