In 2007, a Plymouth County grand jury returned *801indictments charging the defendant and his wife, Carolyn Riley,1 with the murder of their four year old daughter, Rebecca. The defendant and Carolyn were tried separately in 2010. Carolyn was convicted of murder in the second degree; the defendant was convicted of murder in the first degree on a theory of extreme atrocity or cruelty.2 Before us is the defendant’s appeal from his conviction and from the denial of his motions for a new trial and for funds to retain a toxicologist. The defendant argues the following: (1) his trial counsel was ineffective in a number of respects; (2) his motion for a required finding of not guilty on the murder charge should have been allowed because there was insufficient evidence of malice; (3) the prosecutor improperly and excessively relied on evidence of the defendant’s bad character that was unfairly prejudicial; and (4) the judge abused his discretion in denying the defendant’s motion for a new trial without a hearing and the defendant’s related posttrial motion for funds to retain a toxicologist. Last, the defendant asks us to use our power under G. L. c. 278, § 33E, to reduce his conviction to involuntary manslaughter. We affirm the defendant’s judgment of conviction and the denial of his new trial motion and motion for funds, and we decline to reduce his conviction to a lesser degree of guilt.
1. Background. We summarize the facts as the jury could have found them, reserving certain details for our discussion of the issues raised. The defendant and Carolyn had three children: Gerard, aged eleven at the time of Rebecca’s death on December 13, 2006; Kaitlynne, aged six; and Rebecca, aged four. At that time, the defendant, Carolyn, Gerard, and Kaitlynne were each receiving Social Security disability benefits.3
As of June, 2004, the family lived in Weymouth. In August, *8022004, when Rebecca was a little over two years old, the defendant and Carolyn took Rebecca to Dr. Kayoko Kifuji, a child psychiatrist who was already treating Kaitlynne,4 and complained to Dr. Kifuji that Rebecca was very hyperactive, hardly slept, and was violent toward her siblings. Dr. Kifuji diagnosed Rebecca with attention deficit hyperactivity disorder (ADHD) and prescribed her clonidine, a medication approved by the Food and Drug Administration (FDA) to treat high blood pressure in adults, but also used “off label” to treat ADHD in children. Approximately two months after Rebecca received her ADHD diagnosis, the defendant initiated a claim for Rebecca for Social Security disability benefits. It was denied. In May, 2005, the defendant and Carolyn took Rebecca back to Dr. Kifuji, who, based on the description of symptoms provided by Carolyn, diagnosed Rebecca, then aged three, with bipolar disorder; as she had for Kaitlynne, Dr. Kifuji prescribed Depakote for Rebecca. See note 4, supra. Thereafter, a request to reconsider the denial of benefits for Rebecca was filed with the Social Security Administration, but was again denied in July, 2005. In December, 2005, the defendant appealed the denial. The appeal had not been heard at the time of Rebecca’s death.
In 2005, the family was living in a public housing development in Weymouth, and in December, 2005, the Weymouth housing authority directed that the defendant could not live there.5 The defendant moved in with his mother, who lived close by, saw and talked to Carolyn almost every day, and continued to drive Carolyn, Rebecca, and the other children to Rebecca’s appointments with Dr. Kifuji.
In January of 2006, Rebecca began attending a preschool program. She showed signs of being overmedicated throughout the school year. She was lethargic, needed assistance on the *803stairs because she was very unsteady on her feet, and also needed assistance when getting off the school bus — someone would have to lift her physically out of her car seat. School personnel were so worried about Rebecca’s appearance that they frequently took her to the nurse’s office. Rebecca exhibited similar signs of overmedication when she returned to school in the fall of 2006, after a summer break.
The defendant moved back to live with his family between the end of November and early December of 2006. At this point the family was living in Hull; Carolyn’s half-brother, James McConnell, his girl friend, Kelly Williams, and her son also were living in the house. Whereas Carolyn used to keep all the Riley children’s medication in the kitchen, once the defendant rejoined the family, medication was kept in his and Carolyn’s bedroom. Additionally, the defendant directed control of when the children received their medication. He frequently yelled at Carolyn, “Give these fucking kids their medicine,” or “Shut the fucking kids up,” when the children appeared to be annoying him, and Carolyn would then administer the medication.6 Further, Carolyn, at the defendant’s direction, began to give the children their nighttime medications earlier in the evening — between 5 and 6 p.m. — and Rebecca would fall asleep within one-half hour thereafter. She would sleep until around 6 a.m., then would be up for approximately one and one-half hours, be given her morning dose of clonidine, and go back to sleep until 11 a.m. or noon. As a consequence, Rebecca was sleeping between twelve and fifteen hours per day in the weeks leading up to her death. Those at school noted that Rebecca’s condition progressively worsened in those weeks: she became even more lackadaisical, did not engage with the other children or staff members, and required an aide to sit behind her to prop up her body.
On her last day at school, Friday, December 8, 2006, Rebecca appeared to have a cold. The cold persisted on Saturday, and *804she developed a barking cough that sounded like a croup cough. Williams suggested to Carolyn that she might want to take Rebecca to a doctor. On Sunday, Rebecca did not eat anything and her cough was forcing her to vomit; she was given adult strength liquid cough medicine to suppress her cough. In light of these symptoms, Williams told the defendant and Carolyn that they should take Rebecca to see a doctor. Carolyn said that she would make an appointment, but did not do so.
On Monday morning, the defendant and Carolyn went to the Social Security office because the defendant was not receiving his disability benefit check. Rebecca vomited numerous times that day and appeared dazed as she wandered around the house. Williams again said that Rebecca should see a doctor, even offering to take Rebecca to the hospital emergency room herself. Carolyn told Williams that she had called the pediatrician and learned there were no more “sick visits” available for Monday, and that she would need to make an appointment for Tuesday. In fact, Carolyn had not called the pediatrician, and did not make an appointment for Tuesday.
On Tuesday morning, the defendant and Carolyn returned to the Social Security office. Rebecca was visibly worse on Tuesday; she was still feverish and was now also dazed and incoherent. She would walk down the hall without focusing on anything. Concerned for Rebecca’s condition and angry at the defendant for not getting her medical attention, McConnell threatened to hurt the defendant to the point where an ambulance would come and pick up the defendant and Rebecca. The defendant told McConnell that it was none of his business because Rebecca was his child.
After that encounter, Rebecca walked to her parents’ bedroom with a lack of focus in her eyes, knocked on the door, and called for her mother; the defendant answered the door and told Rebecca, “Go to your fucking room,” in an annoyed tone of voice. Rebecca went to her bedroom but returned to her parents’ bedroom on two other occasions. Each time, the defendant yelled at her, did not allow her in the room, and sent her back to her own bedroom.
