A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data
The log-normal distribution is often used to model lifetime data due to its non-monotonic hazard rate. However, with left-truncated data the normal approximation fails due to the increased skewness in this distribution. This sometimes results in the poor performance of the confidence interval estima...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36150/1/36150.pdf |
| _version_ | 1796972853407514624 |
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| author | Manoharan, Thirunanthini Arasan, Jayanthi Midi, Habshah Adam, Mohd Bakri |
| author_facet | Manoharan, Thirunanthini Arasan, Jayanthi Midi, Habshah Adam, Mohd Bakri |
| author_sort | Manoharan, Thirunanthini |
| collection | UPM |
| description | The log-normal distribution is often used to model lifetime data due to its non-monotonic hazard rate. However, with left-truncated data the normal approximation fails due to the increased skewness in this distribution. This sometimes results in the poor performance of the confidence interval estimation based on the asymptotic normality of the maximum likelihood estimates, especially when the sample sizes are small. The purpose of this research is to compare and analyze the performance of the Wald, likelihood ratio and jackknife confidence intervals based on the widths of the intervals for the parameters of the log-normal model with fixed covariates through a coverage probability study. A lifetime data is therefore simulated under six different settings; model 1 (no truncation with exact observations), model 2 (low truncation with exact observations), model 3 (high truncation with exact observations), model 4 (no truncation with low censoring), model 5 (low truncation with low censoring) and model 6 (high truncation with low censoring). The comparative study indicates that the Wald, likelihood ratio and jackknife intervals performed reasonably well when no truncation or truncation is present and exact observations are available (model 1, model 2 and model 3) compared to when no truncation or truncation is observed with the presence of censoring (model 4, model 5 and model 6). Additionally, it is also evident from the results that the jackknife method outperformed the Wald and likelihood ratio methods specifically for the covariate parameter of the log-normal model even with small sample sizes when data is left-truncated with the presence of low censoring. |
| first_indexed | 2024-03-06T08:34:28Z |
| format | Article |
| id | upm.eprints-36150 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:34:28Z |
| publishDate | 2015 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| record_format | dspace |
| spelling | upm.eprints-361502015-08-30T09:56:00Z http://psasir.upm.edu.my/id/eprint/36150/ A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data Manoharan, Thirunanthini Arasan, Jayanthi Midi, Habshah Adam, Mohd Bakri The log-normal distribution is often used to model lifetime data due to its non-monotonic hazard rate. However, with left-truncated data the normal approximation fails due to the increased skewness in this distribution. This sometimes results in the poor performance of the confidence interval estimation based on the asymptotic normality of the maximum likelihood estimates, especially when the sample sizes are small. The purpose of this research is to compare and analyze the performance of the Wald, likelihood ratio and jackknife confidence intervals based on the widths of the intervals for the parameters of the log-normal model with fixed covariates through a coverage probability study. A lifetime data is therefore simulated under six different settings; model 1 (no truncation with exact observations), model 2 (low truncation with exact observations), model 3 (high truncation with exact observations), model 4 (no truncation with low censoring), model 5 (low truncation with low censoring) and model 6 (high truncation with low censoring). The comparative study indicates that the Wald, likelihood ratio and jackknife intervals performed reasonably well when no truncation or truncation is present and exact observations are available (model 1, model 2 and model 3) compared to when no truncation or truncation is observed with the presence of censoring (model 4, model 5 and model 6). Additionally, it is also evident from the results that the jackknife method outperformed the Wald and likelihood ratio methods specifically for the covariate parameter of the log-normal model even with small sample sizes when data is left-truncated with the presence of low censoring. Institute for Mathematical Research, Universiti Putra Malaysia 2015-01 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36150/1/36150.pdf Manoharan, Thirunanthini and Arasan, Jayanthi and Midi, Habshah and Adam, Mohd Bakri (2015) A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data. Malaysian Journal of Mathematical Sciences, 9 (1). pp. 127-144. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol9/9.%20thirunanthini.pdf |
| spellingShingle | Manoharan, Thirunanthini Arasan, Jayanthi Midi, Habshah Adam, Mohd Bakri A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title | A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title_full | A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title_fullStr | A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title_full_unstemmed | A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title_short | A coverage probability on the parameters of the log-normal distribution in the presence of left-truncated and right-censored survival data |
| title_sort | coverage probability on the parameters of the log normal distribution in the presence of left truncated and right censored survival data |
| url | http://psasir.upm.edu.my/id/eprint/36150/1/36150.pdf |
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