Parameters proportional hazards models. Medical search. Frequent questions

However, it is recommended to use Cox's proportional hazards model as it provides a more suitable method for this type of case. (xlstat.com)
Cox's proportional hazards model is another unexpected finding: by using only the ranking information in the data, and hence a partial likelihood, one can eliminate entirely an infinite dimensional nuisance parameter, i.e., the baseline hazard. (imstat.org)
The clinical value of SAA level as a prognostic parameter was evaluated using the Cox's proportional hazards model. (biomedcentral.com)

A likelihood ratio or Wald X² test formally tests the hypothesis of whether the model fits the data better than no model. (analyse-it.com)
A software program developed for this research finds the maximum likelihood estimates of the parameters and the likelihood ratio test of the null hypothesis of a single regime against the alternative of a mixture of two regimes. (suny.edu)
A weak association was observed between prenatal pH1N1 vaccination and increased risk of asthma (adjusted hazard ratio 1.05, 95% confidence interval 1.02 to 1.09) and decreased rates of gastrointestinal infections (adjusted incidence rate ratio 0.94, 0.91 to 0.98). (bmj.com)
In this case study I have to assume a baseline Weibull distribution, and I'm fitting an Accelerated Failure Time model, which will be interpreted by me later on regarding both hazard ratio and survival time. (stackexchange.com)
Every parameter was firstly calculated by the univariate and multivariate Cox proportional hazards regression model and resulted as hazard ratio (HR) and 95% confidence interval (CI). (researchsquare.com)
We study this improper proportional hazards model in both interior and boundary cases by maximum likelihood method, and develop a likelihood ratio test for the presence of an immune proportion in a population. (edu.hk)

Using these models, clinicians are in a better position to provide prognostic information to patients with IPF and to improve the selection of the most appropriate patients for lung transplantation or other standard or novel therapeutic interventions. (nih.gov)
OBJECTIVES: The aim of this study was to determine the prognostic significance of changes in parameters derived from diffusion tensor imaging (DTI) that occur in response to treatment with bevacizumab and irinotecan in patients with recurrent glioblastoma multiforme. (duke.edu)
The objective of this study was to determined whether SAA level could be used as a prognostic parameter in patients with esophageal squamous cell carcinoma (ESCC). (biomedcentral.com)
In this study, we measured the preoperative SAA levels in 167 patients with ESCC to evaluate the clinical value of SAA as a prognostic parameter in those patients. (biomedcentral.com)
Multivariate Cox proportional hazards regression demonstrated that the independent prognostic risk factors associated with PC were age, stage T, N and M, and grade, with a moderate c-index of 0.732 [95% confidence interval (CI), 0.706-0.757] in development group and 0.743 (95% CI, 0.703-0.782) in verification group. (researchsquare.com)
Meier curves and Cox proportional hazards regression was used to identify prognostic factors. (cdc.gov)

An ingenious flipping, from probability space to parameter space, created an exceedingly influential paradigm for statistical inference. (imstat.org)
This transformation model, coupled with proposed inference procedures, provides many alternatives to Cox proportional hazards models for survival analysis with long-term survivors. (edu.hk)

Understand models for human mortality, including how to compute and interpret the life table in a variety of contexts and models for forecasting morality. (southampton.ac.uk)
Comparison of models of mortality: Binomial, Poisson and multiple-state models. (southampton.ac.uk)
Combining demographic, immune and viral parameters, the best predictive models for mortality comprised IFNB1 or age, viral ORF7a and ACE2 receptor transcripts. (nature.com)
Impella improves parameters of shock severity but is associated with higher bleeding complications and has no significant effect on 30-day mortality compared with the use of IABP. (bmj.com)
10.5 Modeling the impact of new screening modalities on reduction of mortality from lung cancer. (who.int)

The hazard ratios for each variable with confidence intervals are also displayed. (xlstat.com)
Propensity score weighting was used to adjust hazard ratios, incidence rate ratios, and risk ratios for potential confounding. (bmj.com)
Cox proportional models were used to estimate adjusted hazard ratios (aHR), with follow-up accrued from birth through cancer diagnosis, death or last contact. (deepdyve.com)
Identified outliers changed the direction of hazard ratios, standard errors, or the strength of association with the risk of developing IA. (lu.se)

Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter(s), denoted β i {\displaystyle \beta _{i}} below, without any consideration of the full hazard function. (wikipedia.org)
The parameter estimate, corresponding standard deviation, Wald's Chi 2 , the corresponding p-value and the confidence interval are displayed for each variable of the model. (xlstat.com)
Typically, the Cox proportional hazards model is applied to estimate a single regime survival regression function. (suny.edu)
The objectives of this study are to estimate its prevalence, factors associated, and possible health hazards. (who.int)

Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. (wikipedia.org)
and the effect parameters, describing how the hazard varies in response to explanatory covariates. (wikipedia.org)
The proportional hazards condition states that covariates are multiplicatively related to the hazard. (wikipedia.org)
The principle of the proportional hazards model is to link the survival time of an individual to covariates. (xlstat.com)
This table displays a series of statistics for the independent model (corresponding to the case where there is no impact of covariates, beta=0) and for the adjusted model. (xlstat.com)
Third, using an agnostic model screening approach, we explored the issue of what covariates to include and how much variance they explain. (elifesciences.org)
The null hypothesis states that all the parameters for the covariates are zero against the alternative that at least one parameter is not equal to zero. (analyse-it.com)
However the model proposed by Kuk and Chen (1992) does not have a proportional hazards structure for the survival function of the entire population, this structure is a desirable property in survival analysis models when doing covariates and is extensively used in survival analysis. (edu.hk)
In this dissertation, we will investigate an alternative mixture model with covariates, which does have a proportional hazards structure and is proposed by Maller and Zhou (1996) via the different motivation of the model from other cure models and is not further investigated so far. (edu.hk)
In this dissertation, we consider a class of semiparametric transformation models derived from the aforesaid 'improper' PH model, which assume a linear relationship between an unknown transformation of the survival time under the proportional hazards model and the covariates. (edu.hk)
The random errors are modeled by an 'improper' extreme value distribution, which is parametricaly specified with unknown parameters and covariates. (edu.hk)

After adjustment for age and baseline vitamin D levels in a linear regression model, the ALSFRS-R score decline was smaller in patients taking vitamin D at 9 months (p=0.02) but was not significantly different at 3 or 6 months. (vitad.org)
Background: Outliers can influence regression model parameters and change the direction of the estimated effect, over-estimating or under-estimating the strength of the association between a response variable and an exposure of interest. (lu.se)
Results: Extreme vitamin B 12 observations that were cases of IA had a stronger influence on the Cox regression model than non-cases. (lu.se)

Risk factors for RP recurrence were analysed using a Cox proportional hazards model, and Kaplan-Meier survival curves were drawn. (springer.com)

An inequality concerning estimation in a two-parameter statistical problem plays a key role in the proof. (projecteuclid.org)
Parameter estimation and statistical inferences can be easily achieved via a partial likelihood function. (amstat.org)
Parameters estimation for condition based maintenance with uncorrelated and correlated observations. (polymtl.ca)
The maximum likelihood estimation and approximate partial likelihood estimation are proposed to obtain the parameter estimators. (edu.hk)
11.4 The data and parameter estimation. (who.int)

Inspired by the works of Potts (2004) and Linoff (2004), in this dissertation we will review some existing discrete time survival models which have already been proposed to analyze survival data from social and behavioral science by these authors, and then generalize these models to accommodate survival data with long-term survivors. (edu.hk)
As a natural extension of the continuous cases discussed in Chapters 1-4, in Chapter 5 of this dissertation we will predominantly focus on modeling discrete-time survival data which may accommodate proportional hazards structure and propose an alternative discrete time cure model which does have proportional hazards structure. (edu.hk)
Since most durations of economic interest are continuous by nature but artificially grouped into discrete intervals, a further important contribution of Chapter 2 is to show that the proposed discrete-time duration model can be linked to an underlying continuous-time process. (lu.se)
More specifically, the choice of hazard specification in the discrete-time framework is motivated by the asymptotic distribution of threshold excesses of a continuous duration variable. (lu.se)
Since the cloglog model is the discrete-time analogue of the Cox model, the Pareto model can be used to test the proportional hazards assumption imposed by the Cox model, even when duration times are coarsely grouped. (lu.se)
Chapter 3 contains an extensive discussion of the ineligibility of the predominantly used continuous-time duration models for the analysis of trade survival, and provides empirical evidence supporting the use of discrete-time models in this context. (lu.se)

