BFLCRM: A Bayesian functional linear Cox regression model for predicting time to conversion to Alzheimer’s disease

Annals of Applied Statistics - Tập 9 Số 4 - 2015
Eunjee Lee1, Hongtu Zhu1, Dehan Kong1, Yalin Wang2, Kelly S. Giovanello1, Joseph G. Ibrahim1
1Departments of Statistics and Operation Research, Biostatistics, and Psychology and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
2School of Computing, Informatics, and Decision Systems Engineering Arizona State University Tempe, AZ 85287-8809 [email protected].

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Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>64</b> 583–639.

Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>58</b> 267–288.

Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. <i>Biometrika</i> <b>57</b> 97–109.

Cox, D. R. (1972). Regression models and life-tables. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>34</b> 187–220.

Yao, F., Müller, H.-G. and Wang, J.-L. (2005). Functional linear regression analysis for longitudinal data. <i>Ann. Statist.</i> <b>33</b> 2873–2903.

Jack, C. R., Petersen, R. C., Xu, Y. C., Waring, S. C., O’Brien, P. C., Tangalos, E. G., Smith, G. E., Ivnik, R. J. and Kokmen, E. (1997). Medial temporal atrophy on MRI in normal aging and very mild Alzheimer’s disease. <i>Neurology</i> <b>49</b> 786–794.

Reiss, P. T. and Ogden, R. T. (2010). Functional generalized linear models with images as predictors. <i>Biometrics</i> <b>66</b> 61–69.

Sinha, D., Ibrahim, J. G. and Chen, M.-H. (2003). A Bayesian justification of Cox’s partial likelihood. <i>Biometrika</i> <b>90</b> 629–641.

Fan, J. and Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. <i>Statist. Sinica</i> <b>20</b> 101–148.

Albert, M. S., DeKosky, S. T., Dickson, D., Dubois, B., Feldman, H. H., Fox, N. C., Gamst, A., Holtzman, D. M., Jagust, W. J., Petersen, R. C., Snyder, P. J., Carrillo, M. C., Thies, B. and Phelps, C. H. (2011). The diagnosis of mild cognitive impairment due to Alzheimer’s disease: Recommendations from the national institute on aging-Alzheimer’s association workgroups on diagnostic guidelines for Alzheimer’s disease. <i>Alzheimers Dement.</i> <b>7</b> 270–279.

Anderson, N. D., Ebert, P. L., Jennings, J. M., Grady, C. L., Cabeza, R. and Graham, S. J. (2008). Recollection- and familiarity-based memory in healthy aging and amnestic mild cognitive impairment. <i>Neuropsychology</i> <b>22</b> 177–187.

Apostolova, L. G., Dinov, I. D., Dutton, R. A., Hayashi, K. M., Toga, A. W., Cummings, J. L. and Thompson, P. M. (2006a). 3D comparison of hippocampal atrophy in amnestic mild cognitive impairment and Alzheimer’s disease. <i>Brain</i> <b>129</b> 2867–2873.

Apostolova, L. G., Dutton, R. A., Dinov, I. D., Hayashi, K. M., Toga, A. W., Cummings, J. L. and Thompson, P. M. (2006b). Conversion of mild cognitive impairment to Alzheimer disease predicted by hippocampal atrophy maps. <i>Arch. Neurol.</i> <b>63</b> 693–699.

Bryant, C., Giovanello, K. S., Ibrahim, J. G., Chang, J., Shen, D., Peterson, B. S., Zhu, H. and ADNI (2013). Mapping the genetic variation of regional brain volumes as explained by all common SNPs from the ADNI study. <i>PloS One</i> <b>8</b> e71723.

Chen, K. H., Chuah, L. Y., Sim, S. K. and Chee, M. W. (2010). Hippocampal region-specific contributions to memory performance in normal elderly. <i>Brain and Cognition</i> <b>72</b> 400–407.

Colom, R., Stein, J. L., Rajagopalan, P., Martinez, K., Hermel, D., Wang, Y., Álvarez-Linera, J., Burgaleta, M., Quiroga, M., Shih, P. C. and Thompson, P. M. (2013). Hippocampal structure and human cognition: Key role of spatial processing and evidence supporting the efficiency hypothesis in females. <i>Intelligence</i> <b>41</b> 129–140.

