Estimation of failure criteria in multivariate sensory shelf life testing using survival analysis

Estimation of failure criteria in multivariate sensory shelf life testing using survival analysis

Accepted Manuscript Estimation of failure criteria in multivariate sensory shelf life testing using survival analysis Ana Giménez, Andrés Gagliardi, ...

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Accepted Manuscript Estimation of failure criteria in multivariate sensory shelf life testing using survival analysis

Ana Giménez, Andrés Gagliardi, Gastón Ares PII: DOI: Reference:

S0963-9969(17)30192-8 doi: 10.1016/j.foodres.2017.04.031 FRIN 6690

To appear in:

Food Research International

Received date: Revised date: Accepted date:

25 January 2017 28 April 2017 29 April 2017

Please cite this article as: Ana Giménez, Andrés Gagliardi, Gastón Ares , Estimation of failure criteria in multivariate sensory shelf life testing using survival analysis, Food Research International (2017), doi: 10.1016/j.foodres.2017.04.031

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ACCEPTED MANUSCRIPT Manuscript for submission to Food Research International

Estimation of failure criteria in multivariate sensory shelf life testing using survival

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analysis

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Ana Giménez*, Andrés Gagliardi, Gastón Ares

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Sensometrics & Consumer Science, Instituto Polo Tecnológico de Pando. Facultad de Química. Universidad de la República. By Pass de Rutas 8 y 101 s/n. C.P. 91000. Pando,

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Canelones, Uruguay.

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* Corresponding author: Ana Giménez [[email protected]]

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ACCEPTED MANUSCRIPT Research highlights  Consumer-based failure criteria in multivariate shelf life testing were estimated.  A deterioration index was determined using PCA on trained assessors’ data.  Consumer rejection was modelled as a function of samples’ coordinates in PC1.

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 The proposed failure criteria may increase the accuracy of shelf life estimations.

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ACCEPTED MANUSCRIPT Abstract For most food products, shelf life is determined by changes in their sensory characteristics. A predetermined increase or decrease in the intensity of a sensory characteristic has frequently been used to signal that a product has reached the end of its shelf life. Considering all attributes change simultaneously, the concept of multivariate shelf

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life allows a single measurement of deterioration that takes into account all these sensory changes at a certain storage time. The aim of the present work was to apply survival analysis

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to estimate failure criteria in multivariate sensory shelf life testing using two case studies,

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hamburger buns and orange juice, by modeling the relationship between consumers’ rejection of the product and the deterioration index estimated using PCA. In both studies, a

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panel of 13 trained assessors evaluated the samples using descriptive analysis whereas a panel of 100 consumers answered a “yes” or “no” question regarding intention to buy or

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consume the product. PC1 explained the great majority of the variance, indicating all sensory characteristics evolved similarly with storage time. Thus, PC1 could be regarded as index of

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sensory deterioration and a single failure criterion could be estimated through survival

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analysis for 25 and 50% consumers’ rejection. The proposed approach based on multivariate shelf life testing may increase the accuracy of shelf life estimations.

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Keywords: sensory shelf life; multivariate; deterioration index

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ACCEPTED MANUSCRIPT 1. Introduction Shelf life dating has several economic, environmental and moral consequences, as it determines products’ maximum commercialization time. It has been identified as one of the causes of food waste at both retail and household levels, particularly in developed countries (European Commission, 2010). Shelf life is usually defined as the storage time during which

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a food product remains safe and retains its physical, chemical and sensory characteristics (IFST, 1993). However, the shelf life of most food products is determined by changes in their

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sensory characteristics, as they occur before their safety is compromised (Lawless &

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Heymann, 2010).

