Confidence interval estimation for lognormal data with application to health economics

Computational Statistics and Data Analysis

Volumn 53, Issue 11, 2009, Pages 3755-3764

  Zou, Guang Yong ^a,b   Taleban, Julia ^a   Huo, Cindy Y ^c  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b ROBARTS RESEARCH INSTITUTE   (Canada)

^c INSTITUTE FOR CLINICAL EVALUATIVE SCIENCES   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONFIDENCE INTERVAL; CONFIDENCE INTERVAL ESTIMATION; CONFIDENCE LIMIT; GENERAL APPROACH; HEALTH BENEFITS; HEALTH ECONOMICS; LOG-NORMAL; SCIENTIFIC INQUIRY; SIMULATION RESULT;

HEALTH;

EID: 67349173219     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2009.03.016     Document Type: Article

References (67)

1. Agresti A., and Coull B.A. Approximate is better than "exact" for interval estimation of binomial proportions. American Statistician 52 (1998) 119-126
2. Aitchison J., and Brown J.A.C. The Log-normal Distribution (1957), Cambridge University Press, Cambridge
3. Bartlett M.S. Approximate confidence intervals. 2. More than one unknown parameter. Biometrika 40 (1953) 306-317
4. Bebu I., and Mathew T. Comparing the means and variances of a bivariate log-normal distribution. Statistics in Medicine 27 (2008) 2684-2696
5. Bradu D., and Mundlak T. Estimation in lognormal linear models. Journal of the American Statistical Association 65 (1970) 198-211
6. Briggs A., Nixon R., Dixon S., and Thompson S.G. Parametric modelling of cost data: Some simulation evidence. Health Economics 14 (2005) 421-428
7. Briggs A.H., O'Brien B.J., and Blackhouse G. Thinking out of the box: Recent advances in the analysis and presentation of uncertainty in cost-effectiveness studies. Annual Review of Public Health 23 (2002) 337-401
8. Burick R.K., and Graybill F.A. Confidence Intervals on Variance Components (1992), Dekker, New York
9. Chen H. Comparison of lognormal population means. Proceedings of the American Mathematical Society 121 (1994) 915-924
10. Chen Y.H., and Zhou X.H. Interval estimates for the ratio and difference of two lognormal means. Statistics in Medicine 25 (2006) 4099-4113
11. Crow E.L., and Shimizu K. The Log-normal Distributions: Theory and Applications (1988), Dekker, New York
12. Diciccio T.J., and Efron B. Rejoinder of "bootstrap confidence intervals". Statistical Science 11 (1996) 223-228
13. Diehr P., Yanez D., Ash A., Hornbrook M., and Lin D.Y. Methods for analyzing health care utilization and cost. Annual Review of Public Health 20 (1999) 125-144
14. Dinh P., and Zhou X.H. Nonparametric statistical methods for cost-effectiveness analyses. Biometrics 62 (2006) 576-588
15. Drummond M.F., Sculpher M.J., Torrance G.W., O'Brien B.J., and Stoddart G.L. Methods for the Economic Evaluation of Health Care Programmes. 3rd ed. (2005), Oxford University Press, New York
16. El-Shaarawi A.H., and Viveros R. Inference about the mean in log-regression with environmental applications. Environmetrics 8 (1997) 569-582
17. Fletcher D. Confidence intervals for the mean of the delta-lognormal distribution. Environmental and Ecological Statistics 15 (2008) 175-189
18. Gill P.S. Small-sample inference for the comparison of means of log-normal distributions. Biometrics 60 (2004) 525-527
19. Graybill F.A., and Wang C.M. Confidence intervals on nonnegative linear combinations of variances. Journal of the American Statistical Association 75 (1980) 869-873
20. Hall P. On the removal of skewness by transformation. Journal of the Royal Statistical Society, B 54 (1992) 221-228
21. Hoch J.S., Briggs A.H., and Willan A.R. Something old, something new, something borrowed, something blue: A framework for the marriage of health econometrics and cost-effectiveness analysis. Health Economics 11 (2002) 415-430
22. Howe W.G. Approximate confidence limits on the mean of X + Y where X and Y are two tabled independent random variable. Journal of the American Statistical Association 69 (1974) 789-794
23. Kowalski C.J. On the effects of non-normality on the distribution of the sample product-moment correlation coefficient. Applied Statistics 21 (1972) 1-12
24. Krishnamoorthy K., and Mathew T. Inferences on the means of lognormal distributions using generalized p-vlaues and generalized confidence intervals. Journal of Statistical Planning and Inference 115 (2003) 103-121
25. Krishnamoorthy K., Mathew T., and Ramachandran G. Generalized p-values and confidence intervals: A novel approach for analyzing lognormally distributed exposure data. Journal of Occupational and Environmental Hygiene 3 (2006) 642-650
26. Land C.E. An evaluation of approximate confidence interval estimation methods for lognormal means. Technometrics 14 (1972) 145-158
27. Lecoutre B., and Faure S. A note on new confidence intervals for the difference between two proportions based on an Edgeworth expansion. Journal of Statistical Planning and Inference 137 (2007) 355-356
28. Lee Y.H., Shao J., and Chow S.C. Modified large-sample confidence intervals for linear combinations of variance components: Extension, theory, and application. Journal of the American Statistical Association 99 (2004) 467-478
29. Limpert E., Stahel W.A., and Abbt M. Log-normal distributions across the sciences: Keys and clues. BioScience 51 (2001) 341-352
30. Mohn E. Confidence estimation of measures of location in the log normal distribution. Biometrika 66 (1979) 567-575
