DOI: 10.7910/dvn/xqweit
title: The CHRISTMAS study. Correlation≠causation: How Retrospective Inference → Spectacles That Make Arms Shorter.

description: Presbyopia is the progressive loss of elasticity in the lens of the eye. Typically occurring in middle age, it leads to gradual impairment in near-vision and accommodation, with progressive elongation of the focal length. Most subjects initially compensate for mild-to-moderate presbyopia by holding reading material at increasingly far distances from their face. When people finally present to request reading glasses they frequently “complain that their arms have ‘become too short’ to hold reading material at a comfortable distance”. Rather than arms becoming too short, we felt that a far more plausible explanation was that people present for their first reading glasses when their progressively increasing focal length nears or even exceeds their fixed arm length. 
We designed an observational study to test the hypothesis that subjects with presbyopia who have long arms do not request reading glasses until presbyopia becomes severe and, by contrast, that subjects with short arms are more likely to request reading glasses earlier and at a milder stage of presbyopia. The association between arm length and the age of requesting reading glasses for presbyopia has not previously been tested in medical literature. We undertook not to make any causal inferences. Specifically, we did not consider reading glasses to be an independent exposure lest we be tempted by a positive correlation to infer that early requests for reading glasses somehow cause our arms to shrink. 
 Even if our observational study support our hypothesis and demonstrate a strong correlation between arm length and the age of first request for reading glasses, it would still be absurd to treat reading glasses as an independent exposure and to make the causal inference that by requesting reading glasses at a young age, patients are somehow causing their arms to shrink. 
 This is a study intended to both “make the readers laugh and then make them think”. We address a deeply serious concern about a frequent abuse of statistical methodology in evidence-based medicine; namely making inappropriate causal inferences from retrospective and observational studies. Retrospective and prospective observational studies aim to identify associations between exposures and outcomes. However these associations may be due to multiple confounding factors, selection bias, or reverse causality and should not be used to infer causation. Making far reaching causal inferences based on data from retrospective and observational studies is very shortsighted. 
 
Specific methodology:

 We conducted a cross-sectional retrospective and prospective observational study of subjects who presented with new-onset impaired near-vision requesting their first pair of reading glasses. 
 The study was conducted from January to July 2022 in the following optometry clinics in Israel: Hadassah University Medical Center, Ein Karem, Jerusalem; Optica Doron in Malka Shopping Mall, Jerusalem; and Einit (Eyewear and Opticians), Beit Shemesh. The study protocol was approved by the Institutional Review Board of Hadassah Medical Organization (protocol number 0367-21-HMO). All participants signed an informed consent form. 

 Subjects were included if they met the following inclusion criteria: 1. Subjects requesting their first pair of reading glasses due to presbyopia, based on reduced near-vision and/or impaired accommodation; 2. Men and women aged 38-55 years at the time of their sentinel examination. This study consisted of two arms. In the prospective arm, we assessed new subjects presenting to optometry clinics who met inclusion criteria. In the retrospective arm, we advertised for subjects meeting inclusion criteria who had received their first pair of reading glasses in the previous 12 months and invited them to attend one of the optometry clinics in the study. 
 Subjects were not enrolled if they met the following exclusion criteria: inability to read the small print in the consent form (although large print laminated copies of the consent form and a wide array of spectacles were available), inability to understand the consent form, refusal to participate, prior habitual use of corrective lenses for myopia, inability to fully extend either arm or thumb, or pregnancy at the time of the optometry assessment. 
 We recorded the following variables: 1. Demographic variables: sex, date of birth, height, hand dominance; 2. Age at first request for reading glasses and age at first complaint of difficulty with near-vision and accommodation. 3. Optometry: uncorrected visual acuity of each participant was measured with Snellen chart at distance (6m, decimal units) and Rosenbaum Pocket Vision Screener at near (40cm, Jagger units). Objective refraction (WAM 700, Essilor Ltd, Créteil, France or Huvitz HRK-8000A Autorefractor, Gyeonggi-do, South Korea) and subjective refraction were measured to evaluate the required refractive correction for distance and near-vision (additions or “Adds”) in each eye (dioptre sphere units). We also measured the amplitude of accommodation of each eye (push-away method, dioptre units) and pupil size (mm units) in daylight using the autorefractometer. 4. Arm length was measured for both arms from the acromion to the tip of the thumb (see supplementary file). Arm length was measured by a blinded investigator, unaware of the optometry data. 
Statistical methods: Correlations between continuous or interval measures were assessed using Pearson’s correlation coefficient. General linear models were constructed controlling for the study covariates. We report regression coefficients, 95% confidence intervals (95% CI) and two-sided p values. Statistical significance of 0.05 was considered significant. Analyses used SPSS version 26 (IBM corporate Inc.).