Several physical, chemical and microbiological changes occur simultaneously during

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storage, causing a decrease in the sensory quality of the product (Derossi, Mastrandrea, Amodio, de Chiara, & Colelli, 2016). Therefore, sensory shelf life studies usually involve

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measuring the intensity of different sensory characteristics throughout storage, until they reach a failure criteria or cut-off point, which corresponds to the maximum tolerable

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deterioration (Giménez, Ares & Ares, 2012). Shelf life can be limited by an increase in the

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intensity of a sensory defect or a decrease in the intensity of a desirable characteristic (Garitta, Hough, & Sánchez, 2004). Therefore, failure criteria for each of the evaluated sensory attributes are needed.

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This approach has several disadvantages. First of all, the consideration of a different

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failure criterion for each sensory attribute can lead to different shelf life estimations. Besides, the estimation of a failure criterion for each sensory attribute is tedious and time-consuming. Finally, it should be taken into account that all the sensory characteristics of the product change simultaneously. Consumers’ reaction towards a product with high intensity of a single defect can be different from their reaction towards a product with several sensory defects. Thus, selecting the most relevant sensory attribute to establish the end of a product’s shelf life might be cumbersome. For this reason, it is necessary to obtain a single measurement of the sensory deterioration of products.

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ACCEPTED MANUSCRIPT In this context, Pedro & Ferreira (2006) introduced the concept of multivariate shelf life. In this approach, Principal Component Analysis (PCA) is applied on the dataset containing the average value of a set of product characteristics at different moments of storage to identify the main sources of variability in the dataset. The first component of the PCA usually summarizes the evolution of all product characteristics with storage time and

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can be regarded as a deterioration index. This approach has been applied to a limited number of situations (Derossi et al., 2016; Pedro & Ferreira, 2006; 2009; Richards, De Kock,

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& Buys, 2014).

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The main challenge of multivariate shelf life testing is how to determine the failure criterion of the deterioration index in order to estimate the product’s shelf life. Derossi et al.

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(2016) determined a failure criterion by setting maximum values for specific attributes based on previous studies. However, consumer perception has been recognized as a key input for

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the selection of failure criteria for shelf life estimation (Giménez et al., 2012). In this sense, Hough, Langohr, Gómez, & Curia (2003) stressed that sensory shelf life does not only

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depend on changes in the sensory characteristics of the product, but rather on how

storage time or not.

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consumers react to these changes, as they decide to consume a product after a certain

Survival analysis has become one of the most popular methodologies for shelf life

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estimation based on consumers’ perception (Giménez et al., 2012). This methodology

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focuses on the risk of consumers rejecting a product that has been stored for a certain time (Hough, 2010). Survival analysis can also be used for estimating the maximum tolerable intensity of a sensory defect (Hough, Garitta, & Sánchez, 2004). Therefore, survival analysis could be used to estimate failure criteria for multivariate sensory shelf life testing by modelling the relationship between consumers’ rejection of the product and the deterioration index estimated using PCA. The application of survival analysis in the context of multivariate shelf life estimation would allow the estimation of failure criteria based on consumers’ perception instead of the arbitrary criteria commonly used. Accurate estimations of failure criteria for multivariate shelf life estimation are particularly relevant when shelf life

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ACCEPTED MANUSCRIPT estimations should be obtained under different storage conditions, as they allow working with trained assessor panels, which is usually simpler and cheaper than conducting several consumer studies. In this context, the aim of the present work was to exemplify the application of survival analysis to estimate failure criteria in multivariate sensory shelf life testing using two case

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studies with different product categories, hamburger buns and orange juice, in which shelf life has been reported to be mainly determined by changes in their sensory characteristics

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(Gray & Bemiller 2003; Moshonas & Shaw, 1989).

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2. Materials and Methods

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2.1. Study 1 - Hamburger buns

2.1.1. Samples and storage conditions

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Hamburger buns were obtained from a local bread industry which elaborates different

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kinds of breads and keeps them frozen until commercialization. Samples from one batch were packaged in polypropylene (PP) bags containing 4 buns each, and stored at -18ºC. In order to have samples with different degree of deterioration from one batch, hamburger buns

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were defrosted at given times prior to evaluation day (Gacula & Kubala, 1975). Hamburger

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buns were defrosted at 20ºC for 6 h, at different times before evaluation (0, 2, 4, 7, 9, and 11 days), and kept at ambient temperature (20ºC) inside polypropylene packages, simulating commercial storage conditions.

