Gamma Log Research Articles

An empirical assessment of breast cancer treatment charges by survival status.

e11541 Background: Breast cancer treatment can be costly, but it remains unknown if charges differ between patients who die during treatment compared to survivors. The objective of this study was to assess annualized mean charges by survival status in patients with a diagnosis of breast cancer. Methods: The University of Utah Enterprise Data Warehouse was used to analyze patients ≥18 years with a diagnosis of breast cancer identified by ICD-9 code (initial diagnosis defined as index date) treated at the Huntsman Cancer institute (HCI) from 2002-2010. The HCI Tumor Registry was used to determine stage at diagnosis and other cancers. Cause and date of death was captured from the Utah Population Database. Cancer-related (CR) and non-CR charges were by ICD-9 codes from index date until death or end of the follow-up period, were weighted by the inverse probability of survival, and annualized. Generalized linear models (GLM) with gamma distribution and log link function were used to examine charges by survival status, while adjusting for baseline characteristics including demographics, stage, and comorbidities. Results: There were 1783 patients included, of which 296 (17%) died. Compared to survivors, deceased patients were older (mean age 62 vs. 56), more were diagnosed with stage IV disease (17% vs. 3%), and fewer with stage I (24% vs. 45%); all p<0.001. Mean unadjusted annualized CR charges were not different between groups (deceased $34,310 vs. alive $32,797; p=0.64), but non-CR charges were higher for deceased patients ($39,926 vs. $16,538; p<0.001). GLM results indicated deceased patients had 90% higher annualized CR charges relative to survivors (p<0.001) and higher charges for stages I, II, and III (125%, 86%, and 69%, respectively; all p<0.001). Deceased patients had 124% higher annualized non-CR charges relative to survivors (p<0.001) and higher charges for stages I, II, and III (174%, 146%, and 107%, respectively; all p<0.001). Charges did not differ between groups for stage IV patients. Conclusions: When adjusting for confounders, death was associated with higher CR and non-CR charges, except in patients with stage IV disease at diagnosis. Patients who died during treatment may have had more aggressive disease leading to higher charges.

Geophysical borehole logging for control of driller’s records: hydrogeological case study from Voltaian sedimentary rocks in northern Ghana

The low borehole yielding potential and the high drilling failure rate of the Voltaian sedimentary rocks of Northern Ghana have been of concern to many local hydrogeologists and international donors. Consequently, several donor-supported projects have been instituted within the last few years with the view to study the hydrogeological characteristics of this ‘difficult’ rock system. One such project is the geophysical borehole logging of 13 boreholes drilled into the Voltaian sedimentary rocks of Northern Ghana to enhance detailed hydrogeological assessment. Natural gamma detectors embedded in the five exploratory logging tools employed for the study ensured depth control by comparing their individual gamma log signatures. The combined gamma and formation resistivity/conductivity response logs provided more detailed lithological information than were shown in the driller’s/geologist’s logs. Significant discrepancies between the logging results and the reported drilled depths, construction depths, and screen settings were observed in seven of the thirteen investigated boreholes. Thus, the reliability of driller’s borehole records seems questionable, which will hamper hydrogeological studies and the mapping of groundwater resources. Further, it may be supposed that the productivity of most wells in Ghana is compromised by poor depth control of screen placement.

A NOTE ON THE q-ANALOGUE OF KIM'S p-ADIC log GAMMA TYPE FUNCTIONS ASSOCIATED WITH q-EXTENSION OF GENOCCHI AND EULER NUMBERS WITH WEIGHT α

In this paper, we introduce the <TEX>$q$</TEX>-analogue of <TEX>$p$</TEX>-adic log gamma functions with weight alpha. Moreover, we give a relationship between weighted <TEX>$p$</TEX>-adic <TEX>$q$</TEX>-log gamma functions and <TEX>$q$</TEX>-extension of Genocchi and Euler numbers with weight alpha.

