Segmented Linear Regression Models Research Articles

Impact of a Medicaid Copayment Policy on Prescription Drug and Health Services Utilization in a Fee-for-Service Medicaid Population

Copayments (copays) for prescription drugs are a common policy among state Medicaid programs. Research exploring the effects of copays on pharmacy and health care utilization in Medicaid patients is limited, especially among patients with chronic disease. The goal of this research was to quantify the impact of a copay policy for prescription drugs on medication and health services utilization overall and among subjects with several common chronic diseases enrolled in a state Medicaid program. Using aggregated pharmacy claims, segmented linear regression models were used to evaluate changes in overall and disease-specific pharmacy utilization after implementation of a copay policy. Trends in emergency department encounters, office visits, and hospitalizations were used to evaluate the impact of this policy on unintended consequences. Utilization among cohorts of patients with several chronic conditions were analyzed to determine if a differential response existed by drug indication. After copay implementation, utilization of prescription drugs declined significantly by 17.2% (P < 0.0001). This pattern was observed at varying degrees for all drug classes investigated. Rates of emergency department encounters, office visits, or hospitalizations did not increase after the policy was introduced. Subjects with diabetes, respiratory disease, and schizophrenia immediately reduced their use of nonindicated drugs significantly more than drugs indicated for their condition. Among Medicaid recipients, nominal copays are associated with significant reductions in use of clinically important drug classes. However, patients with chronic disease exhibited a differential response depending on the disease indication of the drug class.

Analysis of FMR1 gene expression in female premutation carriers using robust segmented linear regression models

Fragile X syndrome is caused by the absence or reduction of the fragile X mental retardation protein (FMRP) because FMR1 gene expression is reduced. Alleles with repeat sizes of 55-200 are classified as premutations, and it has been demonstrated that FMR1 expression is elevated in the premutation range. However, the majority of the studies reported were performed in males. We studied FMR1 expression in 100 female fragile X family members from the northern region of Spain using quantitative (fluorescence) real-time polymerase chain reaction. Of these 100 women, 19 had normal alleles, 19 were full mutation carriers, and 62 were premutation carriers. After confirming differences between the three groups of females, and increased levels of the FMR1 transcript among premutation carriers, we found that the relationship between mRNA levels and repeat size is nonlinear. These results were obtained using a novel methodology that, based on the size of the CGG repeats, allows us to find out the most probable threshold from which the relationship between CGG repeat number and mRNA levels changes. Using this approach, a significant positive correlation between CGG repeats and total mRNA levels has been found in the premutation range <100 CGG, but this correlation diminishes from 100 onward. However, when correcting by the X inactivation ratio, mRNA levels increase as the number of CGG repeats increases, and this increase is highly significant over 100 CGG. We suggest that due to skewed X inactivation, mRNA levels tend to normalize in females when the number of CGG repeats increases.

Modeling distortion product otoacoustic emission input/output functions using segmented regression

Distortion product otoacoustic emissions (DPOAEs) are low-level acoustic signals, the detection of which involves extraction from a background of noise. Boege and Janssen [J. Acoust. Soc. Am. 111, 1810-1818 (2002)] described a method for modeling the presence and growth of these responses. While improving growth function parameter estimation, this technique excludes a significant fraction of the data (especially low-level responses), and relies on ad hoc model fit acceptance criteria. The statistical difficulties associated with these limitations are described, and a weighted segmented linear regression model that avoids them is proposed. A simple test is presented for the presence of DPOAE growth. This technique is compared to that of Boege and Janssen in a dataset of 9 556 input/output (I/O) functions collected over 4 years on 866 ears from 379 construction apprentices and 63 age-matched controls. Comparisons are made on the entire dataset and within audiometric hearing loss categories. Segmented regression avoids the statistical pitfalls of the previous method, allows estimation of the threshold and slope of auditory response on a far greater number of I/O functions, and improves estimation of these parameters in this dataset. The potential for this method to yield more sensitive metrics of hearing function and compromise is discussed.