Around 6:30 p.m. that evening, the defendant and Carolyn left the house to take trash that had been piling up in the yard to *805Carolyn’s mother’s house. Before leaving, Rebecca had been given her nighttime medication. While Williams was watching Rebecca in the defendant’s and Carolyn’s absence, Rebecca walked down the hall toward her parents’ bedroom, incoherent and unresponsive. Even when Rebecca’s name was called, she did not respond; she looked “like a zombie.” When Williams picked her up, she was very cold and clammy but still was feverish; her body was limp, almost as though she were dead weight. The defendant and Carolyn returned hours later, and Williams, in a state of panic, told them that they needed to take Rebecca to a doctor immediately. She even suggested that they call an ambulance and noted that she had considered calling one herself.7 The defendant told Williams that Rebecca had an appointment with her pediatrician at 8 a.m. the next day; no appointment had been made. Carolyn then picked up Rebecca and returned her to the bedroom she shared with Kaitlynne. Around this time, Rebecca was given cough medicine and an extra tablet of clonidine.
At approximately 10 p.m., Rebecca again walked down the hall to her parents’ bedroom. The defendant opened the door, grabbed Rebecca by the arm, turned her around, pushed her back toward her bedroom, and yelled, “Go to your fucking room.” Rebecca cried, calling for her mother and saying that she did not feel well. Rebecca kept returning to her parents’ bedroom. After her parents turned Rebecca away from their bedroom several more times, McGonnell kicked the defendant’s and Carolyn’s door and, in a panicked tone, told them that they needed to call an ambulance. Williams picked up Rebecca, who was stiff, and brought the child back to her bedroom.
At approximately 1 a.m. (now Wednesday, December 13), Blaine Groetzinger, a friend of Williams who was staying in the basement of the house, heard Rebecca faintly calling out for her mother in her bedroom. On hearing this, he knocked on McConnell’s door to tell him that he should get Carolyn. At the time, Rebecca was gurgling and choking, and when McGonnell went to her, Rebecca spit up a red liquid onto his pants. Mc-Gonnell went to the defendant’s and Carolyn’s door and kicked *806it in after nobody answered it; he then kicked their bed to awaken them. The defendant asked McGonnell what he wanted, and McGonnell said that Rebecca was worse and again brought up that they needed to take her to the emergency room, asking, “What if she dies?” According to McGonnell, the defendant acted like “[i]t was a big joke.”
Carolyn thereafter brought Rebecca into the bedroom she shared with the defendant. Rebecca was stiff, gasping for air, and moaning. At the defendant’s direction, Rebecca received at least one-half pill more of clonidine, and was placed on her parents’ bedroom floor with a blanket and pillow. When the defendant and Carolyn awoke around 6:30 a.m. that morning, Rebecca was dead. Her body was stiff and cold, and a pink-tinged foamy liquid had secreted from her nose and mouth.
Rebecca died from intoxication due to the combined effects of clonidine and the other sedating drugs found in her system, or from pneumonia, or from a combination of both intoxication and pneumonia. A toxicology report revealed that the level of clonidine in Rebecca’s femoral blood amounted to twelve nano-grams per milliliter (ng/ml), which constituted approximately three times the therapeutic range for adults —■ one-half to four ng/ml — and six times a suggested therapeutic range for children — one-half to two ng/ml.8 In addition, the toxicology report reflected that Rebecca’s blood tested positive for drugs with a sedating effect that are contained in cough and cold medicines. See note 9, infra, and accompanying text. According to the medical examiner, Dr. Elizabeth Bundock, these drugs in Rebec*807ca’s system in combination with the clonidine, or the clonidine level alone, were sufficient to cause her death. According to two other pathologists who testified at trial, Dr. Sarah Vargas and Dr. Jonathan Arden, at the time of her death Rebecca had pneumonia, which itself caused or contributed to her death.
Originally the defendant and Carolyn were to be tried together. On the first day of their joint trial, however, the Commonwealth assented to Carolyn’s motion to sever. Carolyn was tried in January and February of 2010; the defendant was tried in March of 2010. The judge instructed the jury in the defendant’s case on murder in the first degree (theories of deliberate premeditation and extreme atrocity or cruelty), murder in the second degree, and manslaughter; as mentioned, the jury found the defendant guilty of murder in the first degree committed with extreme atrocity or cruelty. Following his conviction, the defendant filed a motion for funds for a toxicologist, which the trial judge denied, and later filed a motion for a new trial. The trial judge denied the motion in a written decision and order; he did not hold a hearing. We review the denial of the defendant’s motion for a new trial and motion for funds for a toxicologist as part of our plenary review pursuant to G. L. c. 278, § 33E. See Commonwealth v. Morgan, 449 Mass. 343, 353 (2007).
2. Discussion, a. Ineffective assistance of counsel. The defendant’s principal argument in this appeal is that he was denied the effective assistance of counsel at trial in a number of respects, and that the motion judge, who was also the trial judge, abused his discretion in denying the defendant’s motion for a new trial that raised the ineffectiveness claim.
“Because the defendant has been convicted of murder in the first degree, we consider his claim of ineffectiveness of counsel to determine whether there exists a substantial likelihood of a miscarriage of justice, as required under G. L. c. 278, § 33E, which is more favorable to a defendant than the constitutional standard for determining ineffectiveness of counsel.” Commonwealth v. Gonzalez, 443 Mass. 799, 808 (2005), citing Commonwealth v. Wright, 411 Mass. 678, 682 (1992). See Commonwealth v. Leng, 463 Mass. 779, 781 (2012) (“Where the denial of the defendant’s motion for a new trial is considered in conjunction with his direct appeal from a conviction of murder *808in the first degree, our review proceeds under the more exacting standard required by G. L. c. 278, § 33E”). “Thus, we consider whether there was error during the course of the trial, and, if so, whether the error was ‘likely to have influenced the jury’s conclusion.’ ” Commonwealth v. Williams, 453 Mass. 203, 205 (2009), quoting Wright, supra. Under this standard of review, we consider a defendant’s claim even if the action by trial counsel does not “constitute conduct falling ‘measurably below’ that of ‘an ordinary fallible lawyer.’ ” Commonwealth v. MacKenzie, 413 Mass. 498, 517 (1992), quoting Commonwealth v. Saferian, 366 Mass. 89, 96 (1974). Nevertheless, “[w]here defense counsel made a strategic or tactical decision that the defendant now challenges, we determine whether the decision was ‘manifestly unreasonable’ when made, recognizing that ‘[m]any decisions of defense counsel that are characterized in hindsight as errors may have been reasonable tactical or strategic decisions when made.’ ” Commonwealth v. Walker, 460 Mass. 590, 598-599 (2011), quoting Commonwealth v. Mosher, 455 Mass. 811, 827 (2010).
i. Failure to investigate reliability of femoral blood analysis. In the course of performing the autopsy of Rebecca, the medical examiner drew blood from Rebecca’s heart and from the femoral artery in her leg to enable the blood to be tested for, among other things, the presence of drugs. The blood was sent to the laboratory at the University of Massachusetts Memorial Medical Center (UMass Memorial laboratory) for toxicological testing, and the director of the UMass Memorial laboratory in turn sent samples of the blood from the heart and femoral artery to the National Medical Services (NMS) laboratory in Pennsylvania to perform more sophisticated tests for specific drugs than the UMass Memorial laboratory could do at the time; these drugs included clonidine, dextromethorphan, and chlorpheniramine.9 The analysis of the heart blood revealed the presence of cloni-dine at a concentration of nineteen ng/ml; the femoral blood analysis measured clonidine at a concentration of twelve ng/ml.
