A new method for modelling precipitation variability in relation to climate change

Among several environmental processes, spatiotemporal variability in precipitation has an important role in regional climatology (Coffel & Horton 2015; Khan et al. 2021; Wolski et al. 2021). In recent years, the perpetual increase in climate warming threatens to deteriorate the role of flood and drought mitigation, climatic, ecological, and regional environmental policies (Perkins-Kirkpatrick & Gibson 2017). Similar to the other socioeconomic and financial sectors, extreme temperature and high concentration in rainfall have direct severe negative effects on agricultural economics (Powell & Reinhard 2016). In particular, extreme events such as floods and droughts badly affect crop growth and yield production seasons. For instance, the US economy bears $220 million in losses in 2010 and 2012 due to high night-time temperatures and warm winter (Melillo 2014). In recent research, Azad et al. (2022) assessed the patterns of monsoon precipitation in 29 stations of Bangladesh. Islam et al. (2020) discovered the spatiotemporal trend in precipitation under various statistical models. Therefore, the accurate quantification of precipitation with its variability patterns aids in making long-term policy and climate monitoring modules.

Accordingly, the regional distribution of extreme temperature has significant importance for defining regional climatology and watersheds (Courty et al. 2018). Hence, the simultaneous study of these hydrological factors increases hydrological research's impact and reliability. In several previous research, time-series data of precipitation and rainfall are jointly configured to make inferences in climate research and forecasting (Coles & Tawn 1991; Guler et al. 2007; Mahdian et al. 2009; Diacono et al. 2013; Xu et al. 2014; Rahman & Islam 2019; Praveen et al. 2020). Recently, Saunders et al. (2017) have considered spatial distributions of rainfall using the max-stable spatial model in South-East Queensland, Australia. Baek et al. (2017) have made a joint analysis of the seasonal climatic variation using the correlation between precipitation and temperature. Other recent studies include Gehman et al. (2018), Dado & Takahashi (2017), Longman et al. (2018), Zscheischler et al. (2017), etc.

Besides the use of advanced statistical and geospatial tools, precise estimates and accuracy in reporting any random phenomenon are the key factors for reliable inferences and conclusions. In previous research, numerous studies are based on the precise estimation of climatic variables (Gabella & Notarpietro 2004; Germann & Joss 2004; Ahmad et al. 2017) and studying their temporal changes (Carrera-Hernández & Gaskin 2007). However, to improve and update the rainfall statistics, the role of auxiliary information on the recording and reporting stage of rainfall data is not considered in the literature.

For developing countries, it is essential to review the standard monitoring and data recording modules (Mirza 2003; Hussein et al. 2013). From these perspectives, precise quantification of precipitation and other climate factors using optimized gauge monitoring networks present a challenge (Chebbi et al. 2013). However, the existence of and setting of severally available optimized gauge networks reduces the scope of the optimization approaches. Contrarily, geospatial analysis and prediction using geostatistical tools are the alternative way to explore and infer. One drawback of these methods is the use of raw data. That is, no remedy is suggested or made for unreliable and unrepresentative data. This leads to an increase in uncertainty about the results of these models.

In order to increase the precision and accuracy of precipitation estimates, integrated auxiliary information-based sampling estimators are proposed (Cochran 2007; Mauro et al. 2017; West 2017). Several studies have developed various efficient estimators that utilize auxiliary information under different sampling strategies (Sahai & Ray 1980; Lohr & Prasad 2003; Hou et al. 2017). Furthermore, many researchers have used auxiliary variables in various statistical models (Zhu & Lin 2010; Apaydin et al. 2011; Paloscia et al. 2013).

In previous research, Oliver (1980) developed a coefficient of variation-based index called the Precipitation Concentration Index (PCI). The PCI characterizes and classifies the behavior of precipitation of its annual variability structure. Several studies have used the PCI and extended its methodologies in various regional studies in recent years. These include Huang et al. (2015, 2018), Li et al. (2017) and Bartolini et al. (2018). The PCI explores the yearly distribution of rainfall at a single station. In the original and later modified versions of the PCI, no external sources of variation were addressed in their estimation procedure. Moreover, rainfall data does not account for the prolonged behavior of precipitation (Montazerolghaem et al. 2016) and the size of the catchment. Furthermore, many other meteorological factors such as temperature, wind speed and runoff are also neglected.

