We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.
Photodynamic therapy (PDT), a treatment that uses a photosensitizer, molecular oxygen, and light to kill target cells, is a promising cancer treatment method. However, a limitation of PDT is its dependence on light that is not highly penetrating, precluding the treatment of tumors located deep in the body. Copper-cysteamine nanoparticles are a new type of photosensitizer that can generate cytotoxic singlet oxygen molecules upon activation by X-rays. In this paper, we report on the use of copper-cysteamine nanoparticles, designed to be targeted to tumors, for X-ray–induced PDT. In an in vivo study, results show a statistically significant reduction in tumor size under X-ray activation of pH-low insertion peptide–conjugated, copper-cysteamine nanoparticles in mouse tumors. This work confirms the effectiveness of copper-cysteamine nanoparticles as a photosensitizer when activated by radiation and suggests that these Cu-Cy nanoparticles may be good candidates for PDT in deeply seated tumors when combined with X-rays and conjugated to a tumor-targeting molecule.
Big data are data on a massive scale in terms of volume, intensity, and complexity that exceed the capacity of standard analytic tools. They present opportunities as well as challenges to statisticians. The role of computational statisticians in scientific discovery from big data analyses has been under-recognized even by peer statisticians. This article summarizes recent methodological and software developments in statistics that address the big data challenges. Methodologies are grouped into three classes: subsampling-based, divide and conquer, and online updating for stream data. As a new contribution, the online updating approach is extended to variable selection with commonly used criteria, and their performances are assessed in a simulation study with stream data. Software packages are summarized with focuses on the open source and packages, covering recent tools that help break the barriers of computer memory and computing power. Some of the tools are illustrated in a case study with a logistic regression for the chance of airline delay.
IMPORTANCE It is unknown how treatment with radical prostatectomy (RP) and adjuvant external beam radiotherapy (EBRT), androgen deprivation therapy (ADT), or both (termed MaxRP) compares with treatment with EBRT, brachytherapy, and ADT (termed MaxRT). OBJECTIVE To investigate whether treatment of Gleason score 9-10 prostate cancer with MaxRP vs MaxRT was associated with prostate cancer-specific mortality (PCSM) and all-cause mortality (ACM) risk. DESIGN, SETTING, AND PARTICIPANTS The study cohort comprised 639 men with clinical T1-4,N0M0 biopsy Gleason score 9-10 prostate cancer. Between February 6, 1992, and April 26, 2013, a total of 80 men were consecutively treated with MaxRT at the Chicago Prostate Cancer Center, and 559 men were consecutively treated with RP and pelvic lymph node dissection at the Martini-Klinik Prostate Cancer Center. Follow-up started on the day of prostate EBRT or RP and concluded on October 27, 2017. EXPOSURES Of the 559 men managed with RP and pelvic lymph node dissection, 88 (15.7%) received adjuvant EBRT, 49 (8.8%) received ADT, and 50 (8.9%) received both. MAIN OUTCOMES AND MEASURES Treatment propensity score-adjusted risk of PCSM and ACM and the likelihood of equivalence of these risks between treatments using a plausibility index. RESULTS The cohort included 639 men, with a mean (SD) age of 65.83 (6.52) years. After median follow-ups of 5.51 years (interquartile range, 2.19-6.95 years) among 80 men treated with MaxRT and 4.78 years (interquartile range, 4.01-6.05 years) among 559 men treated with RP-containing treatments, 161 men had died, 106 (65.8%) from prostate cancer. There was no significant difference in the risk of PCSM (adjusted hazard ratio, 1.33; 95% CI, 0.49-3.64; P = .58) and ACM (adjusted hazard ratio, 0.80; 95% CI, 0.36-1.81; P = .60) when comparing men who underwent MaxRP vs MaxRT, with plausibility indexes for equivalence of 76.75% for the end point of the risk of PCSM and 77.97% for the end point of the risk of ACM. Plausibility indexes for all other treatment comparisons were less than 63%. CONCLUSIONS AND RELEVANCE Results of this study suggest that it is plausible that treatment with MaxRP or MaxRT for men with biopsy Gleason score 9-10 prostate cancer can lead to equivalent risk of PCSM and ACM.
PURPOSE Adjuvant compared with early salvage radiation therapy (sRT) following radical prostatectomy (RP) has not been shown to reduce progression-free survival in randomized controlled trials. However, these trials might have missed a benefit in men with adverse pathology at RP given that these men were under-represented and immortal time bias might have been present; herein, we investigate this possibility. METHODS We evaluated the impact of adjuvant versus early sRT on all-cause mortality (ACM) risk in men with adverse pathology defined as positive pelvic lymph nodes (pN1) or pGleason score 8-10 prostate cancer (PC) and disease extending beyond the prostate (pT3/4). We used a treatment propensity score to minimize potential treatment selection bias when estimating the causal effect of adjuvant versus early sRT on ACM risk and a sensitivity analysis to assess the impact that varying definitions of adverse pathology had on ACM risk adjusting for age at RP, PC prognostic factors, site, and the time-dependent use of post-RP androgen deprivation therapy. RESULTS After a median follow-up (interquartile range) of 8.16 (6.00-12.10) years, of the 26,118 men in the study cohort, 2,104 (8.06%) died, of which 539 (25.62%) were from PC. After excluding men with a persistent prostate-specific antigen, adjuvant compared with early sRT was associated with a significantly lower ACM risk among men with adverse pathology at RP when men with pN1 PC were excluded (0.33 [0.13-0.85]; P = .02) or included (0.66 [0.44-0.99]; P = .04). CONCLUSION Adjuvant radiation therapy should be considered in men with pN1 or pGleason score 8 to 10 and pT3/4 PC given the possibility that a significant reduction in ACM risk exists.
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