*809Most of the Commonwealth’s expert witnesses,10 as well as the defendant’s expert, testified that to measure drug concentrations postmortem, heart blood is not used because its drug concentrations are artificially high due to postmortem redistribution.11 According to the experts, the heart blood is sometimes used in an initial screening process to identify which drugs need to be further tested. The femoral blood is then tested, and the concentration of a particular drug measured in the femoral blood provides a good proxy for the drug’s concentration in the individual’s blood at the time of death.
The defendant contends that his trial counsel failed to investigate adequately the premise that the femoral blood concentration measurement of twelve ng/ml, obviously a postmortem determination, was a reliable indication of the level of clonidine in Rebecca’s blood at the time of her death (i.e., antemortem measurement). He claims that what investigation would show is that postmortem femoral blood measurement has shown to be “consistently” higher than antemortem measurement, and therefore could not properly be used in this case to gauge how much clonidine had been given to Rebecca before she died, contrary to the Commonwealth’s death-by-overdose theory of the case. In the defendant’s view, the motion judge erred in focusing on whether trial counsel contested the Commonwealth’s overdose theory at trial — which counsel admittedly did — rather than on whether he sufficiently investigated the essential “assumptions” of that theory in order to expose their fatal flaws.12
The defendant’s argument fails. A review of the trial record *810makes clear that this is not a case where, through defense counsel’s lack of preparation and advocacy at trial, the defendant was deprived completely of a defense. Compare Commonwealth v. Farley, 432 Mass. 153, 156-157 (2000), S.C., 443 Mass. 740, cert. denied, 546 U.S. 1035 (2005) (defense counsel initially put forth defense that another committed crime, but then completely failed to develop defense through investigation or, at trial, through presentation of supporting evidence, cross-examination, or closing argument). Rather, as the judge found, trial counsel effectively presented a theory about cause of death that served to provide a reasonable alternative to the Commonwealth’s overdose theory. The defendant’s theory, presented through a forensic pathologist, Dr. Arden, was that although the level of clonidine in Rebecca’s blood clearly was elevated at the time of her death, an overdose of clonidine did not kill her, but rather she died of a fulminant necrotizing pneumonia — a pneumonia that became extremely serious and indeed fatal extremely quickly.13
The defense theory that Rebecca died of a fast-acting pneumonia rather than a drug overdose was far from an unsupported flight of fancy. Arden was highly credentialed and his explanation was well reasoned. More significantly, one of the Commonwealth’s own expert pathologists, Dr. Vargas, agreed with Arden that a cause of death was pneumonia (although Vargas opined as well that the pneumonia was acting in the context of clonidine, and that clonidine overdose by itself also could have been the cause of death). The record contains no persuasive indication that the defendant’s counsel presented the alternative explanation of cause of death because of a lack of investigation of the toxicology evidence on which the Commonwealth was *811relying.14 His retention and use of Arden indicates otherwise. Compare Commonwealth v. Baker, 440 Mass. 519, 528-529 (2003) (defense counsel did not seek to retain expert to examine item of evidence [a single hair] on which Commonwealth’s entire theory of case was built). Further, while affirmatively presenting this alternative theory of cause of death, trial counsel vigorously attacked the validity of the Commonwealth’s overdose theory through his cross-examination of the Commonwealth’s expert witnesses. He brought out in cross-examination of Dr. George Behonick, one of the toxicologists testifying for Commonwealth, that there were no studies of volume of distribution among children; he also repeatedly pointed out through his questioning of the Commonwealth’s experts that the use of clonidine for treating ADHD and bipolar disease had not been approved by the FDA and that there were no studies generally of children’s use of clonidine or of clonidine toxicity or overdose among children.15
*812We turn to the defendant’s specific criticisms of his trial counsel’s performance in relation to the toxicological evidence. He complains that trial counsel should have reviewed the testimony of the two toxicologists who testified as defense experts at Carolyn’s trial; the argument seems to be that counsel should have called these experts to testify at the defendant’s trial, because they, in contrast to the defendant’s expert, Arden, would likely have testified that the postmortem femoral blood measurement was not reliable. The argument is not persuasive. While the two experts presumably would have testified at the defendant’s trial, consistently with their testimony at Carolyn’s, that the postmortem femoral blood measurement of twelve ng/ml was not a reliable measure of Rebecca’s antemortem clonidine concentration, the reasons they gave at Carolyn’s trial for this opinion did not include that postmortem femoral blood measurements are consistently higher than antemortem measurements. See note 19, infra. It is perhaps more important that until right before Carolyn’s trial began, the defendant and Carolyn were going to be tried together. We infer from this — although trial counsel implies otherwise in his affidavit — that trial counsel must have been aware of the thrust of these two experts’ expected testimony; the inference is supported by the fact that counsel used one of these expert’s reports in cross-examining the medical examiner at the defendant’s trial. Moreover, trial counsel of course was aware before the defendant’s trial began that Carolyn had just been convicted of murder in the second degree — i.e., her defense had not been successful.16
The defendant argues that his trial counsel was ineffective *813because he did not request a so-called Lanigan17 hearing to test the reliability of the overdose theory being advanced by the experts testifying on behalf of the Commonwealth. This argument lacks merit. The trial judge here also presided over Carolyn’s trial where the Commonwealth had presented the same toxicological evidence, and despite a defense request to do so, the judge had not held a Lanigan hearing in Carolyn’s case. In the circumstances, a motion for a Lanigan hearing in this case was likely to have been futile.18,19
Finally, the defendant claims that his counsel was ineffective because he failed to cross-examine the Commonwealth’s expert witness Behonick about his electronic mail message (e-mail) addressed to the medical examiner. See note 14, supra. Counsel certainly could have done so, and perhaps it would have been a wise course to follow.20 But it is significant that the e-mail was written before Rebecca’s femoral blood was tested, and Behon-ick explained in the e-mail that he was seeking a test of the femoral blood in order to obtain a more accurate estimate of the clonidine concentration in Rebecca’s blood at the time she died. *814Moreover, it is possible that the opinion on the volume of distribution issue to which Behonick testified at trial, which he stated was based on information he received from another expert during his work on this case, reflected a change of opinion from when he wrote the e-mail.
In summary, what the record indicates is that the defendant’s trial counsel made a strategic decision to pursue a theory of defense that provided an affirmative answer to the Commonwealth’s overdose theory, and with which one of Commonwealth’s own experts basically agreed. The question is whether that strategic decision was manifestly unreasonable. See, e.g., Commonwealth v. Acevedo, 446 Mass. 435, 446 (2006); Commonwealth v. Denis, 442 Mass. 617, 625 (2004). It was not. The judge did not abuse his discretion in denying the defendant’s claim that his counsel was ineffective in handling the critical issue of toxicological evidence at trial.
ii. Failure to challenge Commonwealth’s theory that defendant directed Rebecca’s overmedication. The defendant claims that trial counsel was ineffective because he did not present evidence to combat the Commonwealth’s argument at trial that it was the defendant who, over the course of years, directed the administration of medications and overdosing to Rebecca and her siblings; the argument is that trial counsel failed to do so even though it was clear that Carolyn was the only one who physically gave the children their pills, and even though the defendant was not living with his family for the year preceding Rebecca’s death. According to the defendant, a comparison of the number of pills obtained by Carolyn during 2006 to the number of pills obtained by the family in 2005 indicates that, in 2006, when the defendant was not permitted to live with his family, “the drug use soared.”