Pakistan is considered one of the most three countries with the highest levels of water stress in the world (Farooqi et al. 2005). The average value of rainfall in Pakistan is 287.75 mm. The water shortage in Pakistan is reaching an alarming level that is posing a serious threat to the stability of the country. Accordingly, drought hazards due to the water shortage and the periodic drought events are the serious challenges (El Kharraz et al. 2012; Lal 2018). There are a number of people that lost their lives due to the drought events that occurred in the Tharpaker district (Rana & Naim 2014). Moreover, the water scarcity and drought phenomena effect of the agriculture and livestock sectors and caused a problem in hydropower energy generation. Consequently, the country bears severe economic crises and a shortfall in Gross Domestic Product (GDP). These crises are transpired due to a huge disparity between the demand and supply of energy. Although the development of a large number of the water reservoirs is being progressed. Nevertheless, the climate change and global warming have been formed several other challenges that related the existing water reservoirs in Pakistan.

The objective of this research is the precise and accurate measurement of precipitation concentration and spatiotemporal variability in their patterns. Using an auxiliary information-based sampling estimator, we postulated that the use of temperature as auxiliary information can be used to improve precipitation estimates. This is logical, as many authors have provided evidence of the use of auxiliary information. In our recent research, we have used a number of information-based auxiliary estimators to analyze drought in Pakistan (Ali et al. 2020a, 2021a, 2021b; Jiang et al. 2020). By acknowledging the positive role of auxiliary information in the estimation phase, this study is based on integrating extreme (minimum and maximum) temperature as an auxiliary variable to improve the estimation of precipitation. The specific questions which drive the research are: (1) How can we improve the raw rainfall data by modeling the relationship between temperature and rainfall in the context of global warming and (2) how to examine and assess the patterns of precipitation. In this article, a new technique of measuring precipitation-related statistics such as mean and its variability is provided. The proposed technique uses improved time-series data of precipitation estimates for defining precipitation patterns. Consequently, this research proposed a new formula for measuring precipitation variability: The Regional Contextual Temperature Index of Precipitation Concentration (RCTIPC). To illustrate all the steps involved in estimating RCTIPC, time-series data of monthly total precipitation, minimum temperature and maximum temperature of 54 meteorological stations of Pakistan have been considered. The proposed method's performance is compared with PCI using spatial correlation and spatial predictive maps of various precipitation patterns under the spatial Poisson Log Normal (PLN) model.

This section configures the role of temperature as an auxiliary variable in the estimation process of precipitation. First, we describe the geostatistical settings of environmental variables and their estimation process. Second, we use Mukerjee et al. (1987) estimator to configure extreme temperature as auxiliary information for estimating regional precipitation. Mukerjee et al. (1987) estimator is a generic method that utilizes multiple auxiliary information in the estimation process in which the marginal effect and temporal fluctuation of related variables are accounted.

Here, we recall the definition of geostatistical data. Let be the location points in a certain region. In geo-statistics and geospatial analysis, such data are often collected at spatially sampled locations of continuous phenomenon of a discrete set of locations at particular regions (Diggle et al. 1998). To assemble these settings in rainfall recordings, let z be the total monthly precipitation measured at a certain location ⁠. In the theory of survey sampling (Cochran 2007) this z can be considered as a sample information of the whole region for which we are going to generalize the findings. Therefore, the selection of this location point should be well spatially representative (Henry & Cassidy 1978; Joss et al. 1990; Thornton & Running 1999; Eslamian 2014).

To assess the effect of the auxiliary variable, we extended and analyzed the results of precipitation estimates to check the precipitation variability. Therefore, instead of using a simple average in the denominator of Equation (3), we suggest a regression estimation method for precipitation average. Using this proposal, dissemination of regional variation and classification will incorporate more regional representativeness, reduce sampling error, and account for the effect of extreme temperature. We hypothesize that a more efficient estimator gives more information. The efficiency measures extracted information in terms of variance of an unbiased estimator, which means smaller variance and greater efficiency. Without using the mathematical theory, here we use the traditional mean and the mean of regression estimator proposed by Mukerjee et al. (1987) on real datasets. In this research, the minimum temperature is used as the first auxiliary variable, and the maximum temperature is used as a second.

