Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study.

Sentinel lymph node biopsy is associated with improved survival compared to level I & II axillary lymph node dissection in node negative breast cancer patients

OBJECTIVE: The few long-term follow-up data for sentinel lymph node (SLN) negative breast cancer patients demonstrate a 5-year disease-free survival of 96-98%. It remains to be elucidated whether the more accurate SLN staging defines a more selective node negative patient group and whether this is associated with better overall and disease-free survival compared with level I ; II axillary lymph node dissection (ALND). METHODS: Three-hundred and fifty-five consecutive node negative patients with early stage breast cancer (pT1 and pT2< or =3 cm, pN0/pN(SN)0) were assessed from our prospective database. Patients underwent either ALND (n=178) in 1990-1997 or SLN biopsy (n=177) in 1998-2004. All SLN were examined by step sectioning, stained with H;E and immunohistochemistry. Lymph nodes from ALND specimens were examined by standard H;E only. Neither immunohistochemistry nor step sections were performed in the analysis of ALND specimen. RESULTS: The median follow-up was 49 months in the SLN and 133 months in the ALND group. Patients in the SLN group had a significantly better disease-free (p=0.008) and overall survival (p=0.034). After adjusting for other prognostic factors in Cox proportional hazard regression analysis, SLN procedure was an independent predictor for improved disease-free (HR: 0.28, 95% CI: 0.10-0.73, p=0.009) and overall survival (HR: 0.34, 95% CI: 0.14-0.84, p=0.019). CONCLUSIONS: This is the first prospective analysis providing evidence that early stage breast cancer patients with a negative SLN have an improved disease-free and overall survival compared with node negative ALND patients. This is most likely due to a more accurate axillary staging in the SLN group.

Elderly age is not a negative predictive factor for virological response to therapy with pegylated interferon-α and ribavirin in chronic hepatitis C virus patients

BACKGROUND & AIMS: Age is frequently discussed as negative host factor to achieve a sustained virological response (SVR) to antiviral therapy of chronic hepatitis C. However, elderly patients often show advanced fibrosis/cirrhosis as known negative predictive factor. The aim of this study was to assess age as an independent predictive factor during antiviral therapy. METHODS: Overall, 516 hepatitis C patients were treated with pegylated interferon-α and ribavirin, thereof 66 patients ≥60 years. We analysed the impact of host factors (age, gender, fibrosis, haemoglobin, previous hepatitis C treatment) and viral factors (genotype, viral load) on SVR per therapy course by performing a generalized estimating equations (GEE) regression modelling, a matched pair analysis and a classification tree analysis. RESULTS: Overall, SVR per therapy course was 42.9 and 26.1%, respectively, in young and elderly patients with hepatitis C virus (HCV) genotypes 1/4/6. The corresponding figures for HCV genotypes 2/3 were 74.4 and 84%. In the GEE model, age had no significant influence on achieving SVR. In matched pair analysis, SVR was not different in young and elderly patients (54.2 and 55.9% respectively; P = 0.795 in binominal test). In classification tree analysis, age was not a relevant splitting variable. CONCLUSIONS: Age is not a significant predictive factor for achieving SVR, when relevant confounders are taken into account. As life expectancy in Western Europe at age 60 is more than 20 years, it is reasonable to treat chronic hepatitis C in selected elderly patients with relevant fibrosis or cirrhosis but without major concomitant diseases, as SVR improves survival and reduces carcinogenesis.

Positive affect moderates the effect of negative affect on cardiovascular disease-related hospitalizations and all-cause mortality after cardiac rehabilitation

BACKGROUND Little is known as to whether negative emotions adversely impact the prognosis of patients who undergo cardiac rehabilitation. We prospectively investigated the predictive value of state negative affect (NA) assessed at discharge from cardiac rehabilitation for prognosis and the moderating role of positive affect (PA) on the effect of NA on outcomes. METHODS A total of 564 cardiac patients (62.49 ± 11.51) completed a comprehensive three-month outpatient cardiac rehabilitation program, filling in the Global Mood Scale (GMS) at discharge. The combined endpoint was cardiovascular disease (CVD)-related hospitalizations plus all-cause mortality at follow-up. Cox regression models estimated the predictive value of NA, as well as the moderating influence of PA on outcomes. Survival models were adjusted for sociodemographic factors, traditional cardiovascular risk factors, and severity of disease. RESULTS During a mean follow-up period of 3.4 years, 71 patients were hospitalized for a CVD-related event and 15 patients died. NA score (range 0-20) was a significant and independent predictor (hazard ratio (HR) 1.091, 95% confidence interval (CI) 1.012-1.175; p = 0.023) with a three-point higher level in NA increasing the relative risk by 9.1%. Furthermore, PA interacted significantly with NA (p < 0.001). The relative risk of poor prognosis with NA was increased in patients with low PA (p = 0.012) but remained unchanged in combination with high PA (p = 0.12). CONCLUSION The combination of NA with low PA was particularly predictive of poor prognosis. Whether reduction of NA and increase of PA, particularly in those with high NA, improves outcome needs to be tested.