On Eulerian log-gamma integrals and Tornheim–Witten zeta functions

Stimulated by earlier work by Moll and his coworkers (Amdeberhan et al., Proc. Am. Math. Soc., 139(2):535–545, 2010), we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim–Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate $$\mathcal{LG}_n=\int_0^1 \log^n\varGamma(x) \,\mathrm{d}x $$ for 1≤n≤4 and make some comments regarding the general case. The subsidiary computational challenges are substantial, interesting and significant in their own right.

Disposition of Aquifer System, Geo-electric Characteristics and Gamma-log Anomaly in the Kuttanad Alluvium of Kerala

Abstract: Kuttanad near the western coast of Kerala is a low lying area below mean sea level. The hydrogeological scenario in this wet land dominated tract, known as kole lands, was investigated by using the lithological and geophysical data generated under the R&amp;D exploration programme of Central Ground Water Board (CGWB) during the year 2000, as also other related data generated till the year 2009. The hydrogeology of the tract is complex, and the presence of carbonaceous and organic matter in the soil and sub-soil influences the geochemical and geo-electric characteristics of the sub-surface geological formations as reflected by SP and resistivity logs. The lithologs and geophysical logs of bore wells were used to define the aquifer geometry. While the lateral and vertical variations of the aquifer systems identified were high, the bottom aquifer was relatively brackish over a large area. The gamma log behavior in these granular zones is anomalous and misguiding in nature. The radioactivities recorded against clay horizons were in the range of 130 to 200cps and in the granular zones 150 to 350 cps. The presence of monazite bearing sands at certain depths was responsible for anomalously high gamma counts against granular zones. The water quality in the granular zones was inferred from the electrical logs. The depth of occurrence of high radiation sand beds was also demarcated.

An economic evaluation of perioperative adverse events associated with spinal surgery

Besides their clinical impact, the economic impact of health care-related adverse events (AEs) is significant. Although a number of studies have attempted to estimate the economic impact of AEs, few have directly linked costs to clinician-reported event severity. To estimate the economic impact in terms of the incremental cost and length of stay (LOS), attributable to different severity grades of AEs that occurred during perioperative spinal surgery. Health economic evaluation of data from a prospective observational study from the perspective of an academic hospital. Consecutive patients at a single, tertiary-quaternary care institution who have undergone inpatient spinal surgery. The cost and LOS impacts with respect to the severity of the AEs. We analyzed 4 years of patient discharges between January 1, 2007 and December 31, 2010. The Spine Adverse Events Severity instrument was completed by the surgical team at discharge. Clinical impacts of the AEs were graded as I (requires no/minimal treatment), II (requires treatment and is not likely to cause long-term [>6 months] sequelae), III (requires treatment and is most likely to cause long-term sequelae), and IV (death). A total of 1,815 records were linked with the patient-level costing information. We matched each AE case with four control cases based on their propensity score for the risk of experiencing an AE, regressed against case characteristics. We estimated an incremental cost and LOS for each severity grade by calculating the differences in means across cases and controls. We conducted a sensitivity analysis by estimating the alternate models using generalized linear model (GLM) regression with a gamma log link. Adverse events were reported in 316 (17.4%) cases, with 126 of these patients (40.2%) experiencing multiple events. The incremental cost/LOS for each severity grade are as follows: I=$4,224 (p=.0351)/3.63 days (p=.0001); II=$23,500 (p<.0001)/14.03 days (p<.0001); III=$147,285 (p=.0036)/74.50 days (p=.0018); and IV=$121,366 (p=.0323)/46.44 days (p=.0036). The total cost in millions/LOS (days) associated with each grade over the 4-year study period are as follows: I=$0.66 million/569.9 days; II=$2.96 million/1,767.8 days; III=$4.27 million/2,160.5 days; and IV=$0.49 million/185.8 days. Our sensitivity analysis produced comparable overall results using alternate modeling techniques. Overall, AEs contributed an estimated $8.38 million (16.0% of the total costs for all patients in the sample) in incremental costs and 4,684 additional bed days over the 4-year study period. In this surgical spine cohort, AEs accounted for 16% of the total cost of in-hospital care. Higher severity AEs were progressively more costly on a per-case basis; however, the more frequent lower severity events (ie, Grade I and II) also had a substantial aggregate cost (43%). These results suggest that a strong business case exists for patient safety strategies focused not only on severe AEs but also on the reduction of lower severity events that may be more amenable to prevention efforts.