2.1.2. Trained assessors panel The sensory panel consisted of thirteen assessors, ages ranging from 25 to 47 years old. Assessors had been selected according to the guidelines of the ISO 8586:2012 standard (ISO, 2012) and had prior experience in discriminative and descriptive analysis of different food products.

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ACCEPTED MANUSCRIPT In a first session, assessors were presented with 4 samples of hamburger buns with different storage times (0, 3, 6 and 10 days) to identify the changes in the sensory characteristics of the products most likely to appear due to prolonged storage. They were asked to generate their individual descriptors using a modified grid method (Damasio & Costell, 1991). By open discussion with the panel leader, assessors agreed on the best

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descriptors to describe differences among samples, their definitions and how to evaluate them. The selected descriptors were firmness (texture), softness (texture), cohesiveness,

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(texture) off-odour (odour), dryness (texture), and off-flavour (flavour).

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Assessors were trained in the quantification of the selected descriptors using unstructured scales 10-cm scales. Assessors were presented with samples with different

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intensity of each of the sensory attributes. In the first sessions, they used paired comparisons and ranking for sample evaluation, whereas in the following sessions they used unstructured

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scales for attribute rating. A total of eight 20 min sessions, performed on separate days, were considered to train the panel. Once the training phase ended, samples were evaluated using

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10-cm unstructured line scales anchored from ‘low’ to ‘high’.

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A whole hamburger bun was presented to each assessor on a white plastic plate, coded with a 3-digit random number. The six samples were presented following a Williams’ Latin square design. Two replications of each sample were evaluated by each assessor in

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two sessions, conducted on the same day with a waiting time of 4 hours between sessions.

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Assessors rinsed their mouths with mineral water two times during a 15s interval between samples. The testing was carried out in a sensory laboratory designed in compliance with ISO 8589 (ISO, 2007), under artificial daylight and temperature control (22ºC). Data collection was performed using paper ballots.

2.1.3. Consumer panel Consumers were recruited from the consumer database of the Sensometrics & Consumer Science group of Universidad de la República (Uruguay) based on their interest to participate in the study and their consumption frequency of hamburger buns (at least once a

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ACCEPTED MANUSCRIPT month). One-hundred consumers, ages ranging between 18 and 60 years, 60% female and 40% male, participated in the study. Each consumer received the six samples of bread, one for each storage time (0, 2, 4, 7, 9, and 11 days). The samples were presented in odorless open plastic containers labeled with three digit random numbers. Consumers had to try each of the samples and to answer

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“yes” or “no” to the following question: “Imagine you have just bought this hamburger bun at the supermarket and when you arrive home you try it. Would you purchase it again?”.

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The test was conducted in a sensory laboratory that was designed in accordance with

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ISO 8589 (ISO, 2007) with individual booths with artificial daylight type illumination,

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temperature control (between 22 and 24 ºC) and air circulation.

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2.2. Study 2 – Orange juice

2.2.1. Samples and storage conditions

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Samples of a commercial orange juice (13.6º Brix) made by reconstitution of a

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Uruguayan concentrate (65º Brix) of the orange variety ‘Salustiana’ were used. The juice was aseptically packaged in 1 litre TetraBrik® packages (all filled from the same batch). Three storage temperatures were considered: 25ºC, 35ºC, and 55ºC.

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A reversed design was used for the shelf life study conducted at 25ºC because it was

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not feasible to gather consumers repeatedly over the period of time that the study required. Six industrial batches were stored at 25ºC immediately after produced to obtain samples with different storage time at the time of the study. Samples were stored at 25ºC at the following 0, 100, 183, 267, 338, and 433 days before the study. Previous studies proved that the industrial process variation or this product was minimal in terms of the juices’ physicochemical and sensory characteristics. Furthermore, no significant differences in acidity (0.76-0.79% citric acid, p>0.25) and total soluble solids (13.8-14.3ºBrix, p>0.08) existed between the batches considered in the present study.