This claim has no merit for at least three reasons. First, the trial evidence essentially was undisputed that Carolyn, and not the defendant, was completely in charge of administering medication to Rebecca and the other children, and also that Carolyn was the parent who personally met and talked with Rebecca’s psychiatrist, Dr. Kifuji. Trial counsel was not obliged to introduce additional evidence on this point. See Commonwealth v. Drew, 447 Mass. 635, 650 (2006), cert. denied, 550 U.S. 943 (2007) *815(“The failure to offer cumulative evidence is not ineffective assistance of counsel”). Second, the most relevant time period in this case was the time closely preceding Rebecca’s death, and the defendant by then had returned to living in the house with the family. Evidence of the defendant’s role in relation to Rebecca’s medication earlier in 2006 or before, while it could provide context, was not directly on point, because, as the evidence showed, clonidine does not stay in the body permanently,21 and there was no evidence — nor did the Commonwealth claim — that Rebecca’s death at four years of age was caused by the cumulative effect of her taking clonidine for the two preceding years. Third, the Commonwealth’s theory in this case was that the defendant and Carolyn were acting as participants in a joint venture, the judge so charged, and the defendant does not challenge the sufficiency of the evidence to warrant such a charge. If the jury concluded that Carolyn and the defendant were aiding and abetting each other — a conclusion well supported by the trial evidence — whether the defendant directed Carolyn’s administration of medication or she acted more independently would not be important, because as participants in a joint venture, each was bound by the acts of the other.22
iii. Failure to introduce evidence and argue that a reasonable person would not recognize that Rebecca likely would die without medical treatment. The defendant argues there was evidence showing that at various times on the Monday and Tuesday before her death on Wednesday morning, Rebecca seemed to other witnesses not to be so sick, or to be improving. He contends that trial counsel failed both to present such evidence and to argue in his closing that, in the circumstances, the defendant reasonably would not have known on Monday or even Tuesday that there was “a plain and strong likelihood” Rebecca would die without medical treatment. Despite another fall-on-his-sword *816observation by trial counsel in his affidavit,23 we disagree that counsel was ineffective. For example, at trial, counsel highlighted Williams’s observations of Rebecca in the two days before her death that served to minimize the degree of illness, including that she, Williams, did not think Rebecca would die. As for counsel’s closing argument, he focused for some time on the question of what the defendant as Rebecca’s parent reasonably would have recognized in the two days before her death, and as the defendant’s appellate counsel acknowledges, he explicitly and correctly framed the question to be answered — “As of Tuesday night, as a reasonable parent, looking at their child, would they understand, or have reason to believe, that if they don’t act to get medical attention, the child will die?” — and then attempted to answer it. That trial counsel perhaps might have presented a more focused answer does not mean that a substantial likelihood of a miscarriage of justice occurred.24
iv. Failure to move for preclusion of prosecutor’s argument on defendant’s money motive for killing Rebecca. The defendant argues trial counsel was ineffective because he did not file a motion in limine to preclude the Commonwealth from advancing the theory that the defendant and Carolyn essentially fabricated symptoms of bipolar disease as well as ADHD in all three of their children in order to qualify them for Social Security disability benefits that would be paid to the family on the children’s behalf. The defendant’s position is that there was substantial evidence that the three children did exhibit “abnormal behavior,” so that the prosecutor’s introduction of evidence of allegedly fabricated or “faked” symptoms should have been opposed, and if there had been opposition by counsel, it would have carried the day.
*817A review of the record makes clear that the Commonwealth was well within its rights to present this evidence and make the argument. The Appeals Court’s analysis of Carolyn’s argument about this same evidence is equally applicable here:
“[E]vidence suggesting that the defendant had devised a scheme to secure psychiatric medications for [his] children in order to obtain Social Security disability benefits was probative of the defendant’s motive and intent for giving them unnecessary medication and for doing so regardless of the contraindications. Furthermore, because the Social Security Administration twice had denied Rebecca’s application for benefits, such evidence also was probative of the defendant’s motive and intent in causing or deliberately allowing Rebecca to die.”
Commonwealth v. Riley, 84 Mass. App. Ct. 272, 284-285 (2013). It does not follow that because there was some evidence supporting the proposition that the Riley children’s symptoms of mental illness were real, the Commonwealth should have been precluded from introducing, and arguing the import of, contrary evidence.
v. Failure to object to bad act evidence and to combat inappropriate sympathy-seeking by Commonwealth. Before trial, defense counsel filed a motion in limine to prevent introduction of bad act evidence on the defendant’s part, including in particular evidence concerning alleged incidents of striking his son or any other child. The judge ultimately allowed the motion in part, ruling that only prior evidence concerning the defendant’s interactions with his children that occurred during Rebecca’s lifetime (April of 2002 to December of 2006) would be admissible. On appeal, the defendant claims his counsel was ineffective for not objecting to testimony by an acquaintance of Carolyn, Laurie Perry, that when she visited Carolyn and the Riley family in September of 2002, she observed the defendant strike his son, and also observed a serious diaper rash on Rebecca; and for not objecting to testimony of McConnell that during his visits with the Riley family in 2003 and 2004, the children spent most of their time in their bedrooms because the defendant would swear at them if they came out, and the defendant hit Rebecca’s siblings on the backs of their heads.
*818The judge did not abuse his discretion by allowing the Commonwealth to introduce evidence of prior conduct by the defendant that concerned his relationship with Rebecca and his other two children during Rebecca’s four-year life: the evidence bore on the defendant’s state of mind vis-a-vis Rebecca herself — obviously a relevant consideration — and the brevity of Rebecca’s life made its entire span relevant. See, e.g., Commonwealth v. Dung Van Tran, 463 Mass. 8, 11, 14-15 (2012) (defendant’s abusive behavior toward wife and child for years while living together admissible to show motive and intent to commit armed assault with intent to murder another child). Insofar as acts toward the defendant’s other two children are concerned, where, as here, all three children were living in the same household and there was no evidence that the defendant treated any of his children in a noticeably different manner, it was not error for the judge to conclude that this evidence was relevant to an evaluation of his relationship with and state of mind in relation to Rebecca.25 See Commonwealth v. Gallison, 383 Mass. 659, 672-673 (1981) (evidence of abuse of one child in household relevant to prosecution of homicide of second child in same household, as it was relevant to defendant’s state of mind and demonstrated “common course of conduct regarding the two children”). Accordingly, because the admission of evidence about Perry’s and McConnell’s observations of the defendant fit within the time frame permitted by the judge, it is likely that any objection or motion of the defendant to exclude this particular evidence at trial would have been denied. Counsel was not ineffective for failing to do so.26 See, e.g., Commonwealth v. LeBeau, 451 Mass. 244, 259 n.15 (2008).
