2018 tallied facial soft tissue thicknesses for adults and sub-adults

Highlights

• Overall, >227,400 facial soft tissues have been collected in the literature.

• Since 2008, data for >5450 new individuals have been reported.

• Herein, updated grand and rolling means are described for the 1883–2017 data.

• The grand means triangulate on population parameters for improved accuracy.

• The new grand means yield a standard error of the estimate = 3.7 mm.

Abstract

The tallied facial soft tissue thicknesses (or T-Tables) represent grand means of published facial soft tissue thickness sample means. These sample means have been drawn from across the full-breadth of the facial soft tissue thickness (FSTT) literature, including forensic science, anthropology and odontology. The report of new summary statistics for >1290 new sub-adults and >2200 new adults since the last T-Table calculation, in 2008 for sub-adults and 2013 for adults respectively, makes their update timely. The maximum sample sizes at any landmark now stand at 3023 for individuals aged 0–11 years old (g–g′); 3145 for individuals aged 12–17 years old (n–se′); and 10,333 for adults (n–se′). Following the recalculation of grand weighted means and comparison to the original 2008 data, some shifts in the T-Table statistics are evident at specific landmarks, namely: 2–2.5 mm increases at gonion (go–go′) and mid-mandibular border (mmb–mmb′) for adults; 3.5 mm decrease at gonion (go–go′) for 12–17 year olds; and 2.0 mm decrease at menton (me–me′) for 0–11 year olds. Differences at all other landmarks (91–100% depending on the dataset) were minimal being <1.0 mm. Performance tests of the new grand means as point estimators (using individuals with known FSTT size from the C-Table), show the 2018 T-Table statistics to produce marginally less error than the 2013 means: 2018 standard error of the estimate = 3.7 mm in contrast to 2013 standard error of the estimate = 3.9 mm. The long run nature of the T-Table statistics (i.e., big data) and quantified performance test accuracies on known subjects, earmark the 2018 T-Table as the premier FSTT standard for craniofacial identification casework. In the distant future, this is likely to change as the C-Table raw data repository grows, allowing shorths and shormaxes to be calculated for large samples. Given current raw data repository sample sizes of 0–1574 for T-Table landmarks (notably lower for younger individuals), there is some way to go before enhanced central tendency estimators can entirely replace untrimmed arithmetic means.

Introduction

Facial soft tissue thicknesses (FSTTs) set the primary basis for method quantification and standardization in facial approximation and craniofacial superimposition. Over the last 120 years numerous FSTT studies have been conducted, but typically using samples of ≤40 individuals in any case. This applies even to larger samples which are often subject to sub-categorization by factors such as sex, age and ancestry [1], [2], [3].

Due to the nuances of sample selection and difficulty in obtaining completely random draws of human subjects, it is rare that size measurement averages for any morphological features calculated from two, especially small, samples will be precisely identical, even if draws are made from the same parent population [2], [3], [4]. In fact, even when the draws are entirely random, different sample means would still likely result (some individuals are likely different between each subject selection), and this range in means is known as the sampling distribution of the mean. The deviation of any sample mean from the population mean is measured by the standard error of the mean: $SEM=s/\sqrt{n}$; where s = standard deviation of the sample and n = sample size.

Differences between means of repeat sample draws are even more likely to occur when different investigators are responsible for drawing the samples due to inter-observer errors that are typically larger than intra-observer errors. In other words, the sample means are likely to differ from each other and from the population mean not only due to chance effects of sampling, but also due to errors included in the experimental protocol. Consequently, in real life contexts, sample means are likely to be different from each other even if drawn from the same parent population, and some sample means will be better estimators of population parameters, i.e., more representative, than others.

In the FSTT literature, the above mentioned factors have been ignored to a relatively large degree with small differences between FSTT means taken at face-value and interpreted as encoding meaningful biological differences between different study samples, e.g., ancestry and sex [4]. The consequence of this action has been a sprawling dataset, subcategorized by any observed difference [5], which gives misleading impressions of the size of embedded biological patterns [6]. The over-emphasized differences between groups become apparent when published sample specific means are put to the test—they often perform poorly for their corresponding target sample, and as good or better in test samples for which they were not intended [3].

This noise in the data can be combated by averaging data samples according to well-established principles of the Central Limit Theorem and the Law of Large Numbers to produce a more strategic, less complex, and more useful data suite [1], [3], [4], [5]. The Law of Large Numbers says that a large sample is more likely than a smaller sample to have the characteristics of the whole [2], [7]. In other words, means (${\displaystyle \overline{x}}$) of large samples tend to be more accurate estimators of population means (μ) than means from smaller samples [7] (note that “population” refers here to the statistical notion, not the biological one). The Central Limit Theorem additionally states that the distribution of the means (from multiple samples) will increasingly approximate the normal distribution as the size of the samples increase and that the mean of the sample means will converge on the population mean regardless of the underlying population’s distribution [7], [8].

Pooling independently reported sample means using a weighted mean (or in other words calculating a grand mean) holds the capability to dampen the fluctuations in central tendencies that result from noise. This can be undertaken without access to the raw data, because the mean is a statistic that combines well, i.e., grand means can be calculated from multiple sample means without any re-examination of the raw data. The calculation of grand means, thereby holds the potential to deliver FSTT central tendencies that are less misleading in terms of their precision (errors average out), improved triangulation on population means (samples are large), and increased user-friendliness (fewer data tables without compromised accuracy) [5].

In 2008, these statistical principles and procedures were first applied to the human FSTT data [1], [2] and the product was the Tallied Facial Soft Tissue Depth Tables now commonly referred to as the T-Tables. For adults, data from 55 different and independent studies were pooled at 25 of the most commonly measured landmarks ([9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59.]; Fischer and Moorman (year unknown) cited in Ref. [60]; Köstler (1940), Bankowski (1958), Weining (1958), and Weiβer (1940) cited in Ref. [32]; O’Grady et al. [61] cited in Ref. [62]; Table 1). Similar protocols were also employed for sub-adults aged 0–11 and 12–17 years [2]. Here it is worth noting that the division point of 11.5 years was used as it roughly split the sub-adult data into two, with differences between means typically not exceeding a 2 mm range from the start to the finish point of the age bracket [2]. It is also worth noting that very few studies exist on children aged <6 years of age, and so while additional groups may be warranted in the 0–6 age bracket, the data are too sparse to determine what, if any, separation is justified [2]. Ten years on from the first T-Table calculation, additional sample-specific data from >4170 adults have been reported [22], [63], [64], [65], [66], [67], [68], [69], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81], [82], [83], [84], [85], [86], [87], [88], [89], [90], [91], [92] making a review of the adult T-Table timely. For sub-adults, summary statistics for >1290 individuals have been collectively produced [22], [71], [93], [94], [95], [96], [97]. This includes two studies originally missed in 2008 [22], [97]—one as a result of longstanding mistaken dogma that ‘Russian-type’ methods did not use FSTT averages [98], [99], [100], [101]. For reconceptualization of overarching structure of founding face prediction methods, including addition of means and removal of facial expression muscles to/from so-called “Russian Methods”, see Refs. [22], [102], [103], [104], [105], [106], [107], [108].