Modeling absolute differences in life expectancy with a censored skew-normal regression approach.

Parameter estimates from commonly used multivariable parametric survival regression models do not directly quantify differences in years of life expectancy. Gaussian linear regression models give results in terms of absolute mean differences, but are not appropriate in modeling life expectancy, because in many situations time to death has a negative skewed distribution. A regression approach using a skew-normal distribution would be an alternative to parametric survival models in the modeling of life expectancy, because parameter estimates can be interpreted in terms of survival time differences while allowing for skewness of the distribution. In this paper we show how to use the skew-normal regression so that censored and left-truncated observations are accounted for. With this we model differences in life expectancy using data from the Swiss National Cohort Study and from official life expectancy estimates and compare the results with those derived from commonly used survival regression models. We conclude that a censored skew-normal survival regression approach for left-truncated observations can be used to model differences in life expectancy across covariates of interest.

Dimensional approaches to schizophrenia: A comparison of the Bern Psychopathology scale and the five-factor model of the Positive and Negative Syndrome Scale

The aim was to examine to what extent the dimensions of the BPS map the five factors derived from the PANSS in order to explore the level of agreement of these alternative dimensional approaches in patients with schizophrenia. 149 inpatients with schizophrenia spectrum disorders were recruited. Psychopathological symptoms were assessed with the Bern Psychopathology Scale (BPS) and the Positive and Negative Syndrome Scale (PANSS). Linear regression analyses were conducted to explore the association between the factors and the items of the BPS. The robustness of patterns was evaluated. An understandable overlap of both approaches was found for positive and negative symptoms and excitement. The PANSS positive factor was associated with symptoms of the affect domain in terms of both inhibition and disinhibition, the PANSS negative factor with symptoms of all three domains of the BPS as an inhibition and the PANSS excitement factor with an inhibition of the affect domain and a disinhibition of the language and motor domains. The results show that here is only a partial overlap between the system-specific approach of the BPS and the five-factor PANSS model. A longitudinal assessment of psychopathological symptoms would therefore be of interest.

Mixed effects model in negative exponential curve

Despite many researches on development in education and psychology, not often is the methodology tested with real data. A major barrier to test the growth model is that the design of study includes repeated observations and the nature of the growth is nonlinear. The repeat measurements on a nonlinear model require sophisticated statistical methods. In this study, we present mixed effects model in a negative exponential curve to describe the development of children's reading skills. This model can describe the nature of the growth on children's reading skills and account for intra-individual and inter-individual variation. We also apply simple techniques including cross-validation, regression, and graphical methods to determine the most appropriate curve for data, to find efficient initial values of parameters, and to select potential covariates. We illustrate with an example that motivated this research: a longitudinal study of academic skills from grade 1 to grade 12 in Connecticut public schools. ^

COX-2 expression in operable triple negative breast cancer: A hospital based cross-sectional study

Objectives. Triple Negative Breast Cancer (TNBC) lack expression of estrogen receptors (ER), progesterone receptors (PR), and absence of Her2 gene amplification. Current literature has identified TNBC and over-expression of cyclo-oxygenase-2 (COX-2) protein in primary breast cancer to be independent markers of poor prognosis in terms of overall and distant disease free survival. The purpose of this study was to compare COX-2 over-expression in TNBC patients to those patients who expressed one or more of the three tumor markers (i.e. ER, and/or PR, and/or Her2).^ Methods. Using a secondary data analysis, a cross-sectional design was implemented to examine the association of interest. Data collected from two ongoing protocols titled "LAB04-0657: a model for COX-2 mediated bone metastasis (Specific aim 3)" and "LAB04-0698: correlation of circulating tumor cells and COX-2 expression in primary breast cancer metastasis" was used for analysis. A sample of 125 female patients was analyzed using Chi-square tests and logistic regression models. ^ Results. COX-2 over-expression was present in 33% (41/125) and 28% (35/124) patients were identified as having TNBC. TNBC status was associated with elevated COX-2 expression (OR= 3.34; 95% CI= 1.40–8.22) and high tumor grade (OR= 4.09; 95% CI= 1.58–10.82). In a multivariable analysis, TNBC status was an important predictor of COX-2 expression after adjusting for age, menopausal status, BMI, and lymph node status (OR= 3.31; 95% CI: 1.26–8.67; p=0.01).^ Conclusion. TNBC is associated with COX-2 expression—a known marker of poor prognosis in patients with operable breast cancer. Replication of these results in a study with a larger sample size, or a future randomized clinical trial demonstrating an improved prognosis with COX-2 suppression in these patients would support this hypothesis.^