*819The defendant also criticizes trial counsel for failing to object to a comment by a witness27 or to the prosecutor’s closing argument. We agree that the witness’s comment was improper and an objection to it would have been appropriate. However, it is entirely possible that counsel did not do so because of a concern about drawing more attention to the remark. In any event, the failure to object to this single comment in a very long trial did not create a substantial likelihood of a miscarriage of justice.
With respect to the claimed failure to object to the prosecutor’s closing argument, the defendant focuses on a number of comments about Rebecca’s suffering as she died that he claims were improper appeals to juror sympathy. With one exception, we conclude that the prosecutor’s argument was not objectionable, and therefore that the defendant’s trial counsel was not at fault for failing to object. The prosecutor’s argument generally was hard-hitting, but the comments about Rebecca’s suffering found a basis in the testimony of several expert witnesses about what a person in Rebecca’s extreme medical circumstances — with lungs filling up and unable to breathe — would experience before death. The one exception was the speculative question posed by the prosecutor as to what Rebecca would be asking herself as she was dying.28 This may have been intended as a rhetorical flourish, but it was excessive and unnecessary. An objection would have been warranted. Nevertheless, when considered in the context of the prosecutor’s argument as a whole and the judge’s instructions explaining that closing argu-*820merits are not evidence, we cannot say that this unobjected-to remark created a substantial likelihood of a miscarriage of justice. See Commonwealth v. Tu Trinh, 458 Mass. 776, 785 (2011) (isolated improper remarks did not make closing on whole improper); Commonwealth v. Rodriguez, 437 Mass. 554, 565 (2002), quoting Commonwealth v. Lamrini, 392 Mass. 427, 432 (1984) (“In analyzing a claim of improper argument, the prosecutor’s remarks must be viewed in light of the ‘entire argument, as well as in light of the judge’s instruction to the jury and the evidence at trial’ ”).
vi. Failure to object to jury instruction on violation of parental duty to obtain medical care for a child. In his final jury charge, the trial judge included an instruction on the legal duty of a defendant who is a parent to obtain medical care for his or her child, if in the circumstances that were known to the defendant, a reasonable person would know that the failure to perform it “involved a high degree of likelihood of substantial harm to the child,” or “created a plain and strong likelihood of death to the child.” The judge told the jury that the question whether the defendant violated the duty to obtain medical care was a fact question for them to decide, and that the jury should consider that fact on the question whether the defendant was guilty of any of the crimes at issue — murder in the first degree, murder in the second degree, and manslaughter — and also on whether the elements of any of those crimes had been proved, including the particular intent or mental state required. There was no objection to the judge’s parental duty charge.
The defendant contends on appeal that trial counsel was ineffective for failing to object. He argues that the instruction was objectionable and prejudicial because (1) in relation to murder in the first degree under the theory of extreme atrocity or cruelty, the instruction permitted the jury to consider violation of parental duty of care as an extra, eighth factor under Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983); and (2) the instruction allowed the jury to consider that Rebecca’s death was caused by the failure to obtain medical care, which in turn made it easier for the Commonwealth to prove that one or more of the Cun-neen factors were established.
As to the first point, that the parental duty instruction created *821an eighth Cunneen factor, a reading of the judge’s instructions as a whole essentially defeats it, because they clearly identify the seven Cunneen factors, and explain that to find the defendant guilty of murder committed with extreme atrocity or cruelty, the jury must find that the Commonwealth has proved at least one of those seven factors. See Commonwealth v. Walker, 466 Mass. 268, 284 (2013), quoting Commonwealth v. Owens, 414 Mass. 595, 607 (1993) (“Jury instructions must be construed as a whole to prevent isolated misstatements or omissions from constituting reversible error”). The meaning or import of the defendant’s second point is not clear, and after stating it, the defendant offers no further explanation. We consider the argument waived. See Mass. R. A. P. 16 (a) (4), as amended, 367 Mass. 921 (1975).29
b. Evidence of malice. The defendant argues that his motion for a required finding of not guilty of murder should have been allowed because the evidence of malice was insufficient. In particular, he claims that the evidence failed to establish first prong malice — intent to kill Rebecca — because he and Carolyn purchased cold medicine to help treat Rebecca’s symptoms on Tuesday, and that as to third prong malice, the facts of this case are not meaningfully different from Commonwealth v. Earle, 458 Mass. 341 (2010), where insufficient evidence of malice required reversal of the defendant’s conviction.30
We review the trial record to determine “whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Commonwealth v. Latimore, 378 Mass. 671, 677 (1979), quoting Jackson v. Virginia, 443 U.S. 307, 318-319 (1979). To prove malice, the Commonwealth must prove one of three prongs: (1) intent to kill the victim; (2) intent to cause grievous bodily harm to the victim; or (3) commission of an act that, in the circumstances known to the defendant, a reasonable person would have known *822created a plain and strong likelihood of death. See Commonwealth v. Grey, 399 Mass. 469, 470 n.1 (1987). The requirement of an intentional act
“can be satisfied by a defendant’s omission where the defendant has a duty to act. Thus, as a parent has a duty to provide for the care and welfare of his or her child, ... a failure to discharge that duty can be rendered criminal if the defendant parent had the means to perform it and, depending on the circumstances, can constitute murder or involuntary manslaughter” (citation omitted).
Earle, 458 Mass. at 347-348.
Considering first prong malice first, the evidence was sufficient for the jury to find that the defendant, along with Carolyn, purposefully overdosed Rebecca with the intent to kill her: on the Tuesday before Rebecca’s death on Wednesday, December 13, 2006, they persisted in giving her clonidine substantially in excess of her prescribed dosage as well as adult cold and cough medicines that increased the sedating effect of the clonidine, although Dr. Kifuji had advised Carolyn that clonidine above the amount prescribed could be fatal, and also that cough and cold medications should not be given to children under six — a cohort that included Rebecca.31
There was also sufficient evidence of third prong malice. Witnesses testified that although the defendant physically did not give Rebecca and his other two children their medications, he directed and ordered Carolyn to do so, at least whenever the defendant wanted the children to quiet down or to calm down — which was frequently. Although Rebecca’s school had previously witnessed Rebecca in what appeared to be an overmedi-cated state, witnesses said that in the weeks immediately leading up to her death — the time following the defendant’s return to living with his family — Rebecca’s condition worsened.
Rebecca left school on Friday, December 8, 2006, with what appeared to be a cold, and over the weekend, her symptoms got increasingly more serious: a persistent, severe cough; vomiting; *823and by Sunday a fever. Beginning on Sunday and repeatedly through Tuesday, the defendant’s housemate Williams suggested, then urged, and then pleaded with the defendant and Carolyn to take Rebecca to a doctor and, as time went on, to the emergency room of a hospital. They did not do so, but told Williams that a doctor’s appointment would be scheduled for the next day; it was not. Rather than going to the doctor, on both Monday and Tuesday, the defendant drove Carolyn and Rebecca to the Social Security office to resolve an issue relating to his disability check; Rebecca kept vomiting. By Tuesday, Rebecca was dazed and incoherent to the point that she became unresponsive; her condition continued to deteriorate throughout the day. Nonetheless, the defendant and Carolyn did not seek medical attention for Rebecca, and despite already having given her nighttime clonidine, the defendant and Carolyn gave her another tablet of clonidine at around 10 p.m.