Corder, E. H., Saunders, A. M., Strittmatter, W. J., Schmechel, D. E., Gaskell, P. C., Small, G., Roses, A. D., Haines, J. L. and Pericak-Vance, M. A. (1993). Gene dose of apolipoprotein E type 4 allele and the risk of Alzheimer’s disease in late onset families. <i>Science</i> <b>261</b> 921–923.

Costafreda, S. G., Dinov, I. D., Tu, Z., Shi, Y., Liu, C.-Y., Kloszewska, I., Mecocci, P., Soininen, H., Tsolaki, M., Vellas, B., Wahlund, L.-O., Spenger, C., Toga, A. W., Lovestone, S. and Simmons, A. (2011). Automated hippocampal shape analysis predicts the onset of dementia in mild cognitive impairment. <i>Neuroimage</i> <b>56</b> 212–219.

Cui, Y., Liu, B., Luo, S., Zhen, X., Fan, M., Liu, T., Zhu, W., Park, M., Jiang, T., Jin, J. S. and ADNI (2011). Identification of conversion from mild cognitive impairment to Alzheimer’s disease using multivariate predictors. <i>PloS One</i> <b>6</b> e21896.

Da, X., Toledo, J. B., Zee, J., Wolk, D. A., Xie, S. X., Ou, Y., Shacklett, A., Parmpi, P., Shaw, L., Trojanowski, J. Q., Davatzikos, C. and Alzheimer’s Neuroimaging Initiative (2014). Integration and relative value of biomarkers for prediction of MCI to AD progression: Spatial patterns of brain atrophy, cognitive scores, APOE genotype and CSF biomarkers. <i>Neuroimage Clin.</i> <b>4</b> 164–173.

Desikan, R. S., Cabral, H. J., Fischl, B., Guttmann, C. R. G., Blacker, D., Hyman, B. T., Albert, M. S. and Killiany, R. J. (2009). Temporoparietal MR imaging measures of atrophy in subjects with mild cognitive impairment that predict subsequent diagnosis of Alzheimer disease. <i>American Journal of Neuroradiology</i> <b>30</b> 532–538.

Devanand, D. P., Pradhaban, G., Liu, X., Khandji, A., De Santi, S., Segal, S., Rusinek, H., Pelton, G. H., Honig, L. S., Mayeux, R., Stern, Y., Tabert, M. H. and de Leon, M. J. (2007). Hippocampal and entorhinal atrophy in mild cognitive impairment: Prediction of Alzheimer disease. <i>Neurology</i> <b>68</b> 828–836.

de la Torre, J. C. (2010). Alzheimer’s disease is incurable but preventable. <i>J. Alzheimers Dis.</i> <b>20</b> 861–870.

De Leon, M. J., George, A. E., Golomb, J., Tarshish, C., Convit, A., Kluger, A., De Santi, S., Mc Rae, T., Ferris, S. H., Reisberg, B., Ince, C., Rusinek, H., Bobinski, M., Quinn, B., Miller, D. C. and Wisniewski, H. M. (1997). Frequency of hippocampal formation atrophy in normal aging and Alzheimer’s disease. <i>Neurobiol. Aging</i> <b>18</b> 1–11.

Dickerson, B. C., Wolk, D. A. and Alzheimer’s Disease Neuroimaging Initiative (2013). Biomarker-based prediction of progression in MCI: Comparison of AD signature and hippocampal volume with spinal fluid amyloid-$\beta$ and tau. <i>Front Aging Neurosci.</i> <b>5</b> 55.

Dickerson, B. C., Goncharova, I., Sullivan, M. P., Forchetti, C., Wilson, R. S., Bennett, D. A., Beckett, L. A. and deToledo-Morrell, L. (2001). MRI-derived entorhinal and hippocampal atrophy in incipient and very mild Alzheimer’s disease. <i>Neurobiol. Aging</i> <b>22</b> 747–754.

Fan, Y., Batmanghelich, N., Clark, C. M., Davatzikos, C. and Alzheimer’s Disease Neuroimaging Initiative (2008). Spatial patterns of brain atrophy in MCI patients, identified via high-dimensional pattern classification, predict subsequent cognitive decline. <i>Neuroimage</i> <b>39</b> 1731–1743.