Abstract P6-09-06: Family Members' Burden in Patients with Metastatic and Early Stage Breast Cancer

Abstract BACKROUND: No previous studies have assessed the indirect costs attributable to family members of patients with metastatic breast cancer (MBC). This retrospective database study compared productivity loss and cost associated with family members of patients with MBC vs. early-stage breast cancer (EBC). METHODS: The Thomson Reuters MarketScan Health and Productivity Management (HPM) data (2005–2009) were used. MBC and EBC patients with no other tumors and 12-month continuous enrollment in medical insurance after the index diagnosis date were identified. Adult working family members of these MBC/EBC patients were identified based on their enrollee ID numbers since the enrollees from the same family were assigned the same ID except for the last two digits. The patients' working family members who were eligible for absenteeism and did not have any cancer diagnosis were included and used as a proxy for “caregivers”. The reasons for absenteeism included sickness, personal leave, disability, recreation, Family and Medical Leave Act (FMLA) and others. The productivity loss was measured as the leave days taken under FMLA or personal leave by the family members during a 12-month follow-up period. Associated indirect costs were estimated by multiplying leave days with daily wages obtained from the 2011 Bureau of Labor Statistics. Descriptive analyses and a generalized linear model with log link and gamma distribution were conducted. RESULTS: A total of 209 MBC/1,166 EBC patients' family members were eligible for absenteeism, with a mean age of 50/51 years. 1,373 out of the 1,375 family members were male. Majority of the family members (52%) worked in manufacturing industry, followed by transportation/communication/utilities (28%) and oil gas extraction/mining industry (15%). 52% of the family members had PPO health insurance. Family members of MBC and EBC patients had similar clinical and demographic characteristics. Similar proportions of MBC and EBC patients' family members had overall and individual type of absenteeism. However, MBC patients' family members had more FMLA/personal leave days and higher costs vs. EBC patients (overall mean: 2.8±6.1 vs. 2.1±4.8; $2,366±5,095 vs. $1,741±3,995, both p = .047). Among those who had non-zero FMLA/personal leave days (MBC vs. BC: N=92/44% vs. 502/43%), mean FMLA/personal leave days and costs were 6.4±7.8 vs. 4.8±6.3; $5,375±6,556 vs. $4,043±5,272 respectively, both p = .033. After adjusting for covariates, MBC patients' family members incurred 40% (p = .06) more absenteeism-related costs due to FMLA/personal leave vs. EBC patients' family members. Additionally, occupation in oil/gas extraction/mining (vs. manufacturing non-durable goods industry, p &amp;lt; .001) and Northeast and South regions (vs. West, p &amp;lt; .001) were associated with higher FMLA/personal leave costs. CONCLUSIONS: Productivity loss in MBC patients' family members was substantial and higher than family members of EBC patients, which is expected with the differing goals, type and length of treatment for MBC and EBC. The patients' family members were used as a proxy of the “caregivers” with limitations that prevent generating accurate estimates on caregiver costs. Nevertheless the findings showed that the productivity loss in MBC patients' family members was considerable. Citation Information: Cancer Res 2012;72(24 Suppl):Abstract nr P6-09-06.

A Note on Bayesian and Maximum Likelihood Estimation of Scale Parameter of Log Gamma Distribution

In this paper, the problem of estimating the scale parameter of log gamma distribution under Bayesian and maximum likelihood framework has been addressed. The uniform and Jeffreys priors have been assumed for posterior analysis. The Bayes estimators and associated risks have been derived under five different loss functions. The credible intervals and highest posterior density intervals have been constructed under each prior. A simulation study has been carried out to illustrate the numerical applications of the results and to compare the performance of different estimators. The purpose is to compare the performance of the estimators based on Bayesian and maximum likelihood frameworks. The performance of different Bayes estimators has also been compared using five different loss functions. The study indicated that for estimation of the said parameter, the Bayesian estimation can be preferred over maximum likelihood estimation. While in case of the Bayesian estimation, the entropy loss function under Jeffreys can effectively be employed.

