Degree in a Statistical Science (Laurea) at University of Padua (Italy). Senior statistician in a pharmaceutical company. Interested in statitstics and probability foundations
Usually the conditional probability of A given B is defined as P(A|B=PA&B)/P(B) These short notes... more Usually the conditional probability of A given B is defined as P(A|B=PA&B)/P(B) These short notes deal with the conditional probability considered as a basic concept. The above formula will be a consequence derived from such a basic concept.
The first rules of Probability Calculus explained by the bet idea. This is based on De Finetti... more The first rules of Probability Calculus explained by the bet idea. This is based on De Finetti subjective approach to probability.
An experimental result may affect pre-experimental belief in two ways: it can agree or disagree w... more An experimental result may affect pre-experimental belief in two ways: it can agree or disagree with experimental belief. Such aspects were considered using two concepts of information provided by an experiment: the first due to Lindley, the second to Kullback-Leibler. It can be seen that the Lindley's information is in favour of results which agree with prior belief, while the Kullback-Leibler's information considers more useful results which disagree with prior belief. Finally it is noticed that the maximum likelihood estimator maximizes the Kullback-Leibler information.
Journal of Biopharmaceutical Statistics, Feb 15, 2000
The aim of a stability study is to check whether or not a drug maintains its initial properties (... more The aim of a stability study is to check whether or not a drug maintains its initial properties (over a given range) in a period of time. There are many parameters considered in a stability study, but in this paper only the active content will be considered. Evaluation of this parameter is performed by measuring the content of the active ingredient in the drug at different times and on expiration to see if it is within specification (1). The problem also involves estimating whether the drug will perform satisfactorily and maintain its initial properties in the future. In this paper, we provide a criterion for the evaluation of experimental design used in a stability study for predicting the content of an active ingredient in a drug, starting from the confidence limit calculated following International Conference on Harmonisation of Technical Requirements for the Registration of Pharmaceuticals for Human Use (ICH) recommendations. The point of view adopted is akin to hypothesis testing. The main question is this: "If the drug fulfills the requirements at a given time in the future, what is the probability that the data collected for that drug will show its suitability?" For this purpose, two concepts are used-producer gain and consumer loss-which are defined as follows: producer gain is the advantage (for the producer) of recognizing a drug as "good" (provided it is good and within specification); consumer loss is the loss (for the consumer) when the drug is no longer good, but the data collected indicate that it is good. The aim of the experimental design in this study is to increase the probability of producer gain and maximize it on the basis of a given consumer loss.
Journal of Pharmacological and Toxicological Methods, Sep 1, 2011
Dobutamine stress echocardiography (DSE) is performed to detect subtle ischemic regions in the my... more Dobutamine stress echocardiography (DSE) is performed to detect subtle ischemic regions in the myocardium in patients suffering from stenosed coronary artery disease. While in a clinical and veterinary context DSE is performed daily, in the preclinical context, a very limited application has been described in the literature. In the drug development process, the safety of new chemical entities on the cardiovascular system is a primary requirement for the development of new agents/drugs for administration in humans. There are limited tools to evaluate the impairment of myocardial performance and cardiac contractility in preclinical species and particularly in rodents. In this present paper a possible imaging application is presented. Anesthetised male Crl:CD(SD) rats (n=14) were given single intravenous doses of vehicle (5% w/v Dextrose solution) and dobutamine hydrochloride at 10 μg/kg/min. Echocardiography was performed, starting immediately before the infusion and animals were monitored up to 5 min after the end of infusion. Standard and non-standard echocardiography parameters were evaluated to detect test article related changes compared to vehicle infused animals. Thickening of left ventricle walls and interventricular septum and increased velocity of circumferential stress were observed in dobutamine infused animals compared to those receiving vehicle. These changes were considered to be a direct effect on myocardial contractility, as also confirmed by increased functional parameters (i.e., Ejection Fraction, End Diastolic Volume and decrease of the ratio between pre-ejection period and ejection time of the aortic flow). In dobutamine infused rats the "Tei index" increased up to approximately 32% compared to vehicle animals, showing a clear relationship with increased contractility. As expected dobutamine infusion in the anaesthetised rat is capable of inducing a positive inotropic effect and echocardiography results are a reliable tool for the determination of changes in contractility induced by pharmacological stress testing in the rat.
The paper deals with the problem of finding a better predictor starting from a given one. After i... more The paper deals with the problem of finding a better predictor starting from a given one. After introducing some basic notions of sufficiency in terms of a 'sigma-field', a theorem due to K. Tacheuchi and M. Akahira is used to show criterion leading to a better predictor similar to Rao-Blackwell in statistical estimation theory. Then the wide sense sufficiency is introduced showing a criterion to get a better predictor in presence of a sufficient 'sigma-field ' in a wide sense.