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ACCEPTED MANUSCRIPT Samples from a single batch were stored at 35ºC and 55ºC, following a basic experimental design (Giménez et al., 2012). Seven storage times were considered at each temperature: 0, 31, 46, 62, 76, 92, and 101 days at 35ºC and 0, 7, 17, 24, 28, 31, and 34 days at 55ºC.

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2.2.2. Trained assessors panel The sensory panel consisted of thirteen assessors, ages ranging from 25 to 47 years

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old. The procedure for selecting and training the assessors was identical to that described in

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section 2.1.2. The attributes selected by the panel were off- odour, dark colour, bitterness, orange flavor and off-flavour.

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For the evaluations, samples (50 mL) were served in closed odorless plastic containers at 10ºC. A balanced complete-block experimental design was carried out for duplicate

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evaluation of the samples. Assessors rinsed their mouths with mineral water two times during a 15 s interval between samples. Assessors evaluated a total of 20 samples stored at three

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temperatures. The approach for sample evaluation was adjusted according to the

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experimental design of each storage temperature. The evaluation of the six samples stored at 25ºC was conducted in two sessions conducted on the same day, whereas each of the samples stored at 35ºC and 55ºC were evaluated in separate sessions. The testing was

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carried out in a sensory laboratory designed in compliance with ISO 8589 (ISO, 2007).

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Evaluations were performed under red light, temperature control (between 22 and 24 ºC) and air circulation.

2.2.3. Consumer panel Consumers were recruited among students and workers from Facultad de Química (Montevideo, Uruguay) based on their interest in participating in the study and their consumption frequency of orange juice (at least once a week). One-hundred consumers, ages ranging between 18 and 60, 60% female and 40% male, participated in the study.

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ACCEPTED MANUSCRIPT Consumers only evaluated the six samples stored at 25ºC. Consumers did not evaluate samples stored at 35ºC and 55ºC due to the use of a basic design which would have implied gathering consumers at seven different sessions. Samples were presented in odorless open plastic containers labeled with three digit random numbers, and were evaluated at 10ºC. They were asked to try each of the samples and to answer “yes” or “no” to

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the question “Would you consume this product?”. The test was conducted in a standard

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sensory laboratory (ISO, 2007).

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2.3. Data analysis

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2.3.1. Trained assessors’ data

An analysis of variance (ANOVA) was performed on the trained assessors’ data

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considering storage time as fixed source of variation and assessor, repetition and second order interactions as random effects. Differences were considered significant when p≤0.05.

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A principal component analysis (PCA) was performed on the correlation matrix of

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average scores of the trained assessors’ panel data for each storage temperature. Linear and polynomial regressions were used to model samples’ coordinates in the first principal

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component as a function of storage time.

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2.3.2. Survival analysis

Survival analysis methodology was used to analyse consumers' responses to the yes/no questions. The key concept of this methodology is to focus the hazard on the consumer rejecting the product (Hough et al., 2003). A random variable T was defined as the storage time at which a consumer rejects the sample. The rejection function F(t) can be defined as the probability of a consumer rejecting a product with a storage time lower than t, that is F(t)=P(Tt). Choosing a lognormal distribution for T, the rejection function is given by (Hough, 2010):

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where (•) is the standard normal cumulative distribution function and μ and σ are the model’s parameters. The lognormal distribution was selected to model consumers' rejection in the two studies as it showed the best visual fit to the data. The parameters of the model were obtained by maximizing the likelihood function,

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which is a mathematical expression that describes the joint probability of obtaining the data

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actually observed on the subjects in the study as a function of the unknown parameters of

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the model being considered. Using the estimated parameters shelf life estimations were obtained as the storage time at which 25% and 50% of the consumers rejected the product

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(Giménez et al., 2012).