Electromagnetic‐Induction Logging to Monitor Changing Chloride Concentrations

Water from the San Joaquin Delta, having chloride concentrations up to 3590 mg/L, has intruded fresh water aquifers underlying Stockton, California. Changes in chloride concentrations at depth within these aquifers were evaluated using sequential electromagnetic (EM) induction logs collected during 2004 through 2007 at seven multiple-well sites as deep as 268 m. Sequential EM logging is useful for identifying changes in groundwater quality through polyvinyl chloride-cased wells in intervals not screened by wells. These unscreened intervals represent more than 90% of the aquifer at the sites studied. Sequential EM logging suggested degrading groundwater quality in numerous thin intervals, typically between 1 and 7 m in thickness, especially in the northern part of the study area. Some of these intervals were unscreened by wells, and would not have been identified by traditional groundwater sample collection. Sequential logging also identified intervals with improving water quality-possibly due to groundwater management practices that have limited pumping and promoted artificial recharge. EM resistivity was correlated with chloride concentrations in sampled wells and in water from core material. Natural gamma log data were used to account for the effect of aquifer lithology on EM resistivity. Results of this study show that a sequential EM logging is useful for identifying and monitoring the movement of high-chloride water, having lower salinities and chloride concentrations than sea water, in aquifer intervals not screened by wells, and that increases in chloride in water from wells in the area are consistent with high-chloride water originating from the San Joaquin Delta rather than from the underlying saline aquifer.

A Test for Constant Hazard Against a Change-Point Alternative

In this article, we consider the change-point hazard rate model which arises quite commonly in mechanical or biological systems, which experience a high hazard rate early in their lifetime due to infant mortality and then a constant or steady hazard rate after the threshold time. We first derive the corresponding mean residual life function (MRLF) and observe that the MRLF is initially increasing and then constant. Here, we derive a test statistic for exponentiality against Increasing Initially then Constant Mean Residual Life (ICMRL). We also derive the asymptotic distribution of the test statistic and compare the power of the test with other existing tests such as likelihood ratio, Weibull, and Log gamma tests considered in the literature. The test performs quite well as compared to other alternatives studied.

The hydrocarbon potential of the Nigerian Chad Basin from wireline logs

The need to find an alternative energy source to the Niger Delta has re-enacted interest in the Nigerian Chad (Borno) basin; this work was done in order to evaluate the potential of the basin to generate commercial hydrocarbon. Three (3) Wireline logs from well GUBIO #1, NGAMMA#1 and NGOR#1 of the OPL 419 in the Chad Basin were used for this study. The Gamma ray log, Caliper, Neutron, Density, Sonic, and Resistivity logs were used to identify the reservoir zones (lithology), fractured rock, determine Porosity, identify overpressures zones, and estimate the water and hydrocarbon saturation. In the analysis of the GUBIO#1 well SP and Gamma log were used to predict the environment of the deposition. Fourteen (14), Ten (10), and Eight (8) reservoir zones were delineated for GUBIO #1, NGAMMA#1 and NGOR#1 respectively. With porosity ranging between 4.5-46%, 6-36%,&2.5-44%, apparent resistivity of 0.0012- 35.52Ωm, 0.02-9.23Ωm&0.02-26.25Ωm, estimated water saturation (Sw) that lies within 0-35%, 4.9-45.2%&21-100% for the three wells in that order. The environment of inferred from the SP log shows initial deposition of regressive, and later transgressive to transitional sandstone facies. From this study, the Nigerian Chad basin is a petroleum province with abundant gas than oil and as such can be said to a gas province.