31. Mostafa M.D., and Mahmoud M.W. On the problem of estimation for the bivariate lognormal distribution. Biometrika 51 (1964) 522-527
32. Newcombe R.G. Estimating the difference between differences: Measurement of additive scale interaction for proportions. Statistics in Medicine 20 (2001) 2885-2893
33. Nixon R., and Thompson S.G. Methods for incorporating covariate adjustment, subgroup analysis and between-centre differences into cost-effectiveness evaluation. Health Economics 14 (2005) 1217-1229
34. Owen W.J., and DeRouen T.A. Estimation of the mean for lognormal data containing zeros and left-censored values, with application to the measurement of worker exposure to air contaminants. Biometrics 36 (1980) 707-719
35. Parkhurst D.F. Arithmetic versus geometric means for environmental concentration data. Environmental Science & Technology 88 (1998) 92A-98A
36. Pennington M. Efficient estimators of abundance, for fish and plankton surveys. Biometrics 39 (1983) 281-286
37. Rappaport S.M., and Selvin S. A method for evaluating the mean exposure from a lognormal distribution. American Industrial Hygiene Journal 48 (1987) 374-379
38. Schenker N. Qualms about bootstrap confidence intervals. Journal of the American Statistical Association 80 (1985) 360-361
39. Shen H., Brown L.D., and Zhi H. Efficient estimation of log-normal means with application to pharmacokinetic data. Statistics in Medicine 25 (2006) 3023-3028
40. Shen H., and Zhu Z. Efficient mean estimation in log-normal linear models. Journal of Statistical Planning and Inference 138 (2008) 552-567
41. Shimizu K. UMVU estimation for covariance and first product moments of transformed variables. Communications in Statistics 12 (1983) 1661-1674
42. Smith S.J. Evaluating the efficiency of the Δ-distribution mean estimator. Biometrics 44 (1988) 485-493
43. Stinnett A., and Mullahy J. Net health benefit: A new framework for the analysis of uncertainty in cost-effectiveness analysis. Medical Decision Making 18 (1998) S68-S80
44. Taylor D.J., Kupper L.L., and Muller K.E. Improved approximate confidence intervals for the mean of a log-normal random variable. Statistics in Medicine 21 (2002) 1443-1459
45. Thompson S.G., and Barber J.A. How should cost data in pragmatic randomised trials be analysed?. British Medical Journal 320 (2000) 1197-1200
46. Tian L., and Wu J. Confidence intervals for the mean of lognormal data with excess zeros. Biometrical Journal 48 (2006) 149-156
47. Tian L., and Wu J. Inferences on the common mean of several log-normal populations: The generalized variable approach. Biometrical Journal 49 (2007) 944-951
48. Tian L., and Wu J. Inferences on the mean response in a log-regression model: The generalized variable approach. Statistics in Medicine 26 (2007) 5180-5188
49. Tian L.L. Inferences on the mean of zero-inflated lognormal data: The generalized variable approach. Statistics in Medicine 24 (2005) 3223-3232
50. Willan A.R. Analysis, sample size, and power for estimating incremental net health benefit from clinical trial data. Controlled Clinical Trials 22 (2001) 228-237
51. Willan A.R., and Briggs A.H. Statistical Analysis of Cost-effectiveness Data (2006), Wiley, New York
52. Wilson E.B. Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association 22 (1927) 209-212
53. Wu J., Jiang G., Wong A.C.M., and Sun X. Likelihood analysis for the ratio of means of two independent log-normal distributions. Biometrics 58 (2002) 463-469
54. Wu J., Wong A.C.W., and Wei W. Interval estimation of the mean response in a log-regression model. Statistics in Medicine 25 (2006) 2125-2135
55. Wu J.R., Wong A.C.M., and Jiang G.Y. Likelihood-based confidence intervals for a log-normal mean. Statistics in Medicine 22 (2003) 1849-1860
56. Zhou X.H. Inferences about population means of health care costs. Statistical Methods in Medical Research 11 (2002) 327-339
57. Zhou X.H., and Dinh P. Nonparametric confidence intervals for the one- and two-sample problems. Biostatistics 6 (2005) 187-200
58. Zhou X.H., and Gao S. Confidence intervals for the lognormal mean. Statistics in Medicine 16 (1997) 783-790
59. Zhou X.H., Gao S., and Hui S.L. Methods for comparing the means of two independent log-normal samples. Biometrics 53 (1997) 1129-1135
60. Zhou X.H., Li C., Gao S., and Tierney W.M. Methods for testing equality of means of health care costs in a paired design study. Statistics in Medicine 20 (2001) 1703-1720
61. Zhou X.H., and Qin G.S. A supplement to: "A new confidence interval for the difference between two binomial proportions of paired data". Journal of Statistical Planning and Inference 137 (2007) 357-358
62. Zhou X.H., and Tu W. Confidence intervals for the mean of diagnostic test charge data containing zeros. Biometrics 56 (2000) 1118-1125
63. Zou G.Y. Toward using confidence intervals to compare correlations. Psychological Methods 12 (2007) 399-413
64. Zou G.Y. On the estimation of additive interaction by use of the four-by-two table and beyond. American Journal of Epidemiology 168 (2008) 212-224
65. Zou G.Y., and Donner A. Construction of confidence limits about effect measures: A general approach. Statistics in Medicine 27 (2008) 1693-1702
66. Zou G.Y., Huang W., and Zhang X. A note on confidence interval estimation for a linear function of binomial proportions. Computational Statistics and Data Analysis 53 (2009) 1080-1085
67. Zou G.Y., Huo C.Y., and Taleban J. Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20 (2009) 172-180