Survival analysis was also used to identify the relationship between trained’ data and

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consumers’ responses to the yes/no questions. Samples’ coordinates in the first principal component of the PCA performed on sensory data replaced storage time in the approach

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described above. In order to avoid negative values in the survival analysis model, samples’

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coordinates were transformed to non-zero values. This was done by subtracting the coordinate of the fresh sample to all the samples, given that the fresh sample was always located at the highest negative values of PC1.

3. Results

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Hough (2010).

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Calculations were performed in R (R Core Team, 2014) using the scripts provided by

3.1. Study 1 – Hamburger buns

3.1.1. Trained assessors’ data The intensity of all the sensory attributes was significantly affected by storage time (p<0.001). As expected, the intensity of the attributes off-odour, firmness, dryness, and off-

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ACCEPTED MANUSCRIPT flavour significantly increased with storage time, whereas cohesiveness and smoothness decreased (data not shown). The first component (PC1) of the PCA performed on the average intensity of the sensory characteristics across time explained 94.62% of the variance of the experimental data, which indicates that attributes were influenced by storage time in a similar way. As

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shown in Figure 1a, PC1 was positively correlated with the sensory attributes that increased with deterioration and negatively correlated with the attributes that characterized the fresh

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product. Samples were located along PC1 in ascending order according to their storage time,

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from the fresh sample to the sample with 11 days of storage (Figure 1b).

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Insert Figure 1 around here

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3.1.2. Survival analysis

The maximum likelihood estimates of the parameters of the lognormal distribution

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performed on consumer rejection to purchase again the hamburger buns as a function of

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storage time corresponded to  = 1.70  0.20 and  = 0.85  0.15. As expected, consumer’ rejection to purchase again the hamburger buns increased with storage time (Figure 2a). Shelf life can be estimated as the storage time at which a pre-determined percentage of

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consumers reject the product. Shelf life estimations corresponding to 25% and 50%

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consumers’ rejection are shown in Table 1.

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Survival analysis was also performed considering samples’ coordinates in the first principal component of the PCA of trained assessors’ data (PC1). The maximum likelihood estimates of the parameters of the lognormal distribution for the lognormal model performed corresponded to  = 1.56  0.11 and

= 0.47  0.11. The proportion of consumers rejecting

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ACCEPTED MANUSCRIPT to purchase again the hamburger buns increased as samples’ coordinates in PC1 increased (Figure 2b). Based on the model shown in Figure 2b, sample’s coordinates corresponding to different percentages of consumers rejecting to purchase the product again were estimated and results are shown in Table 1.

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Insert Table 1 around here

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3.1.3. Samples’ coordinates in the first component of the PCA of trained assessors’

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data as a function of storage time

As shown in Figure 3, a second order polynomial showed a good fit to samples’

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coordinates in the first component of the PCA as a function of storage time. Using the failure criteria for PC1 estimated using survival analysis (Table 1), the sensory shelf life of

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hamburger buns can be estimated as (3.2  0.7) and (4.9  1.0) for 25% and 50% of

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consumer rejecting to purchase the product again, respectively.

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Insert Figure 3 around here

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3.2. Study 2 – Orange juice

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3.2.1. Trained assessors’ data The influence of storage time on the sensory characteristics of the orange juice samples was similar, regardless of the storage temperature. The intensity of the attributes dark colour, off-flavour, bitter and off-odour significantly increased with storage time (p<0.001), whereas the intensity of orange flavour significantly decreased. The first component (PC1) of the PCA performed on the average intensity of the sensory characteristics across time explained the great majority of the variance of the experimental data (ranging from 96.99% to 98.74%) for juices stored at the three

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ACCEPTED MANUSCRIPT temperatures. Figure 4a shows the representation of the variables for the juices stored at 25ºC. The sensory attributes that were characteristic of the sensory deterioration of the juices were positively correlated with PC1, whereas orange flavour intensity, which characterized the fresh juice, was negatively correlated with PC1. The distribution of sensory attributes along the first principal component was almost identical for the juices stored at 35ºC and

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55ºC (data not shown).