Abstract P242: Trending Positive Clinical Benefits &amp; Significantly Lower Costs With Niacin Extended-Release Compared to Ezetimibe in Patients Receiving On-Going Statin Therapy

Objective: To compare cardiovascular (CV) and economic outcomes among a community-based population initiating adjunct therapy with niacin extended-release (NER) for broader management of the lipid panel vs. ezetimibe (EZE) for continued LDL-C reductions. Methods: Statin-treated (simvastatin 20 mg/day or equivalent) patients aged ≥30 years initiating adjunct therapy with NER or EZE between 1/1/05-11/30-08 (index date) and ≥1 pre-index lipid panel (LDL-C &lt;100 mg/dL and HDL-C &lt;50 or &lt;55 mg/dL for men and women, respectively) within the Healthcore Integrated Research Database were included. Patients with AST/ALT elevations or liver disease were excluded. Primary outcome was first occurrence of a major adverse CV event (MACE), defined as IHD, PVD, revascularization, or stroke; secondary outcomes were MACE+all-cause mortality and the total of MACE-related medical costs and pharmacy charges for anti-hyperlipidemic therapy. CV risk between NER and EZE were compared using Cox proportional hazards models with a pair-wise approach while generalized linear models with a log link function and gamma distribution were used to compare costs. Multivariate analyses controlled for age, gender, geographical region, co-morbidities, and baseline lipid values. Results: A total of the 452 patients initiated adjunct therapy with NER (n=186) and EZE (n=22). The NER cohort was younger (58.3±9.7 vs 60.4±9.7, P =0.0235), less likely to be female (17.7% vs 34.6%, P &lt;0.0001), and had a shorter follow-up period (200.0 vs 363.2 days, P &lt;0.0001). The NER cohort had a lower frequency of MACE (1.6%) vs EZE (4.5%), with an adjusted hazard ratio (aHR) of 0.39 (95%CI: 0.09-1.65). A similar trend was observed for the MACE+all-cause mortality with an aHR of 0.30 (95%CI: 0.08-1.27). These findings correspond to significantly lower adjusted costs for patients receiving NER ($2706; 95%CI: 2347-3119) vs EZE ($3489; 95%CI: 3101-3926) ( P &lt;0.0001). Conclusions: The trend of positive clinical benefits from this real-world analysis are consistent with those of the ARBITER-6/HALTS study and suggest that treating beyond LDL-C with NER in secondary risk patients receiving simvastatin 20 mg/day or equivalent may reduce CV risk and associated costs.

On p-adic multiple zeta and log gamma functions

Text We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. We conclude with a Laurent series expansion of the p-adic multiple log gamma function for ( p-adically) large x which agrees exactly with Barnesʼs asymptotic expansion for the (complex) multiple log gamma function, with the fortunate exception that the error term vanishes. Indeed, it was the possibility of such an expansion which served as the motivation for our functions, since we can use these expansions computationally to p-adically investigate conjectures of Gross, Kashio, and Yoshida over totally real number fields. Video For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=I9Bv_CycEd8.

Factors Influencing Costs of Inpatient Ischaemic Stroke Care in Singapore

Introduction: Stroke is a major public issue in Singapore, accounting for almost 10,000 admissions annually and the burden of disease is set to increase with an ageing population. We therefore seek to examine the factors influencing the cost of acute stroke care in Singapore. Methods: This is a retrospective analysis of 2,087 discharges with a primary discharge diagnosis of stroke from a tertiary hospital in Singapore from 1 January 2007 to 31 December 2008. Data including age, gender, length of hospital stay, components of direct cost and discharge disposition were obtained. A generalised linear model with a log link function and gamma distribution was used to determine the predictors of total hospital cost. Results: Mean age was 67.8 ± 12.4 years and 54.5% were males. Mean length of stay was 12.3 ± 16 days and mean total overall cost was S$6,783. Ward costs accounted for 48% of total cost. Length of stay strongly correlated to total cost. Being discharged to step-down facilities, death, receiving inpatient rehabilitation and length of stay significantly incurred higher total cost in multivariate analysis. However, there was an inverse relationship between age and total cost, possibly as a result of higher costs incurred for radiological, laboratory investigations and expert care. Conclusion: Further research is needed to examine factors influencing the cost of treatment particularly for those being discharged to step-down facilities and receiving inpatient rehabilitation as they have been found to incur higher total cost. This would impact on the planning of the continuum of healthcare facilities for stroke management.

