Participants with ASD
Participants with ASD were users of a language therapy app that was made available gratis at all major app stores in September 2015 48–52. Once the app was downloaded, caregivers were asked to register and to provide demographic details, including the child’s diagnosis and age. Caregivers provided informed consent to participate in the study and completed the language comprehension assessment called the Mental Synthesis Evaluation Checklist (MSEC) 26,53. The first evaluation was administered approximately one month after the download. The subsequent evaluations were administered at approximately three-month intervals for up to three years. To enforce regular evaluations, the app became unusable at the end of each three-month interval and parents were required to complete an evaluation to regain its functionality.
Inclusion criteria
Inclusion criteria were identical to our previous studies of this population 49,54–60. Specifically, we selected participants based on the following criteria
1) Consistency: Participants’ caregivers must have filled out at least three evaluations, and the interval between the first and the last evaluation was six months or longer. Among the selected participants, the average number of evaluations was 5.3 ± 3.4 (range 3–75). The average number of days between the 1st and the last evaluation was 624 ± 425 (range 160–2,696).
2) Diagnosis: Parent-reported ASD diagnosis at the end of the study. Children without ASD diagnosis were excluded from the study. Autism level (mild/Level 1, moderate/Level 2, or severe/Level 3) was reported by caregivers. Pervasive Developmental Disorder and Asperger Syndrome were combined with mild autism for analysis as recommended by DSM-5 24. A good reliability of parent-reported diagnosis was demonstrated previously 61.
Exclusion criteria:
1) Maximum age: Participants older than 22 years of age at the time of their first evaluation were excluded from this study.
2) Minimum age: Participants younger than two years of age at the time of their first evaluation were excluded from this study.
After excluding participants that did not meet these criteria, there were 15,183 total participants. 78% were males.
Syntactic language comprehension measure
Assessing syntactic language comprehension is more challenging than evaluating language production 62. Clinicians face time constraints during assessments, and a child may fail to respond or respond only half-heartedly, making it difficult to gauge their true comprehension abilities. While clinicians can only spend a few hours with a child, parents’ interaction with a child is a continuous behavioral experiment. Parents might say “Tomorrow we will go to the playground.” A child who does not understand verb tenses can react to the word “playground” and immediately brings sneakers, implying that s/he expects to go to the playground right now. Conversely, a child who understands verb tenses may show an immediate disappointment on his face indicating that s/he understands that s/he has to wait for the playground until tomorrow. Similar situations can occur about a child’s favorite food, a child’s favorite movie, visiting a relative, and so on. When cleaning a child’s room, parents can ask the child to put pencils on the table, while leaving balls and dolls under the table; to put the socks inside the dirty clothes bin, while not putting crayons into the bin; and so on. A child’s performance in these tasks provides unambiguous cues about his/her comprehension of spatial prepositions. Parents play with their children using toys. Any two animal toys (a horse and a lion) can be arranged into “a horse carrying a lion” or “a lion carrying a horse,” “a horse riding a lion” or “a lion riding a horse,” thus, providing information on the child’s understanding of the change in meaning when the order of words is changed. Parents normally read books to their children. Books commonly require children to imagine novel situations. For example, Dr. Seuss’ “Hop on Pop” book details two situations: “Mouse on house” and “House on mouse,” with pictures representing both arrangements. It is only natural for a parent to interact with their child by asking “Show me: mouse on house,” “Show me: house on mouse.” The child’s answers would unambiguously demonstrate his/her “understanding of the change in meaning when the order of words is changed.”