At 1 a.m., after going into Rebecca’s room and hearing her gurgling and choking, McConnell kicked in the defendant’s bedroom door. He screamed at the defendant and Carolyn and insisted that they needed to take Rebecca to the emergency room to get her medical attention, asking, “What if she dies?” Carolyn brought Rebecca into the defendant’s and her bedroom, and the defendant insisted that Rebecca should receive more clonidine.32
The evidence indicated that the amount of clonidine in Rebecca’s system was at least three times more than the upper level of the accepted therapeutic level in adults and approximately six times the upper estimated therapeutic level in children. In addition, multiple days’ dosages of clonidine were missing from the pill tray that Carolyn used to organize Rebecca’s and Kait-lynne’s pills. The defendant himself had taken clonidine on previous occasions and indicated that it “wiped [him] out.” As the Commonwealth argues, it is a matter of common knowledge that a person can die from taking too many sleeping pills, and *824the defendant’s own statement to the police indicated that he directed clonidine to be given to Rebecca in order to make her sleep. Given the outward signs of Rebecca’s increasingly serious condition of which the defendant was necessarily aware, his housemates’ explicit concerns that Rebecca needed immediate medical attention,33 and what reasonably can be inferred about the defendant’s knowledge of the effects of clonidine, a reasonable person in the same circumstances would know by at least Tuesday that the combination of failing to seek medical care for Rebecca and providing her with yet more clonidine was plainly likely to result in Rebecca’s death. The evidence was sufficient to make out third prong malice.
Earle is distinguishable. There, the defendant’s boy friend stomped on her twenty-one month old daughter while the defendant was away from their apartment. Earle, 458 Mass. at 345-346. The next morning, the child was “greenish-blue or greenish-gray,” whimpering consistently, and vomiting a green substance, and seemed to have considerable pains in her abdomen. Id. at 342-343. In concluding the evidence was insufficient to show the “plain and strong likelihood of death” needed for third prong malice, we noted that the defendant had not observed the underlying trauma inflicted on her child, id. at 350, and that other witnesses who saw the victim in the hours before her death did not react as though her appearance indicated she was likely to die. Id. at 352. Here, by contrast, the defendant was directly privy to the underlying trauma, in that (the jury could find) he directed that Rebecca be given clonidine in excess of her daily prescribed amount and watched her get progressively more sick. Further, the witnesses who were present immediately before Rebecca’s death (Williams and McGonnell) expressed concern over Rebecca’s condition numerous times, with increasing urgency, insisting that she needed immediate medical attention; McGonnell explicitly raised a question about Rebecca dying. See Riley, 84 Mass. App. Ct. at 283-284 (distinguishing *825Earle from Carolyn’s case on same grounds).34 Earle is simply different.
c. Prior bad act evidence. The defendant also argues that he was prejudiced by the Commonwealth’s extensive reliance on bad act evidence. He principally objects to the admission of (1) the defendant’s practice of hitting and swearing at his other two children; (2) the assault on Gerard in October, 2006; and (3) the fact that the defendant showed no emotion after Rebecca’s death. There was no error in admitting this evidence, and no impropriety in the prosecutor’s use of it at trial.35
With respect to the assault on Gerard, as has been discussed, the defendant’s abuse toward him was probative of his state of mind toward Rebecca, see Gallison, 383 Mass. at 672-673, and the judge so instructed the jury, explaining that they could not consider the evidence of the assault on Gerard for general bad character purposes. See Commonwealth v. Gonzalez, 465 Mass. 672, 681 (2013) (“The jury are presumed to follow [the judge’s] instructions”). As to the defendant’s lack of emotion in the wake of Rebecca’s death, a trial judge may, in his or her discretion, admit evidence of acts committed after the charged offense to show, among other things, intent or state of mind at the time of the charged offense. Commonwealth v. Cardarelli, 433 Mass. 427, 434 (2001). See Commonwealth v. Rice, 427 Mass. 203, 210 (1998). The evidence cannot be too remote in time. Cardarelli, supra. The references to the defendant’s lack of emotion after Rebecca’s death were close in time to her death and directly related to events that were tied to it.36 Again, the judge did not abuse his discretion in admitting the evidence, and the *826prosecutor therefore properly could use and comment on it. See Cardarelli, supra at 434-436 (defendant’s gambling, credit card use, and depletion of joint financial resources in two weeks after he killed victim were properly admitted, but defendant’s interstate travels from one to three months later were too remote in fact and time and therefore inadmissible).
d. Denial of motions for new trial without hearing and for funds to retain toxicologist. The defendant argues that the judge erred in denying his motion for a new trial without an evidentiary hearing, specifying that the toxicology issue alone presented in the motion for a new trial raised a substantial issue. “Whether to hold a hearing on a motion for a new trial is within the judge’s discretion . . . , and the judge may ‘decide a motion for a new trial without an evidentiary hearing where no substantial issue is raised by the motion or affidavits’ ” (citation omitted). Commonwealth v. Morgan, 453 Mass. 54, 64 (2009), quoting Commonwealth v. Wallis, 440 Mass. 589, 596 (2003). Where, as here, the motion judge is also the trial judge, he may use his “knowledge and evaluation of the evidence at trial in determining whether to decide the motion for a new trial without an evidentiary hearing.” Wallis, supra.37 See Commonwealth v. Burgos, 462 Mass. 53, 73, cert. denied, 133 S. Ct. 796 (2012). The judge properly concluded that an evidentiary hearing was not warranted.
Turning to the defendant’s claim that the judge abused his discretion in denying the defendant’s posttrial motion for funds to retain a forensic toxicologist, we discern nothing that justifies disturbing the judge’s decision, especially in light of our conclusion that the defendant’s motion based on ineffective assistance of counsel with respect to the toxicology evidence did not create *827a substantial likelihood of a miscarriage of justice. See Commonwealth v. Dubois, 451 Mass. 20, 33 (2008).
e. Review under G. L. c. 278, § 33E. We have carefully reviewed the entire record of this case pursuant to our obligation under G. L. c. 278, § 33E. We find no reason to grant relief to the defendant, but consider here one issue, not raised by the defendant, concerning the trial judge’s instruction on parental duty to obtain medical care.
The judge explained that a parent has a duty to obtain medical care for his or her child when, in the circumstances known to the parent, a reasonable person would know that the child is suffering from a serious illness or condition and the failure to obtain medical treatment either (1) involved a high degree of likelihood of substantial harm to the child (first alternative); or (2) created a plain and strong likelihood that death would result (second alternative). In explaining to the jury that they could consider a violation of this parental duty in relation to all the crimes at issue, however, the judge failed to explain that with respect to the charge of murder, only a violation of the duty to obtain medical care when there was a plain and strong likelihood of the child’s death — the second alternative — would be relevant, whereas for the charge of manslaughter, violation of the duty when there was a likelihood of substantial harm to the child — the first alternative — would suffice. See Earle, 458 Mass. at 347-348 & n.9. In the circumstances of this case, however, the judge’s omitted explanation did not create a substantial likelihood of a miscarriage of justice.