Resolving scales of aquifer heterogeneity using ground penetrating radar and borehole geophysical logging

Accurate and reliable characterization of aquifer heterogeneity remains one of the foremost problems in hydrogeology. In this study, ground penetrating radar (GPR) and borehole geophysical logging are used to investigate scales of heterogeneity present locally (<500 m laterally) within an outwash deposit comprised of inter-bedded and cross-bedded sands and gravels of glaciofluvial origin. At a small scale (<15 m laterally), gamma log data in adjacent boreholes show evidence of fining upward sequences, occasional coarsening upward sequences, and abrupt changes in grain sizes, which appear to be laterally continuous at scales of 10 m. At the site scale (<500 m laterally), GPR profiles show a strong reflection interpreted as the water table. Reflectors in the unsaturated zone are more clearly defined than those beneath the water table due to signal attenuation within the saturated sediments. Undulating to discontinuous reflectors at scales of 10–15 m are interpreted to result from interbedded and cross-bedded sands and gravels. A few laterally continuous horizontal to sub-horizontal reflectors, which extend at least up to 360 m, are interpreted as unconformities, based on evidence of gravel bars, truncation of underlying units, as well as scour and fill features in a nearby gravel pit exposure. Overall, the integration of these two geophysical methods provided evidence of unit correlation at the two scales of investigation.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian estimates, depend on the accuracy of the prior parameters, but example simulations show that the performance can be substantially improved compared to maximum likelihood or state-of-the-art nonparametric estimators.

Linear independence of digamma function and a variant of a conjecture of Rohrlich

Let ψ ( x ) denote the digamma function. We study the linear independence of ψ ( x ) at rational arguments over algebraic number fields. We also formulate a variant of a conjecture of Rohrlich concerning linear independence of the log gamma function at rational arguments and report on some progress. We relate these conjectures to non-vanishing of certain L-series.

Transcendence of the log gamma function and some discrete periods

We study transcendental values of the logarithm of the gamma function. For instance, we show that for any rational number x with 0 < x < 1 , the number log Γ ( x ) + log Γ ( 1 − x ) is transcendental with at most one possible exception. Assuming Schanuel's conjecture, this possible exception can be ruled out. Further, we derive a variety of results on the Γ-function as well as the transcendence of certain series of the form ∑ n = 1 ∞ P ( n ) / Q ( n ) , where P ( x ) and Q ( x ) are polynomials with algebraic coefficients.

Models for count data with endogenous participation

We present several extensions of the Poisson and negative binomial models for count data based on the lognormal model for latent heterogeneity in the conditional means. The lognormal model provides a versatile specification that is more flexible than the familiar log gamma form, and provides a platform for several “two part” extensions that have appeared in the literature, including zero inflation, hurdle and sample selection models. We then extend these received two- part models by allowing for endogeneity of the participation equation. We conclude with a detailed application using the data employed in a recent study of the German health care system.

Properties of the Solute-Stationary Liquid Interactions in Gas Liquid Chromatography

The solute-stationary liquid interaction in gas liquid chromatography (GLC) was determined using Eyring's model. The interaction was determined to be the physical adsorption. The descriptor sigma(M) was derived and estimated by van der Waals interactions. The CH/pi interaction energies were calculated by Tsuzuki et al. using the high-level ab initio calculations. The CH/pi interaction energy was concluded to consist of the dispersion energy (Edis) rather than the electrostatic (Ees) and charge-transfer (Ect) energies. These energies were in good agreement with our descriptor sigma M. Furthermore, the macroscopic sigma M also had microscopic support through the weak CH/pi interactions. In substituted benzenes, regression analyses were carried out using sigma M for the relative retention values, log gamma, as a measure of the solute-stationary liquid interaction. The analyses revealed good results under non-polar conditions. The log gamma values therefore consisted primarily of contributions from the dispersion interaction and the CH/pi complex. Moreover, these values were useful when added to the electrostatic term (our descriptor sigma es) for polar solutes. That is, the log gamma values were estimated by the regression analyses using both sigma M and sigma es, and were in good agreement with the predicted values.