For example, the values in the model diagnostics section of the results (AIC, partial log likelihood, negative two times the partial log-likelihood, and pseudo R-squared) are commonly used to compare the specified model to the null model. (graphpad.com)
AIC is an information theory approach that is used to determine how well the data supports each model, taking into account the partial log-likelihood for each model as well as the number of parameters contained within each model. (graphpad.com)
The option to report the partial log-likelihood (and negative two times the partial likelihood) for the selected model is also available on the Options tab of the Cox proportional hazards regression dialog. (graphpad.com)
Similar to the AIC, the LRT also uses the partial log-likelihood to determine which model is preferred. (graphpad.com)
Adding parameters to a model (very nearly) always increases the partial log-likelihood of the model. (graphpad.com)

Recently, Kuk and Chen (1992) proposed a model which is a semiparametric generalization of a parametric model above, which combines a logistic formulation for the probability of occurrence of the event with a proportional hazards specification for the time of occurence of the event. (edu.hk)
Their idea is to extend Cox model with a parametric or completely unspecified baseline to 'improper' Cox model of which the baseline can be modeled as an improper and semiparametric structure of a combination of the probability of occurrence of the event with a proper survival function for the time of occurrence of the event. (edu.hk)

each unit increase in x {\displaystyle x} results in proportional scaling of the hazard. (wikipedia.org)
If the data contains only uncensored or right-censored observations, it is possible, with this function, to reproduce the results of a Cox model. (xlstat.com)
Because of this, a lot of what we generally look at as "interpretation" of the results of a single model is actually cleverly disguised comparisons of different competing models. (graphpad.com)
The risk of incident osteoporotic fractures (including hip, vertebrae, humerus, forearm, pelvis and ribs) was estimated by time-dependent Cox proportional-hazards models, statistically adjusted for lifestyle parameters, comorbidities and comedications.RESULTS: Among 12 351 patients with RA (mean age of 68 years, 69% women), 1411 osteoporotic fractures occurred. (maastrichtuniversity.nl)
D T Levy, Pacific Institute for Research and Evaluation, Results: The model validates well against survey data. (who.int)

When the p-value is small, you can reject the null hypothesis and conclude that at least one parameter is not zero. (analyse-it.com)
This makes it possible to identify the cross-sectional unit that violates the homogeneity assumption in case the null hypothesis of equal parameters is rejected. (lu.se)

The risk of incident osteoporotic fractures (including hip, vertebrae, humerus, forearm, pelvis and ribs) was estimated by time-dependent Cox proportional-hazards models, statistically adjusted for lifestyle parameters, comorbidities and comedications. (maastrichtuniversity.nl)
An SCD competing risks score was derived from demographics, comorbidities, and GEH parameters. (elsevierpure.com)

Although models can be reliably fit using randomly generated cases, repetition would reduce variability in parameter estimates. (cdc.gov)