RCTIPC measures the annual precipitation variability within a single monitoring station. However, RCTIPC is based on regionally improved mean precipitation under global warming contest, unlike simple precipitation mean. Similar to PCI, the classification of various patterns can be configured by classifying the range of RCTIPC. Table 3 shows the range and corresponding patterns of annual precipitation distribution.

This section aims to illustrate the efficiency of the proposed index through numerical examples and comparisons. The main objective is to show that the proposed index is more sensitive to climate warming than the existing one. Here, we consider the time-series data of rainfall and temperature of district Jhelum for the year 2017. Table 4 shows the summary statistics of the regression model. We observed that precipitation is strongly correlated with minimum and maximum temperatures. That is, the study variable has a correlation value (r = 0.6635) with minimum temperature and (r = 0.4356) with maximum temperature. And the least square multiple regression lines are significant (P-value = 0.00497 with 9 degrees of freedom) (see Table 4). In this example, the estimated quantitative values of rainfall (66.44167) and PCI (17.77721) observed irregular behavior in the year 2017. In contrast, the proposed estimator produced high concentration patterns with an improved rainfall estimate of 59.671 and RCTIPC values of 22.0404 (see Table 2). This indicates that the high variability in annual precipitation is observed after employing extreme temperature. In Table 5, the detailed summary of the Jhelum station is shown with regression and correlation coefficient of the study variable and auxiliary variables. We observed that the sum of a square and mean value of the study variable for each year from 1971 to 2017 have random behavior. And the effect of minimum temperature is positive with high slope and correlation values between rainfall and minimum temperature (see Table 2). On the other hand, the maximum temperature has less slope value than the minimum temperature for all year. Also, there is a low correlation between the study variable and maximum temperature. Finally, minimum temperature has more effect on rainfall than the maximum temperature. In the last two columns of Table 5, results of PCI and RCTIPC are given for all years 1971–2017. In general, significant differences in PCI and RCTIPC have been observed each year.