The judge’s instructions on murder in the first degree committed by extreme atrocity or cruelty (as well as murder in the second degree) clearly defined malice as a necessary element, and in particular defined the third prong of malice in language38 that echoed exactly the language of the second alternative in the judge’s definition of parental duty. Similarly, the judge’s instruction on manslaughter channeled the language of the first altema-*828tive in the parental duty definition. It is reasonable to assume that in finding the defendant guilty of murder in the first degree committed with extreme atrocity or cruelty, the jury focused directly on the judge’s explanation of the necessary elements of the crime, and therefore considered whether the Commonwealth had proved beyond a reasonable doubt at least the third prong of malice; put another way, it is not reasonable to assume that the judge’s instruction on parental duty led the jury to conclude that the third prong of malice could be satisfied by proof that the defendant failed to secure medical care for Rebecca in circumstances when a reasonable person in the defendant’s position would know only that such failure created a high likelihood of substantial harm to her, not a plain and strong likelihood of death. See Commonwealth v. Stewart, 460 Mass. 817, 824 (2011) (when evaluating jury instructions, look to what meaning reasonable juror would give to instruction).
3. Conclusion. We affirm the judgment of conviction and the orders denying the motion for a new trial and the motion for funds to retain a toxicologist.
So ordered.
Because the defendant, Carolyn Riley, and their children all share the same last name, we refer to all of them by their first names with the exception of the defendant.
The jury did not find the defendant guilty of murder in the first degree on a theory of deliberate premeditation. The jury were not provided with a theory of felony-murder in the first degree.
Gerard was receiving his Social Security benefits based on his diagnoses of bipolar disorder and possible attention deficit hyperactivity disorder (ADHD). The record suggests that Kaitlynne’s benefits were based on the same or similar diagnoses. See note 4, infra.
Kaitlynne originally saw Dr. Kayoko Kifuji in Springfield, where the family resided at the time. She was diagnosed with bipolar disorder and possibly ADHD and received a prescription for Depakote, a drug used to treat bipolar disorder in adults. In July of 2003, Dr. Kifuji moved her practice to Boston. The defendant and Carolyn drove from Springfield to Boston to take Kaitlynne to see Dr. Kifuji because there was no psychiatrist in Springfield who would continue to prescribe her Depakote.
Carolyn and the three children remained in the same apartment without the defendant.
With respect to the administration of clonidine to Rebecca and her sister, although both of them were prescribed one-half pill of clonidine three times a day, the jury could infer that the children did not receive one-half pills, but only whole pills. Carolyn’s administration of whole pills rather than one-half pills preceded the defendant’s return to the household.
Williams did not do so because her mother, who worked for an insurance company, informed her that only the child’s parents could call for an ambulance.
The clonidine prescriptions for Rebecca and Kaitlynne were refilled on December 7, 2006, and if the girls were given their prescribed dosage between December 7 and December 13, there should have been twenty-six pills remaining in the Riley household; fewer than that number were recovered. Clonidine pills were also missing from a number of the compartments in the pill tray that held the pills Rebecca was scheduled to take on the three days following the Wednesday on which she died. In addition, a comparison of the number of clonidine pills that were prescribed for Rebecca during the year (specifically, 351 days) before she died and the number of such pills that were actually obtained from pharmacies showed that 205.5 extra clonidine pills were obtained in that time frame; 205.5 pills equals the quantity of clonidine prescribed for Rebecca for 58.6 days. (On this point, there was evidence that on a number of occasions, Carolyn would report to Dr. Kifuji or the pharmacy that she had lost the medication or that it “was filled with water” and secure a replacement prescription.)
Dextromethorphan is a drug used to suppress coughs, and is found in many medications sold without prescription; chlorpheniramine is an antihistamine, and is also found in many over-the-counter medications taken for cold and flu symptoms.
One of the Commonwealth’s four experts did not testify about the difference and accuracy with respect to testing heart and femoral blood.
Postmortem distribution refers to the phenomenon where, after death, because the heart is no longer pumping blood throughout the body, drugs in the body diffuse across organs, leading to an increased concentration in certain organs and areas of the body; the heart is one of those organs.
According to the defendant, these uninvestigated but erroneous assumptions were that (1) the postmortem femoral blood level of a drug (specifically, clonidine) is equivalent to the level of the drug at the time of Rebecca’s death; (2) the volume of distribution of a drug (clonidine) in a person’s body is the same for adults as for children; and (3) the measurement of clonidine in a postmortem sample of whole blood would be the same as the measurement in a sample of blood serum or plasma. Volume of distribution refers to the *810extent to which a drug moves from the blood plasma into the tissue of the organs. See Goodman & Gilman’s The Pharmacological Basis of Therapeutics 20 (10th ed. 2001).
With respect to the elevated clonidine level, Dr. Jonathan Arden testified that he did not consider it to be significant in the analysis of cause of death because the medical literature, which had been cited and discussed by the Commonwealth’s experts, indicated that although there were many examples of children receiving overdoses of clonidine, the number of deaths as a result of an overdose were very few and the amount of clonidine involved in those cases where death had occurred far exceeded twelve ng/ml.
Trial counsel submitted an affidavit in support of the defendant’s motion for a new trial, and in it he avers, among other things, that he did not but should have investigated further the same assumptions of the Commonwealth’s overdose theory that the defendant highlights on appeal (see note 12, supra). Trial counsel states that he did not have a copy of, or a memory of having seen, an electronic mail message (e-mail) written by one of the Commonwealth’s expert toxicologists, Dr. George Behonick; and that if counsel had seen it, he could have used it to attack the assumption advanced by Behonick at trial that the volume of distribution in an adult and a child are the same. In fact, as the motion judge was likely aware, trial counsel did have a copy of the Behonick e-mail at the time of trial because he had attached it to a pretrial motion. Based on the judge’s memorandum of decision denying the new trial motion, we agree with the Commonwealth that the judge implicitly discredited trial counsel’s affidavit with its series of “mea culpas.” It was within the province of the judge to do so. Cf. Commonwealth v. Dubois, 451 Mass. 20, 29 (2008) (court assumed motion judge, in implicitly denying defendant’s posttrial motion for discovery of exculpatory information, did not credit defendant’s affidavit, noting that “[t]he judge was not required to credit the affidavit, even if undisputed”). Cf. also Commonwealth v. Thomas, 399 Mass. 165, 167 (1987) (judge deciding posttrial motion has discretion to determine credibility of witness’s affidavit, especially if judge also presided at trial).
The defendant further asserts that trial counsel was ineffective in not investigating whether the postmortem femoral blood level — which was a whole blood measure — would be the same as the blood serum measures used in calculating the therapeutic ranges. The defendant does not present any argument as to what impact the whole blood measure versus blood serum measure would have had, or how it would have made a difference in the defendant’s *812trial. Furthermore, a review of the literature that the defendant cites indicates that the ratio of whole blood to serum measures are drug specific," and the defendant has not provided anything to indicate what that ratio might be for clonidine.