This approach to survival data is called application of the Cox proportional hazards model, sometimes abbreviated to Cox model or to proportional hazards model. (wikipedia.org)
The first proportional hazard model, introduced by Cox in 1972, works with uncensored data and right censored data. (xlstat.com)
The purpose of the proportional hazard model with interval censored data is, therefore, the same as for the Cox model, but it will also be possible to model survival times for interval-censored data, uncensored data, left censored data or right censored data. (xlstat.com)
The options available on this tab allow you to specify a second model (with different combinations of predictor variables, interaction terms, and/or transformations), and compare how well each model fits the entered data. (graphpad.com)
However, if the difference is not very big (say 40% vs. 60%), you wouldn't know for sure which model was better, and you'd want to collect more data. (graphpad.com)
Importantly, AIC can be used to compare any two models on the same data set. (graphpad.com)
Modelling survival data in medical research. (southampton.ac.uk)
By using historical data from experimental human infections with diverse P. vivax strains, survival analysis models were used to obtain quantitative estimates of the incubation period and time to first relapse for P. vivax malaria in broad geographic regions. (cdc.gov)
Knowing the distribution model of the data helps you to continue with the right analysis. (originlab.com)
It is common to test whether the model fits the data better than the null model with no parameters. (analyse-it.com)
Data were correlated with clinicopathological parameters and patient outcomes. (researchsquare.com)
hence, the triggering scheme of event occurrence shall be considered when modeling such data. (amstat.org)
This is an attractive approach to analyzing survival data with long-term survivors, in that it contains two parts which can be interpreted separately by adding structure to the standard survival model. (edu.hk)
Fully parametric approaches have had a long history and recent attention has focused on test for the presence of long-term survivors in the data for mixture model. (edu.hk)
The proposed models and approaches can be directly applied to analyze survival data from social and behavioral science such as the economic values for customer retention with long-life customers. (edu.hk)
The second part discusses more advanced topics such as modeling of nonlinear effects and analysis of longitudinal and clustered data, as well as sample-size and power considerations when designing a study. (stata.com)
Using simulated data and data on US unemployment durations, Chapter 2 shows that the Pareto model works very well in practice, and that it also allows for covariate effects that are entirely different from those implied by both the cloglog and the logit specification. (lu.se)
8.3 Model-based evaluation of liver focal lesion data. (who.int)
Analysis of Survival Data with Non-proportional Hazards and Crossings of Survival Functions (Vilijandas B. Bagdonavic?ius and Mikhail S. Nikuline). (who.int)
To assess the impact of detected outliers, data were analyzed using the extended time-dependent Cox model with robust sandwich estimator. (lu.se)
The purpose of an Interaction Profile is to evaluate data on the toxicology of the "whole" priority mixture (if available) and on the joint toxic action of the chemicals in the mixture in order to recommend approaches for the exposure-based assessment of the potential hazard to public health. (cdc.gov)
A cross-sectional study was conducted of nursing students using a questionnaire that included sociodemographic and employment data, reasons for working, possible health hazards in the workplace, and perceived effects on academic performance. (who.int)

However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky. (wikipedia.org)

5.4 Modeling cancer incidence. (who.int)

Histopathological-based models may be used to stratify patients into low- and high-risk classes 9 and further identify patients at risk of aggressive early-stage OSCC, thus contributing to disease predictability in terms of clinical progression and treatment outcomes. (nature.com)
Secondary outcomes were parameters of shock severity at the early postimplantation phase. (bmj.com)
It describes the important aspects of regression models for continuous, binary, survival, and count outcomes-all commonly encountered in medical research. (stata.com)

The same problem arises in a proportional-hazards context. (cdc.gov)

To approximate the therapeutic effect in intention-to-treat analyses, they used proportional-hazard models. (medscape.com)

The supported regression models are linear, logistic and Poisson regression and the Cox Proportional Hazards model. (belnet.be)
The regression models covered include linear regression, logistic regression, Cox regression, and Poisson regression. (stata.com)

A two-regime parametric mixture is proposed to model the effect of a single covariate on the event time. (suny.edu)

The diversity in these estimates of key epidemiologic parameters for P. vivax supports the need for elucidating local epidemiology to inform clinical follow-up and to build an evidence base toward global elimination of malaria. (cdc.gov)
The chapter proposes a new poolability test based on the Hausman principle, whereby two estimates of the cointegration parameters - one individual and one pooled - are compared. (lu.se)
A further advantage is that the test statistic is based on the maximum difference between the individual and the pooled parameter estimates. (lu.se)

Use the interval-censored proportional hazard model to model survival time based on quantitative or qualitative explanatory variables. (xlstat.com)
TY - BOOK AU - Edler,Lutz AU - Kitsos,Christos P. TI - Recent advances in quantitative methods in cancer and human health risk assessment SN - 0470857560 U1 - 616.994071015118 22 PY - 2005/// CY - New York PB - Wiley KW - Neoplasms KW - Risk factors KW - Models, Theoretical N1 - Preface. (who.int)
DTEM) has developed and coordinated a mixtures program that includes trend analysis to identify the mixtures most often found in environmental media, in vivo and in vitro toxicological testing of mixtures, quantitative modeling of joint action, and methodological development for assessment of joint toxicity. (cdc.gov)

