Öz
Missing data are unavoidable in longitudinal studies and can lead toserious problems, such as loss
of power and biased estimates, which should be solved in the statistical analysis of clinical studies. In
this paper, three different techniques for handling missing data are shown using an example from a
rheumatologic study. It is also shown how sensitive the conclusions of the study can be in terms of how
the incomplete data are analyzed. The missing data process is studied in the framework of longitudinal
data. The common approaches to handling missing longitudinal clinical trial data because of dropout
are complete case (CC) and last observation carried forward (LOCF) analyses. These methods, while
intuitively appealing, require tough assumptions to reach valid statistical conclusions. A relatively new
and up to date statistical method for analyzing data with incomplete repeated measures is “likelihoodbased
ignorable method” which has less constraints and fewer tough assumptions than those required
for CC and LOCF. We apply these three methods to data set of a rheumatologic trial comparing
disease groups in terms of the joint pain scores using a mixed model. No significant differences were
found between the methods of analysis. It can be concluded that attention to the mechanisms of
missing data should be very important part of the analysis of rheumatologic data.
Anahtar Kelimeler
Last observation carried forward Complete case analysis Longitudinal data Rheumatology Missing data process Mixed models
Kaynakça
- van Riel PCLM, van Gestel AM, Welsing PMC. Evaluation and outcome of the patient with established rheumatoid arthritis. In: Hochberg MC et al (eds) Rheumatology, 3rd edn. Mosby Elsevier: Philadelphia, 2003; 893-905.
- Little RJA, Rubin DB. Statistical Analysis with Missing Data, 2nd ed. Wiley: New York, 2002.
- Schafer JL, Graham JW. Missing data: Our view of the state of the art. Psychological Methods 2002; 7 (2): 147-177.
- Jansen I, Beunckens C, Molenberghs G, Verbeke G, Mallinckrodt C. Analyzing incomplete discrete longitudinal clinical trial data. Statistical Science 2006; 21: 52–69.
- Molenberghs G, Thijs H, Jansen I, Beunckens C, Kenward M G, Mallinckrodt C. Carroll R J. Analyzing incomplete longitudinal clinical trial data. Biostatistics 2004; 5: 445–464.
- Fitzmaurice GM. Methods for handling dropouts in longitudinal clinical trials. Statistica Neerlandica 2003; 57: 75–99
- Cay HF, Sezer I, Firat MZ, Kaçar C. Which is the dominant factor for perception of rheumatic pain: meteorology or psychology? Rheumatol Int 2011;31(3):377-85.
- Harris ED. Clinical features of rheumatoid arthritis. In: Harris ED et al (eds) Kelley’s textbook of rheumatology, 7th edn. Elsevier Saunders: Amsterdam, 2005; 1043–1078.
- Olivieri I, van Tubergen A, Salvarani C, van der Linden S. Seronegative spondyloarthritides. Best Pract Res Clin Rheumatol 2002; 16(5):723–739
- Dennison E, Cooper C. Osteoarthritis: epidemiology and classification. In: Hochberg MC et al (eds) Rheumatology, 3rd edn. Mosby Elsevier: Philadelphia, 2003; 1781–1791.
- SAS Institute. SAS/STAT Software, Version 8. Author, Cary, NC, 2008.
- Kincaid C. Guidelines for selecting the covariance structure in mixed model analysis. SUGI 30 Proceedings: Paper 198-3, 2005.
- Larid NM, Ware JH. Random-effect models for longitudinal data. Biometrics 1982; 38: 963–974.
- Diggle PJ, Liang KY, Zeger SL. The Analysis of Longitudinal Data. Oxford University Press: Oxford, 1994.
- Oman SD. Multiplicative effects in mixed model analysis of variance. Biometrika 1991; 78: 729–739.
- Wolfinger R. Covariance structure selection in general mixed models. Commun.Stat-Simul. C 1993; 22: 1079– 1106.
- Akaike H. A new look at the statistical model identification. IEEE Transaction on Automatic Control 1974; AC-19: 716-723.