Fennema-Notestine, C., Hagler, D. J. Jr, McEvoy, L. K., Fleisher, A. S., Wu, E. H., Karow, D. S., Dale, A. M. and Alzheimer’s Disease Neuroimaging Initiative (2009). Structural MRI biomarkers for preclinical and mild Alzheimer’s disease. <i>Hum. Brain Mapp.</i> <b>30</b> 3238–3253.

Fleming, T. R. and Harrington, D. P. (2011). <i>Counting Processes and Survival Analysis</i> <b>169</b>. Wiley, Hoboken, NJ.

Frankó, E., Joly, O. and ADNI (2013). Evaluating Alzheimer’s disease progression using rate of regional hippocampal atrophy. <i>PloS One</i> <b>8</b> e71354.

Gauthier, S., Reisberg, B., Zaudig, M., Petersen, R. C., Ritchie, K., Broich, K., Belleville, S., Brodaty, H., Bennett, D., Chertkow, H., Cummings, J. L., de Leon, M., Feldman, H., Ganguli, M., Hampel, H., Scheltens, P., Tierney, M. C., Whitehouse, P. and Winblad, B. (2006). Mild cognitive impairment. <i>The Lancet</i> <b>367</b> 1262–1270.

Gomar, J. J., Bobes-Bascaran, M. T., Conejero-Goldberg, C., Davies, P., Goldberg, T. E. and ADNI (2011). Utility of combinations of biomarkers, cognitive markers, and risk factors to predict conversion from mild cognitive impairment to Alzheimer disease in patients in the Alzheimer’s disease neuroimaging initiative. <i>Archives of General Psychiatry</i> <b>68</b> 961–969.

Grundman, M., Sencakova, D., Jack, C. R., Petersen, R. C., Kim, H. T., Schultz, A., Weiner, M. F., DeCarli, C., DeKosky, S. T., van Dyck, C., Thomas, R. G., Thal, L. J. and ADCS (2002). Brain MRI hippocampal volume and prediction of clinical status in a mild cognitive impairment trial. <i>Journal of Molecular Neuroscience</i> <b>19</b> 23–27.

Hastie, T. J. and Tibshirani, R. J. (1990). <i>Generalized Additive Models</i> <b>43</b>. CRC Press, Boca Raton, FL.

Huang, J., Sun, T., Ying, Z., Yu, Y. and Zhang, C.-H. (2013). Oracle inequalities for the LASSO in the Cox model. <i>Ann. Statist.</i> <b>41</b> 1142–1165.

Hung, H. and Chiang, C.-T. (2010). Estimation methods for time-dependent AUC models with survival data. <i>Canad. J. Statist.</i> <b>38</b> 8–26.

Ibrahim, J. G., Chen, M.-H. and Kim, S. (2008). Bayesian variable selection for the Cox regression model with missing covariates. <i>Lifetime Data Anal.</i> <b>14</b> 496–520.

Jack, C. R., Petersen, R. C., O’Brien, P. C. and Tangalos, E. G. (1992). MR-based hippocampal volumetry in the diagnosis of Alzheimer’s disease. <i>Neurology</i> <b>42</b> 183–183.

Jack, C. R. Jr., Knopman, D. S., Jagust, W. J., Shaw, L. M., Aisen, P. S., Weiner, M. W., Petersen, R. C. and Trojanowski, J. Q. (2010). Hypothetical model of dynamic biomarkers of the Alzheimer’s pathological cascade. <i>The Lancet Neurology</i> <b>9</b> 119–128.

James, G. M. (2002). Generalized linear models with functional predictors. <i>J. R. Stat. Soc. Ser. B. Stat. Methodol.</i> <b>64</b> 411–432.

Kaye, J. A., Moore, M. M., Dame, A., Quinn, J., Camicioli, R., Howieson, D., Corbridge, E., Care, B., Nesbit, G. and Sexton, G. (2005). Asynchronous regional brain volume losses in presymptomatic to moderate AD. <i>J. Alzheimers Dis.</i> <b>8</b> 51–56.