This null model is simply a model that contains no predictor variables, and - when compared to the specified model in the analysis - can be used to determine the relative importance of the predictor variables included in the specified model, or to assess the overall "fit" of the specified model. (graphpad.com)
Prism offers two different methods to assess the comparison of the model specified on the model tab and the model specified on the compare tab. (graphpad.com)
We used Cox proportional-hazards models to assess the effect of these parameters on survival. (nih.gov)
Objectives: The primary objective was to identify potential outliers at follow-up visits using interquartile range (IQR) statistic and assess their influence on estimated Cox regression parameters. (lu.se)

We used multivariable logistic regression models to examine the association between rurality and food security, physical activity, and overweight or obesity. (bvsalud.org)
After multivariable adjustment, baseline GEH parameters and large increases in GEH parameters over time were independently associated with SCD. (elsevierpure.com)
In a multivariable model, the highest cancer risk was calculated among nonpersistent statin users. (cdc.gov)

In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. (wikipedia.org)
X_{i})&=\lambda _{0}(t)\exp(\beta _{1}X_{i1}+\cdots +\beta _{p}X_{ip})\\&=\lambda _{0}(t)\exp(X_{i}\cdot \beta )\end{aligned}}} This expression gives the hazard function at time t for subject i with covariate vector (explanatory variables) Xi. (wikipedia.org)
Chapter 2 introduces a novel hazard rate model that is much more flexible with respect to the imposed covariate effects than the conventional cloglog, logit, and probit specifications. (lu.se)

RAS / BRAF status, sidedness, Lynch syndrome, and other baseline parameters were not associated with PFS. (bmj.com)
The effect of vitamin D supplementation was not modified by baseline parameters such as race or ethnicity, sex, body mass index, age, or blood 25-hydroxyvitamin D levels. (medscape.com)

Other types of survival models such as accelerated failure time models do not exhibit proportional hazards. (wikipedia.org)
The accelerated failure time model describes a situation where the biological or mechanical life history of an event is accelerated (or decelerated). (wikipedia.org)
In the simplest case of stationary coefficients, for example, a treatment with a drug may, say, halve a subject's hazard at any given time t {\displaystyle t} , while the baseline hazard may vary. (wikipedia.org)
accelerated failure time models. (southampton.ac.uk)
Here, we compared Bayesian logistic and time-to-event approaches to modeling hypertension. (elifesciences.org)
Given that the lifetime risk is so high, we first investigated whether a proportional hazards model in time-to-event analysis yields a better fit than logistic regression. (elifesciences.org)
Second, as time-to-event analysis assumes that the event will occur, that is, that every individual will become hypertensive if they live long enough, we investigated a proportional hazards model including a fraction of individuals that will never become hypertensive and hence are true epidemiological controls. (elifesciences.org)
I'm fitting a model using the function Weibullreg() in R. The survival function is built reading TimeSurv as the time measures and IndSurv as the indicator of censoring. (stackexchange.com)
In this paper, we extend the Cox proportional hazard model with time-varying information of previous events to enhance the model fitness and prediction. (amstat.org)

A Cox proportional hazard model identified four risk factors for hypokalaemia: YK administration (not YKCH) (HR 3.093, 95% CI 1.408 to 6.798), co-administration of LPIDs (HR 2.743, 95% CI 1.754 to 4.289), hypoalbuminaemia at baseline (HR 2.145, 95% 1.360 to 3.384), and full dosage administration (7.5 g/day) (HR 1.600, 95% CI 1.005 to 2.549). (bmj.com)
Following, the univariate and multivariate Cox proportional hazards regression was respectively used to explore the possible risk factors of PC. (researchsquare.com)
Relative-rate models of exposure-response produce unstable near-zero baseline risk and unbounded coefficients, especially when age confounding requires baseline age dependence. (cdc.gov)
The addition of GEH parameters to clinical characteristics improves SCD risk prediction. (elsevierpure.com)
13.4 Dose-response models in risk assessment. (who.int)

Recently, much attention has been attracted to semiparametric transformation model, which provides many interesting statistical models and approaches. (edu.hk)

10.4 Review of modeling approaches. (who.int)

The third part concentrates on prediction, and the fourth part briefly covers some alternatives to regression modeling. (stata.com)