- Schwarz G. Estimating the dimension of a model. Annals of Statistics 1978; 6: 461-464.
- Kim JO, Curry J. The Treatment of Missing Data in Mu ltivariate Analysis. Sociological Methods Research,1977; 6: 215-240.
- Allison, PD. Multiple Regression: A Primer. Pine Forge Press, Thousand Oaks, 1999.
- Shao J, Zhong B. Last Observation Carry-Forward and Last Observation Analysis. Statistics in Medicine 2003; 22: 2429-2441.
- Mallinckrodt CH, Clark WS, David SR. Accounting for Dropout Bias Using Mixed-Effects Models. Journal of Biopharmaceutical Statistics 2001; 11: 9-21.
- Mallinckrodt CH, Kaiser CJ, Watkin JG, Detke MJ, Molenberghs G, Carroll RJ. Type I Error Rates from Likelihood-Based Repeated Measures Analyses of Incomplete Longitudinal Data. Pharmaceutical Statistics 2004; 3: 171-186.
- Gadbury GL, Coffey CS, Allison DB. Modern Statistical Methods for Handling Missing Repeated Measurements in Obesity Trials: Beyond LOCF. Obesity Reviews 2003; 4: 175-184.
- Little RJA, Rubin DB. Statistical Analysis with Missing Data. New York: Wiley, 1987.
- Diggle PJ, Kenward MG. Informative drop-out in longitudinal data analysis (with discussion). Applied Statistics 1994; 43: 49–93.
- Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. New York: Springer, 2000.
Boylamsal Bir Romatoloji Çalışmasında Kayıp Verilerin Üstesinden Gelen Yöntemlerin Karşılaştırılması
Öz
Boylamsal çalışmalarda eksik veriler kaçınılmazdır ve klinik çalışmaların istatistiksel analizinde
çözülmeleri gereken yanlı tahminler ve güç kaybı gibi ciddi sorunlara yol açabilirler. Bu makalede,
romatolojik bir çalışmadan alınan örnek kullanılarak eksik verilerin üstesinden gelen üç farklı
teknik gösterilmiştir. Ayrıca çalışmanın sonuçlarının, eksik verilerin analiz edilme şekli açısından
ne kadar hassas olabileceği gösterilmiştir. Eksik veri süreci boylamsal veriler için incelenmiştir.
Ayrılmalar nedeniyle eksik boylamsal klinik çalışma verilerinin üstesinden gelen yaygın yaklaşımlar,
tam vaka (CC) ve son gözlemi ileri taşıma (LOCF) analizleridir. Sezgisel olarak çekici olmalarına
rağmen bu yöntemler, geçerli istatistiksel sonuçlar üretmek için kısıtlayıcı varsayımlar gerektirirler.
Eksik tekrarlanan ölçümleri içeren verileri analiz etmek için nispeten yeni ve modern bir istatistiksel
yöntem, CC ve LOCF’ye göre daha az sınırlamaya ve kısıtlayıcı varsayımlara sahip olan “olabilirlik
tabanlı” yöntemdir. Bu üç yöntemi, karışık bir model kullanarak eklem ağrı skorları açısından hastalık
gruplarını karşılaştıran romatolojik bir çalışma setine uyguladık. Analiz yöntemleri arasında anlamlı
bir fark bulunmamıştır. Eksik veri mekanizmalarına dikkatin romatolojik verilerin analizinde ayrılmaz
bir parçası olması gerektiği sonucuna vardık.
Anahtar Kelimeler
Tam vaka analizi Son gözlem ileriye taşıma boylamsal veriler Romatoloji Eksik veri süreci Karışık modeler
Kaynakça
- van Riel PCLM, van Gestel AM, Welsing PMC. Evaluation and outcome of the patient with established rheumatoid arthritis. In: Hochberg MC et al (eds) Rheumatology, 3rd edn. Mosby Elsevier: Philadelphia, 2003; 893-905.
- Little RJA, Rubin DB. Statistical Analysis with Missing Data, 2nd ed. Wiley: New York, 2002.