Kesslak, J. P., Nalcioglu, O. and Cotman, C. W. (1991). Quantification of magnetic resonance scans for hippocampal and parahippocampal atrophy in Alzheimer’s disease. <i>Neurology</i> <b>41</b> 51–54.

Lee, E., Zhu, H., Kong, D., Wang, Y., Giovanello, K. S., Ibrahim, J. G. and ADNI (2016). Supplement to “BFLCRM: A Bayesian functional linear Cox regression model for predicting time to conversion to Alzheimer’s disease.” <a href="DOI:10.1214/15-AOAS879SUPP">DOI:10.1214/15-AOAS879SUPP</a>.

Lorensen, W. E. and Cline, H. E. (1987). Marching cubes: A high resolution 3D surface construction algorithm. In <i>ACM Siggraph Computer Graphics</i> <b>21</b> 163–169. ACM, New York.

Luders, E., Thompson, P. M., Kurth, F., Hong, J. Y., Phillips, O. R., Wang, Y., Gutman, B. A., Chou, Y. Y., Narr, K. L. and Toga, A. W. (2013). Global and regional alterations of hippocampal anatomy in long-term meditation practitioners. <i>Human Brain Mapping</i> <b>34</b> 3369–3375.

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (2004). Equation of state calculations by fast computing machines. <i>The Journal of Chemical Physics</i> <b>21</b> 1087–1092.

Misra, C., Fan, Y. and Davatzikos, C. (2009). Baseline and longitudinal patterns of brain atrophy in MCI patients, and their use in prediction of short-term conversion to AD: Results from ADNI. <i>Neuroimage</i> <b>44</b> 1415–1422.

Mizuno, K., Wakai, M., Takeda, A. and Sobue, G. (2000). Medial temporal atrophy and memory impairment in early stage of Alzheimer’s disease: An MRI volumetric and memory assessment study. <i>Journal of the Neurological Sciences</i> <b>173</b> 18–24.

Monje, M., Thomason, M. E., Rigolo, L., Wang, Y., Waber, D. P., Sallan, S. E. and Golby, A. J. (2013). Functional and structural differences in the hippocampus associated with memory deficits in adult survivors of acute lymphoblastic leukemia. <i>Pediatric Blood &amp; Cancer</i> <b>60</b> 293–300.

Murphy, K. R., Landau, S. M., Choudhury, K. R., Hostage, C. A., Shpanskaya, K. S., Sair, H. I., Petrella, J. R., Wong, T. Z., Doraiswamy, P. M. and Alzheimer’s Disease Neuroimaging Initiative (2013). Mapping the effects of ApoE4, age and cognitive status on 18F-florbetapir PET measured regional cortical patterns of beta-amyloid density and growth. <i>Neuroimage</i> <b>78</b> 474–480.

Okuizumi, K., Onodera, O., Tanaka, H., Kobayashi, H., Tsuji, S., Takahashi, H., Oyanagi, K., Seki, K., Tanaka, M., Naruse, S., Miyatake, T., Mizusawa, H. and Kanazawa, I. (1994). ApoE-$\varepsilon 4$ and early-onset Alzheimer’s. <i>Nature Genetics</i> <b>7</b> 10–11.

Patenaude, B., Smith, S. M., Kennedy, D. N. and Jenkinson, M. (2011). A Bayesian model of shape and appearance for subcortical brain segmentation. <i>Neuroimage</i> <b>56</b> 907–922.

Pennanen, C., Kivipelto, M., Tuomainen, S., Hartikainen, P., Hänninen, T., Laakso, M. P., Hallikainen, M., Vanhanen, M., Nissinen, A., Helkala, E.-L., Vainio, P., Vanninen, R., Partanen, K. and Soininen, H. (2004). Hippocampus and entorhinal cortex in mild cognitive impairment and early AD. <i>Neurobiol. Aging</i> <b>25</b> 303–310.

Perri, R., Serra, L., Carlesimo, G. A. and Caltagirone, C. (2007). Amnestic mild cognitive impairment: Difference of memory profile in subjects who converted or did not convert to Alzheimer’s disease. <i>Neuropsychology</i> <b>21</b> 549–558.