Taken together, modeling of the baseline hazard function of hypertension suggests that there are no true controls and that controls in logistic regression are cases with a late age of onset. (elifesciences.org)

survival and hazard functions. (southampton.ac.uk)

An optimized miPPSPC was constructed by combining clinical parameters. (aging-us.com)

A commonly used approach is to formulate the model as a mixture of two populations, one for 'long-term survivors' (subjects that will never experience the event of interest) and the other for 'susceptibles' (subjects that will 'fail' eventualy). (edu.hk)
In fact, the proposed Pareto hazard model incorporates the most commonly used cloglog and logit specifications as special cases. (lu.se)

4. Biological Carcinogenesis: Theories and Models (Sylvia Solakidi, Constantinos E. Vorgias and Constantine E. Sekeris). (who.int)

9. A Unified Modeling Approach: From Exposure to Disease Endpoints (Chao W. Chen). (who.int)

As described above, these controls should not be used to try and specify the "null model" for comparison, but should only be used to compare two models that contain predictor variables. (graphpad.com)

For example, one common comparison that is made is between the model specified in the analysis and the so-called "empty" or "null" model. (graphpad.com)
In contrast, the controls on the Compare tab of the analysis parameters dialog are designed to compare two models specified by the user (two competing models). (graphpad.com)
Regression Models as a Tool in Medical Research , by Werner Vach, is a practical guide to regression analysis for medical researchers. (stata.com)
Further, a xenograft tumor model showed that Nek2 knockdown could improve the anti-tumor effect of sorafenib, whereas an analysis of tumor proteins showed that Nek2 regulates β-catenin protein levels and its nuclear translocation in vivo. (biomedcentral.com)

Interaction of a high-intensity optical laser beam with a solid target can generate `hot' electrons, which generate radiation hazards (mainly bremsstrahlung photons and neutrons) from interaction of hot electrons with target and the surrounding materials. (lu.se)

Cox proportional hazards and competing risks models evaluated associations between GEH electrocardiographic parameters and SCD. (elsevierpure.com)

High-Temperature Empirical Modeling for the I-V Characteristics of GaN150-Based HEMT [Paper]. (polymtl.ca)
The scenario shows that the simulated dose rate is about 5 times lower than that calculated using the empirical formulae (Daresbury model). (lu.se)

The quote above emphasizes the fact that statistical models rarely (if ever) capture the true complexity of a system or population. (graphpad.com)

For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure. (wikipedia.org)

The problem of loss adaptation is investigated: given a fixed parameter, the goal is to construct an estimator that adapts to the loss function in the sense that the estimator is optimal both globally and locally at every point. (projecteuclid.org)
Secondary outcome parameters include the Core Outcome Measures Index, which investigates pain, back-specific function, work disability, social disability and patient satisfaction. (biomedcentral.com)
Further, western blotting, flow cytometry, and an in vivo xenograft model were used to evaluate the function of Nek2 in HCC sorafenib resistance, whereas rescue experiments were performed to confirm that Nek2 induces sorafenib resistance via β-catenin. (biomedcentral.com)

Anatomy1

Organisms1

Diseases62

Chemicals and Drugs19

Analytical, Diagnostic and Therapeutic Techniques and Equipment90

Psychiatry and Psychology5

Phenomena and Processes28

Disciplines and Occupations3

Anthropology, Education, Sociology and Social Phenomena8

Technology, Industry, Agriculture7

Information Science15

Named Groups11

Health Care81

Geographicals25

Cox's3

Ratio6

Prognostic6

Inference2

Mortality5

Ratios4

Estimate4

Covariates11

Regression model3

Kaplan-Meier1

Estimation5

Discrete time6

Likelihood5

Probability2

Results5

Null hypothesis2

Comorbidities2

Reduce variability1

Data22

Assumption1

Incidence1

Outcomes3

Context1

Analyses1

Poisson2

Parametric1

Estimates3

Quantitative3

Assess4

Multivariable3

Covariate3

Baseline parameters2

Time9

Risk5

Semiparametric1

Approaches1

Alternatives1

Hypertension1

Functions1

Clinical1

Commonly2

Biological1

Chen1

Predictor1

Analysis4

Radiation1

Risks1

Empirical2

Statistical models1

Stroke1

Function3