Model selection for forecasting growth rate of Hepatitis B patients

Transcription

1 Inernaional Journal of Engineering Science Invenion (IJESI) ISSN (Online): , ISSN (Prin): Volume 7 Issue 4 Ver. V April 8 PP 6-65 B.Sarojamma, B.Hari mallikarjuna Redd*, S.V.Subramanam 3 Assisan Professor, Deparmen of Saisics, S.V. Universi, Tirupahi.A.P.,3 Research Scholar, Deparmen of Saisics, S.V. Universi, Tirupahi.A.P. *Corresponding auher: B.Sarojamma Absrac: Hepaiis B is a viral infecion ha affecing liver funcion hroughou he world around wo billion people are infeced b hepaiis B virus. There are man pes of hepaiis s he are hepaiis B, hepaiis A, hepaiis C, hepaiis D, hepaiis E, auoimmune hepaiis, chronic hepaiis, ec. In his paper we proposed hree ime series models for ime series daa of hepaiis B for forecasing growh rae of Hepaiis paiens. The models are esed for is accurac b using R crieria and Roo Mean Square Roo Error (RMSE). Kewords: Hepaiis-B, ime series Model-, ime series Model -, ime series Model-3, R crieria, Roo Mean Square Error (RMSE) Dae of Submission: -4-8 Dae of accepance: I. Inroducion Hepaiis B is a viral infecion ha aracs on liver funcion. Hepaiis is a chronic disease. All over he word wo billion people are infeced b hepaiis B virus. These virus will spread hrough blood o blood conac as like HIV. I will spread hrough sexual acivi and injecing drug users. Hepaiis B is ransmied during oung adul hood hrough sex. Hepaiis B virus is more infecion han HIV. I is 5 o imes more infecion han HIV. There are so man pes of Hepaiis virus he are Alcoholic Hepaiis, Toxic and druginduced Hepaiis, ischemaic hepaiis, gian cell hepaiis, viral hepaiis, hepaiis A, hepaiis B, hepaiis C, Hepaiis D, hepaiis E, auoimmune hepaiis chronic hepaiis, ec. The enire paper divided in o four secions, in firs secion we discussed brief inroducion abou he sud and he res of secions includes deailed proposed models, empirical invesigaion and conclusions respecivel. The model-i Le II. Models for forecasing growh rae. consans of he model. Taking log on boh sides of he above equaion hen we ge modified equaion of form Y i =A-B. i (..) The fied regression model is = β β Model: II Anoher proposed model is as below i consans of he model are respecivel he inercep and slope coefficiens. Taking log on boh sides hen he above equaion we ge Log( ) = log( i ) log log log. i and areknown as he and known as he 6 Page

2 Le Log( ) = Y, log( ) = A, log = B Y i = A+B. i (..) he fied regression model is = β + β Model: III Where = number of Hepaiis B paiens = ime (no of ears), consans of he model are respecivel he inercep and slope coefficiens. Taking log on boh sides of he above equaion we ge Le Log( Log( ) = log( )-log( ) log log log. log. and andareknown as he ) = Y, log( ) = A, log = B, log(β ) = C Y=A-B.-C. (.3.) The fied regression model is = β β +β Generalized model: n... Where = number of Hepaiis B paiens = ime (no of ears), and where areknown as he consans of he model, are, respecivel, he inercep and slope coefficiens. Taking log on boh sides hen we ge Le Log( Log( )=log( )-log( +... ) log log log. log., and... and ) =Y, log( ) = A, log = A, log(β ) = A,...log(β n ) = A n Y=A -A.-A A n n. (.4.) Therefore he fied regression model is = β β +β +.+β n III. Empirical Invesigaions: B uilizing proposed models in secion, for he daa we observed he following resuls. Model I: he firs model for forecasing growh rae is parameers of he model and generall ermed as Inercep and slope erms. and are called he Table 3... Year i=(ear-8.5) Observed i=log paiens (observed deahs) i*i i^ Toal Page

3 The fied model is β & β are obained as follows 386 Y (.896) Table 3.. : The observed expexed number of paiens using model Year Observed paiens expeced value R^ adj R^ Model II: The prosed model is i Table 3.. Year i=log i= Observed (observed (ear-8.5) paiens deahs) i*i i^ Toal The fied model is Y 386 (.896) Model III: Year Table 3..: The Observed and expexed number of paiens using model Year Observed paiens expeced value R^ adj R^ i= (ear- 8.5) The prosed model for forecasing number hepaiis B paiens is Observed paiens i=log (observed deahs) Table 3.3. i*i i* i^ i*i^3 i^ i^3 i^ Toal Page

4 The fied Model is Y (.896) (.9996) Table 3..: The Observed and expexed number of paiens using model 3 Year Observed paiens expeced value r^ adj R^ IV. Conclusions: In order o choose he bes model among proposed models one can use R crieria and Roo Mean Square Error (RMSE). The fied models are presened below: 386 Model-I: Y.896 Model-II : Y 386 (.896) Y Model-III: (.896) (.9996) Forecased values Year Observed paiens expeced value expeced value expeced value Model Equaion R R adjused I 386 Y (.896) MSE Roo Mean Square Error II Y 386 (.896) Y (.896) (.9996) III Las four columns explain R, adjused R, Mean Square Errorand mean square roo error for hree models lised above. The bes model among hree is model3, Though R value resembles in case of model and model3 bu on observaion mean square roo error is minimum for model 3. The presen sud help o forecas he disease before onse and hen mankind can be saved from dreadful disease. 64 Page

5 References []. Akaike, H (973), Informaion heor and an Exension of he Maximum Likelihood Principle, in proceedings of he nd Inernaional Smposium on Informaion heor, ed.b N.Perov and F.Csad K, Budapese: Akademiaikiado, []. Akaike, H (98) Likelihood of an Model and Informaion Crieria, Journal of Economerics, 6, 3-4. [3]. Amemia, T (98), Selecion of Regressors, Inernaional Economeric Review,, [4]. Ames Lopez Bernal, Seven Cumins, Anonio Gasparini, (6) Inerruped ime series regression for he evaluaion of public healh inervenions: a uorial Inernaional Jounral of Epidemiolog. -8. [5]. Ashok Chandra, K (7), Crierion for Selecion of Regressors in Economerics, unpublished Ph.D., Thesis, S.V. Universi, Tirupai, Andhra Pradesh Sae, India. [6]. Balagi, B.H (999), Economerics, nd Ediion, Springer-verlong, New York. [7]. Benerjee, A.N. and Magnus, J.R. (), on he sensiivi of he usual and F-ess o Covariance Misspecificaion, Journal of Economerics, 95, B.Sarojamma " "Inernaional Journal of Engineering Science Invenion (IJESI), vol. 7, no. 4, 8, pp Page