Table 5

Time-series data of the PCI and RCTIPC for district Jehlum

Years .	.	.	.	.	.	.	.	.	PCI .	RCTIPC .
1971	105,023.7	64.67	16.41	31.58	4.88	2.85	0.6	0.29	17.44	18.17
1972	82,853.13	51.91	16.28	31.25	5.28	4.47	0.67	0.4	21.35	21.83
1973	62,614.74	52.03	16.35	30.94	3.85	2.48	0.58	0.36	16.06	15.72
1974	261,649.8	81.92	17.03	30.48	7.56	4.11	0.5	0.24	27.08	28.39
1975	61,342.83	45.98	16.31	30.95	3.53	1.55	0.52	0.22	20.15	19.42
1976	326,375.4	103.2	16.01	30.45	11.9	8.11	0.73	0.42	21.25	17.77
1977	344,041.2	86.93	15.98	29.97	8.59	2.22	0.43	0.1	31.62	26.77
1978	195,575.8	74.97	16.93	30.53	8.47	6.12	0.6	0.34	24.17	25.06
1979	323,594.5	97.46	16.75	30.33	8.64	3.38	0.52	0.19	23.66	23.4
1980	168,011.7	78.1	16.65	30.7	6.08	2.37	0.49	0.18	19.13	19.08
1981	145,289.2	79.63	17.04	30.95	6.28	3.68	0.62	0.35	15.91	17.34
1982	146,982.9	69.73	16.29	30.47	4.02	−0.18	0.36	−0.01	21	20.09
1983	212,170.1	89	16.28	29.17	3.07	0.29	0.23	0.02	18.6	17.92
1984	198,857.3	90.74	15.74	28.98	6.73	5.51	0.57	0.38	16.77	12.22
1985	164,211.5	70.45	16.27	30.48	6.63	3.37	0.59	0.26	22.98	20.95
1986	90,763.92	51.5	16.78	31.38	3.75	1.35	0.39	0.13	23.76	25.06
1987	131,211.7	77.67	16.1	29.59	5.01	2.92	0.52	0.28	15.11	13.01
1988	88,884.94	54.42	16.5	30.95	4.29	3.07	0.48	0.29	20.84	20.94
1989	295,555.6	82.83	17.27	31.36	7.57	2.21	0.42	0.11	29.91	34.74
1990	98,175.92	55.7	16.19	30.68	4.73	2.26	0.5	0.23	21.98	20.3
1991	214,421.1	99.37	17.23	30.38	2.88	−0.35	0.24	−0.03	15.08	15.59
1992	162,396.3	82.19	16.41	29.88	6.17	3.83	0.55	0.32	16.69	14.96
1993	205,957.7	94.53	16.59	29.45	3.61	0.34	0.29	0.02	16	15.75
1994	121,461	63.48	16.52	31.18	4.99	2.25	0.49	0.2	20.93	21.17
1995	307,584	83.29	17.08	30.53	9.31	3.78	0.51	0.19	30.79	33.35
1996	481,962.9	96.49	16.62	30.01	9.28	3.6	0.41	0.15	35.95	33.85
1997	165,023.4	82.43	16.68	30.11	5	2.86	0.47	0.21	16.87	16.25
1998	416,530	111.3	16.69	28.8	10.76	8.81	0.56	0.38	23.35	17.78
1999	185,227.4	80.12	17.11	30.59	6.19	3.83	0.51	0.28	20.04	21.29
2000	74,819.59	52.36	17.77	31.44	3.73	0.65	0.47	0.08	18.95	22.73
2001	152,943.9	70.03	17.4	31.22	6.3	3.71	0.57	0.3	21.66	26.4
2002	109,862.5	62.23	16.91	31.61	6.93	6.51	0.77	0.56	19.7	25.75
2003	50,743.94	44.38	17.76	31.81	3.42	2.46	0.57	0.36	17.89	24.59
2004	159,427.6	80.13	17.46	30.16	4.97	2.15	0.45	0.19	17.25	18.51
2005	162,976.7	71.58	17.82	31.4	5.29	2.7	0.41	0.19	22.09	28.02
2006	82,656.94	55.18	17.08	30.25	2.63	0.35	0.34	0.04	18.85	19.47
2007	393,410.5	102.7	18.35	30.94	9.09	4.12	0.45	0.18	25.88	36.59
2008	117,859.8	69.39	17.1	30.53	3.6	1.36	0.39	0.13	17	17.66
2009	102,923	68.85	17.23	30.23	4.34	3.57	0.54	0.36	15.08	15.46
2010	53,203.38	45.18	17.27	31.44	3.48	2.37	0.54	0.33	18.1	21.68
2011	125,387.8	65.94	17.28	31.48	5.8	3.84	0.59	0.32	20.02	24.79
2012	106,754.6	62.36	16.96	30.78	5.32	3.36	0.6	0.32	19.06	20.28
2013	126,872.1	59.78	16.55	31.17	4.66	2.55	0.46	0.22	24.65	25.23
2014	169,726.4	76.48	17.03	30.72	6.23	4.05	0.54	0.31	20.15	21.47
2015	137,672.2	78.6	16.47	29.63	5.65	3.1	0.63	0.28	15.48	13.88
2016	138,549.4	86.75	16.95	30.19	5	3.63	0.57	0.38	12.79	12.68
2017	113,007.5	66.44	17.2	31.43	6.21	4.56	0.66	0.44	17.78	22.04