Regarding the representation of the samples in PC1, the fresh sample was always

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located at negative values of PC1, whereas the most deteriorated samples were located at positive values of this component. Sample positioning is exemplified in Figure 4b for orange

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juice samples stored at 25ºC.

Although the distribution of samples was similar in the PCA conducted for each of the

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three storage temperatures, the coordinates of the fresh samples differed. This was expected

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as the projection of samples in the PCs depends on the raw data. At 25ºC, the coordinate of the fresh sample in PC1 was -2.69, whereas at 35ºC it was -3.35 and -4.46 at 55ºC. For this reason, in order to use a single failure criterion for PC1, samples stored at 35ºC and 55ºC

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were projected into the PCA of samples stored at 25ºC (Figure 4b). Sample coordinates in

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the projection of the first two components of the PCA of the juices stored at 25ºC provided the same information than the analysis conducted separately at each temperature. The projected sample coordinates were linearly correlated with sample coordinates in the individual PCAs conducted at each storage temperature (R2=1).

3.2.2. Survival analysis for samples stored at 25ºC A lognormal distribution was selected to model rejection to consume data as a function of storage time. The maximum likelihood estimates of the parameters of the lognormal distribution for rejection to consume ( = 5.84  0.17 and  = 0.73  0.17) were used to graph 14

ACCEPTED MANUSCRIPT consumers’ to consume percentage versus storage time, as shown in Figure 5a. Shelf life estimations were obtained by estimating the time necessary to achieve a consumer rejection to consume percentage of 25% and 50%, as shown in Table 2.

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When survival analysis was performed considering samples’ coordinates in the first

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principal component of the PCA of trained assessors’ data (PC1) the estimated parameters

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of the lognormal model corresponded to  = 1.73  0.13 and  = 0.46  0.14. Figure 5b shows how the proportion of consumers rejecting to consume the orange juice increased as

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samples’ coordinates in PC1 increased. Sample’s coordinates corresponding to different percentages of consumers rejecting to consume the orange juice stored at 25ºC are shown

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in Table 2.

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3.2.3. Samples’ coordinates in the first component of the PCA of trained assessors’

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data as a function of storage time

A linear regression was used to model samples’ coordinates in the first component of

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the PCA of trained assessors’ data as a function of storage time for orange juices stored at 25, 35 and 55ºC (Figure 6). As expected, the slope of the lines increased with storage

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temperature, which indicates an increase in deterioration rate. The failure criterion determined for samples stored at 25ºC (Table 2) was used to determine the shelf life of the juices corresponding to 25% and 50% of the consumers rejecting to consume the product. The estimations for each of the three storage temperatures are shown in Table 3.

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Insert Table 3 around here

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4. Discussion and Conclusions In the two studies the first component of the PCA performed on the average intensity of attributes responsible for differences in the sensory characteristics of samples stored for different times explained the great majority of the variance (Figures 1 and 4). This result

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indicates that all the sensory characteristics evolved similarly with storage time, as previously reported by other authors (Derossi et al., 2016; Pedro & Ferreira, 2006; Richards et al.,

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2014).

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The first component of the PCA could be regarded as index of sensory deterioration. In Study 1, changes in the sensory characteristics of the hamburger buns were related to

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texture changes and the generation of defective odours and flavours (Figure 1), which can be attributed to bread staling (Gray & Bemiller, 2003). In Study 2 the relationship between

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sensory attributes was similar, regardless of the storage temperature, which indicates that the reactions responsible for the deterioration of the orange juice did not change between 25

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and 55ºC. As shown in Figure 4, the main sensory changes in the juices with storage time

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were browning and the generation of off-flavour and off-odour, which can be attributed to non-enzymatic browning and oxidation processes (Moshonas & Shaw, 1989; Petersen, Tonder, & Poll (1998).