Therefore, day-to-day conversations, repeated activities, common play, and reading fairy tales aloud collectively provide an ample opportunity to observe a child’s behavior in response to sentences involving spatial prepositions, syntactic structures, verb tenses, and other complex grammatical sentences. These observable behaviors can be used by parents for Bayesian learning of their child’s abilities and can be reported in response to a survey. Accordingly, over a decade ago we developed a parent-reported survey that assesses language comprehension both directly, through items such as “[my child] understands elaborate fairy tales that are read aloud,” “[my child] understands several modifiers in a sentence,” “[my child] understands spatial prepositions” (Table 1: items 1, 2, 6–12, and 20), and indirectly, through items that are strongly related with the syntactic-language-comprehension-phenotype 35. Two related items assess representational drawing (Table 1, items 3 and 4), which has been shown to be associated with the syntactic-language-comprehension-phenotype 63. One item evaluates pretend play (Table 1, item 5), which is a known precursor to syntactic language; lack of pretend play in children with ASD is a strong indicator of challenges in acquisition of the syntactic-language-comprehension-phenotype 64–67. Additionally, seven items measure understanding of complex recursion through arithmetic (Table 1, items 13–19). Arithmetic items extend the MSEC instrument into a range of complex recursion abilities that share the combinatorial nature of syntactic language while being familiar to parents 68,69. At an early level, arithmetic is an extension of syntactic-language. Interpretation of syntactic sentences requires a degree of reasoning that is similar to that of arithmetic. Compare the following two sentences: 1) “The lion lives under the monkey, who lives under the dog,” and 2) “Mom had five flowers; she gave two flowers to Dad; how many flowers does Mom have now?” While the first sentence could come from a fairy tale and the second from an arithmetic book, the two instructions involve the same executive function that can be characterized as reasoning, syntactic logic, or interpreting complex recursive sentences. In other words, the level of arithmetic abilities serves as a proxy for the ability to comprehend complex recursive sentences. For several reasons, a parent survey could not ask about the child’s complex recursive abilities directly. First, most parents do not understand the concept of recursion. Second, even if examples of recursive sentences were provided—such as “The lion lives under the monkey, who lives under the dog”—these sentences are not commonly encountered in everyday activities, and parents would likely not know if their children understood them. Third, the goal of MSEC was to assess comprehension of recursive complexity at multiple levels. This is practically impossible to achieve in a parent-survey directly, but easily accomplished in the arithmetic domain, since most parents are well aware of their child’s arithmetic skills. Therefore, seven arithmetic questions were added to the MSEC to measure the child’s combinatorial recursive abilities: 1) Understands NUMBERS (i.e. two apples vs. three apples); 2) Can perform simple arithmetic: 2 + 3 = ?; 3) Can add larger numbers: 7 + 6 = ?; 4) Can perform simple subtraction: 3–2 = ?; 5) Can subtract larger numbers: 15–7 =?; 6) Can perform simple multiplication: 2 × 2 = ?; 7) Can multiply larger numbers: 6 × 7 =?
The possible answers to each MSEC item are: not true (2 points), somewhat true (1 point), very true (0 points). MSEC consists of 20 questions and a score ranges from 0 to 40 points; a lower MSEC score indicates a better developed language comprehension.
The psychometric quality of MSEC was tested with 3,715 parents of ASD children 53. Internal reliability of MSEC was excellent (Cronbach’s alpha = 0.93). MSEC exhibited adequate test–retest reliability, good construct validity, and good known group validity as reflected by the difference in MSEC scores for children of different ASD severity levels. Another study of 143 autistic children 2 to 22 years of age also demonstrated excellent internal consistency of MSEC (Cronbach’s alpha = 0.96). The Exploratory Factor Analysis and Confirmatory Factor Analysis demonstrated MSEC unidimensionality and suggested that all 20 MSEC items were related to a single underlying factor 70: (1) A single factor explained 71% of the total variance. (2) The off-diagonal fit value of 0.95 suggested an adequate single-factor model fit for the MSEC assessment. (3) The Comparative Fit Index (CFI) was 0.998, and the Tucker-Lewis Index (TLI) was 0.986, indicating a good model fit. (4) The Root Mean Square Error of Approximation (RMSEA) was 0.075, and the Standardized Root Mean Square Residual (SRMR) was 0.124. (5) All items had significant loadings onto the latent factor (p < 0.01). Confirmation of MSEC's unidimensionality is crucial for validating the inclusion of both 'pre-syntactic' items, such as pretend play, and 'post-syntactic' items, such as arithmetic, in the survey.
Multiple studies demonstrated MSEC’s ability to provide information complementary to the expressive language subscale 54,56,59. In one longitudinal study, MSEC was the only outcome measure out of five demonstrating the negative effect of prolonged video and television watching 55. In another longitudinal study, MSEC was the only outcome measure demonstrating the positive effect of meat, eggs, and vegetables consumption as well as gluten-free diet 60. In other studies, MSEC was significantly more sensitive than the expressive language scale to improvements associated with pretend play and joint engagement 58,59.
MSEC norms have been reported earlier 26.
Table 1
Mental Synthesis Evaluation Checklist (MSEC) 71. The answers choices were: not true (2 points), somewhat true (1), very true (0). The subscale score ranges from 0 to 40 points. A lower score indicates better language comprehension ability.