Survival analysis of circulating tumor cells in triple-negative breast cancer

Background. Breast cancer is the most frequently diagnosed cancer and the leading cause of cancer death among females, accounting for 23% (1.38 million) of the total new cancer cases and 14% (458,400) of the total cancer deaths in 2008. [1] Triple-negative breast cancer (TNBC) is an aggressive phenotype comprising 10–20% of all breast cancers (BCs). [2-4] TNBCs show absence of estrogen, progesterone and HER2/neu receptors on the tumor cells. Because of the absence of these receptors, TNBCs are not candidates for targeted therapies. Circulating tumor cells (CTCs) are observed in blood of breast cancer patients even at early stages (Stage I & II) of the disease. Immunological and molecular analysis can be used to detect the presence of tumor cells in the blood (Circulating tumor cells; CTCs) of many breast cancer patients. These cells may explain relapses in early stage breast cancer patients even after adequate local control. CTC detection may be useful in identifying patients at risk for disease progression, and therapies targeting CTCs may improve outcome in patients harboring them. Methods . In this study we evaluated 80 patients with TNBC who are enrolled in a larger prospective study conducted at M D Anderson Cancer Center in order to determine whether the presence of circulating tumor cells is a significant prognostic factor in relapse free and overall survival . Patients with metastatic disease at the time of presentation were excluded from the study. CTCs were assessed using CellSearch System™ (Veridex, Raritan, NJ). CTCs were defined as nucleated cells lacking the presence of CD45 but expressing cytokeratins 8, 18 or 19. The distribution of patient and tumor characteristics was analyzed using chi square test and Fisher's exact test. Log rank test and Cox regression analysis was applied to establish the association of circulating tumor cells with relapse free and overall survival. Results. The median age of the study participants was 53years. The median duration of follow-up was 40 months. Eighty-eight percent (88%) of patients were newly diagnosed (without a previous history of breast cancer), and (60%) of patients were chemo naïve (had not received chemotherapy at the time of their blood draw for CTC analysis). Tumor characteristics such as stage (P=0.40), tumor size (P=69), sentinel nodal involvement (P=0.87), axillary lymph node involvement (P=0.13), adjuvant therapy (P=0.83), and high histological grade of tumor (P=0.26) did not predict the presence of CTCs. However, CTCs predicted worse relapse free survival (1 or more CTCs log rank P value = 0.04, at 2 or more CTCs P = 0.02 and at 3 or more CTCs P < 0.0001) and overall survival (at 1 or more CTCs log rank P value = 0.08, at 2 or more CTCs P = 0.01 and at 3 or more CTCs P = 0.0001. Conclusions. The number of circulating tumor cells predicted worse relapse free survival and overall survival in TNBC patients.^

Estudio del rendimiento bajo presión en los tiros libres en baloncesto, y su influencia sobre el porcentaje de acierto durante el último minuto de juego