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The strong correlation between the evaluated sensory attributes indicates that the

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identification of a single critical attribute that determines the end of the sensory shelf life, as previously done by Curia & Hough (2009) and Martínez, Mucci, Santa Cruz, Hough & Sánchez (1998), might be cumbersome. The estimation of separate failure criteria for individual sensory attributes (Garitta et al., 2004) does not accurately represent how the sensory characteristics of products change during storage. Instead, it seems more appropriate to determine a single failure criterion for the sensory deterioration of the product based on the index identified using PCA. Besides, In the case of accelerated shelf life studies, the consideration of a deterioration index can enable the estimation of a single

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ACCEPTED MANUSCRIPT acceleration coefficient instead of acceleration coefficients for each sensory attribute (Richards et al., 2014). The evolution of samples’ position along the first component of the PCA as a function of storage time enables to model the evolution of product deterioration. In the case of hamburger buns, the evolution of the deterioration index with storage time fitted a second

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order polynomial (Figure 3). Meanwhile, for orange juice a linear model showed the best fit to the experimental data, indicating a zero order kinetic model (Figure 6). This reaction order

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has been previously reported by Burdurlu & Karadeniz (2003) for non-enzymatic browning in

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apple juice concentrate.

The combination of survival analysis and multivariate approaches enabled the

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estimation of a global failure criterion for the product’s deterioration based on consumers’ perception. Failure criteria were determined for 25 and 50% consumers’ rejection (Tables 1

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and 2), which are the most common cut-off points considered in survival analysis (Giménez et al., 2012). This approach may increase the accuracy of shelf life estimations based on

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multivariate shelf life testing respect to other more arbitrary criteria. In this sense, Lareo,

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Ares, Ferrando, Lema, Gámbaro & Soubes (2009) showed that arbitrary criteria (e.g. a value of 50% on an intensity scale) can lead to a large percentage of consumers rejecting the product at the end of the shelf life, which can increase food waste and decrease consumers’

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confidence in the brand or store that sells the product.

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Using the estimated failure criteria and the model, sensory shelf life estimations were obtained as the time needed for the deterioration index to reach that value. For hamburger buns and orange juice stored at 25ºC, the shelf life estimations obtained using this approach were similar to those obtained considering the usual application of survival analysis (modelling consumers’ rejection as a function of storage time), which supports their validity of the proposed approach. In Study 2 the failure criterion estimated in the study conducted at 25ºC was used to estimate shelf life at 35 and 55ºC (Table 3). This approach makes it not necessary to conduct

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ACCEPTED MANUSCRIPT consumer tests for the evaluation of samples stored at 35 and 55ºC, which leads to a reduction in the amount of money and time needed for sensory shelf-life estimation. To conclude, the use of a multivariate approach allowed to take into account the contribution of each dependent variable on the overall quality when estimating shelf life, without the need to select a cut-off criterion based on a single attribute. This approach may

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increase the accuracy of shelf life estimations since it encompasses the changes of sensory characteristics of a product as a whole over storage time. Moreover, the combination of this

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multivariate approach with survival analysis allowed the estimation of a global failure criterion

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that took into account consumers’ decision to accept or reject the product. Therefore, the risk of food waste or consumer dissatisfaction due to under- or overestimating the shelf life of

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a product might be reduced.

Acknowledgments

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The authors gratefully acknowledge funding from Comisión Sectorial de Investigación

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Científica - Universidad de la República (Uruguay).

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ACCEPTED MANUSCRIPT Derossi, A., Mastrandrea, L., Amodio, M.L., de Chiara, M.L.V., & Colelli, G. (2016). Application of multivariate accelerated test for the shelf life estimation of fresh-cut lettuce. Journal of Food Engineering, 169, 122-130. European Commission. (2010). Preparatory study on food waste across EU 27. Available at: ec.europa.eu/environment/archives/eussd/pdf/bio_foodwaste_report.pdf.