In addition, we have reviewed the testimony offered by the two experts at Carolyn’s trial, Dr. Robert Middleberg and Dr. David Benjamin. While both of them testified that the postmortem femoral blood measurement of twelve ng/ml was not a reliable indication of clonidine concentration in Rebecca’s blood at the time of her death, their explanations of the opinion were diffuse, and at least in the case of Benjamin, his opinion appeared to have been based on factually incorrect assumptions that Rebecca died with vomit present in her mouth, and that the autopsy was performed and blood drawn one day or more after her death. Middleberg presented a different problem: his report stated that if Rebecca had been given the quantity of clonidine that was prescribed, *813she would not have died. This statement could be understood to mean that in fact what had occurred was that Rebecca had been given a great deal more clonidine than she was prescribed, which would point a finger directly at the defendant and Carolyn.
Commonwealth v. Lanigan, 419 Mass. 15, 25-26 (1994). See Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 592-595 (1993).
In its decision affirming Carolyn’s conviction, the Appeals Court concluded that there was no error in the judge’s decision not to hold a Lanigan hearing in that case. See Commonwealth v. Riley, 84 Mass. App. Ct. 272, 274 (2013).
The defendant further argues that even if no Lanigan hearing were held, his counsel should have used two research studies suggesting that postmortem femoral blood measurements consistently are higher to challenge more effectively the Commonwealth’s theory of the case. While there was a great deal of testimony by the experts about research studies, it appears that the studies in question were located by the defendant’s appellate counsel after the conclusion of the defendant’s trial. None of the many toxicologists and pathologists who testified at Carolyn’s and the defendant’s trials — a total of seven different experts — referenced these two articles or suggested that postmortem femoral blood measurements generally are higher than antemortem measurements. It is not at all clear what, if any, impact these two articles would have had if used for cross-examination at the defendant’s trial.
In the e-mail, Behonick states that “the Volume of Distributions in children are [sic] frequently different from young adult or adult values,” whereas at the defendant’s trial he testified that he had been informed there was no real difference between them.
Clonidme has a “half-life,” which refers to the amount of time that it takes for the drug concentration to be lowered by fifty per cent after reaching peak concentration. See Stedman’s Medical Dictionary 847 (28th ed. 2006).
The issue whether the defendant actually was directing Carolyn’s administration of medication perhaps might have more significance if the jury had found the defendant guilty of deliberately premeditated murder. But the jury did not do so.
Trial counsel states in his affidavit: “I should have highlighted this evidence [i.e., certain testimony of Williams and McConnell relating to Tuesday night, December 12, 2006,] in closing. It would have been more effective and it would have solidified the argument that the Commonwealth failed to prove malice.”
Contrast Commonwealth v. Farley, 432 Mass. 153, 157 (2000), S.C., 443 Mass. 740, cert. denied, 546 U.S. 1035 (2005) (among other failings in conducting defense at trial, counsel “simply recited the evidence” in his closing and did not marshal it); Commonwealth v. Triplett, 398 Mass. 561, 568-569 (1986) (counsel in his closing essentially admitted his client’s guilt and abdicated client’s defense).
The judge was careful in his jury instructions specifically to limit the use of any evidence of the defendant’s hitting Gerard or more generally his conduct toward the other two children to the issue of his state of mind or intent vis-a-vis Rebecca — and not as evidence of bad character or propensity to abuse children.
In concluding that the judge properly permitted the Commonwealth to present Laurie Perry’s and James McGonnell’s observations of the defendant, we also reject the defendant’s separate argument that evidence of the defendant’s swearing and hitting his children was bad act evidence that was far more prejudicial than probative and that it should not have been introduced or used by the prosecutor. See Commonwealth v. Simpson, 434 Mass. 570, 578-579 (2001) (“Whether evidence is relevant and whether its probative value is *819substantially outweighed by its prejudicial effect are matters entrusted to the trial judge’s broad discretion and are not disturbed absent palpable error”). The evidence was admissible, and therefore the prosecutor was entitled to introduce it and use it at trial.
The comment was made by Dr. Michele Bums Ewald, a toxicologist and emergency department physician who testified on behalf of the Commonwealth. In the course of his direct examination, the prosecutor showed Dr. Bums and the jury a photograph of Rebecca lying dead on the floor of her parents’ bedroom, at which point Dr. Burns stated to the jury, “So first of all, it’s probably pretty difficult for all of us to view this photo. So imagine Rebecca having to have endured this.”
The prosecutor stated: “Can you imagine the amount of suffering that went into this little girl as she lay on the floor inches from her father’s bed, coughing, choking, gurgling in her own fluids, wondering, why won’t my Daddy help me” (emphasis added)?
We return to the judge’s instruction on parental duty to obtain medical care in our consideration of G. L. c. 278, § 33E, infra.
The defendant does not address the second prong of malice (intent to cause grievous bodily injury) because, he states, the prosecutor did not argue it to the jury at trial. We also do not address this prong.
While the evidence was sufficient to establish first prong malice, we infer that the jury did not so find from the fact that the jury did not find the defendant guilty of deliberately premeditated murder.
The defendant told an investigating State police trooper that Carolyn only gave Rebecca one-half tablet of clonidine around 1 a.m. However, there was other evidence that the defendant and Carolyn never gave their children one-half pills of clonidine such that the jury reasonably could infer that Rebecca was given a full pill of clonidine at this time.
In addition to the insistent reminders of Rebecca’s dire condition provided by Williams and McGonnell, one of the physician witnesses testified that “when a child comes in with even one or two extra tablets of [c]lonidine, they look incredibly sick. They’re not breathing well. Their heart rates are low. Their blood pressures are low. They look like they are about to die” (emphasis added).
See also Commonwealth v. Robidoux, 450 Mass. 144, 145-146 (2007) (affirming murder conviction where defendant withdrew his son from solid food while observing resulting starvation); Commonwealth v. Fickling, 434 Mass. 9, 14 (2001) (leaving toddler alone with dying mother without alerting anyone as to toddler’s presence was sufficient to establish third prong malice).
We previously considered whether the defendant’s hitting and swearing at the other children was properly admitted (see notes 25 and 26, supra, and accompanying text) and do not further discuss this point here. We address only the specific instance involving Gerard and the defendant’s affect.
The evidence concerned the defendant’s demeanor (1) when talking with first responders who were investigating Rebecca’s death; (2) when going to Rebecca’s and his other children’s schools on the day of Rebecca’s death and the following day; (3) when witnesses offered their condolences on the day of *826Rebecca’s death and days immediately following it; and (4) at Rebecca’s wake and funeral service.
The judge here presided over not only the defendant’s trial but Carolyn’s as well, and therefore heard from multiple experts with respect to the clonidine evidence. Moreover, although the expert witnesses in this case disagreed about the cause of Rebecca’s death, all of them, including the defendant’s, agreed that Rebecca’s clonidine level was elevated significantly. The experts also agreed that testing femoral blood provided the most accurate measure for determining drugs present in the blood stream. Finally, neither of the articles submitted in support of the defendant’s new trial motion discusses clonidine.
The judge defined the third prong of malice in relevant part: “it is . . . malice if the defendant intentionally engaged in conduct which, in the circumstances known to the defendant, a reasonable person would have known that his conduct created a plain and strong likelihood of death to Rebecca” (emphasis added).