Years .	.	.	.	.	.	.	.	.	PCI .	RCTIPC .
1971	105,023.7	64.67	16.41	31.58	4.88	2.85	0.6	0.29	17.44	18.17
1972	82,853.13	51.91	16.28	31.25	5.28	4.47	0.67	0.4	21.35	21.83
1973	62,614.74	52.03	16.35	30.94	3.85	2.48	0.58	0.36	16.06	15.72
1974	261,649.8	81.92	17.03	30.48	7.56	4.11	0.5	0.24	27.08	28.39
1975	61,342.83	45.98	16.31	30.95	3.53	1.55	0.52	0.22	20.15	19.42
1976	326,375.4	103.2	16.01	30.45	11.9	8.11	0.73	0.42	21.25	17.77
1977	344,041.2	86.93	15.98	29.97	8.59	2.22	0.43	0.1	31.62	26.77
1978	195,575.8	74.97	16.93	30.53	8.47	6.12	0.6	0.34	24.17	25.06
1979	323,594.5	97.46	16.75	30.33	8.64	3.38	0.52	0.19	23.66	23.4
1980	168,011.7	78.1	16.65	30.7	6.08	2.37	0.49	0.18	19.13	19.08
1981	145,289.2	79.63	17.04	30.95	6.28	3.68	0.62	0.35	15.91	17.34
1982	146,982.9	69.73	16.29	30.47	4.02	−0.18	0.36	−0.01	21	20.09
1983	212,170.1	89	16.28	29.17	3.07	0.29	0.23	0.02	18.6	17.92
1984	198,857.3	90.74	15.74	28.98	6.73	5.51	0.57	0.38	16.77	12.22
1985	164,211.5	70.45	16.27	30.48	6.63	3.37	0.59	0.26	22.98	20.95
1986	90,763.92	51.5	16.78	31.38	3.75	1.35	0.39	0.13	23.76	25.06
1987	131,211.7	77.67	16.1	29.59	5.01	2.92	0.52	0.28	15.11	13.01
1988	88,884.94	54.42	16.5	30.95	4.29	3.07	0.48	0.29	20.84	20.94
1989	295,555.6	82.83	17.27	31.36	7.57	2.21	0.42	0.11	29.91	34.74
1990	98,175.92	55.7	16.19	30.68	4.73	2.26	0.5	0.23	21.98	20.3
1991	214,421.1	99.37	17.23	30.38	2.88	−0.35	0.24	−0.03	15.08	15.59
1992	162,396.3	82.19	16.41	29.88	6.17	3.83	0.55	0.32	16.69	14.96
1993	205,957.7	94.53	16.59	29.45	3.61	0.34	0.29	0.02	16	15.75
1994	121,461	63.48	16.52	31.18	4.99	2.25	0.49	0.2	20.93	21.17
1995	307,584	83.29	17.08	30.53	9.31	3.78	0.51	0.19	30.79	33.35
1996	481,962.9	96.49	16.62	30.01	9.28	3.6	0.41	0.15	35.95	33.85
1997	165,023.4	82.43	16.68	30.11	5	2.86	0.47	0.21	16.87	16.25
1998	416,530	111.3	16.69	28.8	10.76	8.81	0.56	0.38	23.35	17.78
1999	185,227.4	80.12	17.11	30.59	6.19	3.83	0.51	0.28	20.04	21.29
2000	74,819.59	52.36	17.77	31.44	3.73	0.65	0.47	0.08	18.95	22.73
2001	152,943.9	70.03	17.4	31.22	6.3	3.71	0.57	0.3	21.66	26.4
2002	109,862.5	62.23	16.91	31.61	6.93	6.51	0.77	0.56	19.7	25.75
2003	50,743.94	44.38	17.76	31.81	3.42	2.46	0.57	0.36	17.89	24.59
2004	159,427.6	80.13	17.46	30.16	4.97	2.15	0.45	0.19	17.25	18.51
2005	162,976.7	71.58	17.82	31.4	5.29	2.7	0.41	0.19	22.09	28.02
2006	82,656.94	55.18	17.08	30.25	2.63	0.35	0.34	0.04	18.85	19.47
2007	393,410.5	102.7	18.35	30.94	9.09	4.12	0.45	0.18	25.88	36.59
2008	117,859.8	69.39	17.1	30.53	3.6	1.36	0.39	0.13	17	17.66
2009	102,923	68.85	17.23	30.23	4.34	3.57	0.54	0.36	15.08	15.46
2010	53,203.38	45.18	17.27	31.44	3.48	2.37	0.54	0.33	18.1	21.68
2011	125,387.8	65.94	17.28	31.48	5.8	3.84	0.59	0.32	20.02	24.79
2012	106,754.6	62.36	16.96	30.78	5.32	3.36	0.6	0.32	19.06	20.28
2013	126,872.1	59.78	16.55	31.17	4.66	2.55	0.46	0.22	24.65	25.23
2014	169,726.4	76.48	17.03	30.72	6.23	4.05	0.54	0.31	20.15	21.47
2015	137,672.2	78.6	16.47	29.63	5.65	3.1	0.63	0.28	15.48	13.88
2016	138,549.4	86.75	16.95	30.19	5	3.63	0.57	0.38	12.79	12.68
2017	113,007.5	66.44	17.2	31.43	6.21	4.56	0.66	0.44	17.78	22.04