In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a ... more In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a stability analysis, is to determin the period of time within wich the compound conserve its initial characetris. At each time point an evaluation a previous trend analysis is caried out. The underlining trend is supposed to be linear or reduced to be linear following the equation C = a+b t, where C is the level of active content. The determination of such trend allows the estimation of the content at varous time points, and to check if the level is greater than a fixed value (the specification). This value represent theminimal condition the copmound must fulfill.,that is:ICH and FDA guide-lines recommend that the lower confidence limit is reported too. If such limit at a time point si greater than the specification,then at such time the specification is fulfilled.Such analysis is performed under the condition of classical regression model. An alternative approach is represented by the use of a mixed model in which the batch effect is regarded as a random effect. This approach appear, from a theoretical point of view, more appealing, since it does not reguest to adopt the step wise procedure seen below. The difference between batch is a variability factor whose effect the variability of the observed result. Such variability can be modelled using a suitable covariance matrix.
In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a ... more In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a stability analysis, is to determin the period of time within wich the compound conserve its initial characetris. At each time point an evaluation a previous trend analysis is caried out. The underlining trend is supposed to be linear or reduced to be linear following the equation C = a+b t, where C is the level of active content. The determination of such trend allows the estimation of the content at varous time points, and to check if the level is greater than a fixed value (the specification). This value represent theminimal condition the copmound must fulfill.,that is:ICH and FDA guide-lines recommend that the lower confidence limit is reported too. If such limit at a time point si greater than the specification,then at such time the specification is fulfilled.Such analysis is performed under the condition of classical regression model. An alternative approach is represented by the...
An application of the dose-response curve in the case of dicothomous responses according to a Bay... more An application of the dose-response curve in the case of dicothomous responses according to a Bayesian point of view is presented in this paper. A dose response curve in cases of dichotomous data describes the relationship between the probability of observing an occurence and a dose level. A researcher may sometimes have some ideas of the shape of such a
Usually the conditional probability of A given B is defined as P(A|B=PA&B)/P(B) These short notes... more Usually the conditional probability of A given B is defined as P(A|B=PA&B)/P(B) These short notes deal with the conditional probability considered as a basic concept. The above formula will be a consequence derived from such a basic concept.
The first rules of Probability Calculus explained by the bet idea. This is based on De Finetti... more The first rules of Probability Calculus explained by the bet idea. This is based on De Finetti subjective approach to probability.
An experimental result may affect pre-experimental belief in two ways: it can agree or disagree w... more An experimental result may affect pre-experimental belief in two ways: it can agree or disagree with experimental belief. Such aspects were considered using two concepts of information provided by an experiment: the first due to Lindley, the second to Kullback-Leibler. It can be seen that the Lindley's information is in favour of results which agree with prior belief, while the Kullback-Leibler's information considers more useful results which disagree with prior belief. Finally it is noticed that the maximum likelihood estimator maximizes the Kullback-Leibler information.
Journal of Biopharmaceutical Statistics, Feb 15, 2000
The aim of a stability study is to check whether or not a drug maintains its initial properties (... more The aim of a stability study is to check whether or not a drug maintains its initial properties (over a given range) in a period of time. There are many parameters considered in a stability study, but in this paper only the active content will be considered. Evaluation of this parameter is performed by measuring the content of the active ingredient in the drug at different times and on expiration to see if it is within specification (1). The problem also involves estimating whether the drug will perform satisfactorily and maintain its initial properties in the future. In this paper, we provide a criterion for the evaluation of experimental design used in a stability study for predicting the content of an active ingredient in a drug, starting from the confidence limit calculated following International Conference on Harmonisation of Technical Requirements for the Registration of Pharmaceuticals for Human Use (ICH) recommendations. The point of view adopted is akin to hypothesis testing. The main question is this: "If the drug fulfills the requirements at a given time in the future, what is the probability that the data collected for that drug will show its suitability?" For this purpose, two concepts are used-producer gain and consumer loss-which are defined as follows: producer gain is the advantage (for the producer) of recognizing a drug as "good" (provided it is good and within specification); consumer loss is the loss (for the consumer) when the drug is no longer good, but the data collected indicate that it is good. The aim of the experimental design in this study is to increase the probability of producer gain and maximize it on the basis of a given consumer loss.
Journal of Pharmacological and Toxicological Methods, Sep 1, 2011
Dobutamine stress echocardiography (DSE) is performed to detect subtle ischemic regions in the my... more Dobutamine stress echocardiography (DSE) is performed to detect subtle ischemic regions in the myocardium in patients suffering from stenosed coronary artery disease. While in a clinical and veterinary context DSE is performed daily, in the preclinical context, a very limited application has been described in the literature. In the drug development process, the safety of new chemical entities on the cardiovascular system is a primary requirement for the development of new agents/drugs for administration in humans. There are limited tools to evaluate the impairment of myocardial performance and cardiac contractility in preclinical species and particularly in rodents. In this present paper a possible imaging application is presented. Anesthetised male Crl:CD(SD) rats (n=14) were given single intravenous doses of vehicle (5% w/v Dextrose solution) and dobutamine hydrochloride at 10 μg/kg/min. Echocardiography was performed, starting immediately before the infusion and animals were monitored up to 5 min after the end of infusion. Standard and non-standard echocardiography parameters were evaluated to detect test article related changes compared to vehicle infused animals. Thickening of left ventricle walls and interventricular septum and increased velocity of circumferential stress were observed in dobutamine infused animals compared to those receiving vehicle. These changes were considered to be a direct effect on myocardial contractility, as also confirmed by increased functional parameters (i.e., Ejection Fraction, End Diastolic Volume and decrease of the ratio between pre-ejection period and ejection time of the aortic flow). In dobutamine infused rats the "Tei index" increased up to approximately 32% compared to vehicle animals, showing a clear relationship with increased contractility. As expected dobutamine infusion in the anaesthetised rat is capable of inducing a positive inotropic effect and echocardiography results are a reliable tool for the determination of changes in contractility induced by pharmacological stress testing in the rat.