El minuto final de un partido ajustado de baloncesto es un momento crítico que está sujeto a multitud de factores que influyen en su desarrollo. Así, el porcentaje de acierto en los tiros libres durante ese periodo de tiempo va a determinar, en muchas ocasiones, el resultado final del partido. La disminución de rendimiento (drop) en esta faceta de juego en condiciones de presión, puede estar relacionada con múltiples variables propias del contexto deportivo estudiado, como por ejemplo: los segundos restantes de posesión, la situación en el marcador (ir ganando, empatando o perdiendo), la localización del partido (jugar en casa o fuera), la fase de competición (fase regular o eliminatorias) o el nivel del equipo (mejores/peores equipos). Además, las características del jugador que realiza los lanzamientos tienen una gran importancia respecto a su edad y años de experiencia para afrontar los momentos críticos, así como el puesto de juego que ocupa en el equipo. En este sentido, la combinación de factores del contexto y del jugador, permiten interactuar en el rendimiento del lanzador en los momentos finales de partido durante sus lanzamientos de tiro libre. El presente trabajo de tesis doctoral tiene como objetivo encontrar aquellas variables más relacionadas con la disminución de rendimiento del jugador en los tiros libres durante el último minuto de juego, y la última serie de tiros libres en los partidos ajustados de baloncesto. Para alcanzar el objetivo del estudio se analizaron 124 partidos ajustados (diferencias iguales o inferiores a 2 puntos) de todas las competiciones (fase regular, playoff y copa del Rey) de la liga ACB durante las temporadas 2011-2012 a 2014-2015. Para el registro de variables se analizó el porcentaje de acierto en los tiros libres del lanzador en la liga regular, partido completo, último minuto y última serie. De este modo se trató de analizar qué variables del contexto y del jugador permitían explicar el rendimiento en los tiros libres durante el último minuto, y la última serie de tiros libres del partido. Por otro lado, se trató de conocer el grado de asociación entre el descenso del rendimiento (drop) en los momentos finales de partido, y las variables estudiadas del jugador: puesto de juego, edad, y años de experiencia profesional; mientras que las variables situacionales consideradas fueron: fase de competición, localización, clasificación, tiempo restante, y diferencia parcial en el marcador. Para el análisis de los datos se realizaron dos modelos estadísticos: 1º) un modelo de regresión lineal múltiple para conocer el efecto de las variables independientes en el porcentaje de aciertos del lanzador en el último minuto, y en la última serie de tiros libres del partido; y 2º) un análisis de regresión logística binomial para analizar la relación existente entre la probabilidad de tener un drop (disminución del rendimiento) y las características del lanzador, y las variables situacionales. Los resultados del modelo de regresión lineal múltiple mostraron efectos negativos significativos en el porcentaje de acierto en los tiros libres durante el último minuto, cuando los lanzadores son los pívots (-19,45%). Por otro lado, los resultados durante la última serie mostraron el efecto negativo significativo sobre la posición de pívot (- 19,30%) y la diferencia parcial en el marcador (-3,33%, para cada punto de diferencia en el marcador) en el porcentaje de acierto en los tiros libres. Las variables independientes edad, experiencia profesional, clasificación en la liga regular, fase de competición, localización, y tiempo restante, no revelaron efectos significativos en los modelos de regresión lineal. Los resultados de la regresión logística binomial revelaron que las variables experiencia profesional entre 13 y 18 años (OR = 4,63), jugar de alero (OR = 23,01), y jugar de base (OR = 10,68) están relacionadas con una baja probabilidad de disminuir el rendimiento durante el último minuto del partido; mientras que ir ganando, aumenta esta probabilidad (OR = 0,06). Además, los resultados de la última serie mostraron una menor disminución del rendimiento del jugador cuando tiene entre 13 y 18 años de experiencia (OR = 4,28), y juega de alero (OR = 8,06) o base (OR = 6,34). Por el contrario, las variables situacionales relacionadas con esa disminución del rendimiento del jugador son las fases eliminatorias (OR = 0,22) e ir ganando (OR = 0,04). Los resultados principales del estudio mostraron que existe una disminución del rendimiento del jugador en su porcentaje de acierto en los tiros libres durante el último minuto y en la última serie de lanzamientos del partido, y que está relacionada significativamente con la edad, experiencia profesional, puesto de juego del jugador, y diferencia parcial en el marcador. Encontrando relación también con la fase de competición, durante la última serie de tiros libres del partido. Esta información supone una valiosa información para el entrenador, y su aplicación en el ámbito competitivo real. En este sentido, la creación de simulaciones en el apartado de aplicaciones prácticas, permite predecir el porcentaje de acierto en los tiros libres de un jugador durante los momentos de mayor presión del partido, en base a su perfil de rendimiento. Lo que puede servir para realizar una toma de decisiones más idónea, con el objetivo de lograr el mejor resultado. Del mismo modo, orienta el tipo de proceso de entrenamiento que se ha de seguir, en relación a los jugadores más tendentes al drop, con el objetivo de minimizar el efecto de la presión sobre su capacidad para rendir adecuadamente en la ejecución de los tiros libres, y lograr de esta manera un rendimiento más homogéneo en todos los jugadores del equipo en esta faceta del juego, durante el momento crítico del final de partido. ABSTRACT. The final minute of a close game in basketball is a critical moment which is subject to many factors that influence its development. Thus, the success rate in free-throws during that period will determine, in many cases, the outcome of the game. Decrease of performance (drop) in this facet of play under pressure conditions, may be related to studied own multiple sports context variables, such as the remaining seconds of possession, the situation in the score (to be winning, drawing, or losing) the location of the match (playing at home or away), the competition phase (regular season or playoffs) or team level (best/worst teams). In addition, the characteristics of the player are very important related to his age and years of experience to face the critical moments, as well as his playing position into team. In this sense, the combination of factors in context and player, allows interact about performance of shooter in the final moments of the game during his free-throw shooting. The aim of this present doctoral thesis was find the most related variables to player´s drop in free throws in the last minute of the game and the last row of free-throws in closed games of basketball. To achieve the objective of the study, 124 closed games (less or equal than 2 points difference) were analyzed in every copetition in ACB league (regular season, playoff and cup) from 2011-2012 to 2014-2015 seasons. To record the variables, the percentage of success of the shooter in regular season, full game, last minute, and last row were analyzed. This way, it is tried to analyze which player and context variables explain the free-throw performance in last minute and last row of the game. On the other hand, it is tried to determine the degree of association between decrease of performance (drop) of the player in the final moments, and studied player variables: playing position, age, and years of professional experience; while considered situational variables considered were: competition phase, location, classification, remaining time, and score-line. For data analysis were performed two statistical models: 1) A multiple linear regression model to determine the effect of the independent variables in the succsess percentage of shooter at the last minute, and in the last row of free-throws in the game; and 2) A binomial logistic regression analysis to analyze the relationship between the probability of a drop (lower performance) and the characteristics of the shooter and situational variables. The results of multiple linear regression model showed significant negative effects on the free-throw percentage during last minute, when shooters are centers (-19.45%). On the other hand, results in the last series showed the significant negative effect on the center position (-19.30%) and score-line (-3.33% for each point difference in the score) in the free-throw percentage. The independent variables age, professional experience, ranking in the regular season, competition phase, location, and remaining time, revealed no significant effects on linear regression models. The results of the binomial logistic regression showed that the variables professional experience between 13 and 18 years (OR = 4.63), playing forward (OR = 23.01) and playing guard (OR = 10.68) are related to reduce the probability to decrease the performance during the last minute of the game. While wining, increases it (OR = 0.06). Furthermore, the results of the last row showed a reduction in performance degradation when player is between 13 and 18 years of experience (OR = 4.28), and playing forward (OR = 8.06) or guard (OR = 6.34). By contrast, the variables related to the decrease in performance of the player are the knockout phases (OR = 0.22) and wining (OR = 0.04). The main results of the study showed that there is a decrease in performance of the player in the percentage of success in free-throws in the last minute and last row of the game, and it is significantly associated with age, professional experience, and player position. Finding relationship with the competition phase, during last row of free-throws of the game too. This information is a valuable information for the coach, for applying in real competitive environment. In this sense, create simulations in the section of practical applications allows to predict the success rate of free-throw of a player during the most pressing moments of the game, based on their performance profile. What can be used to take more appropriate decisions in order to achieve the best result. Similarly, guides the type of training process must be followed in relation to the most favorable players to drop, in order to minimize the effect of pressure on their ability to perform properly in the execution of the free-throws. And to achieve, in this way, a more consistent performance in all team players in this facet of the game, during the critical moment in the final of the game.