- Schafer JL, Graham JW. Missing data: Our view of the state of the art. Psychological Methods 2002; 7 (2): 147-177.
- Jansen I, Beunckens C, Molenberghs G, Verbeke G, Mallinckrodt C. Analyzing incomplete discrete longitudinal clinical trial data. Statistical Science 2006; 21: 52–69.
- Molenberghs G, Thijs H, Jansen I, Beunckens C, Kenward M G, Mallinckrodt C. Carroll R J. Analyzing incomplete longitudinal clinical trial data. Biostatistics 2004; 5: 445–464.
- Fitzmaurice GM. Methods for handling dropouts in longitudinal clinical trials. Statistica Neerlandica 2003; 57: 75–99
- Cay HF, Sezer I, Firat MZ, Kaçar C. Which is the dominant factor for perception of rheumatic pain: meteorology or psychology? Rheumatol Int 2011;31(3):377-85.
- Harris ED. Clinical features of rheumatoid arthritis. In: Harris ED et al (eds) Kelley’s textbook of rheumatology, 7th edn. Elsevier Saunders: Amsterdam, 2005; 1043–1078.
- Olivieri I, van Tubergen A, Salvarani C, van der Linden S. Seronegative spondyloarthritides. Best Pract Res Clin Rheumatol 2002; 16(5):723–739
- Dennison E, Cooper C. Osteoarthritis: epidemiology and classification. In: Hochberg MC et al (eds) Rheumatology, 3rd edn. Mosby Elsevier: Philadelphia, 2003; 1781–1791.
- SAS Institute. SAS/STAT Software, Version 8. Author, Cary, NC, 2008.
- Kincaid C. Guidelines for selecting the covariance structure in mixed model analysis. SUGI 30 Proceedings: Paper 198-3, 2005.
- Larid NM, Ware JH. Random-effect models for longitudinal data. Biometrics 1982; 38: 963–974.
- Diggle PJ, Liang KY, Zeger SL. The Analysis of Longitudinal Data. Oxford University Press: Oxford, 1994.
- Oman SD. Multiplicative effects in mixed model analysis of variance. Biometrika 1991; 78: 729–739.
- Wolfinger R. Covariance structure selection in general mixed models. Commun.Stat-Simul. C 1993; 22: 1079– 1106.
- Akaike H. A new look at the statistical model identification. IEEE Transaction on Automatic Control 1974; AC-19: 716-723.
- Schwarz G. Estimating the dimension of a model. Annals of Statistics 1978; 6: 461-464.
- Kim JO, Curry J. The Treatment of Missing Data in Mu ltivariate Analysis. Sociological Methods Research,1977; 6: 215-240.
- Allison, PD. Multiple Regression: A Primer. Pine Forge Press, Thousand Oaks, 1999.
- Shao J, Zhong B. Last Observation Carry-Forward and Last Observation Analysis. Statistics in Medicine 2003; 22: 2429-2441.
- Mallinckrodt CH, Clark WS, David SR. Accounting for Dropout Bias Using Mixed-Effects Models. Journal of Biopharmaceutical Statistics 2001; 11: 9-21.
- Mallinckrodt CH, Kaiser CJ, Watkin JG, Detke MJ, Molenberghs G, Carroll RJ. Type I Error Rates from Likelihood-Based Repeated Measures Analyses of Incomplete Longitudinal Data. Pharmaceutical Statistics 2004; 3: 171-186.
- Gadbury GL, Coffey CS, Allison DB. Modern Statistical Methods for Handling Missing Repeated Measurements in Obesity Trials: Beyond LOCF. Obesity Reviews 2003; 4: 175-184.
- Little RJA, Rubin DB. Statistical Analysis with Missing Data. New York: Wiley, 1987.
- Diggle PJ, Kenward MG. Informative drop-out in longitudinal data analysis (with discussion). Applied Statistics 1994; 43: 49–93.
- Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. New York: Springer, 2000.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Klinik Tıp Bilimleri |
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 12 Temmuz 2021 |
| Gönderilme Tarihi | 21 Mayıs 2020 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 7 Sayı: 2 |