The paper deals with the problem of finding a better predictor starting from a given one. After i... more The paper deals with the problem of finding a better predictor starting from a given one. After introducing some basic notions of sufficiency in terms of a 'sigma-field', a theorem due to K. Tacheuchi and M. Akahira is used to show criterion leading to a better predictor similar to Rao-Blackwell in statistical estimation theory. Then the wide sense sufficiency is introduced showing a criterion to get a better predictor in presence of a sufficient 'sigma-field ' in a wide sense.
In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a ... more In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a stability analysis, is to determin the period of time within wich the compound conserve its initial characetris. At each time point an evaluation a previous trend analysis is caried out. The underlining trend is supposed to be linear or reduced to be linear following the equation C = a+b t, where C is the level of active content. The determination of such trend allows the estimation of the content at varous time points, and to check if the level is greater than a fixed value (the specification). This value represent theminimal condition the copmound must fulfill.,that is:ICH and FDA guide-lines recommend that the lower confidence limit is reported too. If such limit at a time point si greater than the specification,then at such time the specification is fulfilled.Such analysis is performed under the condition of classical regression model. An alternative approach is represented by the use of a mixed model in which the batch effect is regarded as a random effect. This approach appear, from a theoretical point of view, more appealing, since it does not reguest to adopt the step wise procedure seen below. The difference between batch is a variability factor whose effect the variability of the observed result. Such variability can be modelled using a suitable covariance matrix.
In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a ... more In the paper the stability analysis of a pharmaceutical compound is presented. The purpouse of a stability analysis, is to determin the period of time within wich the compound conserve its initial characetris. At each time point an evaluation a previous trend analysis is caried out. The underlining trend is supposed to be linear or reduced to be linear following the equation C = a+b t, where C is the level of active content. The determination of such trend allows the estimation of the content at varous time points, and to check if the level is greater than a fixed value (the specification). This value represent theminimal condition the copmound must fulfill.,that is:ICH and FDA guide-lines recommend that the lower confidence limit is reported too. If such limit at a time point si greater than the specification,then at such time the specification is fulfilled.Such analysis is performed under the condition of classical regression model. An alternative approach is represented by the...
An application of the dose-response curve in the case of dicothomous responses according to a Bay... more An application of the dose-response curve in the case of dicothomous responses according to a Bayesian point of view is presented in this paper. A dose response curve in cases of dichotomous data describes the relationship between the probability of observing an occurence and a dose level. A researcher may sometimes have some ideas of the shape of such a
The aim of a stability study is to check whether or not a drug maintains its initial properties (... more The aim of a stability study is to check whether or not a drug maintains its initial properties (over a given range) in a period of time. There are many parameters considered in a stability study, but in this paper only the active content will be considered. Evaluation of this parameter is performed by measuring the content of the active ingredient in the drug at different times and on expiration to see if it is within specification (1). The problem also involves estimating whether the drug will perform satisfactorily and maintain its initial properties in the future. In this paper, we provide a criterion for the evaluation of experimental design used in a stability study for predicting the content of an active ingredient in a drug, starting from the confidence limit calculated following International Conference on Harmonisation of Technical Requirements for the Registration of Pharmaceuticals for Human Use (ICH) recommendations. The point of view adopted is akin to hypothesis testing. The main question is this: "If the drug fulfills the requirements at a given time in the future, what is the probability that the data collected for that drug will show its suitability?" For this purpose, two concepts are used-producer gain and consumer loss-which are defined as follows: producer gain is the advantage (for the producer) of recognizing a drug as "good" (provided it is good and within specification); consumer loss is the loss (for the consumer) when the drug is no longer good, but the data collected indicate that it is good. The aim of the experimental design in this study is to increase the probability of producer gain and maximize it on the basis of a given consumer loss.
• Long-term stability data of parameters that changes with time are expected to be assessed by IC... more • Long-term stability data of parameters that changes with time are expected to be assessed by ICH guidelines Q1A (R2) and Q1E by a statistical approach in order to support a retest period/shelf-life assignment. • Trend analysis of data is typically performed by making data linear via the more important 3 degradation orders (kinetic): 1. Order 0 : content= a+b*time 2. Order 1 : log(content)=a+b*time 3. Order 2 : 1/content=a+b*time
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