Petersen, R. C., Thomas, R. G., Grundman, M., Bennett, D., Doody, R., Ferris, S., Galasko, D., Jin, S., Kaye, J., Levey, A., Pfeiffer, E., Sano, M., van Dyck, C. H., Thal, L. J. and Alzheimer’s Disease Cooperative Study Group (2005). Vitamin E and donepezil for the treatment of mild cognitive impairment. <i>N. Engl. J. Med.</i> <b>352</b> 2379–2388.

Poulin, S. P., Dautoff, R., Morris, J. C., Barrett, L. F., Dickerson, B. C. and ADNI (2011). Amygdala atrophy is prominent in early Alzheimer’s disease and relates to symptom severity. <i>Psychiatry Research</i>: <i>Neuroimaging</i> <b>194</b> 7–13.

Prestia, A., Caroli, A., van der Flier, W. M., Ossenkoppele, R., Van Berckel, B., Barkhof, F., Teunissen, C. E., Wall, A. E., Carter, S. F., Schöll, M., Choo, I. H., Nordberg, A., Scheltens, P. and Frisoni, G. B. (2013). Prediction of dementia in MCI patients based on core diagnostic markers for Alzheimer disease. <i>Neurology</i> <b>80</b> 1048–1056.

Risacher, S. L., Saykin, A. J., Wes, J. D., Shen, L., Firpi, H. A. and McDonald, B. C. (2009). Baseline MRI predictors of conversion from MCI to probable AD in the ADNI cohort. <i>Current Alzheimer Research</i> <b>6</b> 347–361.

Roberts, G. O., Gelman, A. and Gilks, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. <i>Ann. Appl. Probab.</i> <b>7</b> 110–120.

Rosen, W. G., Mohs, R. C. and Davis, K. L. (1984). A new rating scale for Alzheimer’s disease. <i>Am. J. Psychiatry</i> <b>141</b> 1356–1364.

Saunders, A. M., Strittmatter, W. J., Schmechel, D., George-Hyslop, P. S., Pericak-Vance, M. A., Joo, S. H., Rosi, B. L., Gusella, J. F., Crapper-MacLachlan, D. R., Alberts, M. J., Hulette, C., Crain, B., Goldgaber, D. and Roses, A. D. (1993). Association of apolipoprotein E allele $\varepsilon 4$ with late-onset familial and sporadic Alzheimer’s disease. <i>Neurology</i> <b>43</b> 1467–1467.

Scheltens, P. H., Leys, D., Barkhof, F., Huglo, D., Weinstein, H. C., Vermersch, P., Kuiper, M., Steinling, M., Wolters, E. C. and Valk, J. (1992). Atrophy of medial temporal lobes on MRI in “probable” Alzheimer’s disease and normal ageing: Diagnostic value and neuropsychological correlates. <i>Journal of Neurology</i>, <i>Neurosurgery &amp; Psychiatry</i> <b>55</b> 967–972.

Shaw, L. M., Vanderstichele, H., Knapik-Czajka, M., Clark, C. M., Aisen, P. S., Petersen, R. C., Blennow, K., Soares, H., Simon, A., Lewczuk, P., Dean, R., Siemers, E., Potter, W., Lee, V. M., Trojanowski, J. Q. and ADNI (2009). Cerebrospinal fluid biomarker signature in Alzheimer’s disease neuroimaging initiative subjects. <i>Annals of Neurology</i> <b>65</b> 403–413.

Shi, J., Thompson, P. M., Gutman, B., Wang, Y. and Alzheimer’s Disease Neuroimaging Initiative (2013a). Surface fluid registration of conformal representation: Application to detect disease burden and genetic influence on hippocampus. <i>Neuroimage</i> <b>78</b> 111–134.

Shi, J., Wang, Y., Ceschin, R., An, X., Lao, Y., Vanderbilt, D., Nelson, M. D., Thompson, P. M., Panigrahy, A. and Leporé, N. (2013b). A multivariate surface-based analysis of the putamen in premature newborns: Regional differences within the ventral striatum. <i>PloS One</i> <b>8</b> e66736.

Shi, J., Leporé, N., Gutman, B. A., Thompson, P. M., Baxter, L. C., Caselli, R. L., Wang, Y. and ADNI (2014). Genetic influence of apolipoprotein E4 genotype on hippocampal morphometry: An $N=725$ surface-based Alzheimer’s disease neuroimaging initiative study. <i>Human Brain Mapping</i> <b>35</b> 3903–3918.