1. Understands simple stories that are read aloud
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2. Understands elaborate fairy tales that are read aloud (i.e. stories describing FANTASY creatures)
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3. Draws a VARIETY of RECOGNIZABLE images (objects, people, animals, etc.)
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4. Can draw a NOVEL image following YOUR description (e.g. a three-headed horse)
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5. Engages in a VARIETY of make-believe activities (such as: playing house, playing with toy soldiers, building forts and castles, etc.)
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6. Understands some simple modifiers (i.e. green apple vs. red apple or big apple vs. small apple)
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7. Understands several modifiers in a sentence (i.e. small green apple)
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8. Understands size (can select the largest/smallest object out of a collection of objects)
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9. Understands possessive pronouns (i.e. your apple vs. her apple)
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10. Understands spatial prepositions (i.e. put the apple ON TOP of the box vs. INSIDE the box vs. BEHIND the box)
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11. Understands verb tenses (i.e. I will eat an apple vs. I ate an apple)
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12. Understands the change in meaning when the order of words is changed (i.e. understands the difference between 'a cat ate a mouse' vs. 'a mouse ate a cat')
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13. Understands NUMBERS (i.e. two apples vs. three apples)
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14. Can perform simple arithmetic: 2 + 3 = ?
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15. Can add larger numbers: 7 + 6 = ?
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16. Can perform simple subtraction: 3–2 = ?
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17. Can subtract larger numbers: 15–7 = ?
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18. Can perform simple multiplication: 2 × 2 = ?
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19. Can multiply larger numbers: 6 × 7 = ?
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20. Understands explanations about people, objects or situations beyond the immediate surroundings (e.g., “Mom is walking the dog,” “The snow has turned to water”)
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Statistical approach
The MSEC assessment measures the absolute L1 score. L1 learning-rate corresponds to the derivative of the MSEC score over time. Accordingly, L1 learning-rate can be calculated as the difference between each two consecutive MSEC scores divided by the number of days between the assessments normalized by 365 days. Note that L1 learning-rate can always be converted back into absolute L1 score by calculating the area under the curve.
L1 learning-rate was modeled by a piecewise function in which L1 learning-rate r(t) is a constant from birth to age tc, whereupon it declines exponentially with a time constant τ (this formula was simplified from Hartshorne et al. piecewise sigmoidal function, that was found to best describe L2 learning-rate 10):
where t is age measured in years, tc is age after which learning-rate follows an exponential decline (a critical inflection point 10,11) measured in years, τ is an exponential decline time constant measured in years that controls the steepness of the exponent, and r0 is a constant measured in MSEC units change per year. Thus, r(t) = r0, at t = tc; r(t) = r0 * e − 1, at t = tc + τ; r(t) = r0 * e − 2, at t = tc + 2τ; and so on.
The variability among participants was mathematically reconciled using the following R functions: nlme (Nonlinear Mixed-Effects) from the nlme package 72 and nlsLM (Nonlinear Least-Squares) from the minpack.lm package 73. The nlme function is considered superior since it allows combining fixed and random effects, where fixed effects are assumed to represent those parameters that are the same for the whole population, while random effects are group dependent variables assumed to consider the variance in the data explained over time and subject 74. However, the nlme function is very sensitive to the choice of starting values for the model parameters (r0, tc, and τ). This sensitivity can result in a complete failure to fit the model (no convergence) when starting values for the model parameters are suboptimal. In order to facilitate the discovery of the optimal starting values for the model parameters we employed the nlsLM function. The nlsLM function is also sensitive to the choice of starting values for the model parameters and this sensitivity can result in no convergence, but the nlsLM function is recognized for its robustness even for poorly chosen starting parameters 75.
L1 learning-rate in typically developing children
A convenience sample of 138 neurotypical participants was obtained by approaching parents of young children on a parent community online site and asking if they would be willing to complete a Google form. The data presented in this manuscript includes everyone who agreed to participate and indicated that their child was “Normally Developing” (other diagnostic options included: Mild Language Delay, Attention Deficit Disorder, Autism Spectrum Disorder, Asperger Syndrome, Social Communication Disorder, Specific Language Impairment, Apraxia, Sensory Processing Disorder, Down Syndrome, and Other). All caregivers consented to anonymized data analysis and publication of the results. The mean age of participants was 4.8 ± 1.8 (range, 2–10.6) years, and 47% of them were male. Neurotypical children reach the ceiling MSEC score by around 8 years of age 26, making it unfeasible to assess L1 learning-rate using MSEC in typically developing children older than 7 years of age.