The 2014 chikungunya virus outbreak in the U.S. Virgin Islands: epidemiology, long-term health outcomes, and economic burden

Thesis (Ph.D.)--University of Washington, 2016-06

Improving precision and reducing bias in biological surveys: estimating false-negative error rates

The use of presence/absence data in wildlife management and biological surveys is widespread. There is a growing interest in quantifying the sources of error associated with these data. We show that false-negative errors (failure to record a species when in fact it is present) can have a significant impact on statistical estimation of habitat models using simulated data. Then we introduce an extension of logistic modeling, the zero-inflated binomial (ZIB) model that permits the estimation of the rate of false-negative errors and the correction of estimates of the probability of occurrence for false-negative errors by using repeated. visits to the same site. Our simulations show that even relatively low rates of false negatives bias statistical estimates of habitat effects. The method with three repeated visits eliminates the bias, but estimates are relatively imprecise. Six repeated visits improve precision of estimates to levels comparable to that achieved with conventional statistics in the absence of false-negative errors In general, when error rates are less than or equal to50% greater efficiency is gained by adding more sites, whereas when error rates are >50% it is better to increase the number of repeated visits. We highlight the flexibility of the method with three case studies, clearly demonstrating the effect of false-negative errors for a range of commonly used survey methods.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

Statnote 24: Multiple regression

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. These methods can be used to determine whether there is a linear relationship between the two variables, whether the relationship is positive or negative, to test the degree of significance of the linear relationship, and to obtain an equation relating Y to X. This Statnote extends the methods of linear correlation and regression to situations where there are two or more X variables, i.e., 'multiple linear regression’.