NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Expression, induction and regulation of the cytochrome P450 monooxygenase system in the rat glioma C6 cell line

The cytochrome P450 monooxygenase system consists of NADPH- cytochrome P450 reductase (P450 reductase) and cytochromes P450, which can catalyze the oxidation of a wide variety of endogenous and exogenous compounds, including steroid hormones, fatty acids, drugs, and pollutants. The functions of this system are as diverse as the substrates. P450 reductase transfers reducing equivalents from NADPH to P450, which in turn catalyzes metabolic reactions. This enzyme system has the highest level of activity in the liver. It is also present in other tissues, including brain. The functions of this enzyme system in brain seem to include: neurotransmission, neuroendocrinology, developmental and behavioral modulation, regulation of intracellular levels of cholesterol, and potential neurotoxicity.^ In this study, we have set up the rat glioma C6 cell line as an in vitro model system to examine the expression, induction, and tissue-specific regulation of P450s and P450 reductase. Rat glioma C6 cells were treated with P450 inducers phenobarbital (PB) or benzo(a)anthracene (BA). The presence of P450 reductase and of cytochrome P450 1A1, 1A2, 2A1, 2B1/2, 2C7, 2D1-5 and 2E1 was detected by reverse transcription followed by polymerase chain reaction (RT-PCR) and confirmed by restriction digestion. The induction of P450 1A1 and 2B1/2 and P450 reductase was quantified using competitive PCR. Ten- and five-fold inductions of P450 1A and 2B mRNA after BA or PB treatments, respectively, were detected. Western blot analysis of microsomal preparations of glioma C6 cells demonstrated the presence of P450 1A, 2B and P450 reductase at the protein level. ELISAs showed that BA and PB induce P450 1A and 2B proteins 7.3- and 13.5-fold, respectively. Microsomes prepared from rat glioma C6 cells showed cytochrome P450 CO difference spectra with absorption at or near 450 nm. Microsomes prepared from rat glioma C6 cells demonstrated much higher levels of ethoxyresorufin O-deethylase (EROD) and pentoxyresorufin O-dealkylase (PROD) activity, when treated with BA or PB, respectively. These experiments provide further evidence that the rat glioma C6 cell line contains an active cytochrome P450 monooxygenase system which can be induced by P450 inducers. The mRNAs of P450 1A1 and 2B1/2 can not bind to the oligo(dT) column efficiently, indicating they have very short poly(A) tails. This finding leads us to study the tissue specific regulation of P450s at post-transcriptional level. The half lives of P450 1A1 and 2B1/2 mRNA in glioma C6 cells are only 1/10 and 1/3 of that in liver. This may partly contribute to the low expression level of P450s in glial cells. The induction of P450s by BA or PB did not change their mRNA half lives, indicating the induction may be due to transcriptional regulation. In summary of this study, we believe the presence of the cytochrome P450 monooxygenase system in glial cells of the brain may be important in chemotherapy and carcinogenesis of brain tumors. ^

Hypogonadism in male cancer patients: A cross-sectional study

Introduction. Cancer is the second most common cause of death in the USA (2). Studies have shown a coexistence of cancer and hypogonadism (9,31,13). The majority of patients with cancer develop cachexia, which cannot be solely explained by anorexia seen in these patients. Testosterone is a male sex hormone which is known to increase muscle mass and strength, maintain cancellous bone mass, and increase cortical bone mass, in addition to improving libido, sexual desire, and fantasy (14). If a high prevalence of hypogonadism is detected in male cancer patients, and a significant difference exists in testosterone levels in cancer patients with cachexia versus those without cachexia, testosterone may be administered in future randomized trials to help alleviate cachexia. Study group and design The study group consisted of male cancer patients and non-cancer controls aged between 40 and 70 years. The primary study design was cross-sectional with a sample size of 135. The present data analysis is done on a subset convenience sample of 72 patients recruited between November 2006 and January 2010. ^ Methods. Patients aged 40-70 years with or without a diagnosis of cancer were recruited into the study. All patients with a BMI over 35, significant edema, non-melanomatous skin cancer, current alcohol or illicit drug abuse, concomitant usage of medications interfering with gonadal axis, and anabolic agents, patients on tube feeds or parenteral nutrition within 3 months prior to enrollment were excluded from the study. The study was approved by the Institutional Review Board of Baylor College of Medicine and is being conducted at the Michael E. DeBakey Veterans Affairs Medical Center at Houston. My thesis is a pilot data analysis that employs a smaller subset convenience sample of 72 patients determined by using the data available for the 72 patients (of the intended sample of 135 patients) recruited between November 2006 and January 2010. The primary aim of this analysis is to compare the proportion of patients with hypogonadism in the male cancer and non-cancer control groups, and to evaluate if a significant difference exists with respect to testosterone levels in male cancer patients with cachexia versus those without cachexia. The procedures of the study relevant to the current data analysis included blood collection to measure levels of testosterone and measurement of body weight to categorize cancer patients into cancer cachexia and cancer non-cachexia sub-groups. ^ Results. After logarithmic transformation of data of cancer and control groups, the unpaired t test with unequal variances was done. The proportion of patients with hypogonadism in the male cancer and non-cancer control groups was 47.5% and 22.7% with a Pearson chi2 statistic of 1.6036 and a p value of 0.205. Comparing the mean calculated Bioavailable testosterone in male cancer patients and non-cancer controls resulted in a t statistic of 21.83 and a p value less than 0.001. When the cancer group alone was taken, the mean free testosterone, calculated bioavailable testosterone and total testosterone levels in the cancer non-cachexia sub-group were 3.93, 5.09, 103.51 respectively and in the cancer cachexia sub-group were 3.58, 4.17, 84.08 respectively. The unpaired t test with equal variances showed that the two sub-groups had p values of 0.2015, 0.1842, and 0.4894 with respect to calculated bioavailable testosterone, free testosterone, and total testosterone respectively. ^ Conclusions. The small sample size of this exploratory study, resulting in a small power, does not allow us to draw definitive conclusions. For the given sub-sample, the proportion of patients with hypogonadism in the cancer group was not significantly different from that of patients with hypogonadism in the control group. Inferences on prevalence of hypogonadism in male cancer patients could not be made in this paper as the sub-sample is small and therefore not representative of the general population. However, there was a statistically significant difference in calculated Bioavailable testosterone levels in male cancer patients versus non-cancer controls. Analysis of cachectic and non-cachectic patients within the male cancer group showed no significant difference in testosterone levels (total, free, and calculated bioavailable testosterone) between both sub-groups. However, to re-iterate, this study is exploratory and the results may change once the complete dataset is obtained and analyzed. It however serves as a good template to guide further research and analysis.^