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Hough, G., Garrita, L., & Sánchez, R. (2004). Determination of consumer acceptance limits to sensory defects using survival analysis. Food Quality and Preference, 15, 729–734

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ACCEPTED MANUSCRIPT Lareo, C., Ares, G., Ferrando, L., Lema, P., Gámbaro, A., & Soubes, M. (2009). Influence of temperature on shelf life of butterhead lettuce leaves under passive modified atmosphere packaging. Journal of Food Quality, 32, 240–261. Lawless, H., & Heyman, H. (2010). Sensory evaluation of food. Principles and practices. New York: Springer.

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mayonnaise. Journal of Sensory Studies, 13, 331-346.

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R Core Team. (2014). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Richards, M., De Kock, H.L., Buys, E.M. (2014). Multivariate accelerated shelf-life test of low fat UHT milk. International Dairy Journal, 36, 38-45.

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ACCEPTED MANUSCRIPT Figure captions

Figure 1. Representation of sensory attributes (a) and samples (b) in the first and second components of the principal component analysis performed on data from the trained assessors’ panel for the evaluation of hamburger buns with different storage time. Samples

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are identified by their storage time (in days).

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Figure 2. Survival analysis results of the hamburger buns study: (a) Probability of consumers

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rejecting to purchase again the product as a function of storage time for the lognormal model and (b) Probability of consumers rejecting to purchase again the product as a function of

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samples’ coordinates in the first component of the principal component analysis performed

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on trained assessors’ data for the lognormal model.

Figure 3. Samples’ coordinates in the first component of the principal component analysis of

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trained assessors’ data as a function of storage time for hamburger buns.

Figure 4. Representation of sensory attributes (a) and samples (b) in the first and second components of the principal component analysis performed on data from the trained

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assessors’ panel for the evaluation of orange juices with different storage time at 25ºC.

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Samples represented in blue correspond to the projection of samples stored at 35ºC and 55ºC. Samples are identified by their storage time (in days), followed by their storage temperature.

Figure 5. Survival analysis results of the orange juice study: (a) Probability of consumers rejecting to consume the product as a function of storage time at 25ºC for the lognormal model and (b) Probability of consumers rejecting to consume the product as a function of samples’ coordinates in the first component of the principal component analysis performed on trained assessors’ data of juices stored at 25ºC for the lognormal model.

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Figure 6. Samples’ coordinates in the first component of the principal component analysis of trained assessors’ data as a function of storage time for orange juice samples stored at 25,

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35 and 55ºC.

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ACCEPTED MANUSCRIPT Tables

Table 1. Shelf life estimations (days) and sample coordinates in the first principal component (PC1) of trained assessors’ data, corresponding to different percentage of consumers rejecting to purchase the products again, estimated using a lognormal model in survival

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analysis, for the hamburger bun study.

Storage time (days)

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3.10.6 5.51.0

Sample’s coordinates in PC1 of trained assessors’ data -0.820.42 0.480.49

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Percentage of consumers rejecting to purchase the product again (%)

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ACCEPTED MANUSCRIPT Table 2. Shelf life estimations (days) and sample coordinates in the first principal component (PC1) of trained assessors’ data, corresponding to different percentage of consumers rejecting to consume the product, estimated using a lognormal model in survival analysis, for orange juices stored at 25ºC.

25 50

21038 34355

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Storage time (days)

Sample’s coordinates in PC1 of trained assessors’ data 0.50.0.59 2.080.57

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Percentage consumers rejecting to purchase the product again (%)

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ACCEPTED MANUSCRIPT Table 3. Shelf life estimations (days) obtained considering the failure criterion determined for sample coordinates in the first principal component (PC1) of trained assessors’ data using survival analysis, for orange juices stored at 25ºC, 35ºC and 55ºC.

Shelf life estimated using PC1 coordinates (days) 25% rejection 50% rejection 23480 341120 8730 12620 144 238

Storage temperature (ºC)

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25 35 55

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Consumer rejection percentages after removing consumers who rejected the fresh samples are shown. Dotted lines correspond to linear or polynomial regressions for overall liking data, whereas for consumer rejection they correspond to the exponential model (Studies 1 and 2) and the Weibull model (Studies 3 and 4).

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Graphical abstract

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