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In recent research, a large number of applications related to the geostatistical count data are based on Gaussian random fields. The initial proposal of the PLN model mainly for the analysis of spatiality correlated count data (Aitchison & Ho 1989). By assuming the total number of various patterns of rainfall is spatially correlated variable, the use of the PLN model appears to the appropriate model for modeling the count of rainfall patterns. In this paper, the spatial PLN model was used for exploring the predictive distribution precipitation patterns observed from RCTIPC and PCI. This is due to the fact that the data of various categories is spatially counted. In previous research, Ali et al. (2020a, 2020b) used PLN to explore the various patterns of drought for Pakistan. A brief description on PLN is as follows:

Suppose the pairs (x_i; y_i) where x_i is the reference points and y_i is the observed value of the counts of patterns, where the spatial distribution of y_in is abnormal. Diggle et al. (1998) introduced a class of generalized linear spatial models (GLSM): PLN and binomial logit normal spatial models for non-Gaussian spatial data sets. These models are helpful for modeling spatial count data sets when the spatially varying attribute of interest is functionally related to a realization of a non-Gaussian random field (Zhang 2002). Several studies used GLSM to model spatial count data in various disciplines (Cameron & Trivedi 2013). Royle & Wikle (2005) adopted the spectre parameterization of the spatial varied mean of a PLN model in order to obtain a maps of avian count data. Wakefield (2006) applied a general linear model with spatial autocorrelation for mapping the illness of esophageal cancer incidence data. They suggested that GLSM approach for modeling and mapping spatial counts of disease incidence is efficient and robust for inference. Furthermore, using the PLN spatial model is a naturally good candidate for modeling spatial count data (Jing & De Oliveira 2015). However, it is impossible to estimate the parameters and posterior sampling due to the high dimensional integral of likelihood. One solution is to employ numerical algorithms such as Markov chain Monte Carlo (MCMC) with the help of advanced methods such as Langevin–Hastings algorithms, data-based transformations, and group updating may incorporate in their estimation. In the current study, geo-count (Jing & De Oliveira 2015) and geoRglm (Christensen & Ribeiro 2002) R packages are employed to implement the model using MCMC algorithms. Moreover, the segregated maps of all patterns are prepared to compare the distributional behavior of RCTIPC and PCI.

This section performs spatial comparative analysis using Tjostheim's coefficient index (Tjøstheim 1978) and modified t-test (Dutilleul et al. 1993). Tjostheim's coefficient and modified t-test are widely used to measure the association between two stochastic processes observed over space. We have used spatiotemporal regional spatial count data (see Table 6) of irregular, uniform, and moderate patterns observed under RCTIPC and PCI methods in all the selected stations. In computation, this research employed SpatialPack (Osorio et al. 2016) R package for assessing the spatial association.

Table 7 gives numerical estimates of spatial association among the counts of patterns of precipitation variability assessed from PCI and RCTIPC. In uniform patterns of frequency counts, there is a low spatial correlation (P < 0.05) between PCI and RCTIPC. Irrespective to the uniform pattern, there is a significant high correlation between PCI and RCTIPC. However, RCTIPC is highly correlated with PCI in other patterns. This shows that, the extreme temperature has significant impact on varying precipitation estimates under spatial configuration.

The objectives of this study were to examine the relation of precipitation with temperature and develop a better method for measuring precipitation concentration. For this purpose, the current research proposes a new approach that incorporates temperature as a piece of auxiliary information for analyzing regional precipitation variability. Under the climate warming scenario, regression analysis revealed that the additional input can potentially improve the precipitation estimates under the appropriate sampling estimator. This is the first study that has documented the impact of climate warming on measuring precipitation concentration. Overall, this study strengthens the analysis of precipitation concentration under climate warming. Empirical findings from this research provide some guidance for government and experts. A more reliable statistical procedure is needed to increase the meteorological products by employing advanced probabilistic and machine learning techniques which would encourage the researchers to propagate more reliable climatological information.

A few limitations of the study are the subjective selection of the auxiliary information-based sampling estimator and the contemplative inference of the interpolation techniques. Therefore, future research may be based on the optimum selection of the sampling estimator or techniques such as bootstrapping and the most appropriate interpolation methods.

All the data were analyzed using R software. The data and code used to support the findings of this study are available from the corresponding author upon request.

The manuscript is prepared in accordance with the ethical standards of the responsible committee on human experimentation and with the latest (2008) version of Helsinki Declaration of 1975.

The authors have not received any funding from any project.

The authors declare that they have no competing interests.

All authors have equal contribution.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.