The phrase "a second study by the same" is not complete and lacks clarity, but it is grammatically correct.
You can use it when referring to a follow-up study conducted by the same author or research team, although it would typically need additional context to be fully understandable.
Example: "In a second study by the same researchers, the results were further validated."
Alternatives: "a follow-up study by the same" or "another study by the same".
In a second study by the same multicenter group, 142 patients with advanced dysplasia were treated.
A second study by the same group, published in 2009, found that children born after their mothers lost weight had lower birth weights and were three times less likely to become severely obese than their older siblings.
A second study by the same author showed that treatment with progesterone resulted in a delay in bleeding and no change in the headache pattern [65].
In a second study by the same group, poultry products labeled "no antibiotics added" carried antibiotic-resistant E. coli and Enterococcus (another bacteria that causes invasive disease in humans), although the microbes were less prevalent than on conventionally raised birds.
In a second study by the same group [ 32], blood transfusions allowed five anemic COPD patients, in whom trials of weaning from a respirator before the transfusions had been unsuccessful, to be successfully weaned after the transfusions.
In a second study by the same group, 120 patients with hypertensive nephropathy and CKD stage 2, all taking ACE inhibitors, were randomized in a blinded fashion to receive 0.5 mEq/kg/day sodium bicarbonate, sodium chloride, or matching placebo.
The same seems to be true of other cephalopods, according to a second study in the same journal by Thomas Cronin of the University of Maryland Baltimore County and his colleagues.
A second study in the same issue, led by Adi Gazdar of the University of Texas Southwestern Medical Center in Dallas, yielded similar results.
A second study in the same journal was conducted in both Tanzania and Kenya, and it shows the vaccine is indeed improved by using a better adjuvant.
In a second study, though, the same procedure was used.
A second study of same-sex couples, the first such investigation by HUD, revealed starker discrimination against gay and lesbian renters.