Sinha, D., Chen, M.-H. and Ghosh, S. K. (1999). Bayesian analysis and model selection for interval-censored survival data. <i>Biometrics</i> <b>55</b> 585–590.

Strittmatter, W. J., Saunders, A. M., Schmechel, D., Pericak-Vance, M., Enghild, J., Salvesen, G. S. and Roses, A. D. (1993). Apolipoprotein E: High-avidity binding to beta-amyloid and increased frequency of type 4 allele in late-onset familial Alzheimer disease. <i>Proc. Natl. Acad. Sci. USA</i> <b>90</b> 1977–1981.

Tabert, M. H., Manly, J. J., Liu, X., Pelton, G. H., Rosenblum, S., Jacobs, M., Zamora, D., Goodkind, M., Bell, K., Stern, Y. and Devanand, D. P. (2006). Neuropsychological prediction of conversion to Alzheimer disease in patients with mild cognitive impairment. <i>Arch. Gen. Psychiatry</i> <b>63</b> 916–924.

Vemuri, P., Gunter, J. L., Senjem, M. L., Whitwell, J. L., Kantarci, K., Knopman, D. S., Boeve, B. F., Petersen, R. C. and Jack Jr, C. R. (2008). Alzheimer’s disease diagnosis in individual subjects using structural MR images: Validation studies. <i>Neuroimage</i> <b>39</b> 1186–1197.

Wang, Y., Zhang, J., Gutman, B., Chan, T. F., Becker, J. T., Aizenstein, H. J., Lopez, O. L., Tamburo, R. J., Toga, A. W. and Thompson, P. M. (2010). Multivariate tensor-based morphometry on surfaces: Application to mapping ventricular abnormalities in HIV/AIDS. <i>NeuroImage</i> <b>49</b> 2141–2157.

Wang, Y., Song, Y., Rajagopalan, P., An, T., Liu, K., Chou, Y.-Y., Gutman, B., Toga, A. W. and Thompson, P. M. (2011). Surface-based TBM boosts power to detect disease effects on the brain: An $N=804$ ADNI study. <i>Neuroimage</i> <b>56</b> 1993–2010.

Young, J., Modat, M., Cardoso, M. J., Mendelson, A., Cash, D. and Ourselin, S. (2013). Accurate multimodal probabilistic prediction of conversion to Alzheimer’s disease in patients with mild cognitive impairment. <i>NeuroImage</i>: <i>Clinical</i> <b>2</b> 735–745.

Zhang, D., Shen, D. and ADNI (2012). Predicting future clinical changes of MCI patients using longitudinal and multimodal biomarkers. <i>PloS One</i> <b>7</b> e33182.

Ramsay, J. O. and Silverman, B. W. (2005). <i>Functional Data Analysis</i>, 2nd ed. Springer, New York.

Ibrahim, J. G., Chen, M.-H. and Sinha, D. (2005). <i>Bayesian Survival Analysis</i>. Wiley Online Library.

Kalbfleisch, J. D. and Prentice, R. L. (2002). <i>The Statistical Analysis of Failure Time Data</i>, 2nd ed. Wiley, Hoboken, NJ.

Biswas, A., Datta, S., Fine, J. P. and Segal, M. R. (2008). <i>Statistical Advances in the Biomedical Sciences</i>: <i>Clinical Trials</i>, <i>Epidemiology</i>, <i>Survival Analysis</i>, <i>and Bioinformatics</i>. Wiley, Hoboken, NJ.

Ferraty, F. and Vieu, P. (2006). <i>Nonparametric Functional Data Analysis</i>: <i>Methods</i>, <i>Theory</i>, <i>Applications and Implementation</i>. Springer, New York.

Li, J. and Ma, S. (2013). <i>Survival Analysis in Medicine and Genetics</i>. Chapman &amp; Hall/CRC, Boca Raton, FL.

Li, S., Okonkwo, O., Albert, M. and Wang, M.-C. (2013). Variation in variables that predict progression from MCI to AD dementia over duration of follow-up. <i>Am. J. Alzheimers Dis.</i> (<i>Columbia</i>) <b>2</b> 12–28.