Extensive exercise is not harmful in amyotrophic lateral sclerosis

Whether physical activity increases risk or promotes progression of motor neurone degeneration in amyotrophic lateral sclerosis (ALS) is still debated. Current pathophysiological hypotheses include excitotoxicity, oxidative stress and increased calcium loads as causes of selective degeneration of vulnerable motor neurones. Vigorous exercise might amplify these factors by increasing firing rates at motor neurones. To test this hypothesis, we constrained a transgenic mouse model of ALS overexpressing the mutant human form of the Cu/Zn superoxide dismutase-1 (SOD-1) to a lifetime exercise on motor-driven running wheels for 10 h daily (active group, n = 12). Onset and progression of disease were assessed by grip strength, stride length and tight rope test. Data were compared with SOD-1 mice placed in running wheels set to slow speed (sedentary group, n = 13). Untreated SOD-1 mice were an additional control group (n = 12). We found no differences in disease onset, which was determined by a change-point analysis using an iterative fitting of segmented linear regression models, or in disease progression. However, the running group showed a non-significant 6-day improvement in survival (133.7 +/- 3.2 days) compared with the sedentary group (127.2 +/- 3.2 days) and a 4-day improvement compared with the control group (129.1 +/- 2.5 days). We demonstrate that a lifetime of vigorous exercise does not promote onset or progression of motor degeneration in SOD-1-mediated ALS. Moreover, the results suggest that the level of excitatory input and calcium turnover at motor neurones, both of which should be increased by running activity, do not interfere with the pathophysiology of SOD-1-mediated ALS.

Maximal Voluntary and Functional Performance Needed for Independence in Adults Aged 65 to 97 Years

Age-related loss of muscle mass and cardiovascular endurance can lead to impairments in muscle force production and cardiac function that, in turn, limit performance in activities essential to everyday living. The purposes of this study were: (1) to identify the "breakpoint" or threshold of maximal voluntary performance and performance in ordinary daily function and (2) to evaluate the predictive validity of the threshold to identify the ability to live independently without self-reported functional limitation. Men and women (N=192; mean age=76 years, SD=7, range=65-97) were recruited from single-family community dwellings or retirement communities with multiple levels of care. Physical function was measured with the Continuous-Scale Physical Functional Performance Test (CS-PFP). Maximal voluntary performance measures included peak oxygen consumption (VO(2peak)) and isokinetic knee extensor torque (KET). Segmented linear regression models of the CS-PFP on the physical performance measures were used to determine the threshold values and their confidence intervals. A logistic regression model was used to evaluate the ability of the CS-PFP scores to identify those living independently and to further illustrate the concepts of threshold and physical reserve. Threshold values identified for VO(2peak) (20 mL x kg(-1) x min(-1)) and KET (2.5 N x m/[kg x m(-1)]) were associated with an average of CS-PFP score of 57 units. The threshold accurately predicted individuals reporting functional limitations. The thresholds provide a mechanism for easily estimating an individual's physical reserve, predicting dependency in living status, and providing unbiased guidance for intervention in late-life independence.

Rate of increase and critical amount of nuclear polyhedrosis virus in lepidopterous larvae estimated from survival time assay data with a birth-death model.

A birth-death model developed for pathogens of vertebrates was used to estimate the in vivo rate of increase (alpha) and the doubling time (td) from survival time assay data. Host-pathogen combinations used in this study were two Autographa californica nuclear polyhedrosis virus isolates in Trichoplusia ni and Heliothis zea NPV in H. zea. The alpha's, estimated as he negative reciprocal of the slope of the linearly decreasing section of the plot of median survival times against the logarithm of inoculum concentration, were calculated in two ways. First, simple regression was used to fit a line through the linearly decreasing part using data points selected by eye; secondly, a three-phase segmented linear regression model was used and alpha was estimated from the slope of the middle segment. Estimates of alpha (and td) were 0.338 (2.05), 0.274 (2.53) and 0.243 h-1 (2.85 h) using the simple regression method, and 0.385 (1.80), 0.305 (2.27) and 0.223 h-1 (3.11 h) using the 3-phase segmented linear regression model for AcMNPV-1A, AcMNPV-HOB and HzSNPV, respectively. Although AcMNPV-HOB killed larvae faster (6 to 13 h) than AcMNPV-1A, it multiplied more slowly. Estimates for the critical number ranged from 4.8 x 10(9) to 4.5 x 10(14) genome copies for HzSNPV in H. zea larvae and AcMNPV-1A in T. ni larvae, respectively. The significance of the calculated critical numbers is discussed.

Segmented linear regression models applied to the analysis of data from a cross‐sectional growth experiment

AbstractSeveral different methods of analysis are applied to data consisting of weight measurements, taken at specified post‐treatment times, of harvested thyroids from rats given one of four treatments. Previous studies of this type of data indicated that the growth is initially rapid, and that a second phase of less rapid growth is followed by a final phase in which little additional growth occurs. The data are further characterized by increasing variance through time.The primary purpose of the analysis is to study the effect of the treatments at the end of the study period. One‐way analysis of variance tests among groups are performed on each day, but the results are not particularly helpful. However, results from two‐way analyses of variance (over subsets of days and groups) are consistent with the three phase model and accordingly indicate significant group differences during each. Finally, maximum likelihood methods are used to fit a three part segmented linear regression model.