This basket trial will enroll prepubertal children and adolescents with clinically diagnosed and genetically confirmed (if applicable) TS, SHOX-D, SGA, or ISS between ages of ≥2 and <18 years with open growth plates. The purpose of the study is to see how well treatment with once-weekly lonapegsomatropin works compared to treatment with daily somatropin. Approximately 186 participants will be distributed equally (1:1), to receive either lonapegsomatropin for 2 years or somatropin for 1 year followed by lonapegsomatropin for 1 year. This trial will be conducted in the United States, France, Germany, Italy, Romania, Spain and South Korea.

Inclusion Criteria:

1. Chronological age between ≥2 and <18 years, at start of screening.

2. Naïve to growth hormone and growth hormone promoting therapies.

3. Prepubertal.

4. Able to stand without assistance.

5. Diagnosis of TS, SHOX-D, SGA, or ISS with impaired growth or short stature, according to the following disease-specific criteria:

   TS or SHOX-D (Léri-Weill dyschondrosteosis):

   1. Diagnosis confirmed by a genetic test. NOTE: Historical test results are acceptable for proof of diagnosis. For karyotypes, a minimum of 20 cells must be counted.
   2. Impaired growth or short stature defined as:

   (i.) AHV <25th percentile over a time span of 6-16 months prior to screening utilizing a historical height properly documented in a health care setting (self-measurement record is not accepted) OR (ii.) Height <5th percentile for sex and age according to the Centers for Disease Control Growth Charts for the United States

   SGA without catch-up growth:

   c. Birth weight and/or birth length < -2.0 SDS for gestational age according to the 2006 World Health Organization Child Growth Standards. For infants born premature, the Fenton Preterm Infant Growth Chart (Fenton 2013) should be used.

   d. Impaired growth or short stature defined as: (i.) AHV <25th percentile over a time span of 6-16 months prior to screening properly documented in a health care setting (self-measurement record is not accepted) OR (ii.) Height < -2.0 SDS for age and sex according to the 2000 Centers for Disease Control Growth Charts for the United States for children ≥ 3 years or height < -2.5 SDS for age and sex according to the for children ≥ 2 years and < 3 years

   ISS:

   e. Height < -2.25 SDS for sex and age according to the Centers for Disease Control Growth Charts for the United States with no identifiable cause for short stature.

   f. Documented normal GH-IGF-1 axis, defined as either: (i.)IGF-1 SDS >0 at screening based on central laboratory OR (ii.)Historical documentation of normal peak GH upon stimulation test (as defined by local institution) g. 46,XX chromosome as determined by karyotype or microarray if female. For karyotypes, a minimum of 30 cells must be counted.

6. If on hormone replacement therapies for any hormone deficiencies other than growth hormone (e.g., adrenal, thyroid), must be on adequate and stable doses for ≥4 weeks prior to and throughout screening.

7. Written, signed informed consent provided by parent(s) or legal guardian(s) of the participant. Assent should be signed by participant as required by IRB/HREC/IEC.

Exclusion Criteria:

1. Advanced bone age X-ray by central reading defined as >20% above chronological age in months (Greulich 1959).

2. Closed epiphyses as defined as bone age of ≥14.0 years in females or ≥16.0 years in males.

3. Current clinical diagnosis of diabetic retinopathy

4. Any diagnosis or presence at screening of the following:

   1. Untreated moderate or severe sleep apnea as determined by formal (local) read of an inpatient or at-home sleep study.
   2. Prader Willi syndrome with severe obesity, history of severe upper airway obstruction, or severe respiratory impairment.

5. Signs/symptoms of intracranial hypertension, active proliferative retinopathy.

6. Uncontrolled hypo- or hyperthyroidism.

7. Uncontrolled diabetes mellitus (defined as: HbA1c >7.5% from central laboratory at screening).

8. Known history or diagnosis of any gastrointestinal inflammatory condition, HIV, radiation exposure, other skeletal dysplasias, growth hormone deficiency, and/or cardio-thoracic surgery due to their independent effects on growth.

9. Any significant hepatic or renal abnormality, such as abnormal renal function (defined as eGFR <60 mL/min/1.73m2).

10. Undiagnosed or uncontrolled hypertension.

11. Receiving treatment with any agent that might influence growth or interfere with GH secretion or action including any sex steroids and stimulants for attention-deficit/hyperactivity disorder (ADHD).

12. High dose inhaled glucocorticoid for more than 28 consecutive days total over the course of 12 months.

13. Female who is pregnant, plans to be pregnant, or breastfeeding.

14. Participation in another interventional clinical trial involving an investigational compound within 90 days prior to screening or in parallel to this trial.

15. Any disease or condition that, in the judgement of the investigator, may make the participant unlikely to comply with the requirements of the protocol or any condition that presents undue risk from the investigational product or trial procedures.

16. Exclusion Criteria only applicable to TS:

    1. Presence of Y chromosome material on genetic testing without history of gonadectomy.
    2. Less than 10% of 45,X mosaicism.
    3. Any known, clinically significant, congenital or acquired cardiovascular dysfunction that might interfere with growth.

17. Exclusion Criteria only applicable to SGA:

    a. Any known clinically significant abnormality likely to affect growth or the ability to evaluate growth with standing height measurements: (i.)Chromosomal aneuploidy, significant gene mutations, or medical syndromes with short stature, including but not limited to Turner syndrome, Laron syndrome, Noonan syndrome, Prader-Willi syndrome, abnormal SHOX-1 gene analysis or absence of GH receptors.

    (ii.)Congenital abnormalities (causing skeletal abnormalities), including but not limited to skeletal dysplasias.

18. Exclusion Criteria only applicable to ISS:

    1. Known history of any condition that causes disproportionate short stature (i.e. skeletal dysplasias), chromosomal aneuploidy, significant gene mutations, or medical syndromes with short stature, including but not limited to Turner syndrome, Laron syndrome, Noonan syndrome, Prader-Willi syndrome, abnormal SHOX-1 gene analysis or absence of gH receptors.